spectroscopy and mass spectrometry of state-selected...

이학박사 학위논문

분광학과 질량분석법을 이용한 상태 선택된

벤젠족 분자 이온들의 연구

Spectroscopy and Mass Spectrometry of State-selected Benzenoid Molecular Ions

2004년 2월

서울대학교 대학원 화학부 물리화학전공

권 찬 호

Copyright(c)2002 by Seoul National University Library. All rights reserved.(http://library.snu.ac.kr)

2004/01/28 17:41:01

분광학과 질량분석법을 이용한 상태 선택된

벤젠족 분자 이온들의 연구

Spectroscopy and Mass Spectrometry of State-selected Benzenoid Molecular Ions

지도교수 김 명 수

이 논문을 이학박사 학위논문으로 제출함

2003년 11월

서울대학교 대학원

화학부 물리화학전공

성 명 권 찬 호

권찬호의 이학박사 학위논문을 인준함

2003년 12월 5일

위 원 장

부위원장

위 원

위 원

위 원


2004/01/28 17:41:01

A Ph. D. Dissertation

Spectroscopy and Mass Spectrometry of State-Selected Benzenoid Molecular Ions

By Chan Ho Kwon Supervisor : Prof. Myung Soo Kim

School of Chemistry Seoul National University

February 2004


2004/01/28 17:41:01

Abstract

Presence of benzene cation in a long-lived (10 µsec or longer) excited

electronic state, presumably 2E2g, was found through photodissociation kinetics

and charge exchange ionization mass spectrometry. In a subsequent work, a

method based on charge exchange in collision cells of a modified double focusing

mass spectrometer was developed to search routinely the long-lived excited states

with conventional mass spectrometry. This is based on the criterion that charge

exchange between polyatomic species is efficient only when the energy of

reaction is close to zero or negative ( ), or the exoergicity rule. Therefrom,

the 2B2 states of chlorobenzene, bromobenzene, benzonitrile, and phenyl

acetylene cations were found to have long lifetimes (ten microseconds or longer)

while excited electronic states with long lifetime were not detected for

fluorobenzene, iodobenzene, toluene, nitrobenzene, and styrene cations. The long-

lived states found were those generated by removal of an electron from the in-

plane nonbonding p orbitals of halogens or in-plane π orbitals of the triple bonds,

displaying well-resolved vibrational structures in the photoelectron spectra.

B~

0≤∆E

B~

For spectroscopic investigation of the benzenoid cations in excited electronic

states, firstly, continuously tunable vacuum ultraviolet (VUV) light source in the

104 ∼ 125 nm range has been developed by utilizing four-wave sum frequency

mixing in Hg vapor. Then, vibrational spectra of benzenoid cations in the ground

electronic states ( X ) and in the excited electronic states ( ), which consisted

mostly of fundamentals with proper symmetries, have been measured by one-

photon mass-analyzed threshold ionization (MATI) spectroscopy using VUV

radiation generated by four-wave mixing in Kr gas or Hg vapor. Vibrational

assignments were made by referring to the previous results, comparing with

~ B~

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2004/01/28 17:41:01

calculated frequencies, and invoking the selection rule for one-photon process.

Geometric change upon ionization, was calculated quantum chemically and used

to explain the prominent overtones of some vibrational modes and combinations

involving these. Furthermore, Franck-Condon factors calculations to utilize

spectral intensity information, were found to be extremely useful for reliable

vibrational assignment.

While, to aid the spectral analysis for Jahn-Teller benzenoid cations, the Jahn-

Teller coupling parameters for four e2g modes of C6X6+ (X=H, D, F) in the ground

electronic state were calculated from the topographical data of the potential

energy surface at the density functional theory (DFT) level. These were used to

calculate the energies of the Jahn-Teller states and upgraded through the

multimode fit to the experimental data. Excellent agreement between the

experimental and calculated frequencies was achieved. The vibrations which are

not linear Jahn-Teller active were observed and could be assigned by referring to

the frequencies obtained at the DFT level.

Keywords : Benzenoid Cation, Long-lived Excited Electronic State, Jahn-

Teller Effect, Vibrational Spectra, Vacuum Ultraviolet Radiation, Mass-

analyzed Threshold Ionization Spectroscopy, Charge Exchange Ionization

Mass Spectrometry, Quantum Chemical Calculation, Photodissociation

Kinetics, Franck-Condon Factor, Potential Energy Surface.

Student Number : 99305-802

ii


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Contents

Abstract (in English) ......................................................................... i

Contents ............................................................................................. iii

List of Tables ...................................................................................... viii

List of Figures .................................................................................... xii

Chapter

1 Introduction ........................................................................................ 1

1.1 Why the Excited State? ................................................................... 1

1.2 Mass Spectrometry .......................................................................... 3

1.2.1 Ionization Methods ................................................................... 5

1.2.2 Mass Analyzers ......................................................................... 10

1.2.3 Theory of Mass Spectra ............................................................ 10

1.2.4 Long-lived Excited Electronic State ......................................... 12

1.3 MATI and ZEKE Spectroscopies ................................................... 13

1.3.1 Historical Background .............................................................. 13

1.3.2 General Principles ..................................................................... 16

1.3.3 One-photon MATI Scheme and Apparatus ............................... 19

1.3.4 Application to Excited Electronic State of Ions ........................ 26

References ............................................................................................. 28

2 Discovery of Isolated Electronic State by Mass Spectrometry 34

iii


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2.1 Initial Discovery : Benzene Cation ................................................. 35

2.1.1 Experimental Setup ................................................................... 36

2.1.2 Energetics of Benzene Ion ........................................................ 40

2.1.3 Photodissociation Kinetics ........................................................ 42

2.1.4 Quenching of Photodissociation ............................................... 47

2.1.5 Charge Exchange Ionization by Benzene Cation ...................... 53

2.1.6 Conclusions ............................................................................... 58

2.2 Method to Detect Isolated Electronic States ................................. 60


2.2.2 Principle of Method .................................................................. 63

2.2.3 Utilization of Method ................................................................ 64

2.2.4 Conclusions ............................................................................... 74

2.3 Monosubstituted Benzene Cations ................................................. 74

2.3.1 Charge Exchange Ionization and Exoergicity Rule .................. 75


2.3.3 Results ....................................................................................... 77

2.3.4 Conclusions ............................................................................... 93

References .............................................................................................. 95

3 Coherent Vacuum Ultraviolet Radiation ................................. 101 3.1 VUV Generation in Gaseous Nonlinear Medium ......................... 101

3.1.1 General Principles ..................................................................... 101

3.1.2 Wavelength Calibration ............................................................. 103

3.1.3 Measurements of VUV Intensity .............................................. 105

3.2 Four-wave Difference Frequency Mixing in Kr Gas .................... 107

3.3 Four-wave Sum Frequency Mixing in Hg Vapor .......................... 107

3.4 Development of Coherent VUV source at 104 – 108 nm .............. 109

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3.4.2 VUV Generation at 104 – 108 nm ............................................ 115

References .............................................................................................. 119

4 VUV-MATI Spectroscopy of Benzenoid Molecules ............. 121 4.1 Determination of Ionization Energies ............................................ 122

4.2 Selection Rules in One-photon MATI Spectra .............................. 125

4.3 Franck-Condon Factor Calculations ............................................. 128

4.4 VUV-MATI Spectroscopy of Monohalobenzenes ......................... 129

4.4.1 Vibrational Spectra in the Ground Electronic States, ........... 131 X~

4.4.1.1 Chlorobenzene Cation .................................................. 131

4.4.1.2 Bromobenzene Cation .................................................. 137

4.4.1.3 Iodobenzene Cation ...................................................... 138

4.4.1.4 Fluorobenzene Cation..................................................... 141

4.4.2 Vibrational Spectra in the Excited Electronic States, ........... 144 B~

4.4.2.1 Chlorobenzene Cation .................................................. 144

4.4.2.2 Bromobenzene Cation .................................................. 151

4.4.2.3 Iodobenzene Cation ...................................................... 151

4.4.3 Conclusions ............................................................................... 155

4.5 VUV-MATI Spectroscopy of Difluorobenzenes ............................ 158

4.5.1 Computational ........................................................................... 158

4.5.2 Molecular Geometry Calculation .............................................. 159

4.5.3 Ionization Energies .................................................................... 160

4.5.4 p- difluorobenzene Cation ......................................................... 164

4.5.5 m- difluorobenzene Cation ........................................................ 165

4.5.6 o- difluorobenzene Cation ......................................................... 172

4.5.7 Geometrical Change upon Ionization and Vibrational Progressions

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..................................................................................................... 179

4.5.8 Conclusions ............................................................................... 181

4.6 VUV-MATI Spectroscopy of Phenylacetylene and Benzonitrile . 182

4.6.1 Quantum Chemical Calculations .............................................. 183

4.6.2 Ionization Energies .................................................................... 184

4.6.3 Phenylacetylene Cation ............................................................. 188

4.6.4 Benzonitrile Cation ................................................................... 195

4.6.5 Conclusions ............................................................................... 201

References .............................................................................................. 202

5 The Jahn-Teller Effect in Benzenoid Cations ......................... 206 5.1 General Descriptions ....................................................................... 206

5.2 Computation .................................................................................... 208

5.2.1 The Jahn-Teller Potential Energy Surfaces and Coupling Constants..................................................................................................... 208

5.2.2 The Jahn-Teller Parameters and Vibronic Energies .................. 210

5.3 C6H6+ and C6D6

+ in the State ................................................... 211 X~

5.3.1 Ionization Energies...................................................................... 213

5.3.2 Jahn-Teller Effect and Vibronic Splitting ................................. 214

5.3.3 Vibrational Analysis .................................................................. 215

5.3.4 Conclusions ............................................................................... 228

5.4 C6H6+ and C6D6

+ in the State ................................................... 229 B~

5.4.1 Jahn-Teller Effect and Vibronic Splitting ................................... 231

5.4.2 Selection Rule ........................................................................... 232


5.4.4 Radiationless B~ 2E2g → X~ 2E1g transition .............................. 245

5.4.5 Conclusions ............................................................................... 247

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5.5 C6F6+ in the State ...................................................................... 247 X~

5.5.1 MATI Spectrum and Ionization Energy .................................... 248

5.5.2 Calculated Results ..................................................................... 250


5.5.4 Conclusions ............................................................................... 262

References .............................................................................................. 264

Abstract (in Korea) ........................................................................... 267

Acknowledgement ............................................................................. 269

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List of Tables

1.1

1.2

2.1

2.2

2.3

2.4

2.5

3.1

3.2

4.1

4.2

Classification of components consisting of mass spectrometer. ............ 4

Recombination energies of gaseous ions. ............................................... 8

Ion source pressure (P), collision frequency (Zc), source residence time (tR),

and number of collisions (Ncoll) suffered by ions exiting the ion source at

some benzene pressures. ......................................................................... 50

Ionization Energies and the ratios of molecular ion intensities generated by

charge exchange ionization (CI) with benzene ion and by electron ionization

(EI). ........................................................................................................ 57

Collision gases, their ionization energies (IE) in eV, and success/failure to

generate their ions by charge exchange with some precursor ions. ....... 79

Recombination energies of the X~ 2B1, A~ 2A2, B~ 2B2, and C~ 2B1 electronic

states of some monosubstituted benzene cations and the calculated oscillator

strengths of the radiative transitions from the B~ 2B2 states. .................. 80

Recombination energies (RE) of some excited hole states of fluorobenzene

cation and the calculated oscillator strengths of some radiative transitions.

.................................................................................................................. 81

Tunable generation in rare gases. ........................................................... 104

Tunable generation in metal vapors. ...................................................... 104

Ionization energies (IE) to the ground ( X~ 2B1) and B~ 2B2 excited states of

chloro-, bromo-, iodo-, and fluorobenzene cations, in eV. ..................... 132

Vibrational frequencies (in cm-1) and their assignments for the ground state

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( X~ 2B1) chlorobenzene cation. ............................................................... 134

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

4.11

4.12


( X~ 2B1) bromobenzene cation. ............................................................... 140


( X~ 2B1) iodobenzene cation. .................................................................. 143


( X~ 2B1) fluorobenzene cation. ................................................................ 146

Vibrational frequencies (in cm-1) and their assignments for the

chlorobenzene cation in the B~ 2B2 excited state. .................................. 150

Vibrational frequencies (in cm-1) and their assignments for the

bromobenzene cation in the B~ 2B2 excited state. .................................. 153

Geometrical parameters of p-difluorobenzene in the ground state ( X~ 1Ag)

and those of the cation in the ground state ( X~ 2B2g) calculated at the

B3LYP/6-311++G (2df, 2pd) level. ........................................................ 161

Geometrical parameters of m-difluorobenzene in the ground state ( X~ 1A1)

and those of the cation in the ground state ( X~ 2B1) calculated at the

B3LYP/6-311++G (2df, 2pd) level. ........................................................ 162

Geometrical parameters of o-difluorobenzene in the ground state ( X~ 1A1)

and those of the cation in the ground state ( X~ 2B1) calculated at the

B3LYP/6-311++G (2df, 2pd) level. ........................................................ 163

Ionization energies (IE) to the ground states of p-, m-, and o-difluorobenzene

cations, in eV. ......................................................................................... 166

Frequencies (in cm-1) of the totally symmetric modes of the p-

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difluorobenzene cation in the ground electronic state ( X~ 2B2g) calculated at

the B3LYP level with various basis sets. ................................................ 167

4.13

4.14

4.15

4.16

4.17

4.18

4.19

4.20

5.1

5.2

Vibrational frequencies (in cm-1) and their assignments for the p-

difluorobenzene cation in the electronic ground state ( X~ 2B2g).. ........... 169

Vibrational frequencies (in cm-1) and their assignments for the m-

difluorobenzene cation in the ground electronic state ( X~ 2B1). ............. 174

Vibrational frequencies (in cm-1) and their assignments for the o-

difluorobenzene cation in the ground electronic state ( X~ 2B1). ............. 177

Vibrational frequencies (in cm-1) of phenylacetylene neutral and cation in the

ground electronic states calculated at the B3LYP, B3PW91, and BP86 levels

with the 6-311++G (2df, 2pd) basis set and experimental data for the neutral.

.................................................................................................................. 185

Vibrational frequencies (in cm-1) of benzonitrile neutral and cation in the

ground electronic states calculated at the B3LYP, B3PW91, and BP86 levels

with the 6-311++G (2df, 2pd) basis set and experimental data for the neutral.

.................................................................................................................. 186

Ionization energies (IE) of phenylacetylene and benzonitrile, in eV. ..... 188

Vibrational frequencies (in cm-1) and their assignments for phenylacetylene

cation in the ground electronic state ( X~ 2B1). ........................................ 191

Vibrational frequencies (in cm-1) and their assignments for benzonitrile

cation in the ground electronic state ( X~ 2B1). ........................................ 198

Ionization energies (IE) to the ground states of C6H6+ and C6D6

+, in eV. 215

Vibrational frequencies (in cm-1) and assignments for C6H6+ in the ground

electronic state ( X~ 2E1g). ........................................................................ 215

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Vibrational frequencies (in cm-1) and assignments for C6D6+ in the ground

electronic state ( X~ 2E1g). ........................................................................ 222

5.3

5.4

5.5

5.6

5.7

5.8

5.9

Ionization energies (IE) to the excited states of C6H6+ and C6D6

+, in eV. 234

Vibrational frequencies (in cm-1) and assignments for C6D6+ in the excited

electronic state ( B~ 2E2g). ......................................................................... 238

Vibrational frequencies (in cm-1) and assignments for C6H6+ in the excited

electronic state ( B~ 2E2g). ......................................................................... 243

Ionization energies (IE) of hexafluorobenzene, in eV. ........................... 251

Vibrational frequencies (in cm-1) of hexafluorobenzene cation in the ground

electronic state ( X~ 2E1g) measured by the one-photon MATI and their

assignments. ........................................................................................... 253

Calculated and experimental Jahn-Teller coupling parameters for the four e2g

vibrational modes of C6F6+. .................................................................... 260

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List of Figures

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

1.10

Illustrated diagram of photophysical processes. Radiation by straight arrows

(F=fluorescence, P=phosphorescence) and radiationless processes by wavy

arrows (IC=internal conversion, ISC=intersystem crossing, VR=vibrational

relaxation)................................................................................................. 2

Diagram of EI source.. ............................................................................. 6

The (a) EI and (b) self-CI mass spectra of benzene. ................................ 9

Comparison between the ZEKE and the photoelectron spectroscopies by

one-photon and resonance-enhanced multiphoton ionization schemes. .. 15

Schematics of the ZEKE/MATI process. ................................................. 17

Ionization threshold and higher states having their own individual Rydberg

series. High Rydberg states near n=100 are converted into special ZEKE

states which have an abnormal lifetime by external fields....................... 18

Experimental scheme for perpendicular TOF mass spectrometer. 4 mm × 50

mm size slit-electrode assemblies were used to enhance ion collection

efficiency. ................................................................................................. 20

Timing sequence for various pulses adopting according to (a) broadband

MATI scheme or (b) narrowband MATI scheme. .................................. 22

Schematic drawing of the four-wave mixing Kr cell and VUV MATI

instrument. (a) top and (b) side views. ................................................... 24

Schematic drawing of the four-wave mixing Hg cell and VUV MATI

instrument. (a) top and (b) side views. ................................................... 25

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2.1

2.2

2.3

2.4

2.5

2.6

Schematic diagram of the double focusing mass spectrometer with reversed

geometry (VG ZAB-E) modified for photodissociation study. The inset

shows the details of the electrode assembly. .......................................... 37

Circuit diagram devised to pulse the electron beam. MA3104-003D indicates

the main board circuits controlling the ion source of ZAB-E mass

spectrometer . ........................................................................................... 39

Energy diagram of the benzene molecular ion. The lowest reaction threshold

(E0) is 3.66 eV for C6H6+•→C6H5

++H•. ktot denotes the total rate constant

for dissociation in the ground electronic state predicted from previous studies.

.................................................................................................................. 41

PD-MIKE profile for the production of C4H4+• from the benzene ion at

357nm obtained with 2.1kV applied on the electrode assembly. Experimental

result is shown as filled circles. Reproduction of the profile using the rate

constant distribution centered at 6.3×107 s-1 obtained by experimental data is

shown as the solid curve. The positions marked A and B are the kinetic

energies of products generated at the position of photoexcitation and after

exiting the ground electrode, respectively. ............................................. 44

The total RRKM dissociation rate constant of benzene ion as a function of

the internal energy calculated with molecular parameters in ref. 8. The

internal energies corresponding to the dissociation rate constants of

( 5 . 5±1 .1 )×107 and (5±3 )×106 s-1 for PDs at 357 and 488.0 nm,

respectively, are marked. ........................................................................ 46

Pressure dependences of the precursor (C6H6+•) intensity (–––) and

photoproduct (C4H4+•) intensities at 357 (·····) and 488.0 (–––) nm. Pressure

in the CI source was varied continuously to obtain these data. The abscissa

shows the pressure read by an ionization gauge located outside of the source.

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The inside source pressures estimated using eqn. (1) at three ionization

gauge readings are marked. The scale for the precursor intensity is different

from that for photoproduct intensities. ..................................................... 54

2.7

2.8

2.9

2.10

2.11

The ratios of molecular ion intensities generated by charge exchange

ionization (CI) with benzene ion and by electron ionization (EI) are plotted

as a function of the sample ionization energy. • and o are for CI intensities

measured at the ion source pressure of 0.013 and 0.09 Torr, respectively.

.................................................................................................................. 56

Schematic diagram of the double focusing mass spectrometer with reversed

geometry (VG ZAB-E). The inset shows details of the first collision cell

assembly modified for charge exchange study. ...................................... 62

MIKE spectrum of the C6H6+• primary ion generated by EI. CS2 was

introduced into the second collision cell. The acceleration energy for C6H6+•

was 4002 eV. The collision cell potential was 3902 V. The peak types are

denoted. The peak marked 77+(MID) is due to the metastable ion

decomposition of C6H6+• to C6H5

+ occurring in the field-free region between

the magnetic and electric sectors. ........................................................... 66

Mass spectra obtained under the single-focusing condition. The acceleration

energy in the source was 4004 eV and the collision cell potential was 3929 V.

C6H6 and CS2 were introduced into the ion source and the first collision cell,

respectively. C6H6 was ionized (a) by EI and (b) by CI at the 0.02 Torr

source pressure. (c) C6D6 and CH3Cl were introduced into the ion source and

the first collision cell, respectively and C6D6 was ionized by EI. The

instrument was tuned to maximize the type III ion signals. The types of the

major signals are denoted. ...................................................................... 68

MIKE spectrum recorded by setting the magnetic field to transmit the

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C32S2+•(III) ion in Figure 3(b) and scanning the electric sector. ............ 69

2.12

2.13

2.14

2.15

2.16

Relative yields of the reagent gas ions, I(A+•)/I(C6H6+•), vs. the primary ion

translational energy. Benzene ions were generated by CI at (a) 0.02 Torr

(CI1) and at (b) 0.1 Torr (CI2) source pressures. Charge exchange ionization

was done in the first collision cell. For consistency, the instrument was tuned

to maximize the primary ion signal. In (a), CH3F+• and CH4+• signals were

hardly detectable at low energy while CS2+•, CH3Cl+•, CH3F+•, and CH4

+•

were not detectable at low energy in (b). ............................................... 71

Partial mass spectrum of C6H5Cl generated by 20 eV EI recorded under the

single focusing condition with 4006 eV acceleration energy is shown in (a).

(b) and (c) are mass spectra in the same range recorded with CH3Cl in the

collision cell floated at 3910 and 3960 V, respectively. Type II signals at m/z

49.3 and 50.3 in (b) and at m/z 49.6 and 50.6 in (c) are due to collision-

induced dissociation of C6H5Cl+• to C4H2+• and C4H3

+, respectively. The

peaks at m/z 50.6 in (b) and at m/z 50.8 in (c) are due to collision-induced

dissociation of C6H5+

to C4H3+. .............................................................. 82

Ion kinetic energy spectrum recorded by setting the magnetic field to

transmit the type III CH335Cl+• ion in Fig. 2 (b) and scanning the electric

sector. ...................................................................................................... 83

Partial mass spectrum obtained under the single focusing condition with

C6H5Br and CH3Br introduced into the ion source and collision cell,

respectively. C6H5Br was ionized by 20 eV EI and acceleration energy was

4008 eV. Collision cell was floated at 3907 V. ....................................... 85

Partial mass spectrum obtained under the single focusing condition with

C6H5CN and CH3Cl introduced into the ion source and collision cell,

respectively. C6H5CN was ionized by 20 eV EI and acceleration energy was

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4007 eV. Collision cell was floated at 3910 V. Type II signals at m/z 49.3,

50.3, and 51.3 are due to collision-induced dissociation of C6H5CN+• to

C4H2+•, C4H3

+, and C4H4+•, respectively. Those at m/z 49.6 and 50.6 are due

to collision-induced dissociation of C6H4+• to C4H2

+• and C4H3+, respectively.

.................................................................................................................. 88

2.17

3.1

3.2

3.3

3.4

3.5

Ion kinetic energy spectra recorded by introducing C6H5Br+• ((a) and (b))

and C6H5CH3+• ((c)) in the second cell filled with CH3Br. The molecular ions

were accelerated to 4 keV in the ion source. The second collision cell was

floated at (a) 3910, (b) 3943, and (c) 3910 V. Arrows indicate the expected

positions for ions from collision gases generated by charge exchange with

the precursor ions. The major peaks appearing at 3957 and 3974 eV in (a)

and (b), respectively, are due to collision-induced dissociation of C6H5Br+• to

C6H5+. The major peak appearing at 3960 eV in (c) is due to unimolecular

dissociation of C7H8+• to C7H7

+ occurring outside the collision cell, but

between the magnetic and electric sectors. ............................................ 89

The number of photoions by ion chamber currents measured as function of

the pressure of No/He. Voltage between two electrodes in ion chamber is 50

V. ............................................................................................................ 106

Schematic diagram for four-wave difference frequency mixing in Kr gas. 108

Schematic diagram for four-wave sum frequency mixing in Hg vapor. .. 110

Apparatus for VUV generation by four-wave sum frequency mixing in Hg

vapor. The laser beams were aligned off-center of LiF lens to separate the

VUV light from the residual UV and visible lights at the interaction region

with the molecular beam. ....................................................................... 111

Schematic diagram of the experimental apparatus including the Hg cell with

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a cone type glass capillary, monochromator, and photoionization chamber.

.................................................................................................................. 114

(a) Spectral profile of VUV generated by frequency tripling in Hg at ω1

~312.8 nm. (b) and (c) show spectral profiles of VUV generated by FWSM

via 71S0 - 61S0 transition in Hg recorded using the Au plate monitor and

photoionization of benzene, respectively. PHg ∼ 1 torr and PHe ∼ 2 torr. .. 116

3.6

3.7

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

Spectral profiles of VUV generated by FWSM via 61D2 - 61S0 measured

using (a) the Au plate monitor and (b) photoionization of benzene. PHg ∼ 1

torr and PAr ∼ 0.5 torr. ............................................................................. 118

Lowering of the ionization potential due to an electric field. ................ 124

Illustration of the Franck-Condon principle and intensity distributions for

small and large displacement, respectively. ........................................... 130

Ground state one-photon MATI spectra recorded by monitoring (a)

C6H535Cl+• and (b) C6H5

37Cl+•. ............................................................... 133

Ground state one-photon MATI spectra recorded by monitoring (a)

C6H579Br+• and (b) C6H5

81Br+•. .............................................................. 139

Ground state one-photon MATI spectrum recorded by monitoring C6H5I+•.

.................................................................................................................. 142

Ground state one-photon MATI spectrum recorded by monitoring C6H5F+•.

.................................................................................................................. 145

B~ 2B2 state one-photon MATI spectrum of C6H535Cl+•. The x-axis of the

inset, ion energy, denotes energy scale referred to the position of the 0-0

band. ....................................................................................................... 149

B~ 2B2 state one-photon MATI spectrum of C6H579Br+•. The x-axis of the

xvii


2004/01/28 17:41:01

inset, ion energy, denotes energy scale referred to the position of the 0-0

band. ....................................................................................................... 152

4.9

4.10

4.11

4.12

4.13

4.14

4.15

B~ 2B2 state one-photon MATI spectrum of C6H5I+•. .............................. 154

Equilibrium geometries of (a) C6H5F and C6H5F+• and (b) C6H5Cl and

C6H5Cl+• calculated at the B3LYP/6-311++G** level. Atomic displacements

upon ionization are drawn as broken arrows in the drawings of the neutrals.

The 6a eigenvectors of the cations are drawn as arrows in the drawings of the

cations. Bond lengths in Å and angles in degree. ................................... 156

One-photon MATI spectrum of p-C6H4F2 recorded by monitoring p-

C6H4F2+• in the ground electronic state. The x-scale at the top of the figure

corresponds to the vibrational frequency scale for the cation. ............... 168

One-photon MATI spectrum of m-C6H4F2 recorded by monitoring m-

C6H4F2+• in the ground electronic state. The x-scale at the top of the figure

corresponds to the vibrational frequency scale for the cation. ............... 173

One-photon MATI spectrum of o-C6H4F2 recorded by monitoring o-C6H4F2+•

in the ground electronic state. The x-scale at the top of the figure

corresponds to the vibrational frequency scale for the cation. Its origin is at

the 0-0 band position. Spectrum in the 100~800 cm-1 region magnified by

30 is shown as an inset to demonstrate the quality of the MATI spectra

obtained in this work. ............................................................................. 176

Equilibrium geometries of (a) neutral and (b) cation of p-C6H4F2. Arrows

in (a) indicate atomic displacements upon ionization magnified by 10.

Arrows in (b) indicate the eigenvector of the mode 6 of the cation. ...... 180

One-photon MATI spectrum of C6H5C≡CH recorded by monitoring

C6H5C≡CH+ in the ground electronic state. The x-scale at the top of the

xviii


2004/01/28 17:41:01

figure corresponds to the vibrational frequency scale for the cation whose

origin is at the 0-0 band position. Spectrum in the 50 ∼ 2500 cm-1 region

magnified by 15 is shown as an inset to demonstrate the quality of the MATI

spectrum obtained in this work. ............................................................... 190

4.16

5.1

5.2

5.3

5.4

One-photon MATI spectrum of C6H5C≡N recorded by monitoring

C6H5C≡N+ in the ground electronic state. The x-scale at the top of the figure

corresponds to the vibrational frequency scale for the cation whose origin is

at the 0-0 band position. Spectrum in the 50 ∼ 2200 cm-1 region magnified

by 15 is shown as an inset to demonstrate the quality of the MATI spectrum

obtained in this work. ............................................................................. 197

One-photon MATI spectrum of C6H6 recorded by monitoring C6H6+ in the

ground electronic state. The x-scale at the top of the figure corresponds to

the vibrational frequency scale for the cation. Its origin is at the 0-0 band

position. Spectrum in the 100~2100 cm-1 region magnified by 30 is shown

as an inset to demonstrate the quality of the MATI spectrum obtained in this

work. Relative intensity of the peak marked by asterisk (*) changed with

the beam expansion condition. ............................................................... 216

One-photon MATI spectrum of C6D6 recorded by monitoring C6D6+ in the


the vibrational frequency scale for the cation. Its origin is at the 0-0 band

position. Spectrum in the 100~2100 cm-1 region magnified by 40 is shown

as an inset to demonstrate the quality of the MATI spectrum obtained in this

work. ....................................................................................................... 221

Photoionization spectrum of C6H6 measured as a function of the VUV

photon energy (in cm-1). ......................................................................... 236

One-photon MATI spectrum of C6D6 recorded by monitoring C6D6+ in the

xix


2004/01/28 17:41:01

excited electronic state B~ 2E2g. The x-scale at the top of the figure

corresponds to the vibrational frequency scale for the cation, or the ion

internal energy. Its origin is at the 0-0 band position. Spectrum in the

0~1900 cm-1 region magnified by 10 is shown as an inset to demonstrate the

quality of the MATI spectrum obtained in this work. ............................ 237

One-photon MATI spectrum of C6H6 recorded by monitoring C6H6+ in the

excited electronic state B~ 2E2g. The x-scale at the top of the figure

corresponds to the vibrational frequency scale for the cation, or the ion

internal energy. Its origin is at the 0-0 band position. Spectrum in the

0~1900 cm-1 region magnified by 10 is shown as an inset to demonstrate the

quality of the MATI spectrum obtained in this work. ............................ 242

5.5

5.6

5.7

5.8

One-photon MATI spectrum of C6F6 recorded by monitoring C6F6+ in the


the vibrational frequency scale for the cation whose origin is at the 0-0 band

position. Spectrum in the 50 ~ 1900 cm-1 region magnified by 20 is shown as

an inset to demonstrate the quality of the MATI spectrum obtained in this

work. ....................................................................................................... 249

The optimized geometries for the (a) 2E1g (D6h), (b) 2B2g (D2h), and (c) 2B3g

(D2h) states of C6F6+ calculated at the B3LYP/6-311++G (2df) level. Values

in parentheses in (a) are the bond lengths in the neutral. ....................... 252

The Jahn-Teller potential energy surfaces along each normal coordinate of

the four e2g modes of C6F6+ in the ground electronic state. Only the portions

in the 2B3g side are drawn. ...................................................................... 259

xx


2004/01/28 17:41:01

Chapter 1

Introduction

1.1 Why the Excited State?

Controlling the outcome of chemical reaction has been a long-standing goal of

chemists. The reaction dynamics has attempted to understand a chemical reaction

at the single molecule level and considerably been progressed together with rapid

development in laser technology. Particularly, photochemistry has long been a

prominent area of reaction dynamics.1-3 Many experimental and theoretical

approaches have been proposed to comprehend and even control a photochemical

process.4-13

In general, most photochemical processes involve first the electronic transition

by absorption or scattering of one or more photons, followed by nuclear motion

on the excited electronic state(s), crossed back to the ground electronic state, and

finally relaxed into minima representing photoproducts. Practically, scattering and

multiphoton processes require the intense light fields available only from lasers.

Multiphoton and light scattering processes are called nonlinear optical phenomena,

because unlike stimulated absorption, they do not depend linearly on the

excitation power.

Most excited electronic states have only a short lifetime, namely the excess

energy of an excited state can be dissipated through unimolecular photophysical

processes which are illustrated schematically in Fig. 1.1. Followings are some

important processes on the excited electronic states:

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2004/01/28 17:41:01

S1

S0

T1

hv

P

F

ISC

VRVR

IC

VR

E

PhotoproductsPhotoproducts

Fig. 1.1 Illustrated diagram of photophysical processes. Radiation by straight arrows (F=fluorescence,

P=phosphorescence) and radiationless processes by wavy arrows (IC=internal conversion, ISC=intersystem

crossing, VR=vibrational relaxation).

2

Copyright(c)2002 by Seoul N

ational University L

ibrary. All rights reserved.(http://library.snu.ac.kr) 2004/01/28 17:41:01

• Fluorescence : stimulated and spontaneous emission.

• Phosphorescence : lower energy spontaneous emission occurring from

longer-lived excited states, usually triplet multiplicity.

• Intersystem Crossing : transitions between excited electronic state manifolds

of different spin multiplicity.

• Internal Conversion : transitions from higher to lower lying excited states or

ground state, having the same spin multiplicity.

• Vibrational Relaxation : dissipation such as heat to the vibrational ground

state.

• Photochemical Reactions : photodissociation, photosynthesis, photoinduced

electron-transfer.

After comprehending about the creation and evolution of excited electronic

states, selectively preparing and storing these excited state ions may be especially

useful for the investigation of the state-specific unimolecular and bimolecular

reactions, even though it was difficult to prepare state-selected ions due to various

limitations. Furthermore, the study of the structure and dynamics of excited

electronic states14-18 will be useful to predict a photochemical process, to induce

new reaction control scheme, even to completely control a chemical reaction,

because of their important roles in chemical reactions.

1.2 Mass Spectrometry

Mass spectrometry19-21 has progressed considerably and rapidly during the last

decade and raised to an outstanding position for analytical methods. The

development of modern mass spectrometers has been related to advances in laser

and signal-processing technologies, ion optics and detection, fast and high-

3


2004/01/28 17:41:01

performing electronics, etc. This has been particularly true for the time-of-flight

(TOF) mass spectrometry,20 which recently plays an increasingly important role in

all of the biological research areas as well as ion reaction dynamics field.

Table 1.1 Classification of components consisting of mass spectrometer.20

Ionization Methods Mass Analyzers Detectors

Electron ionization (EI) Magnetic (B) Faraday cup

Chemical ionization (CI) Double-focusing (EB) Electron multiplier (EM)

Fast atom bombardment (FAB) Ion cyclotron resonance (ICR) Photon multiplier (PM)

Field Ionization (FI) Quadrupole (Q) Microchannel plate (MCP)

Photoionization (PI) Quadrupole ion trap (ITMS) Array detectors

Multiphoton ionization (MPI) Time-of-flight (TOF) Image currents

Electrospray (ESI) Fourier transform (FTMS)

Matrix-assisted laser

desorption/ionization (MALDI)

Mass spectrometers can be characterized by the ionization sources, mass

analyzers, and detectors that are used. In general, they have been made up of

appropriate components according to the features of interesting system and

continuous/pulsed types, even possible to hybrid. For example, double focusing

mass spectrometer with reversed geometry (EI/CI-BE-PM) and TOF mass

spectrometer (PI/MATI-TOF-MCP) are used to study state-selected benzenoid

molecular ions.

4


2004/01/28 17:41:01

1.2.1 Ionization Methods

A molecule (M) can be generally ionized through interaction with the

energetic electrons, particles, or photons.

−+ +→+ eMEM (1.1)

Here, ionization energy (IE) is defined as the minimal energy required on removal

of an electron in molecule. Ionizations can occur through various methods such as

electron ionization (EI), charge exchange ionization (CI), photoionization (PI),

electrospray ionization (ESI), matrix-assisted laser desorption ionization

(MALDI) that can be chosen, depending on the volatility, thermal stability, and

physical state of molecule.21

• Electron Ionization (EI): This is the oldest and most widely used method in

organic mass spectrometry. As shown in Figure 1.1, sample molecules (M) be

volatilized into the ionization chamber are bombarded with electrons which are

obtained from a heated filament in vacuum and accelerated by voltage (V), thus

have energy eV, where e is the electronic charge. Standard mass spectra are

usually obtained at 70 V because of maximum ionization efficiency and good

reproducibility for most organic molecules near this voltage.

(1.2) −•+− +→+ eMeM 2

However, this technique induces extensive fragmentation due to excess internal

energy in molecular ion formed by high electron energy, even though it can be

useful to identify its structure. Therefore, EI method capable to form the

molecular ion with large internal energy is not adequate in state-selective or

energy-selective reaction study.

• Charge Exchange Ionization22 (CI): The interaction of a reactant ion (A+) with

a neutral molecule (M) may lead to charge exchange, if the recombination energy

5


2004/01/28 17:41:01

Ion accelerating potential

Feedback by trap current

Filament heater potential

Electron accelerating

potential

Repeller

e-

Filament

Trap

M+•

Fig. 1.2 Diagram of EI source.

6


2004/01/28 17:41:01

(RE) of the reactant ion is greater than the ionization energy (IE) of the neutral

molecule.

AMAM +→+ ++ =∆ (1.3) )RE(AIE(M)E +−

The RE of A+ is defined as the electron affinity and normally has the same

numerical value of the IE to ground state of A+. In some cases, ions of reactant or

product may be formed in an excited electronic state. A selection of RE is

presented in Table 1.2. Molecular ion formed by the CI will have an internal

energy determined by the exothermicity (∆E) and hence, the product distribution

from the CI will depend on the ∆E of the reaction. This is ‘soft’ method of

ionization, resulting in little fragmentation as shown in Figure 1.3.

Charge exchange ionizations of polyatomic molecules could have been

utilized to measure the rate constants of unimolecular reactions, namely, to

energy-selective study. However, although the CI can forms the molecular ions

with less excess of internal energy than the case in the EI, it is not effective

method to select a state of molecule.

• Photoionization (PI): Photoionization method (PI) employs photons to ionize a

molecule. The photons are generated by high-power lamps or by lasers. Ionization

processes depend on the photon energy, with either direct transition to the ionic

state A+ or multiphoton absorptions, namely,

−+ +→ν+ eMhM 1 (1.4)

or

−+ +→ν+ eMnhM 2 . (1.5)

Practically, single-photon ionization occurs in the vacuum ultraviolet (VUV)

region and is the most general and cleanest photoionization method. In addition,

7


2004/01/28 17:41:01

Table 1.2 Recombination energies of gaseous ions.

Ion RE, eVa

Kr+•

2P3/2 14.0

2P1/2 14.7

CO+• 14.0

CO2+•

13.8

Xe+• 2P3/2 12.1

2P1/2 13.4

COS+• 11.2

CS2+•

X~ 10.08

A~ 12.84

C6H6+• 9.243

a From ref. 22

8


2004/01/28 17:41:01

30 40 50 60 70 80m/z

Inte

nsity

(arb

itrar

yun

its)

30 40 50 60 70 80m/z

Inte

nsity

(arb

itrar

yun

its)

(b)

(a)

Fig. 1.3 The (a) EI and (b) self-CI mass spectra of benzene.

9


2004/01/28 17:41:01

the resolution of photon energy reached to rotational levels as well as the

vibrational levels of molecular systems. However, regardless of extremely high

energy resolution achieved by development of laser technique, it still remains the

problem in the resolution of photoionization because of removal electron with

significant kinetic energy. For the study of state-selected molecular ion, new

ionization technique which produces the threshold photoelectron with near zero

kinetic energy by one-photon PI, would be required.23

1.2.2 Mass Analyzers

The ions which are produced from an ion source, can be separated to their

masses by many different analyzers. Scanning analyzers successively transmit

ions of different masses along a time scale, which are either magnetic or

quadrupole analyzers. While, some simultaneously allow the transmission of all

ions such as the time-of-flight, the ion trap, the ion cyclotron resonance analyzers.

Also, the analyzers can be distinguished by three main characteristics, the upper

mass limit, the transmission, and the resolution. Considering the purpose and the

interested system, instruments combined several analyzers in sequence, namely,

the tandem mass spectrometers (MS/MS), are increasingly common because a

mass spectrum resulting from the dissociation of an ion selected in the first

analyzer can be obtained.

1.2.3 Theory of Mass Spectra

Theory of mass spectra, or RRKM (Rice-Ramsperger-Kassel-Marcus)-QET

(quasi- equilibrium theory), has been successful in explaining fragmentation of

polyatomic (four atoms or more) molecular ions produced by various means and

mass spectra formed thereby. One of the main assumptions of RRKM-QET is that

the internal energy, either electronic or vibrational, acquired at the time of

10


2004/01/28 17:41:01

molecular ion formation redistributes rapidly prior to fragmentation.24 In

particular, rapid redistribution of the former means that internal conversion from

the excited electronic states to the ground state occurs efficiently for polyatomic

ions such that all the dissociation reactions occur in the latter state, even though

cases to the contrary are frequently observed for simpler diatomic and some

triatomic ions. From the very inception of the theory, efforts have been made to

find evidences against the assumption of rapid internal conversion such as the

occurrence of dissociation in an excited electronic state, or ‘isolated’ state, and

rapid radiative decay of the electronic energy. Various mass spectrometric and

spectroscopic techniques have been used for this purpose such as photoelectron-

photoion coincidence spectrometry,25-34 tandem mass spectrometry utilizing

collision-induced dissociation35-38 or photodissociation,39-44 and emission

spectroscopy.45-48 Tens of cases of isolated state dissociation have been reported,

most abundant having been dissociations in repulsive electronic states.26-33,39-43

Rapid dissociations in such states can compete effectively against the internal

conversion and the nonstatistical nature of the reactions is manifest in the

experimental breakdown graph, kinetic energy release distribution, or dissociation

anisotropy. Cases25,36-38 of slow internal conversion have been reported also,

CD2O+• ( A ) → CDO~ + + D• being the best known example. To measure the

lifetime, both radiative and nonradiative, of an excited electronic state lying below

the dissociation threshold, optical emission and laser-induced fluorescence

spectroscopies have been used.45-48 When the transition from the first excited

electronic state to the ground state is electric dipole allowed, absence of emission

is an indication of very rapid internal conversion. Similar conclusions have often

been drawn45-48 when emission is absent from an excited state whose radiative

transitions to the lower states are electric dipole forbidden, such as the B~ 2E2g

state of benzene cation, even though extremely slow decay of such a state is also

11


2004/01/28 17:41:01

compatible with the experimental observation.14-18

1.2.4 Long-lived Excited Electronic State

There are some cases where the hypothesis of rapid conversion from an

excited to ground electronic states prior to dissociation is not valid. The most

frequently observed are the cases of direct dissociation in a repulsive excited

electronic state. 26-33,39-43 Predissociation via bound-to-repulsive transition has

been observed for dissociation of simple molecular cations also. Dissociation in a

bound excited state, or an ‘isolated’ electronic state, has been hardly observed in

ionic cases.14-18 Hence searching for isolated electronic states of polyatomic

cations remains a mission yet to be fulfilled.

In our recent investigation on photodissociation of benzene cation,14 We found

evidences for a very long lifetime (20 µsec or longer) of its B~ 2E2g state. In a

subsequent work,15 a method based on charge exchange in collision cells of a

modified double focusing mass spectrometer was developed for routine search for

long-lived excited states with conventional mass spectrometry. Then, the overall

scheme was applied to find long-lived excited electronic states of the molecular

ions of some benzene derivatives generated by electron ionization.17 It was found

that the B~ 2B2 excited electronic states of chlorobenzene, bromobenzene,

benzonitrile, and phenylacetylene cations had very long lifetimes (tens of

microsecond or longer). These are the states generated by removal of an electron

from the in-plane nonbonding p orbitals of halogens or in-plane π orbitals of the

triple bonds. Halogen p orbitals or π orbitals of triple bonds in ethene derivatives

also split into two just as in the benzene derivatives, one in-plane and the other

out-of-plane. All of the long-lived excited electronic states of benzenoid

molecular cations investigated by mass spectrometry are described with details in

next chapter.

12


2004/01/28 17:41:01

1.3 MATI and ZEKE spectroscopies

1.3.1 Historical Background

Spectroscopy of molecular cations is of important for the study of combustion,

atmospheric chemistry, cosmochemistry, etc.49-51 Analysis of a vibrational

spectrum, with rotational resolution in particular, provides useful structural

information. Availability of reliable ionic spectral database is also essential for the

development and test of quantum chemical methods especially for the open shell

systems.

Unlike neutrals, it is difficult to perform infrared or Raman spectroscopy to

obtain vibrational spectra of molecular cations.52,53 Optical emission spectroscopy

is not generally applicable either because emission is not observed for most of the

polyatomic ionic species.54 Probably the simplest way to obtain vibrational

information of a molecular cation is to record the photoelectron spectrum (PES)55

of the corresponding neutral. However, the resolution of this technique is rather

poor (typically ∼10 meV, or 80 cm-1, for high resolution photoelectron

spectrometer)56-58 and hence is not adequate to obtain detailed vibrational

information. A different form of PES on the basis of the photoionization

experiments which already utilized a photon monochromator, called threshold

photoelectron spectroscopy (TPES),23 was developed with slightly better

resolution than that of the PES. The PES and TPES spectra are linked by the

energy conservation law:

)(eE)(ME)(eE)(ME)(MEhv kikki−+−++ +≈++= (1.6)

where Ei (M+) is the internal energy of the photoion, Ek (M+) is the kinetic energy

of the ion, while Ek (e-) is the kinetic energy of the departing electron. By

conservation of momentum, Ek (M+) ≈ 0 and becomes identically zero in TPES for

13


2004/01/28 17:41:01

which Ek (e-) = 0. Namely, this method is to detect the electrons with zero kinetic

energy produced from an ionic state when the photon energy matches an

ionization threshold. Since these electrons are prompted with no kinetic energy,

the angular dispersion is negligible, which enables to increase the collection

efficiency of electron energy analyzer. Most of the work in TPES has been done

with synchrotron light sources, which are excellent sources of continuously

tunable short-wavelength light. However, TPES of which resolution is limited

largely by the synchrotron light source, is also not sufficient method to well-

resolve the molecular ionic states. A related technique in parallel with the

development of TPES using synchrotron radiation is the resonance-enhanced

multiphoton ionization (REMPI)-photoelectron spectroscopy (PES)59,60 which

ionizes a neutral by REMPI using coherent laser pulses of high sensitive and

resolution and determines the ion internal energy by measuring the electron

kinetic energy. Even though REMPI-PES has some advantages over PES such as

the intermediate state selection, spectral resolutions of the two are comparable.

A new technique for extreme high-resolution photoelectron spectroscopy which

combines REMPI and TPES, was developed by Schlag and coworkers. The

technique, called the pulsed-field ionization zero kinetic energy (PFI-ZEKE)61-63

photoelectron spectroscopy, takes advantages of both the high photon energy

resolution and the pulsed excitation provided by tunable pulsed dye lasers, in

addition, high photoelectron energy resolution due to the delayed pulsed field

ionization used for threshold detection. Here, one can detect the field-ionized

electrons from high Rydberg states or the corresponding positive ions. The latter

type of detection scheme first developed by Johnson has come to be known as

mass-analyzed threshold ionization (MATI) spectroscopy.64-66 Even though the

resolution of MATI is inferior to that of ZEKE at the moment, capability to identify

the ionic species responsible for a spectral peak is the advantage of the former.

14


2004/01/28 17:41:01

M

M*

M+

hv1

hv2hvHe(I)

e-

e-

PES

REMPI-PES

M

M*

M+

hvVUV

hv1

hv2

e- (Ek=0)

ZEKE (TPES)

Fig. 1.4 Comparison between the ZEKE and the photoelectron spectroscopies

by one-photon and resonance-enhanced multiphoton ionization schemes.

15


2004/01/28 17:41:01

1.3.2 General Principles

ZEKE spectroscopy67,68 was originally developed as extremely high resolution

version of TPES, adopting the pulsed nature of REMPI to introduce a delay time

between excitation to high Rydberg states of neutrals and extraction of the

Rydberg electrons by small pulsed electric field. The basic idea of ZEKE was that

after any electrons formed with small kinetic energy would drift away from the

excitation position during the delay time, electrons with zero kinetic energy only

leaved to await the extraction and detection. This results the stimulated study on

the real mechanism of ZEKE process and Schlag and coworkers found that the

responsible ZEKE signals come not from electrons formed by photoionization at

just above threshold but Rydberg electrons which are bound weakly to very high n

Rydberg states just below the ionization threshold by the pulsed field ionization.

Namely, high Rydberg state electrons generated by photon absorption in field-free

region, are so loosely bound that it is easily extracted by pulsed field ionization.

This ZEKE process is shown schematically in Fig. 1.5. The resolution in ZEKE

spectroscopy is generally determined by not the bandwidth of exciting laser but

the depth of field ionization. In the presence of the electric field, ionization

threshold is lowered by FE α=∆ and the value of is between 4 and 6,

depending on whether the field ionization is diabatic or adiabatic. While, it must

be remembered not only that Rydberg series of n>100 at ionization threshold lead

up to a narrow set of ZEKE states in a typical 8 cm

α

-1 bandwidth by external field,

but also that this is true for all the individual excited ionic states above the IP, as

shown in Fig. 1.6. Hence, the electrons from the ZEKE states of individual ionic

states are extracted by the pulsed field ionization and these ZEKE signals

recorded as function of photon energy are called the ZEKE spectrum.

Many efforts have been made to understand the mechanism of Stark ionization

16


2004/01/28 17:41:01

High Rydberg stateHigh Rydberg state

M+e-

hvhvCoulomb Coulomb potentialpotential

EE

M+e-

Low Rydberg stateLow Rydberg state

e-M+e-

M+M+ e-Continuum (Cation)

Direct ion(electron)Direct ion(electron)

++ ––

ee--

ee--

ee--

RRMM++

MM++

RR

RR

++ ––

ee--

ee--

ee--

MM++

MM++

MM++

MM++ee--

++ ––

MM++ee--ZEKEZEKE

MATIMATI

0V

Laser pulse

Delay time, ~µs

Spoil Field

PFI

TOF spectrumdirect electrons

PFIPFI--ZEKE signal ZEKE signal

Pulsed field ionization (PFI)

Fig. 1.5 Schematics of the ZEKE/MATI process.

17




g

n=100

n=50

n=30

E=hv

ZEKE states

ZEKE states

ZEKE states

ZEKE states

ZE

KE

spec

trum

n=200Ground

state

v1

v2

v3

0-0

v 1v 2

v 3

Fig. 1.6 Ionization threshold and higher states having their own individual Rydberg series. High Rydberg states

near n=100 are converted into special ZEKE states which have an abnormal lifetime by external fields.

18




of Rydberg state. ZEKE state surviving for several µs, has been another issue

and investigated both theoretically and experimentally, even though not

conclusive thought.68-70

1.3.3 One-photon MATI Scheme and Apparatus

Two color 1+1’ excitation is the most widely used scheme in ZEKE or MATI

spectroscopy, namely excitation of a molecule to a high-lying Rydberg state via

an intermediate state, which is followed by pulsed-field ionization.61-66 In this

scheme, the measured spectral transitions would be governed by the nature of

the intermediate state. This sometimes helps spectral assignment. The fact that

detailed spectroscopic information on the excited electronic states is not

available for most of the molecules is one of the difficulties in routine

application of the 1+1’ scheme. Even though difficulty lies in the fact that the

first excited electronic states are located 6.2 eV (200 nm) or more above the

ground states and not accessible by one photon absorption of a commercial dye

laser output in most of the cases. Also to be mentioned in that excitation to these

states often result in diffuse spectra either due to rapid dissociation or relaxation.

In such cases, one can not expect good ZEKE or MATI signals when the 1+1’

scheme is used. Recently, we developed one photon MATI scheme using

vacuum ultraviolet irradiation and studied the spectra of the polyatomic ions.16

Presence of an appropriate intermediate state is no longer a requirement in this

scheme because the molecules are prepared in the Rydberg states by direct one-

photon absorption from the ground state. In addition, every possible dipole

allowed transition makes up complex spectra, which show rich vibrational

structures.

The TOF mass spectrometer consists of two differentially pumped chambers

and a 60 cm flight tube with a dual microchannel plate detector equipped at the

19


2004/01/28 17:41:01

skimmer

VUV laserE3

E2

E1

temperature-controlled pulsed nozzle

G

MCP

TOF

Fig. 1.7 Experimental scheme for perpendicular TOF mass spectrometer. 4

mm × 50 mm size slit-electrode assemblies were used to enhance ion

collection efficiency.

20


2004/01/28 17:41:01

end. A sample seeded in He at the stagnation pressure of ∼2 atm was

supersonically expanded through a temperature–controlled pulsed nozzle (dia.

500 µm, General Valve) and introduced to the ionization chamber through a

skimmer (dia. 2 mm, Beam Dynamics) placed about 3 cm downstream from the

nozzle orifice. The background pressure in the ionization chamber was typically

∼ 10-8 Torr. The VUV laser pulse was collinearly overlapped with the molecular

beam in a counter-propagation manner to maximize the laser-molecular beam

interaction volume. Instead of the usual circular aperture, 4 mm × 50 mm size

slit-electrode assemblies were used to enhance ion collection efficiency, Fig. 1.7.

Spoil field of 0 ~ 0.2 V/cm was applied in the ionization region to remove

directly produced ions. To achieve pulsed-field ionization (PFI) of neutrals in the

ZEKE state, an electric field of 10 ~ 80 V/cm was applied with the field

direction perpendicular to that of the molecular and laser beams. Then, ions were

accelerated, flied through a field-free region, and were detected by a dual

microchannel plate (MCP) detector. It is well known that the spoil field must be

kept low to obtain a MATI spectrum with good resolution, which requires use of

a long time delay between VUV absorption and PFI. Use of a time delay longer

than 10 ns led to rapid decay of MATI signal in our apparatus. We could

lengthen the lifetime of the VUV-excited neutrals tremendously, however, by

applying a short pulse of scrambling field at the laser irradiation time. This

allowed the use of a very long delay time, ~ 25 µs, and low spoil field. Timing

sequence for various pulses is shown in Fig. 1.8. MATI signal detected by MCP

was preamplified and A/D converted by a digital storage oscilloscope (LeCroy

9370L). Either the full time-of-flight mass spectrum or selected regions of the

spectrum as needed were transferred to a personal computer in real time.

The tunable VUV light was generated by resonant four-wave mixing (ωVUV±

= 2ωUV ± ωS) in Kr and Hg in the region of 130 ∼ 143 nm and 106.6 ∼ 117 nm,

21


2004/01/28 17:41:01

(a) Broad-band MATI scheme

E1

E2

E31500V

1250V

-0.3V

photon

25 µs

(b) Narrow-band MATI scheme

E1

E2

E3 20V

2000V

-0.3V

photon

25 µs

1750V

Fig. 1.8 Timing sequence for various pulses adopting according to (a)

broadband MATI scheme or (b) narrowband MATI scheme

22


2004/01/28 17:41:01

respectively. VUV generation in Kr will be described with details in Chapter 4.

A schematic diagram of the experimental apparatus is in Fig. 1.9. Briefly, to

excite the Kr 5p[1/2]0 – 4p6 transition, the light at 212.5 nm (∼0.5 mJ/pulse) was

generated by frequency tripling of 637.6 nm output of a dye laser (Continuum

ND6000) pumped by the second harmonic of an Nd:YAG laser (Continuum

PL8000). Another dye laser output (410 ∼ 570 nm) pumped by the third

harmonic of the second Nd:YAG laser (Continuum Surelite II) was combined

with the 212.5 nm light and loosely focused with a fused silica lens (f = 50 cm)

in the Kr cell to generate the VUV light tunable in the 130 ∼ 143 nm range. A

MgF2 lens (f = 25 cm) was placed at the exit of the Kr cell and the laser beams

were aligned off-centered at the lens to separate the residual light beams (UV

and visible) from the VUV light that was focused onto the molecular beam. The

optimized Kr pressure in the cell was 5 ∼ 15 Torr.

VUV in the region of 106.6 ∼ 117 nm used to measure the spectra of the

cations in the excited states was generated by four-wave sum frequency mixing

in Hg. A schematic diagram of the experimental apparatus is in Fig. 1.10. The

UV light (ωUV = 312.8 nm, ∼ 2 mJ/pulse), which excites the Hg 61S0 – 71S0

transition via the two-photon resonance, was generated by frequency-doubling of

an output of a dye laser (Continuum ND6000) pumped by the second harmonic

of an Nd:YAG laser (Continuum PL8000) with ∼ 7 nsec pulse duration and 10

Hz repetition rates. ωS (2 ∼ 6 mJ/pulse) at 335 ∼ 470 nm was generated by the

second dye laser (Lambda Physik SCANMATE 2E) pumped by the second or

third harmonic of another Nd:YAG laser (Continuum PL8010). The two laser

beams were combined with a dichroic mirror and tightly focused using an

achromatic lens (f = 20 cm) onto the Hg vapor. The four-wave mixing Hg cell

was designed similar to that of Hilbig et. al.74 A LiF lens (f = 20 cm) was placed

23


2004/01/28 17:41:01

molecular beamVUVE3

E2E1G

TOF

Kr cell

MgF2 lens(R=103mm)

Dichroic mirror

PI chamber

50cm lens

(a) top view

(b) side viewT

OF

MCP

Au plate

ωUV

ωS

Temp.-controlledPulsed valve

Fig. 1.9 Schematic drawing of the four-wave mixing Kr cell and VUV

MATI instrument. (a) top and (b) side views.

24


2004/01/28 17:41:01

molecular beam

PI chamber

(b) side viewT

OF

MCP

LiF lens(R=103mm)

(a) top view

Achromaticlens(f=200mm)

Fused silicawindow

Hg cell

Dichroicmirror

ωUV

ωS

Temp.-controlledPulsed valve

VUV E3

E2E1G

TOF

Hg

Heatingblock

Ar

Water inWater in

Fig. 1.10 Schematic drawing of the four-wave mixing Hg cell and VUV

MATI instrument. (a) top and (b) side views.

25


2004/01/28 17:41:01

at the exit of the Hg cell and the laser beams were aligned off-center to separate

the VUV light from the residual UV and visible lights at the interaction region

with the molecular beam. The VUV output in the 106.6 ∼ 117 nm region was

optimized at the Hg vapor pressure close to 0.9 Torr with Ar buffer (1 ∼ 2 Torr).

The spectral resolution was ∼ 1 cm-1 and 1010 ∼ 1011 photons /pulse were

generated. A small portion of a dye laser output was used to calibrate its

frequency based on the optogalvanic effect in a Fe/Ne hollow cathode lamp. Its

precision was ± 0.5 cm-1 in the visible region. A gold wire was placed in the

VUV beam path as a beam monitor. Its output was used to normalize the

intensity of each vibrational peak in the MATI spectra.

1.3.4 Application to Excited Electronic States of Ions

When vibrational peaks in the PES band of an excited electronic state of a

molecular cation are resolved,56-58 one can expect to obtain a well resolved

vibrational spectrum for this state. The states of benzene and chlorobenzene

cations studied previously by various methods are such states. The above are the

hole states generated by removal of an electron from an orbital lying below the

highest occupied orbital of the neutral. Various difficulties appear when one

attempts ‘1+1’ ZEKE or MATI for such a case. A useful technique here is to

prepare molecular cations in the ground electronic state and record the

multiphoton dissociation spectrum occurring via resonance excitation to the

excited electronic state of interest, or REMPD.

B~

B~

75,76 An alternative is to prepare

neutrals in highly excited Rydberg states and observe their ionization induced by

another laser, or photoinduced Rydberg ionization (PIRI) spectroscopy.77,78

REMPD and PIRI can suffer some complications when the transition involved is

electric dipole forbidden, such as the ← transitions for the benzene and

chlorobenzene cations. Here again, the simplest approach is to obtain ZEKE or

X~

26


2004/01/28 17:41:01

MATI spectrum with the one-photon scheme using appropriate VUV radiation.

The one-photon MATI scheme has been found to be especially useful to

obtain the cation ground state spectrum because knowledge on the neutral

intermediate states is not required. In the study of excited electronic states, the

fact that ionization occurs only to the hole states in MATI is an additional

advantage. One-photon ZEKE scheme has been utilized already to obtain

vibrational spectra of simple cations in the ground and excited states.16,71-73 The

present study has demonstrated that one-photon MATI scheme can be routinely

used to obtain vibrational spectra of polyatomic cations also once coherent VUV

radiation becomes available over a wide spectral range.

27


2004/01/28 17:41:01

References

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3. J. Laane, H. Takahashi, and A. Bandrauk, Structure and Dynamics of

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51. C. R. Cowley, An Introduction to Cosmochemistry (Cambridge University

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65. H. Krause and H. J. Neusser, J. Chem. Phys. 97, 5923 (1992).


67. J. W. Hepburn, Chem. Soc. Rev. 25, 281 (1996).

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69. A. Held, L. Y. Baranov, H. L. Selzle, and E. W. Schlag, Chem. Phys. Lett.

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74. R. Hilbig and R. Wallenstein, IEEE J. Quantum Electron. QE-19, 1759

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75. X. Ripoche, I. Dimicoli, J. LeCalve, F. Piuzzi, and R. Botter, Chem. Phys.

124, 305 (1988).

76. K. Walter, U. Boesl, and E. W. Schlag, Chem. Phys. Lett. 162, 261 (1989).

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33


2004/01/28 17:41:01

Chapter 2

Discovery of Isolated Electronic State by

Mass Spectrometry

One of the main assumptions in the original formulation of the theory of

mass spectra1 was that the rate of dissociation of an ion be slow relative to the

rate of redistribution of energy of the internal degrees of freedom, both

electronic and vibrational. Namely, a molecular ion generated in an excited

electronic state would undergo a rapid radiationless transition to the ground

electronic state. Then, statistical distribution of the internal energy, which is now

in the form of the vibrational energy in the ground electronic state, would

determine the reaction rate. With this assumption, the theory becomes equivalent

to the Rice-Ramsperger-Kassel-Marcus (RRKM) theory2 for unimolecular

reaction in the ground electronic state. The theory has been successful to explain

most of the mass spectral features. Regardless, validity of the assumption of the

rapid conversion to the ground electronic state has been the focus of

investigations over the years.3-5 Cases to the contrary, namely the presence of

isolated electronic states, have been reported. The most obvious of these is

repulsive dissociation from an excited electronic state.6-8 Also, elaborate

experiments using techniques such as the photoelectron-photoion coincidence

spectrometry provided evidence for the presence of the isolated electronic states

for some simple systems.9-10

34


2004/01/28 17:41:01

2.1 Initial Discovery: Benzene Cation

The benzene molecular ion is one of the most extensively studied ionic

systems. Various experimental and theoretical methods were used to investigate

the structure and the dissociation dynamics of this ion. It is well established now

that the C6H6+• ion generated by electron ionization of the neutral benzene

precursor retains the benzene structure.11 On the other hand, the nature of its

dissociation dynamics has been a controversial subject since the report by

Andlauer and Ottinger12 that the dissociations to C6H5+ and C4H4

+• were not in

competition according to their charge exchange kinetics data. Rosenstock and

coworkers13 analyzed the photoionization data and suggested that C6H5+and

C6H4+• be formed from the benzene ion ground state while C4H4

+• and C3H3+

from the first excited state. Further investigations14-18 carried out thereafter,

however, showed the statistical character of the benzene ion dissociation. Most

conspicuously, Neusser and coworkers15 found that the production rate constants

for the above four fragment ions measured by photodissociation of the benzene

ion generated by resonance-enhanced two-photon ionization were identical. It

was concluded that the benzene ion excited to the C or electronic

state undergoes a rapid internal conversion to the ground state where the

dissociations occur statistically. Now, the statistical dissociation of the benzene

ion in the ground state is generally accepted. A successful Rice-Ramsperger-

Kassel-Marcus (RRKM) theory modeling of the dissociation rate has been

reported,

~2u

2 A D~ 1u2 E

18 which is in excellent agreement with the recent experimental

data.15,17,18

Various experimental and theoretical efforts have been made also to study

the excited electronic states of benzene ion, a part of the interest arising from the

possible presence of an isolated electronic state mentioned above.19-35 In addition

35


2004/01/28 17:41:01

to the ground electronic state X , several excited electronic states (

, and E~ ) have been identified by the photoelectron

spectroscopy.

~

2uB

g2E

1g2 E B~ g2

2 E ,

C~ 2u2 A , D~ 1u

2 E 2

2

30-32 Compared to the neutral benzene36 and the halogen-substituted

benzene ions,37,38 the first excited electronic state ( ) of benzene ion has

been found to be very difficult to investigate by conventional absorption and

emission spectroscopies.

B~ g22 E

19-22 In particular, lack of fluorescence from this state

has been the subject of great interest,9,12 which forbids the use of the highly

sensitive laser-induced fluorescence technique. This has been attributed to the

rapid internal conversion to the ground electronic state.22 Recently, high

resolution spectra of the B~ state have been obtained with the use of the

modern spectroscopic techniques such as the resonance-enhanced multiphoton

dissociation spectroscopy23 and the photo-induced Rydberg ionization

spectroscopy24 and the properties of this state have begun to be unveiled.

In the course of our photodissociation investigation of the benzene molecular

ion generated by electron impact, we observed an unexpected strong absorption

in the near ultraviolet. A combined kinetic and charge exchange ionization study

showed the presence of a long-lived excited electronic state of benzene ion. The

results from our investigation are discussed in this section.

2.1.1 Experimental Setup

A schematic diagram of the double focusing mass spectrometer with reversed

geometry (VG ZAB-E) modified for photodissociation (PD) study is shown in

Fig. 2.1. Samples were introduced into the ion source via a septum inlet and

ionized using 20 eV electron energy. Ions generated in the ion source were

accelerated to 8 keV and analyzed by conventional and photodissociation mass

36


2004/01/28 17:41:01

Magnetic sector

Ion source

Electrodeassembly

Electric sector

PMT

Chopper

Lens

Argon ion laser

Phase-sensitive detection

Laser beam Prism

Laser beam

Collision cell

R1 R2 R3 R6R4 R7R5

Ion beam

Ion beam

Fig. 2.1 Schematic diagram of the double focusing mass spectrometer with reversed geometry (VG ZAB-E)

modified for photodissociation study. The inset shows the details of the electrode assembly.

37




spectrometries. Two different ion sources were used. To generate ions only by

electron impact, a source with a large conductance was used, which will be

called the electron ionization (EI) source. A source with smaller conductance, a

chemical ionization (CI)39 source, was used to generate ions via ion-molecule

reactions in the presence of the ionizing electron beam. The ion source

temperature was maintained at 150 °C. The CI experiment was done not only for

benzene itself but also for other samples, using benzene as the reagent gas.

Pressure of a sample other than benzene was maintained at ∼1 % of the reagent

gas.

Pressure was monitored with an ionization gauge located outside the ion

source. The pressure inside the CI source, P, was estimated from the ionization

gauge reading, Pig, using the relationship.40

ig)(= PgZS

P (2.1)

Here, Z is the conductance of the source evaluated in the usual way41, S is the

pumping speed estimated according to ref. 40, and g is the gas correction factor

of the ionization gauge available in the literature.42 Also measured was the

average source residence time of an ion exiting the CI source, which was used in

the work to estimate the number of collisions suffered by an ion. For this

purpose, the electron beam was pulsed and the time delay between the electron

and ion pulses was measured. Circuit diagram devised to pulse the electron beam

is shown in Fig. 2.2. The source residence time under the EI condition was

estimated by ion-optical trajectory calculations.43 Adding this to the measured

time delay difference between the CI and EI experiments, the source residence

time was estimated at various ion source pressures.

For the photodissociation study, benzene ion beam was selected by the

38


2004/01/28 17:41:01

Fig. 2.2 Circuit diagram devised to pulse the electron beam. MA3104-

003D indicates the main board circuits controlling the ion source of ZAB-

E mass spectrometer.

39


2004/01/28 17:41:01

magnetic sector and was crossed perpendicularly with a laser beam inside an

electrode assembly located near the intermediate focal point of the instrument as

shown in Fig. 2.1. The UV multiple line with the mean wavelength of 357 nm of

an argon ion laser (Spectra Physics Beamlok 2065-7S) and the 488.0 and 514.5

nm lines of another argon ion laser (Spectra Physics 164-09) were used. The

translational kinetic energy of product ions was analyzed by the electric sector.

Recording the kinetic energy of product ions generated by the dissociation of

mass-analyzed precursor ions is called the mass-analyzed ion kinetic energy

spectrometry (MIKES).44 A MIKE spectrum for PD, or a PD-MIKE spectrum, is

often contaminated by contributions from the same reactions occurring

unimolecularly or by collision of the precursor ions with the residual gas. Hence,

phase-sensitive detection was adopted to record a MIKE spectrum originating

only from PD. To improve the quality of PD-MIKE spectra, signal averaging

was carried out for repetitive scans.

2.1.2 Energetics of Benzene Ion

Adiabatic ionization energy to X was determined recently by

photoelectron spectroscopy

~

22 E

2u

1g2 E

g

31 as 9.243 eV which is essentially the same as 9.244

eV measured by zero kinetic energy spectroscopy.35 Information on the excited

states is limited to those created by loss of an electron from the occupied orbitals

as observed by photoelectron spectroscopy (PES). The second PES band, namely

the band corresponding to the ionic B state, is well resolved. A recent PES

study

~

2 B

31 reported the adiabatic ionization energy of 11.488 eV for this state.

Those to C , and E~ are known less accurately due to the

broad and overlapping nature of the photoelectron bands as ~12, ~13.8 and

~14.7 eV, respectively. No experimental energetics data are available for the

~2u

2 A , D~ 1u2 E

40


2004/01/28 17:41:01

X 2E1g (ground state)

B 2E2g

C 2A2u

D 2E1u

E(eV)

0

5

3

2

4

Dissociation( Products )

~

~

~

~

E 2B2u

~

Electronic states( C6H6

+• )

ktot ~ 107s-1

ktot ~ 104s-1

C6H6+•→ C6H5

+ + H•

6

1

Fig. 2.3 Energy diagram of the benzene molecular ion. The lowest reaction

threshold (E0) is 3.66 eV for C6H6+•→C6H5

++H•. ktot denotes the total rate

constant for dissociation in the ground electronic state predicted from

previous studies.18

41


2004/01/28 17:41:01

excited electronic states associated with the elevation of an electron to

unoccupied orbitals. However, these states are thought to lie well above the

state according to the spectroscopic data for neutral benzene. The lowest

reaction threshold for benzene ion, namely the critical energy

B~ g22 E

18 for the

production of C6H5+ and H• from the ground state benzene ion, is 3.66 eV. These

energetics data are shown schematically in Fig. 2.3.

2.1.3 Photodissociation Kinetics

When the benzene ions generated by EI were irradiated with visible (514.5

and 488.0 nm) or near UV (357 nm) lasers with the corresponding photon

energies of 2.41,

2.54, and 3.47 eV, respectively, noticeable amounts of C4H4+• were produced

with C6H5+, C6H4

+•, C5H3

+, and C3H3+ appearing as minor products. The electron

energy used for ionization hardly affected the photodissociation features, even

though data obtained at 20 eV EI will be presented here for comparison with

other data which will be discussed later. To obtain a rough estimate of the PD

cross section at 357 nm, the PD yields were measured for benzene ion, 1,3,5-

hexatriene, cyclopropylbenzene, and n-butylbenzene ions. The latter three are

the ions whose PD cross sections at 357 nm are available in the literature.46-48

Care was taken such that all the measurements were done under the same

experimental condition, especially the same ion beam-laser beam overlap. Both

the precursor and PD fragment ion intensities were measured to obtain the

relative PD yield in each case. Comparing the PD yield of benzene ion with

those of the other three and using the PD cross sections of the latter ions in the

literature, the PD cross section of benzene ion at 357 nm was estimated. This

was ~9×10-19 cm2, corresponding to a fairly strong dipole-allowed transition. The

42


2004/01/28 17:41:01

PD yields at 488.0 and 514.5 nm were roughly 30 and 20 %, respectively, of that

at 357 nm.

According to previous photodissociation studies of benzene ion trapped in an

ion cyclotron resonance (ICR) spectrometer reported by Freiser and

Beauchamp33 and also by others,34,35 a benzene ion can absorb two visible

photons sequentially via the dipole-allowed C ← transition

( ← is dipole-forbidden), namely via two successive C~ ←

transitions with a rapid internal conversion in-between, and dissociate. Such a

sequential two-photon excitation mechanism is not applicable here because the

ion transit time (~1ns) across the light field is far shorter than in the ICR

experiment (~1s). Even for other dipole-allowed one-photon photodissociation

processes, the product yields detected by the present apparatus are less than

0.001 % of the parent ion intensity. This forms another argument against the

sequential two-photon absorption. Then, the fact that dissociation of benzene ion

could be induced by absorption of one photon with energy less than the reaction

threshold was puzzling. Hence, an attempt was made in this work to estimate the

internal energy of benzene ion undergoing dissociation using the

photodissociation kinetics technique developed previously.

~2u

2 A X~ 1g2 E

B~ g22 E X~ 1g

2 E X~

49-51

The PD-MIKE spectrum at 357 nm was recorded for benzene ion with 2.1

kV applied to the electrode R2 and the remaining electrodes of the electrode

assembly (Fig. 2.1) grounded. With the electric field present in the

photoexcitation region, the kinetic energy of a product ion will change

depending on the position of its formation. The MIKE spectral region

corresponding to the production of C4H4+• is shown in Fig. 2.4. The positions

marked A and B in this figure are the kinetic energies of products generated at

the position of photoexcitation and after exiting the ground electrode (R3 in this

43


2004/01/28 17:41:01

5300 5500 5700 5900

B

A

Inte

nsity

Translational energy, eV

Fig.2.4 PD-MIKE profile for the production of C4H4+• from the benzene

ion at 357nm obtained with 2.1kV applied on the electrode assembly.

Experimental result is shown as filled circles. Reproduction of the profile

using the rate constant distribution centered at 6.3×107 s-1 obtained by

experimental data is shown as the solid curve. The positions marked A and

B are the kinetic energies of products generated at the position of

photoexcitation and after exiting the ground electrode, respectively.

44


2004/01/28 17:41:01

case), respectively. The asymmetric tail in the lower energy side of A is due to

dissociation occurring before R3 on a nanosecond time scale. The method to

evaluate the rate constant (k) by analyzing this time-resolved PD-MIKE profile

is well established now.49-51 The most probable rate constant determined from

several duplicate experiments are (5.5±1.1)×107 s-1. The MIKE profiles for

C6H5+ and C6H4

+• were not well resolved due to the interference from the

precursor signal. The MIKE profiles for C5H3+ and C3H3

+ were very similar to

that in Fig. 2.4, indicating the competitive dissociations. If all the five

dissociation channels are competitive as is currently accepted, the measured rate

constant corresponds to the sum of the individual rate constants. Then, the

average internal energy content of the photodissociating benzene ion can be

determined by comparing with the previous experimental rate-energy data or

with their RRKM fit. Since the present rate constant is a little out of range from

the previous rate-energy data,15,17 the RRKM calculation of Grebner and

Neusser18 was extended to higher internal energy. Production of C5H3+, which

was less than 10 % of the total product intensity, was ignored since the

parameters needed for calculation were not reported by the above investigators.

The RRKM expression of the rate constant for each channel, ki (E), at the

reactant internal energy E is given by

)()-()( 0

EhEEWEk ii

ii ρσ

‡

= (2.2)

Here, h is the Planck constant, ρ is the density of states of the reactant, Wi‡ is the

state sum at the transition state for the ith channel with the critical energy E0i,

and σi is the reaction path degeneracy. Then, the total dissociation rate constant

is obtained by adding rate constants for all the competing channels.

45


2004/01/28 17:41:01

4 5 6 7 8

2

4

6

8

10357 nm PD

488.0 nm PD

log

k, k

in s-1

Internal energy, eV

Fig. 2.5 The total RRKM dissociation rate constant of benzene ion as a

function of the internal energy calculated with molecular parameters in ref.

18. The internal energies corresponding to the dissociation rate constants

of ( 5 . 5±1 .1 )×107 and (5±3 )×106 s-1 for PDs at 357 and 488.0 nm,

respectively, are marked.

46


2004/01/28 17:41:01

∑4

1=total )(=)(

ii EkEk (2.3)

The total rate constant calculated over the internal energy range of interest using

the molecular parameters in ref. 29 is shown in Fig. 2.5. The calculated rate

constants at two internal energy values are marked in Fig. 2.3 also to emphasize

the fact that the photodissociation can be observed with the present nanosecond

apparatus when the internal energy of the photo-excited benzene ion is higher

than the reaction threshold by a few eV. The average internal energy of the

photodissociating benzene ion corresponding to the observed rate constant of

(5.5±1.1)×107 s-1 was read from the calculated rate-energy data, which was

6.1±0.1 eV. Subtracting the 357 nm photon energy (3.47 eV) from this value

results in the average pre-excitation internal energy of 2.6±0.1 eV for benzene

ion undergoing photodissociation. Dissociations in the visible were slower and

the rate constants were beyond the limit that can be determined reliably by the

present technique. My best estimate for PD at 488.0 nm was k= (5±3)×106 s-1

which corresponds to the internal energy of 5.5±0.1 eV. Subtracting the photon

energy of 2.54 eV, the pre-excitation internal energy of benzene ion undergoing

PD at this wavelength becomes 3.0±0.1 eV. A routine explanation for the above

pre-excitation internal energies is that the benzene ions generated in various

excited electronic states by EI undergo rapid internal conversion and the

electronic energies of these excited states are converted to the vibrational energy

in the ground electronic state. Validity of such an explanation can be checked by

observing the decrease in the PD signal as the vibrational energy of the ground

electronic state benzene ion is relaxed in the high pressure ion source.

2.1.4 Quenching of Photodissociation

As an attempt to induce the quenching of the PD signal by collisional

47


2004/01/28 17:41:01

relaxation of the vibrationally hot benzene ions, we introduced a benzene/argon

mixture (benzene:argon=1:50) into the source and recorded the PD signal as a

function of pressure. Even though the Ar+• ion generated by electron ionization

can ionize the neutral benzene by charge exchange, the benzene ion thus

generated would have the internal energy as large as 6.5 eV and dissociate

immediately, not affecting the photodissociation carried out at 22 µs after ion

formation. We could not achieve efficient relaxation of the vibrationally hot

benzene ion in this way, however. Namely, the PD signals increased with the

mixed gas pressure in the ion source almost to the point where the intensity of

the precursor benzene ion itself began to decrease due to various collisional

processes such as deflection and subsequent wall collision. Some of the data

obtained in this experiment will be discussed later.

In the case of molecular ions, it is well known that the resonant charge

exchange17,52 with their neutral counterparts is more efficient for vibrational

relaxation than the usual inelastic processes. In this process, the molecular ion is

converted to a neutral retaining the vibrational energy while the neutral collision

partner becomes an ion with much less vibrational energy. Namely,

C6H6+•* + C6H6 C→ 6H6* + C6H6

+• (2.4)

As an attempt to induce the quenching of the PD signal via charge exchange

collision of vibrationally hot benzene ions in the ion source, we introduced

benzene to the CI source to much higher pressure than normally used in the

electron ionization (EI) mass spectrometry and measured the PD signal as a

function of the benzene pressure. Fig. 2.6 shows the precursor (C6H6+•) intensity

and photoproduct (C4H4+•) intensities at 357 and 488.0 nm as functions of the

pressure measured by an ionization gauge located outside of the source. The

pressure dependence of the photoproduct signal at 514.5 nm was essentially the

48


2004/01/28 17:41:01

same as that at 488.0 nm. At high pressure, the ionization gauge reading can be

converted to the source pressure following the method described in a previous

section. Pressure data at some important points are listed in Table 2.1. Tuning of

the instrument changed a little with the source pressure, the effect of which was

not corrected for in the data. The precursor intensity increases initially as the

pressure increases, as expected. This reaches the maximum at the ionization

gauge reading of 3.5×10-5 Torr which corresponds to the ion source pressure of

∼0.04 Torr and then begins to decrease with the pressure. Various physical and

chemical processes must be responsible for the overall pressure dependence in

the high pressure region. The photoproduct ion signals also rise and fall with the

pressure increase, with the maxima at pressures lower than for the precursor. The

most remarkable observation here is the fact that the maximum in 357 nm PD

occurs at much higher pressure than that in 488.0 nm one. Even in the high

pressure region where the 488.0 nm PD signal disappears completely, the 357

nm signal keeps increasing with the pressure.

Absorption of a photon at 357 and 488.0 nm increases the benzene ion

internal energy by 3.47 and 2.54 eV, respectively. Considering that the critical

energies for the production of the major fragment ions are ∼4 eV,29 rather close

to the 357 nm photon energy, one may attempt to explain the above observation

with the argument that PD at 357 nm would not be easily quenched because the

pre-excitation internal energy needed for dissociation is not large. Such an

argument is not valid in the present experiment, however, because the photo-

excited benzene ion must possess internal energy a few eV above the critical

energy for its dissociation to be detected on a nanosecond time scale (Figs. 2.3

and 2.5). Specifically, the pre-excitation internal energies needed for PDs at 357

and 488.0 nm are comparable, 2.6±0.1 and 3.0±0.1 eV, according to the PD

kinetics data presented above.

49


2004/01/28 17:41:01

Table 2.1. Ion source pressure (P), collision frequency (Zc), source residence

time (tR), and number of collisions (Ncoll) suffered by ions exiting the ion source

at some benzene pressures.

Pig/Torr P/Torr Zc/µs-1 tR/µs Ncolla

4×10-6 0.0051 0.13 4.2 0.6 (1.4)

1×10-5 0.013 0.33 5.8 1.9 (4.5)

2×10-5 0.025 0.63 7.6 4.8 (12)

3×10-5 0.038 0.96 9.0 8.6 (23)

5×10-5 0.063 1.59 11.2 18 (49)

7×10-5 0.088 2.23 13.0 29 (82)

a Numbers in the parentheses are for the Ar reagent gas.

To see if the vibrational relaxation by charge exchange collision, reaction

(2.4), was operative in the actual experiment, we estimated the average number

of collisions suffered by benzene ion exiting the ion source by multiplying the

collision frequency (Zc) by the average residence time in the ion source.

uZ ccc 2= σρ (2.5)

Here, ρc and <u> are the number density and the average speed, respectively. σc

is the cross section for ion-dipole collision which was estimated roughly using

the Langevin formula.53

21

r0

2

c E2'

=

πεαπσ e (2.6)

50


2004/01/28 17:41:01

Here, α′ is the polarizability volume (1.032×10-29 and 1.66×10-30 m3 for C6H6

and Ar, respectively)54 and Er is the relative translational energy which can be

approximated as 23 kT. Collision frequencies, average source residence time, and

average number of collisions suffered by ions exiting the source estimated at

several pressures are listed in Table 2.1. We expect that the number of collisions

thus estimated is accurate within a factor of 2∼3. At the ionization gauge reading

of ∼4×10-6 Torr corresponding to the maximum in the PD intensity at 488.0 nm,

the average number of collisions was 0.60. On the other hand, the same PD

intensity hardly decreased even after 10∼20 collisions in the quenching

experiment with Ar mentioned previously (data not shown). This indicates that

the efficient vibrational relaxation by charge exchange collision be operative in

the ion source at high benzene pressure. In contrast, the average number of

collisions at the ionization gauge reading of 2.5×10-5 Torr corresponding to the

maximum in the PD intensity at 357 nm was 6.7. Namely, the quenching of the

PD signal at 357 nm by charge exchange collision in the ion source is much less

efficient than in the 488.0 nm PD case. Considering that every charge exchange

collision is effective for vibrational relaxation (488.0 nm PD case), very

inefficient quenching of PD at 357 nm can not be explained simply based on the

smaller requirement of the pre-excitation internal energy in this case.

The fact that the collisional quenching behaviors of PDs at 357 and 488.0 nm

are dramatically different can be explained only by assuming that the C6H6+•

precursors for 357 and 488.0 nm PDs be different, either in structure or state. As

was mentioned in a previous section, benzene ion is the most stable of the

C6H6+• isomers and retains its structure. Also, the fact that the recombination

energy of 9.2 eV was found valid for C6H6+• generated from benzene at even

higher source pressure (0.4 Torr)55 than used in this work supports that the

51


2004/01/28 17:41:01

C6H6+• ion investigated here has the benzene structure. This is also supported by

the charge exchange ionization data to be presented later. Then, the remaining

possibility is that the electronic state of benzene ion responsible for PD at 357

nm is different from that at 488.0 nm. If the C ← transition for

benzene ion in the ground electronic state with a large vibrational energy is

responsible for PD at 488.0 nm, the PD at 357 nm must involve a transition from

an electronic state other than the ground state. The fact that no peak was

observed in this spectral region in the absorption spectrum of benzene ion

trapped in the argon matrix

~2u

2 A X~ 1g2 E

20,21 is in agreement with such an assignment.

The assumption that the initial state for PD at 357 nm be an excited

electronic state has some difficulties of its own. The first is that this state should

survive for ∼10µs in the source and also for a few tens of microseconds needed

for the flight from the source to the laser-ion interaction region. This can be

reconciled only by assuming that the electronic state involved is long-lived, with

the lifetime of 10 µs or longer. The second difficulty of the above assumption is

that the collisional relaxation of this excited electronic state is not as efficient as

the vibrational relaxation in the ground electronic state (PD at 488.0 nm). This

can be explained readily, however, considering that the most efficient process in

the collision of the electronically excited benzene ion (C6H6+•†) with the neutral

benzene would be the resonant charge exchange.

C6H6+•† + C6H6 C→ 6H6 + C6H6

+•† (2.7)

The PD yield at 357 nm is maintained at high source pressure because the

resonant charge exchange of C6H6+•† regenerates C6H6

+•† and hence does not

affect the C6H6+• population in the excited electronic state. This is in contrast

with the resonant charge exchange of C6H6+•* which reduces its population.

52


2004/01/28 17:41:01

��

Relaxation of the electronically excited benzene ion by inelastic collisions

must be occurring also, however, considering that decay of the 357 nm PD

signal occurs at lower pressure than that of the total benzene ion current in Fig.

2.6. Then, benzene ion would be mostly in the ground electronic state at a very

high source pressure, for example at ∼ 7×10-5 Torr ionization gauge reading in

Fig. 2.6 which corresponds to ∼ 0.09 Torr source pressure. The relative 357 nm

PD cross section at this pressure was less than 0.1 % of that at much lower

pressure region suggesting that most of the benzene ions are in the ground

electronic state. This may be the reason why the benzene ion recombination

energy of 9.2 eV, which is equivalent to the ionization energy of benzene to the

ionic ground state, was observed by Rao and Fenselau55 in the charge exchange

experiment performed at the benzene pressure of ∼ 0.4 Torr. Two experimental

results, Rao and Fenselau’s and ours, can not be compared quantitatively,

however, because the methods used to measure the pressure might not be the

same.

2.1.5 Charge Exchange Ionization by Benzene Ion in the Excited

Electronic State

Benzene is a well-known reagent in the chemical ionization mass

spectrometry.39 As mentioned above, benzene ion is the reagent ion in this

ionization scheme and ionizes compounds with the ionization energy less than

9.243 eV by charge exchange at a very high source pressure of ∼ 0.4 Torr.

C6H6+• + A → C6H6 + A+• (2.8)

If the benzene ion population in the long-lived excited electronic state is

maintained at a moderately high source pressure such as 1.0×10-5 Torr ionization


2004/01/28 17:41:01

10-6 10-5 10-4

0

0.09 Torr

0.04 Torr

0.013 Torr

Rel

ativ

e in

tens

ity

Ionization gauge reading, Torr

Fig. 2.6 Pressure dependences of the precursor (C6H6+•) intensity (–––)

and photoproduct (C4H4+•) intensities at 357 (·····) and 488.0 (–––) nm.

Pressure in the CI source was varied continuously to obtain these data. The

abscissa shows the pressure read by an ionization gauge located outside of

the source. The inside source pressures estimated using eqn. (1) at three

ionization gauge readings are marked. The scale for the precursor intensity

is different from that for photoproduct intensities.

54


2004/01/28 17:41:01

gauge reading (∼0.013 Torr in source pressure), it should be possible to

determine its recombination energy through charge exchange experiments.

Namely, samples with ionization energy less than the recombination energy of

the electronically excited benzene ion would be ionized efficiently by charge

exchange while those with higher ionization energy would not be ionized.

Samples used in the experiment are listed in Table 2.2 together with their

ionization energies. Since some of the samples are ionized by electron impact

even under the chemical ionization (high source pressure) condition, the

molecular ion intensities were measured under the CI and EI conditions and their

ratios (CI/EI ratio) were evaluated. At the high ion source pressure of 0.09 Torr

(7×10-5 Torr ionization gauge reading), samples with ionization energy larger

than the recombination energy (9.243 eV) of the ground state benzene ion were

hardly ionized, as listed in Table 2.2. This is in agreement with the report by Rao

and Fenselau55 and also with the near complete decay of the electronically

excited benzene ion at this pressure indicated in Fig. 2.6. At lower pressure,

however, the molecular ion intensities of some samples with ionization energy

larger than 9.243 eV increased with the source pressure. The CI/EI ratios for the

molecular ion intensities measured at the low ion source pressure of 0.013 Torr

(1.0×10-5 Torr ionization gauge reading) are listed in Table 2.2. Data at 0.013

Torr are drawn in Fig. 2.7 also. It is remarkable to note that the samples with

ionization energy less than ~11.5 eV can be ionized efficiently by benzene ion at

this pressure while those with ionization energy a little larger than this are

difficult to ionize. This is a strong evidence supporting our proposition that there

exists a long-lived excited electronic state of benzene ion. Also to be mentioned

is that the above experimental recombination energy of ~11.5 eV is much larger

than those for other C6H6+• ions which have been investigated in the

isomerization study.56 Namely, other isomers of C6H6+• can not ionize samples

55


2004/01/28 17:41:01

9 10 11 12 13

0

2

4

6 9.243 eV 11.5 eV

CI/E

I rat

io

Ionization energy, eV

Fig. 2.7 The ratios of molecular ion intensities generated by charge

exchange ionization (CI) with benzene ion and by electron ionization (EI)

are plotted as a function of the sample ionization energy. • and o are for CI

intensities measured at the ion source pressure of 0.013 and 0.09 Torr,

respectively.

56


2004/01/28 17:41:01

Table 2.2. Ionization Energies and the ratios of molecular ion intensities

generated by charge exchange ionization (CI) with benzene ion and by electron

ionization (EI).

Compounds IEa (eV) CI/EI(0.013 Torr)b CI/EI(0.09 Torr)b

Chlorobenzene 9.06 3.6 3.5

Fluorobenzene 9.20 3.9 1.4

Benzonitrile 9.62 5.3 0.06

Chloropentafluorobenzene 9.72 4.7 0.01

Nitrobenzene 9.86 3.8 0.06

Hexafluorobenzene 9.91 2.5 0.02

Ethylene 10.51 3.0 0.02

Methylene chloride 11.32 4.4 0.04

Chloroform 11.37 4.7 0.03

Carbon tetrachloride 11.47 3.4 0.06

Ethane 11.52 0.09 ~0

Dichlorofluoromethane 11.75 0.05 0.04

1-chloro-1,1-difluoroethane 11.98 0.16 0.01

Chlorodifluoromethane 12.2 0.09 0.05

Methane 12.51 0.24 ~0

a All the ionization energy (IE) data are from ref. 57 except that for

dichlorofluoro-methane, which is from ref. 58.

b Ratio of the molecular ion intensities measured under the CI and EI conditions.

The pressure in the parenthesis is the ion source pressure in the CI experiment.

EI experiment was done at much lower pressure to avoid ion-molecule reaction.

57


2004/01/28 17:41:01

with ionization energy close to 11.5 eV by charge exchange. This is another

evidence that the precursor in the PD at 357 nm has the benzene structure. The

difference between the experimentally estimated recombination energy of ~11.5

eV for the excited benzene ion and the first ionization energy of benzene is ~2.3

eV. This is also in remarkable agreement with the average pre-excitation internal

energy of 2.6 eV estimated by the photodissociation kinetics at 357 nm

considering that the benzene ion would possess a few tenth of an eV of thermal

vibrational energy in addition to the electronic energy.

As a further test, we also measured the PD yield at 357 nm with the addition

of a small amount (~1%) of scavenger which can decrease the population of the

excited electronic state of benzene ion. For example, addition of benzonitrile

which has the ionization energy of 9.62 eV decreased the PD yield to ~60% even

though the total precursor current was hardly affected. This is also in agreement

with our proposition.

2.1.6 Conclusions

Photodissociation kinetics and charge exchange ionization mass spectrometry

have shown that there exists a long-lived excited electronic state of benzene ion

at ~2.3 eV above the ground state. The lifetime of the state seems to be longer

than 10 µs, maybe much longer. Even though its presence seems to be certain,

the exact identity of the state is a matter of conjecture because not much is

known about the electronic states of benzene ion. According to the photoelectron

spectroscopy, and C are the electronic states in this energy region

which are accessible by one electron removal from an occupied molecular

orbital of the neutral. is not a likely candidate because the corresponding

photoelectron peak appears as a broad structureless band indicating a rapid

B~ g22 E ~

2uA

2u2 A

C~ 2

58


2004/01/28 17:41:01

radiationless process in this state. The assumption of the rapid internal

conversion of this state needed to interpret the photodissociation in the visible33

as the sequential two-photon process is also against the assignment. This leaves

as the best candidate for the long-lived excited electronic state observed

in this work. In particular, ~2.3 eV energy observed for the long-lived state well

matches with the energy difference of 2.245 eV between B and

Such an assignment is not absolutely certain, however, because of the

controversy concerning the lifetime of the B~ state. Leach and coworkers

B~

X~

g22 E

~g2

2 E

E~

X~

g2

1g2 E .

g22 E

g

22

established that fluorescence from this state is not observable and proposed that

a rapid (>8×1010 s-1) internal conversion to the ground state be responsible.

Köppel27 found theoretically that a new type of conical intersection between the

and states triggered by the Jahn-Teller effect may be responsible for the

rapid internal conversion. However, failure to fluoresce may have an entirely

different origin, namely a very long lifetime. Further spectroscopic study on this

state would be useful, such as the acquisition of a high resolution spectrum and

the determination of the lifetime from the spectral width. If the B~ is the

initial state of the present photo-excitation at 357 nm, the transition involved can

be either ← or ← both of which are electric dipole-

allowed. Appearance of the prominent photodissociation signal at 357 nm is in

agreement with such assignments. Whatever the transition is, the benzene ion

further excited by the absorption of a 357 nm photon must undergo a rapid

internal conversion to the ground state for the RRKM theory to be applicable as

assumed in this work. The broad spectral profiles of the D and bands in the

photoelectron spectrum suggests the feasibility of such an assumption. Even

though not applicable in the present case, a situation may arise in which the

B~

2 E

D~ 1u2 E B~ g2

2 E E~ 2u2 B B~ 2E2

~

59


2004/01/28 17:41:01

dissociation occurs in the B~ state. Then, its kinetics would not be

compatible with the currently accepted model of statistical dissociation in the

ground state.

g22 E

The fact that the observed excited electronic state is very long-lived suggests

the possibility of studying the physics and chemistry of this state by various

means. A useful further development may be the preferential generation and

storage of ions in this state. Then, study of the excited state chemistry on a

practical time scale may become a reality.

2.2 Method to Detect Isolated Electronic States

Using the same techniques introduced in previous section, we attempted to

find the evidence for the presence of the isolated electronic states in other ionic

systems. We have found, however, that the above techniques are not generally

applicable. For the photodissociation kinetic technique to be applicable, the

molecular ion of interest must absorb at the wavelength range covered by strong

continuous wave lasers and also must dissociate on the nanosecond ~ low

microsecond time scale. Furthermore, reliable rate-energy data, which are

needed to compare the experimental results with, are available only for limited

number of ionic systems. In the case of the charge exchange ionization in the ion

source, various complications can arise because both the reagent and sample are

mixed in the ion source and ionized together.39 In fact, the previous study on the

benzene system should be regarded as fortunate because benzene is a well-

known reagent for chemical ionization.55 A better method than the charge

exchange ionization in the ion source would be to separate spatially the

ionization and charge exchange regions. Such apparatuses were built in early

days of the charge exchange ionization mass spectrometry and used to measure

60


2004/01/28 17:41:01

accurately the cross sections, appearance energies, etc.59,60 Instead of building a

sophisticated instrument, we simply modified a commercial double focusing

mass spectrometer, which turned out to be adequate for the present purpose. The

results from the investigation are reported in this paper.



geometry (VG ZAB-E; Manchester, UK) is shown in Fig. 2.8. Benzene was

introduced into the ion source via a glass capillary connected to a reservoir

(septum inlet) and ionized under the electron ionization (EI) or chemical

ionization (CI) condition using 20 eV electron energy. The ion source

temperature was maintained at 140 °C. The CI experiments were done at the

benzene pressure of 0.02 or 0.1 Torr in the CI source. Ions generated in the

source were accelerated with high voltage (VS) of 4 kV. 1,3-Butadiene was

purchased from Matheson (Parsippany, NJ) and other chemicals from Aldrich

(Milwaukee, WI). All the chemicals were of the highest purity commercially

available and were used without further purification.

Collision Cells : To investigate the charge exchange ionization of reagent gases

by benzene ion, two collision cells were utilized, the first cell located between

the ion source and the magnetic sector and the second cell between the magnetic

and electric sectors. The second cell is as designed by the manufacturer and can

be floated at a high voltage. In the original design, the first collision cell was

located after the Y-focusing electrodes. For this work, we redesigned the

assembly such that the collision cell was located in front of the Y-focusing

electrodes (see the inset in Fig. 2.8). Also, the collision cell was modified to be

floatable at a high voltage and a repeller plate was installed. Namely, the first

collision cell in its present form functions as the ion source for the reagent gas

61


2004/01/28 17:41:01

Collision cell assembly

Ion beam

Ion source

Magnetic sector Conversion dynode

EM

Electric sector

Collision Cell Y-lens

Repeller

IonSource

Collision cell assembly

Conversion dynode

PM

SecondCollision

cell

Fig. 2.8 Schematic diagram of the double focusing mass spectrometer with reversed geometry (VG ZAB-E). The

inset shows details of the first collision cell assembly modified for charge exchange study.

62




with the ionization achieved by collision with the primary ions entering the cell.

2.2.2 Principle of the Method

This subsection is to show evidence for the presence of primary ions in long-

lived excited electronic states by observing charge exchange ionization (eqn.

(2.8)) of various reagent gases with different ionization energies occurring in the

collision cell. When the primary ion has large translational kinetic energy, not

only the charge exchange ionization but also other processes such as the

collisional impact ionization can generate ions from the reagent gas.61

Decelerating the primary ion would be necessary to eliminate the latters. However,

when the translational energy of the primary ion is reduced to near thermal level,

it diverges in the collision cell or even before entering the cell, which results in

poor reagent ion signal. It will be seen in the next section that deceleration of the

primary ion to near thermal energy is not needed and fairly good results can be

obtained with deceleration to 50∼100 eV.

When a primary ion, m1+, with translational energy eVS is injected into a

collision cell containing a reagent gas, three types (Ⅰ, Ⅱ, and Ⅲ) of ions may

exit the cell, the primary ion itself (typeⅠ), its collision-induced dissociation

product (m2+, typeⅡ), and the ions generated from the reagent gas (typeⅢ). When

a high voltage, VC ( < VS), is applied on the collision cell, the translational

energies of these ions exiting the cell are as follows.62

TypeⅠ, KⅠ = eVS (2.9)

TypeⅡ, KⅡ = e[VC + (m2/m1)(VS - VC)] (2.10)

TypeⅢ, KⅢ = eVC (2.11)

63


2004/01/28 17:41:01

When the second collision cell is used, these three types of ions can be readily

distinguished by measuring their translational energies with the electric sector.

However, it is not possible to determine whether the typeⅢ ions generated are the

molecular ion of the reagent gas, its fragments or reaction products, or a mixture

of these.

Identity of the typeⅢ ions can be determined by performing experiment using

the first collision cell and analyzing ions with the magnetic sector. The mass (m)

of the ion with the translational energy eV and the magnetic field B of the sector

with radius r needed to transmit it are related63 by

m/z = B2r2e/2V (2.12)

Then, using the translational energies in eqns. (2.9) ∼ (2.11), the peaks in the mass

spectrum recorded by scanning the magnetic field can be identified. As a further

check, one can set the magnetic field to transmit a particular peak in the mass

spectrum and measure its translational energy by scanning the electric sector

potential as in the usual mass-analyzed ion kinetic energy spectrometry

(MIKES)64. All the typeⅢ ions must appear at the trasnslational energy of eVC

(eqn. (2.10)) in the MIKE spectrum. One may also record the typeⅢ ions only by

setting the electric sector potential to transmit ions with the translational energy

eVC and scanning the magnetic field. This is not possible yet with the present

apparatus.

2.2.3 Utilization of Method

Since the ionization energies to the ground and long-lived excited electronic

states of benzene ion are 9.243 and ∼11.5 eV, respectively, we chose five

molecules with ionization energies slightly below or above these values as the

64


2004/01/28 17:41:01

reagents. These are 1,3-C4H6 (butadiene)65, CS2, CH3Cl, CH3F, and CH4 with the

ionization energy66 of 9.08, 10.07, 11.22, 12.47, and 12.51 eV, respectively.

Energetics consideration dictates that only 1,3-C4H6 can be ionized by charge

exchange with the ground state benzene ion while 1,3-C4H6, CS2, and CH3Cl can

be ionized by the benzene ion in the long-lived excited state. Neither of the

benzene states have sufficient electronic energy to ionize CH3F and CH4 by

charge exchange.

We first attempted to study charge exchange ionization of CS2 introduced into

the second collision cell. Benzene ion was generated by 20 eV EI in the ion source,

accelerated to 4002 eV, mass-selected by the magnetic sector, decelerated by

collision cell potential of 3902 V, and introduced to the cell. Then, benzene ion

would have the pre-collision translational energy of 100 eV. The pressure of CS2

in the second collision cell was adjusted to attenuate the primary ion beam

(C6H6+•) intensity by 20 %. A partial MIKE spectrum thus obtained is shown in

Fig. 2.9. Most of the peaks in this spectrum arose from unimolecular (metastable

ion decomposition) and collision-induced dissociations of benzene ion and could

be identified using eqn. (2.9). A peak, marked Ⅲ in the figure, appeared at the

translational energy of 3902 eV which corresponded to the acceleration energy

due to the voltage applied on the collision cell. The position of this peak changed

with the cell potential exactly as dictated by eqn. (2.10), showing that the peak

originated from the reagent gas. As mentioned earlier, however, ions responsible

for this peak can not be identified by MIKE spectrometry. Peaks at the same

position were also observed with 1,3-C4H6 and CH3Cl reagent gases but not with

CH3F and CH4, indicating that charge exchange ionization occurred in the former

three cases.

Similar experiment was done by introducing CS2 in the first collision cell. Fig.

2.10 (a) shows the mass spectrum recorded under the single-focusing condition,

65


2004/01/28 17:41:01

3900 3930 3960 3990

77+(MID)

II

II

II

III

Inte

nsity

Translational Energy, eV

Fig. 2.9 MIKE spectrum of the C6H6+• primary ion generated by EI. CS2 was

introduced into the second collision cell. The acceleration energy for C6H6+•

was 4002 eV. The collision cell potential was 3902 V. The peak types are

denoted. The peak marked 77+(MID) is due to the metastable ion

decomposition of C6H6+• to C6H5

+ occurring in the field-free region between

the magnetic and electric sectors.

66


2004/01/28 17:41:01

namely without using the electric sector. The acceleration voltage in the ion

source was 4004 V and 3929 V was applied on the first collision cell in this case.

The mass scale shown in the spectrum is the one calculated with eqn. (2.12) using

the acceleration voltage in the source, 4004 V. Hence, the peaks appearing near

the integer masses correspond to ions generated in the source by electron

ionization. Two peaks appear at the nominal masses of 74.6 and 76.5. Inserting

the collision cell potential of 3929 V into eqn. (2.12), these can be identified as 12C32S2

+• and 12C32S 34S

+• generated in the collision cell. It is not certain at this

point that these CS2+• ions are generated by charge exchange with C6H6

+•. First of

all, these ions may have been generated by charge exchange with fragment ions

produced together with C6H6+• by 20 eV EI of benzene. Most of the fragment ions

appearing in the EI spectra are even-electron species and their recombination

energies, or ionization energy of the corresponding odd-electron radicals, are

usually lower than the ionization energies of the reagent gases used in this work.

Namely, charge exchange ionization of the reagent gases by the even-electron

fragments can be safely neglected. The same argument does not apply to the odd-

electron species. Among the major odd-electron fragment ions (C6H4+•, C4H4

+•,

and C4H2+•) appearing in the EI spectrum of benzene, only C4H2

+• has literature

recombination energy66 larger than the ionization energy of CS2. In this work, its

intensity was reduced to a negligible level by carrying out electron ionization at

20 eV. The second complication arises from the fact that both the ion source and

the first collision cell are evacuated by the same pumping system in the present

apparatus and hence some CS2 enters the ion source and is ionized there. Even

though the primary CS2+• ion beam intensity thus generated would not be strong,

it may contribute significantly to charge exchange ionization of CS2 in the

collision cell because the reaction is symmetric. Presence of the primary CS2+•

(typeⅠ) can not be judged from the mass spectrum in Fig. 2.10(a) because CS2+•

67


2004/01/28 17:41:01

72 74 76 78 800

50

100

Ι

(b)

(c)

(a)x 5

Ι

Ι

ΙΙΙ

C32S2+· (ΙΙΙ)

Rela

tive

Inte

nsity

, %

m/z

48 50 52 54 56 580

50

100

ΙΙΙΙ

Ι

Ι

CH335Cl+· (ΙΙΙ)

Rela

tive

Inte

nsity

, %

m/z

72 74 76 78 800

50

100

ΙΙΙΙ

x 5

x 5

Ι

C32S2+· (ΙΙΙ)

Rela

tive

Inte

nsity

, %

m/z

Fig. 2.10 Mass spectra obtained under the single-focusing condition. The acceleration energy in the source was 4004 eV and the collision cell potential was 3929 V. C6H6

and CS2 were introduced into the ion source and the first collision cell, respectively. C6H6 was ionized (a) by EI and (b) by CI at the 0.02 Torr source pressure. (c) C6D6

and CH3Cl were introduced into the ion source and the first collision cell, respectively and C6D6 was ionized by EI. The instrument was tuned to maximize the type III ion signals. The types of the major signals are denoted.

68


2004/01/28 17:41:01

3900 3915 3930 3945 3960

Inte

nsity


Fig. 2.11 MIKE spectrum recorded by setting the magnetic field to transmit

the C32S2+•(III) ion in Figure 2.10(b) and scanning the electric sector.

69


2004/01/28 17:41:01

and its isotopomer overlap with benzene ion and its fragment at m/z 78 and 76. To

see the effect of the reagent gas leakage to the ion source more clearly, we

recorded the 20 eV EI mass spectrum of C6D6 with CH3Cl in the first collision

cell, Fig. 2.10(c). In this spectrum, m/z 52, 54, and 56 correspond to the typeⅠ

ions of C4D2+•, C4D3

+, and C4D4+• and m/z 48.7 and 50.6 to the typeⅢ CH3

35Cl+•

and CH337Cl+•, respectively. m/z 50 can be the typeⅠ ions of C4D+, CH3

35Cl+•, or

their mixture. By comparing with mass spectrum recorded in the absence of the

reagent gas, we estimated that 75 % of the m/z 50 intensity was C4D+ and the

remainder CH335Cl+•. Namely, the typeⅠ CH3Cl+• is weaker than the typeⅢ one

in the mass spectrum and is not likely to contribute significantly to the typeⅢ

signal.

An easy way to eliminate the above complications, for the benzene case at

least, is to use a CI source and increase the benzene pressure in the source. Fig.

2.10(b) shows the mass spectrum recorded at the benzene pressure of 0.02 Torr,

so-called CI1 condition in previous section, with CS2 in the first collision cell. Not

only the fragment ions from benzene but also the typeⅠ CS2+• (m/z 76) ions are

virtually absent in this spectrum. Regardless, the typeⅢ CS2+• ions appear

prominently at m/z 74.6. Then, these ions must have been generated by reaction of

CS2 with benzene ion. Further evidences showing that this reaction is the charge

exchange with benzene ion in the long-lived excited electronic state will be

presented later. We will just point out here that this long-lived state persists in the

CI1 condition, namely at the source benzene pressure of 0.02 Torr, according to

previous section. We also recorded the MIKE spectrum with the magnetic sector

set to transmit the typeⅢ CS2+• ion, Fig. 2.11. A single peak appears at 3929 eV

in the MIKE spectrum, as expected for a typeⅢ ion generated in the collision cell

floated at 3929 V.

70


2004/01/28 17:41:01

0 200 400 600 800 100010-6

10-5

10-4

10-3

10-2

10-1

(b) 1,3-C4H6+

CS2+

CH3Cl+

CH3F+

CH4+

Rela

tive

Yiel

d, Ι

(A+. ) /

Ι(C 6H

6+. )

Primary Ion Translational Energy, eV

0 200 400 600 80010-6

10-5

10-4

10-3

10-2

10-1

(a)

Rela

tive

Yiel

d, Ι

(A+. ) /

Ι(C 6H

6+. )

1,3-C4H6+

CS2+

CH3Cl+

CH3F+

CH4+

Primary Ion Translational Energy, eV

Fig. 2.12 Relative yields of the reagent gas ions, I(A+•)/I(C6H6

+•), vs. the primary ion translational energy. Benzene ions were generated by CI at (a) 0.02 Torr (CI1) and at (b) 0.1 Torr (CI2) source pressures. Charge exchange ionization was done in the first collision cell. For consistency, the instrument was tuned to maximize the primary ion signal. In (a), CH3F+• and CH4

+• signals were hardly detectable at low energy while CS2

+•, CH3Cl+•, CH3F+•, and CH4+• were not detectable at low

energy in (b).

71


2004/01/28 17:41:01

We have mentioned earlier that not only the charge exchange but also other

processes such as collisional impact ionization may contribute to the above typeⅢ

ion signal. Checking such a possibility is all the more important because the mass

spectral data presented so far were obtained at the inside-the-cell primary ion

translational energy (K = eVS - eVC) of 50 ~ 100 eV, which is much larger than

thermal. In this regard, we measured the relative yield of the reagent gas ions,

I(A+)/I(C6H6+•), as a function of the primary ion translational energy for the five

reagent gases adopted in this work. The results obtained with benzene ions

generated under the CI1 condition are shown in Fig. 2.12(a). It is to be noted that

the relative yields of 1,3-C4H6+•, CS2

+•, and CH3Cl+•, which can be generated via

electronically exoergic charge exchange with C6H6+• in the long-lived excited

state, remain high up to ~ 100 eV of the primary ion translational energy and then

decrease at higher energy. On the other hand, charge exchanges of CH3F and CH4

with C6H6+• in the long-lived excited state are electronically endoergic and the

corresponding products, CH3F+• and CH4+•, are hardly detectable at low energy.

Their production at higher collision energy (≥400 eV) with much smaller cross

sections than the above exoergic cases is likely due to collision-induced endoergic

charge exchange or collisional impact ionization.67 We are not much interested in

the exact nature68,69 of the mechanism involved in the generation of the reagent

gas ions at high energy. The main highlight of the data in this figure is that

reagent ions which can be generated by exoergic charge exchange with C6H6+• in

the excited state are produced with good yields at the primary ion energy of 50 ~

100 eV and not for ions that require endoergic charge exchange.

As a further test of the method, we repeated the same experiment, but using

benzene ions generated at the higher CI source pressure of 0.1 Torr. This was

called the CI2 condition in the previous work which found that benzene ions were

completely relaxed to the ground electronic state under this condition. The data in

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2004/01/28 17:41:01

Fig. 2.12(b) show that 1,3-C4H6+• is generated with high yield at ~50 eV of the

primary ion translational energy while the molecular ions of the remaining four

reagents were not observable. This is compatible with the fact that charge

exchange of 1,3-C4H6+• with benzene ion in the ground state is electronically

exoergic while those for the other reagents are endoergic. The results in Figures

5(a) and 5(b) strongly suggest that prominent reagent ion signals are due to the

electronically exoergic charge exchange, even at 50 eV of primary ion

translational energy.

Atomic charge exchange processes have been heavily investigated over the

years. 61,70-72 It is well known that the cross section for a symmetric charge

exchange is the maximum at the thermal energy and decreases with increasing

impact velocity. On the other hand, the cross section for non-symmetric charge

exchange is small at low impact velocity, rises to a maximum, and falls off as the

velocity increases. It is also known that the impact velocity at the maximum cross

section is well predicted by the Massey’s adiabatic criterion. Polyatomic charge

exchange has not been as much investigated.59,60 However, it is well known in the

field of chemical ionization mass spectrometry39 that the electronically exoergic

charge exchange is especially efficient. It is thought that the negative energy

defect, or exoergicity, is compensated by vibrational excitation of products,

rendering the process energetically symmetric, or near resonant. We have shown

here that the same reasoning may also hold for the charge exchange by ions in the

excited electronic state. To test the exoergicity rule, we performed additional

charge exchange experiments for the reagent gases used in this work with the

primary ions generated from these gases, in various combinations. The only

exception to the exoergicity rule was the electronically endoergic reaction CH3F+•

+ CH4 → CH3F + CH4+•, which showed a good yield at low translational energy.

This is not surprising, however, because the cross section for this reaction with

73


2004/01/28 17:41:01

very small endoergicity (0.04 eV) is expected to be large even at small primary

ion translational energy according to the Massey’s adiabatic criterion.73

2.2.4 Conclusions

Most of the experimental methods employed so far to find the presence of

isolated electronic states rely on the measurement of dissociation or fluorescence

from these states. These methods are often useless when the excited state of

interest is non-fluorescing and lies well below the dissociation threshold such as

the benzene ion in the B state. Charge exchange ionization in collision cells

investigated in this work can be useful in such cases. The present observation that

the cross sections for electronically exoergic charge exchange reactions are much

larger than and hence can be distinguished from endoergic ones will be

particularly useful to make a reasonable estimate for the energy level of the

excited state involved. Also the fact that large difference in cross sections can be

observed at 50 ~ 100 eV of the primary ion translational energy means that a

simple instrumentation can be used for such an investigation. Even though the

method can detect the presence of long-lived excited electronic states, it is not

adequate to determine the identity of the state. Development of spectroscopy-

based techniques will be needed for this purpose.

2g2E~

2.3 Monosubstituted Benzene Cations

In previous section on photodissociation of benzene cation, we found

evidences for a very long lifetime (20 µsec or longer) of its A~ 2E2g state. In a

subsequent section, a method based on charge exchange in collision cells of a

modified double focusing mass spectrometer was developed for routine search for

long-lived excited states with conventional mass spectrometry. Observations

74


2004/01/28 17:41:01

made were summarized as a hypothesis termed the exoergicity rule (will be

discussed in following subsection).

We have searched for other polyatomic molecular ions in long-lived excited

electronic states using the charge exchange method introduced in the previous

section. Molecules displaying well-resolved vibrational structure in an excited

state photoelectron peak have been chosen as candidates. For molecules

displaying broad excited electronic state photoelectron peaks, rapid internal

conversion of the molecular ions in the excited electronic states generated initially

by electron ionization would result in molecular ions in the ground electronic state,

which can be probed by the above charge exchange method. Some of such

molecules were also investigated as counter examples. Results from investigation

on monosubstituted benzene cations are shown in this section.

2.3.1 Charge Exchange Ionization and Exoergicity Rule

Charge exchange is an important class of ion-molecule reactions. Charge

exchange between atomic species has been heavily investigated over the years.

The cross sections of atomic charge exchange processes are known to be very

sensitive to the absolute value of the change of internal energy (∆E), for the

reaction (2.13):

A+ + B → A + B+, ∆E. (2.13)

∆E = IE(B) – RE(A+) (2.14)

Here, IE and RE denote the ionization and recombination energies, respectively,

both of which are defined as positive quantities. For a resonant (∆E=0) charge

exchange, the cross section is maximum at low collision energy and decreases

rapidly as the collision energy increases. For endoergic (∆E>0) or exoergic

(∆E<0) charge exchange, the cross section increases with the collision energy,

75


2004/01/28 17:41:01

reaches a maximum, then decreases at higher collision energy. The adiabatic

maximum rule, which is a propensity rule based on the analysis of a large volume

of experimental data, can predict the impact velocity (ν) at which the cross section

is maximum with surprising accuracy5 as in (2.15):

hEa ∆

=ν (2.15)

Use of 7 Å for the adiabatic parameter, a, has been reported to be adequate.



geometry (VG Analytical ZAB-E) modified for the present charge exchange study

is shown in Fig. 2.8. Details of the experimental method were described in

previous section.

There are two technical difficulties in the present method of finding the

presence of a long-lived excited electronic state based on ∆ of the charge

exchange reaction. One is the charge exchange by fragment ions generated in the

ion source which have recombination energies comparable to or larger than that of

the excited state being probed. These are usually odd-electron species which are

not as abundant as even-electron species. By lowering the electron energy used

for ionization, say to 20 eV, interference from high recombination energy

fragment ions could be avoided in this work. The second complication arises from

collision gas leakage to the ion source and its ionization in the source. When this

ion enters the collision cell, symmetric charge exchange occurs in the cell and

hence generates collision gas ion. Possibility of such a process must be suspected

when collision gas ion signal generated in the ion source is much larger (by 10 or

more) than the same ion signal generated in the collision cell. As shown in the

E

76


2004/01/28 17:41:01

inset of Fig. 2.8, we installed an additional slit between the ion source chamber

and the collision cell assembly evacuated by analyzer pumping system to improve

the differential pumping. Care was taken in all the measurements such that the

signal due to collision gas ion generated in the ion source is less than or negligible

compared to the signal of the same ion generated in the collision cell.

Both of the above complications can be eliminated by selecting the precursor

ion beam with the magnetic sector and observing charge exchange occurring in

the collision cell (‘second cell’) located between the magnetic and electric sectors

and floated at high voltage (VC′). Then, ions originating from the collision cell

would have the corresponding kinetic energy (eVC′) and can be identified by the

electric sector even though their exact identity cannot be determined. The second

cell experiment, which is complementary to the above first cell one, was also

performed in this work.

Iodobenzene and benzonitrile were purchased from TCI (Tokyo) and WAKO

Pure Chemical (Osaka), respectively. 1,3-butadiene and ethane were purchased

from Matheson (Parsippany, NJ). Other chemicals were purchased from Aldrich

(Milwaukee, WI). All the chemicals were of the highest purity commercially

available and were used without further purification.

2.3.3 Results

As was mentioned in a previous section, three types (I, II, and III) of ions

appear in the mass spectrum obtained by scanning the magnetic sector with charge

exchange reagent gas in the collision cell floated at high voltage (VC). These are

ions generated in the ion source (type I), their collision-induced dissociation

products (type II) generated in the collision cell, and ions originating from the

collision gas (type III) generated by charge exchange. Taking VS as the

77


2004/01/28 17:41:01

acceleration voltage in the ion source, the translational energies after exiting the

collision cell can be expressed as eqns. (2.9) ~ (2.11).

Since the translational energies of type II and III ions differ from that of the

ordinary ions (type I), they will not appear at their ordinary m/z positions in the

spectrum. Measuring their effective m/z positions and analyzing with eqns. (2.9) ~

(2.11), their correct m/z values can be obtained. Also, the fact that their positions

in the spectrum move with the collision cell potential, eqns. (2.9) and (2.10), helps

positive identification of these ions. Ionization energies of collision gases used are

listed in Table 2.3. For each candidate ion, some of the collision gases in the table

were chosen as needed. Recombination energies of the candidate ionic states are

listed in Tables 2.4 and 2.5.

Chlorobenzene was the first molecule chosen for investigation in this work. Its

high resolution photoelectron spectrum has been reported recently,74 which shows

well- resolved vibrational structures for the ground state peak (3b1)−1 X~

B~

2B1 and

the third and fourth peaks corresponding to the hole states (6b2)−1 2B2 and

(2b1)−1 C~ 2B1. The vibrational bandwidths for the B~ 2B2 state were comparable to

those for X~ 2B1 indicating that the band broadening was mostly due to apparatus

rather than rapid relaxation. On the other hand, the vibrational bands for the C~ 2B1

peak were broader than the above states. Hence, the B~ 2B2 state was the prime

candidate in the present search for long-lived excited electronic states. The

recombination energies of the X~

~

2B1, B~ 2B2, and C~ 2B1 states are 9.066, 11.330,

and 11.699 eV,74 respectively, as listed in Table 2.4. Fragment ions with m/z 77,

76, 52, 51, and 50 appear in the 20 eV electron ionization (EI) mass spectrum.

Among these ions, m/z 50 has the highest recombination energy of 10.17 eV

which is less than that of the B 2B2 state of C6H5Cl+• and hence would not

interfere with our investigation. Fig. 2.13 shows the partial mass spectra of

78


2004/01/28 17:41:01

Table 2.3. Collision gases, their ionization energies (IE) in eV, and success/failurea to generate their ions by charge

exchange with some precursor ions.

Precursor ions Collision gas IEb, eV C6H5Cl+• C C6H5Br+• C6H5CN+•

6H5CCH+• C6H5I+• C6H5F+•

(CH3)2CHNH2 8.72 O O O O

1,3-C4H6(butadiene) 9.07

O X O

CS2 10.07 O

CH3Br 10.54 O O O X X

C2H5Cl 10.98 X

CH3Cl 11.28 O X O X

C2H6 11.52 X O

O2 12.07 X

Xe 12.12 X X X

CHF3 13.86 X

a Success and failure indicated by O and X, respectively. Symbols are not drawn when experiments were not done.

b IEs of (CH3)2CHNH2 and CH3Cl taken from ref. 75 and others from ref. 79.

79




Table 2.4 Recombination energiesa of the X~ 2B1, A~ 2A2, B~ 2B2, and C~ 2B1 electronic states of some monosubstituted

benzene cations and the calculated oscillator strengthsb of the radiative transitions from the ~B 2B2 states.

State c C6H5Cl+• C C C6H5Br+•6H5I+•

6H5CN+• C6H5CCH+•

X~ 2B1 9.066 (0.0000000)

8.991 (0.0000000)

8.754 (0.0000000)

9.71 (0.0000000)

8.75 (0.0000000)

A~ 2A2 9.707 (0.0000008)

9.663 (0.0000001)

9.505 (0.0000000)

10.17 (0.0000010)

9.34 (0.0000004)

B~ 2B2 11.330

10.633 9.771 11.84 10.36

C~ 2B1 11.699 11.188 10.541 12.09 11.03

a Taken from refs. 74, 77, 78, 79, and 80 for C6H5Cl+•, C6H5Br+•, C6H5I+•, C6H5CN+•, and C6H5CCH+•,

respectively. In eV. b Results from TDDFT/UB3LYP calculations with the 6-31G** basis set. LanL2DZ used for the iodine atom.

Shown inside the parentheses.

c X~ 2B1 and A~ 2A2 are the states formed by removal of an electron from the b1 and a2 benzene π orbitals of the

neutral, respectively. ~B 2B2 and ~C 2B1 are the states formed by removal of an electron from the in-plane and out-

of-plane halogen nonbonding or triple bond π orbitals of the neutral, respectively.

80




Table 2.5. Recombination energies (RE)a of some excited hole states of

fluorobenzene cation and the calculated oscillator strengthsb of some radiative

transitions.

Oscillator strengthb Statec Characterd RE, eV

From E~ 2B2 state From J~ 2B2 state

X~ 2B1 π2 9.20 0.0000000 0.0000000

A~ 2A2 π3 9.81 0.0000261 0.0000943

B~ 2B2 B(19) 12.24 0.0298871 0.0049450

C~ 2B1 π1 12.24 0.0000000 0.0000000

D~ 2A1 B(18) 13.04 0.0029268 0.0120808

E~ 2B2 B(14), n(F2p‖) 13.89 0.1020018

F~ 2B2 B(16) 14.62 0.0016411

G~ 2A1 B(13) 15.17 0.0126313

H~ 2B1 n(F2p⊥) 16.31 0.0000000

I~ 2A1 B(15) 16.31 0.0000091

J~ 2B2 B(14) , n(F2p‖) 16.70

a Taken from ref. 79. b Calculated at the TDDFT/UB3LYP level with the 6-311G** basis set. c Hole states will be called , , … in order of increasing energy.X~ A~ B~

d π means an electron removal from a benzene π orbital, B(i) from ith orbital of

benzene, n(F2p‖) from in-plane nonbonding 2p orbital of fluorine, and n(F2p⊥)

from out-of-plane nonbonding 2p orbital of fluorine.

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2004/01/28 17:41:01

0

50

100

+

+

+. .

(a)

C 4H4

C 4H3

C 4H2

I

I

I

0

50

100

+

+

+++

++

.. .

.

(b)

C 4H4

CH337

Cl

C 4H2

CH335

Cl

C 4H3

CH237

Cl

CH235

Cl

III

III

III

III

II II II I

I

I

Rela

tive

Inte

nsity

48 49 50 51 520

50

100

+

+

+

+

+

+

+

.

..

.

m/z

(c)

CH 237

Cl

II

II

C 4H4

C 4H3

C 4H2

CH337

Cl

CH335

Cl

CH235

Cl

II/II

I

III

III

III I

I

I

Fig. 2.13 Partial mass spectrum of C6H5Cl generated by 20 eV EI recorded under the single focusing condition with 4006 eV acceleration energy is shown in (a). (b) and (c) are mass spectra in the same range recorded with CH3Cl in the collision cell floated at 3910 and 3960 V, respectively. Type II signals at m/z 49.3 and 50.3 in (b) and at m/z 49.6 and 50.6 in (c) are due to collision-induced dissociation of C6H5Cl+• to C4H2

+• and C4H3+, respectively. The peaks at m/z 50.6 in (b) and at m/z

50.8 in (c) are due to collision-induced dissociation of C6H5+

to C4H3+.

82


2004/01/28 17:41:01

3880 3900 3920 39400

50

100

Rela

tive

Inte

nsity


Fig. 2.14 Ion kinetic energy spectrum recorded by setting the magnetic field

to transmit the type III CH335Cl+• ion in Fig. 2.13 (b) and scanning the

electric sector.

83


2004/01/28 17:41:01

chlorobenzene recorded without (Fig. 2.13 (a)) and with (Figs. 2.13 (b) and 2.13

(c)) CH3Cl in the collision cell. The collision cell was floated at 3910 and 3960 V,

respectively, to obtain Figs. 2.13 (b) and 2.13 (c). All the peaks in the figures have

been identified based on the method described previously. Movement of type II

and III peaks, as evident when Figs. 2.13 (b) and 2.13 (c) are compared, has been

checked also. We also varied the acceleration voltage in the ion source (VS) and

confirmed that only the type II peaks moved with VS (compare eqns. (2.9) and

(2.10)). For further confirmation of type III CH3Cl+•, magnetic field of the sector

was set to transmit this ion in Fig. 2.13 b) and the electric sector potential was

scanned to measure the ion kinetic energy, Fig. 2.14. Excellent agreement

between this measurement and the potential applied to the cell, 3910 V, showed

that this ion was generated from the collision gas indeed. Since the ionization

energy of CH3Cl is 11.28 eV,75 appearance of type III CH3Cl+• and its ion-

molecule reaction product,76 CH2Cl+, means that there is an ionic species in the

precursor ion beam which has the recombination energy equal to or larger than

11.28 eV. As was mentioned earlier, some of the type III ions in this spectrum

might have been generated from CH3Cl+• in the precursor beam which was

produced from CH3Cl leaked into the ion source. CH335Cl+• and CH3

37Cl+• in the

precursor beam which did not suffer collision would appear at m/z 50 and 52,

overlapped with the C4H2+• and C4H4

+• precursor signals. The C4H2+• /C4H3

+ and

C4H4+• /C4H3

+ ratios in Figs. 2.13 (b) and 2.13 (c) are similar to the same ratio in

Fig. 2.13 (a), which indicates that the fraction of CH3Cl+• species in the precursor

beam is negligible. The fact that the collision gas leakage into the ion source is not

significant will be shown with another spectrum to be presented later. We also

attempted to obtain charge exchange signal using C2H6 (IE=11.52 eV) as collision

gas. No type III ions were generated whatsoever. To summarize, type III signals

appear when the ionization energies of collision gases are 11.28 eV or lower while

84


2004/01/28 17:41:01

88 90 92 94 96

0

50

100

+

++

+

..

CH381

Br

CH379

Br

CH281

Br

CH279

Br

III

III

III

III

Rela

tive

Inte

nsity

m/z

Fig. 2.15 Partial mass spectrum obtained under the single focusing

condition with C6H5Br and CH3Br introduced into the ion source and

collision cell, respectively. C6H5Br was ionized by 20 eV EI and

acceleration energy was 4008 eV. Collision cell was floated at 3907 V.

85


2004/01/28 17:41:01

they are absent when the ionization energies are 11.52 eV or larger. Based on the

exoergicity rule ( ) established in the previous section, it is concluded that

the precursor beam contains C

0≤∆E

6H5Cl+• in a long-lived excited electronic state with

the recombination energy in the range 11.28 ~ 11.52 eV, B~ 2B2 state with the

recombination energy 11.330 eV being the best candidate.

We used the same guideline, narrow vibrational bands for an excited

electronic state peak in high resolution photoelectron spectrum, to search for other

long-lived excited electronic states. The B~ 2B2 and C~ 2B1 states of bromobenzene

ion with the recombination energies of 10.633 and 11.188 eV,77 respectively, were

our next targets. A partial mass spectrum of bromobenzene recorded with CH3Br

(IE=10.54 eV) in the collision cell is shown in Fig. 2.15. Type III CH3Br+•

appears prominently in this spectrum together with its ion-molecule reaction

product, CH2Br+, indicating the presence of an ionic species in the precursor beam

with recombination energy 10.54 eV or larger. Also to be noted is that type I

CH3Br+• signals expected at m/z 94 and 96, are hardly observable indicating that

collision gas leak into the ion source is not significant. On the other hand, charge

exchange signal was not obtained with C2H5Cl (IE=10.98 eV), indicating the

presence of a long-lived state with the recombination energy of 10.54 ~ 10.98 eV.

Obviously, B~ 2B2 is such a state. Even though the C~ 2B1 state shows narrow

vibrational bandwidth in the high resolution photoelectron spectrum, this turned

out not to be long-lived in the present work. Namely, we cannot predict long

lifetime of an excited electronic state solely based on the well-resolved vibrational

structure in the photoelectron spectrum. This is due to rather poor resolution of the

high resolution photoelectron spectrometers, ~ 8 meV (64 cm−1).

It is interesting to note that both of the long-lived states found, B~ 2B2 states of

C6H5Cl+• and C6H5Br+•, have the same character, namely elimination of an

86


2004/01/28 17:41:01

electron from a molecular orbital which is essentially halogen nonbonding p

orbital parallel to the benzene ring, n(Cl3p‖) or n(Br4p‖).74,77 The same state of

iodobenzene ion has the recombination energy of 9.771 eV.78 Even though the

vibrational structure is resolved in the corresponding photoelectron peak, each

vibrational band is noticeably broader than that of the ground state band.78 As

expected, none of the collision gas underwent charge exchange with C6H5I+•

except (CH3)2CHNH2 which has ionization energy (8.72 eV)75 smaller than the

recombination energy of the ground state C6H5I+• (8.754 eV).78 In the case of

fluorobenzene, n(F2p‖) is mixed with a σ orbital of the benzene ring resulting in

two photoelectron peaks with partial n(F2p‖) character at 13.89 and ~16.7 eV,

Table 2.5. Even though vibrational splitting is indicated for the former, each

vibrational band is rather broad.79 Failure to observe charge exchange signals

from CH3Cl (IE=11.28 eV),75 Xe (IE=12.12 eV), and CHF3 (IE=13.86 eV) is in

agreement with the above photoelectron spectral feature. A strong charge

exchange signal was observed, of course, with 1,3-butadiene which has ionization

energy (9.07 eV) maller than the recombination energy of C6H5F+• in the ground

state, 9.20 eV.79

Benzonitrile and phenyl acetylene are similar to halobenzenes in the sense that

the cylindrical symmetry of the π electron system of the triple bonds are broken

due to the presence of the benzene ring, resulting in two distinct photoelectron

peaks. Here again, the states corresponding to elimination of an electron from the

in-plane π orbitals of the triple bonds, π(C N≡ ‖) and π(C C≡

≡

‖), seem to show

narrower vibrational bands than those from the out-of-plane π orbitals, π(C N≡ ⊥)

and π(C C≡ ⊥).79,80 Recombination energies of the π(C N‖)−1 B~ 2B2 and

π(C N≡ ⊥)−1 C~ 2B1 states of benzonitrile cation are 11.84 and 12.09 eV,

respectively.79 Then, the charge exchange results in Table 2.3 that collision gases

87


2004/01/28 17:41:01

47 48 49 50 51 52

0

50

100+

+

+

+

+

+

.

.

.

.

C 4H4

CH337

Cl

C 4H2

CH237

Cl

CH335

Cl

CH235

Cl

IIIII

III

III

III

IIIIII

II

I

I

Re

lativ

e In

tens

ity

m/z

Fig. 2.16 Partial mass spectrum obtained under the single focusing

condition with C6H5CN and CH3Cl introduced into the ion source and

collision cell, respectively. C6H5CN was ionized by 20 eV EI and

acceleration energy was 4007 eV. Collision cell was floated at 3910 V.

Type II signals at m/z 49.3, 50.3, and 51.3 are due to collision-induced

dissociation of C6H5CN+• to C4H2+•, C4H3

+, and C4H4+•, respectively. Those

at m/z 49.6 and 50.6 are due to collision-induced dissociation of C6H4+• to

C4H2+• and C4H3

+, respectively.

88


2004/01/28 17:41:01

0

50

100

(a)

0

50

100

(b)

Rela

tive

Inte

nsity

3800 3850 3900 39500

50

100

(c)

Translational Energy, eV Fig. 2.17 Ion kinetic energy spectra recorded by introducing C6H5Br+• ((a) and (b)) and C6H5CH3

+• ((c)) in the second cell filled with CH3Br. The molecular ions were accelerated to 4 keV in the ion source. The second collision cell was floated at (a) 3910, (b) 3943, and (c) 3910 V. Arrows indicate the expected positions for ions from collision gases generated by charge exchange with the precursor ions. The major peaks appearing at 3957 and 3974 eV in (a) and (b), respectively, are due to collision-induced dissociation of C6H5Br+• to C6H5

+. The major peak appearing at 3960 eV in (c) is due to unimolecular dissociation of C7H8

+• to C7H7+

occurring outside the collision cell, but between the magnetic and electric sectors.

89


2004/01/28 17:41:01

As counter examples, we investigated charge exchange by molecular ions of

toluene, nitrobenzene, and styrene. Photoelectron spectra of these molecules do

not show excited state peaks with well-resolved vibrational structure. We will not

show mass spectra of these molecules because the experimental results were

simple and predictable. Namely, charge exchange signals were observed only

when the ionization energy of a collision gas was smaller than the recombination

energy of the ground state ion, or the first ionization energy of the corresponding

neutral.

We also performed second collision cell experiments with various gases

introduced into the cell. Molecular ions generated in the source were accelerated

to 4 keV, mass-selected by the magnetic sector, and decelerated to 50~100 eV by

floating the cell at 3900~3950 V. Fig. 2.17 shows the ionic kinetic energy spectra

obtained by introducing bromobenzene and toluene molecular ions to the cell

filled with CH3Br and by scanning the electric sector potential. Arrows in the

spectra indicate the kinetic energy corresponding to the cell potential, or ions

originating from the collision cell. A prominent peak appeared at this position and

moved with the cell potential when bromobenzene ion was introduced into the cell

(Figs. 2.17(a) and 2.17(b)) while such a peak was absent when toluene ion was

introduced (Fig. 2.17(c)). These are in agreement with the first cell results that

CH3Br is ionized by bromobenzene ion in a long-lived state but not by toluene ion.

The time between bromobenzene ion formation in the ion source and its arrival at

the second cell is ~ 40 µsec. Then, the above observation means that some of the

bromobenzene ions in the B~ 2B2 state have survived as long as 40 µsec. We also

performed similar experiments for other ions. Since the results were the same as

those of the first cell experiments, no further spectra will be presented.

For an excited electronic state to have a very long lifetime (ten microseconds

or longer), neither radiative decay nor nonradiative decay should be efficient.

90


2004/01/28 17:41:01

Even though efficiency of the latter is not easy to investigate, that of the former

can be estimated through the symmetry selection rule and calculation of the

oscillator strength. For chlorobenzene, bromobenzene, benzonitrile, and phenyl

acetylene cations, two electronic states lie below the long-lived excited states

B~

B~

2B2. These are (b1)−1 X~ 2B1 and (a2)−1 A~

~

2A2 correlating with the X~ 2E1g state of

benzene cation. It is to be noted that the electric dipole transition B~ 2B2 → X~

X~

2B1 is

symmetry forbidden while B~ 2B2 → A~ 2A2 is allowed. Very long lifetimes of the 2B2 states require that the oscillator strengths of the latter transitions be very

small even though they are symmetry allowed. In this regard, the oscillator

strengths were calculated with the GAUSSIAN 98 package. Geometries of the

molecular cations in the ground electronic states were optimized at the

UB3LYP/6-31G** level and oscillator strengths were obtained through the time-

dependent density functional theory (TDDFT) calculation. The oscillator strengths

for the B~ 2B2 → A~ 2A2 transitions thus obtained are listed in Table 2.4. These are

10−6 or smaller in all four cases, as required. Similar calculation was done for

iodobenzene cation using the LanL2DZ basis set for the iodine atom, which also

showed negligible oscillator strength for the B~ 2B2 → A~

~

2A2 transition. Then, the

broad vibrational bandwidth for the B peak in the photoelectron spectrum of

iodobenzene and our finding that the B~ state of iodobenzene cation is not very

long-lived must be due to rapid internal conversion. We do not have explanation

at the moment why the internal conversion from the B 2B2 states is slow for the

former four cases while it is fast for iodobenzene cation. We also calculated the

oscillator strengths for the transitions from the C~ 2B1 states. Transitions with

significant strengths were found for all five cases, especially C~ 2B1→2B1.

Namely, consideration of the radiative decay does not allow long lifetime for the

91


2004/01/28 17:41:01

C~

B~

states. This does not mean that the C~ 2B1→ X~ 2B1 radiative transitions can be

observed for these cations because internal conversion from the C~ states may be

even faster. Similar calculations were done for the radiative transitions from the

excited states of fluorobenzene cation with the fluorine nonbonding 2p character.

Both of these states showed radiative decay channels with significant strength,

Table 2.5. Then, absence of any emission from the fluorobenzene cation generated

by electron impact as reported previously19,37 means that nonradiative decay of

these states is even faster.

We also calculated the lowest energy doublet and quartet states with an

electron in the lowest unoccupied molecular orbital (LUMO) of chlorobenzene,

bromobenzene, iodobenzene, benzonitrile, and phenyl acetylene cations at the

TDDFT/UB3LYP level. This was to check the possibility that proximity of these

states to the B~ 2B2 states would affect the lifetime of the latter states. The lowest

doublet states with an electron in LUMO were found at 4.48, 4.39, 4.28, 4.13, and

4.28 eV above the ground states while the lowest quartet states were found at 4.17,

4.39, 3.91, 3.59, and 3.95 eV above the ground states for chlorobenzene,

bromobenzene, iodobenzene, benzonitrile, and phenyl acetylene cations,

respectively. Namely, all these states were found to be located substantially (> 1.5

eV) above the B~ 2B2 states and are not expected to affect the B~ 2B2 state lifetimes.

The most intriguing of the present observations is that the B~ 2B2 state of

iodobenzene cation is not long-lived while the corresponding states of

chlorobenzene, bromobenzene, benzonitile, and phenyl acetylene cations are.

Looking at the photoelectron specta,74,77-80 one finds that the 0−0 band of the 2B2 state is well separated from the lower-lying A

~

~

2A2 state continuum for the

latter four cases while the vibrational bands of the B 2B2 state are overlapped with

the A~ 2A2 state continuum for the iodobenzene cation. Then, efficient internal

92


2004/01/28 17:41:01

conversion of the B~ 2B2 state of iodobenzene cation to the A~ 2A2 state, and

eventually to the X~ 2B1 state, may be responsible for the vibrational band

broadening in the photoelectron spectrum and for the depletion of the B~ 2B2 state

population observed in this work.

2.3.4 Conclusions

Searching for isolated electronic states of polyatomic ions has been one of the

active research areas in the fields of ion chemistry and mass spectrometry. Most

of such states found so far were repulsive states in which dissociation could occur

rapidly prior to internal conversion. For radiative bound states, spectroscopic

techniques have been used to measure the efficiency of their internal conversion

to the ground electronic states. The most difficult to study are the nonradiative

bound states lying below the dissociation thresholds. Absence of emission from

such a state has been usually interpreted as due to rapid internal conversion even

though very long lifetime (ten microseconds or longer) can be an alternative

explanation as suggested for the B~ 2E2g state of benzene cation in previous section.

Measurement of vibrational bandwidth in photoelectron spectra is not helpful to

judge whether the lifetime of the concerned state is very long (ten microseconds

or longer) or very short (picoseconds or shorter) due to rather poor resolution of

the method.

In this section, we have used the charge exchange method to judge whether

some excited states of monosubstituted benzene cations chosen based on narrow

vibrational bandwidths in the photoelectron spectra have long lifetimes. The

method has been found simple and decisive, even though time consuming, in the

sense that the long-lived states were located nearly exactly at the recombination

energies expected from the photoelectron spectra. Present results are further

93


2004/01/28 17:41:01

confirmation on the validity of the exoergicity rule established previously that

charge exchange between polyatomic species is efficient when ∆ , and not

otherwise.

0≤E

Among the monosubstituted benzene cations investigated, C6H5Cl+•, C6H5Br+•,

C6H5CN+•, and C6H5CCH+• have been found to possess long-lived excited

electronic states, all of which are the B~ 2B2 states and show well-resolved

vibrational structures in the photoelectron spectra. It is interesting to note that

these states arise from removal of one electron from in-plane halogen nonbonding

p orbitals or in-plane π orbitals of triple bonds. It is known that these in-plane

orbitals have almost pure halogen p or triple bond π character while the

corresponding out-of-plane orbitals possess some benzene π character.74,77,79,80 We

do not know at the moment whether or how these orbital characters are related to

the efficiency of internal conversion. Regardless, the above correlation suggests

possible presence of long-lived excited states for unsaturated aliphatic molecular

ions with substituents such as halogen and nitrile, which is under investigation in

this laboratory.

94


2004/01/28 17:41:01

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66. Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.;

Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, (Suppl. No. 1).

67. Maier II, W. B. J. Chem. Phys. 1965, 42, 1790-1804.

68. Marx, R. Charge Transfers at Thermal Energies: Energy Disposal and

Reaction Mechanisms, In Kinetics of Ion-Molecule Reactions; Ausloos, P.,

Ed.; Plenum Press.: New York, 1979; p 103.

69. (a) Mauclaire, G.; Dera, R.; Fenistein, S.; Marx, R. J. Chem. Phys. 1979, 70,

4017-4022. (b) Mauclaire, G.; Dera, R.; Fenistein, S.; Marx, R. J. Chem.

Phys. 1979, 70, 4023-4026.

70. Giese, C. F.; Maier II, W. B. J. Chem. Phys. 1963, 39, 197-200.

71. Hasted, J. B. Physics of Atomic Collisions; Butterworths: Washington, 1964.

72. Lehrle, R. S.; Parker, J. E.; Robb, J. C.; Scarborough, J. Int. J. Mass

Spectrom. Ion Phys. 1968, 1, 455-469.

73. See M. S. Kim, Org. Mass Spectrom. 1991, 26, 565-574 for sample

calculations.



Chem. Phys. 254, 385 (2000).

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75. K. Watanabe, T. Nakayama, and J. Mottl, J. Quant. Spectrosc. Radiat.

Transfer 2, 369 (1962).

76. A. A. Herod, A. G. Harrison, and N. A. McAskill, Can. J. Chem. 49, 2217

(1971).








80. J. W. Rabalais and R. J. Colton, J. Electron Spectrosc. Relat. Phenom. 1, 83

(1972/73).

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Chapter 3

Coherent Vacuum Ultraviolet Radiation

One-photon ionization which is the most general and cleanest photoionization

method, usually occurs in the vacuum ultraviolet (VUV) region and the progress in the

field of VUV spectroscopy has been limited by the available VUV light source.1-3

Because there is currently no media able to provide suitable light at shorter

wavelengths than 190 nm, the coherent and tunable VUV radiations have been

developed, which also hold promise for many new applications in atomic and

molecular studies.4-6 The easiest way to generate coherent VUV light is by third

harmonic generation (THG) or four-wave mixing (FWM) in a nonlinear gaseous

medium.1 Of course, all instruments used to study these sources must be evacuated, as

vacuum ultraviolet (VUV) can not travel freely in air. In addition, it is necessary to

separate and monitor the VUV light of interest from the unwanted and residuals.

In this chapter, the basic concepts of nonlinear optics and the generations of

coherent and powerful VUV pulse at 104 ~ 143 nm by four-wave mixing in nonlinear

medium are summarized.

3.1 VUV Generation in Gaseous Nonlinear Medium

3.1.1 General Principles

When a light consisting of electric and magnetic fields propagates through matter, a

macroscopic polarization P which is induced by the electric field E of incident light

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may be described by a power series expansion in )( iE ω :

, (3.1) K+++= 3)3(3

2)2(2

)1( )()()( iii EEEPiii

ωχωχωχ ωωω

Here, is the linear susceptibility of the medium and is related to the refractive

index n by n . The quantities are the nonlinear susceptibilities

and they describe the nonlinear-optical properties of the medium. The importance of

the induced polarization can be understood from the fact that any oscillating dipole

also emits radiation, at the frequency of oscillation. Hence, as a result of the nonlinear

effects, the radiating dipoles can be used to generate light at new frequencies.

(1)iωχ

(1)2i

1 ωχ+= K,, )3(3

)2(2 ii ωω χχ

In general, for a material with inversion symmetry, for example, atomic gases such

as Xe, Kr, or Ne and metal vapors such as Hg, Cd, or Ze, there are no even powers of

the field in the expansion of the polarization for symmetry reason. The lowest-order

nonlinearity is then the cubic term in eqn. (3.1) and this term is responsible for all four-

wave mixing processes (FWM) or third-harmonic generation (THG). Then, in the gas

phase, the number density, , is so low that local field effects are small and hence,

macroscopic susceptibility describing nonlinear polarization induced by the laser is

simply and this polarization may be introduced into the wave equation as a

nonlinear source term, (THG) or (FWM). Furthermore,

the VUV intensity (I

N

VUV =

)3(χN

i3ωω 21VUV 2 ω+ω=ω

VUV) of the radiation generated at frequency is VUVω

)()()()( 3i

2VUV

32VUV kbFINI )( ∆ωωχ∝ω ; THG (3.2)

or

)()()()()( 22

12

VUV32

VUV kbFIINI )( ∆ωωωχ∝ω ; FWM (3.3)

where I is the laser intensity, is the phase-matching factor, b is the beam

confocal parameter (Rayleigh length of the focused Gaussian beam), and

)( kbF ∆

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iVUV 3 ωω −=∆ kkk or ∆ is the wave vector mismatch between the

generated and the incident waves. In a focused beam condition (b<<L), where L is the

length of the nonlinear medium, can be approximated into

21VUV 2 ωωω −−= kkkk

)( kbF ∆

)()( 2∆π=∆ expkbkbF

)(22 1VUV1 nnk −νπ=∆

)0()( <∆∆ kkb

=0 0( ≥ . (3.4) )∆ k

Also, the wavevector mismatch ∆k between the waves is given by

[ ])(2 2VUV2 nn −ν+ . (3.5)

However, one can compensate for the phase mismatch, choosing the harmonic

radiation to lie in the region of anomalous dispersion on the high energy side of a

resonance line and adding a second normally dispersive gas.

Although the nonlinear susceptibilities for gases are generally much smaller than

the corresponding values for metals, the nonlinear processes in rare gases can be easily

accomplished, considering the experimental difficulty in preparation the metal vapors

of high density. Extensive wavelength tunability with rare gases has been achieved by

Hilbig and Wallenstein7 and the typical conversion efficiency for Kr or Xe, was

reported by 10-6. The VUV radiations generated in rare gases are listed in Table 3.1.

While, four-wave mixing (FWM) in metal vapor10 offers advantage of high efficiency,

which can be achieved by using relatively low photon energy and intensity of incident

radiation. Especially, Hg or Mg vapor, was found to be a very efficient nonlinear

medium which demonstrated conversion efficiency of ~ 10-3. The VUV radiations

generated in metal vapors are also listed in Table 3.2.

3.1.2 Wavelength Calibration5

Whenever one performs high-resolution spectroscopy experiments, one should

calibrate the wavelength in the VUV light. The easiest way for wavelength calibration

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Table 3.1 Tunable generation in rare gases.

Wavelength Nonlinear medium Processes

195 ~ 163 Xe 2×266±λs, λia

147 ~ 118 Xe 2×266±λs

147 ~ 140 Xe:Kr 3λDye9

130 ~ 110b Kr 2λUV+λL10

123.5 ~ 120 Kr:Ar 3λDye9

106c Xe 2×31811

a Parametric oscillator with signal and idler wavelengths λs, λi. Ref.7.

b λUV from a range of laser dyes.

c Tunable over a small region.

Table 3.2 Tunable generation in metal vapors.

Wavelength Nonlinear medium Processes Primary Laser

174 ~ 145 Mg 2×459.7+λDye N2-Dye12

160 ~ 140 Mg 2×431.0+λ Dye N2-Dye13

140 ~ 106 Zn 2×358.5+λ Dye KrF-Dye14

125 ~ 117 Hg 2×312.8+λ Dye Nd:YAG-Dye15

115 ~ 104.5 Hg 2×268.8+λ Dye Nd:YAG-Dye16

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is to utilize the optogalvanic effect. The method is to peel off a part of the mixed beam

and pass it through a hollow cathode source. This is useful technique because of

considerably broaden range of available lines to sue as standards and providing the

sharp lines in the UV and VUV. One may use either sealed lamps or open, depending

on the wavelength range. Hybrid fillings of rare gas-metal combinations (for example,

Fe/Ne) are available with the sealed units.

3.1.3 Measurements of VUV Intensity17

To measure the absolute intensity of radiation of any wavelength, a detector of

which gain is known, must be used. This can be calibrated with a standard source

whose intensity of radiation is accurately informed. Calorimetirc measurement of heat

produced by photon would be absolute if photon is completely absorbed and

transformed into heat. However, the fact that the intensity of VUV generated is usually

low partially restricts the use of this measurement due to insensitive. Solar blind

detectors which are inert to UV or visible, can be used with requirement of any

calibration.

The most accurate and reproducible method of measuring absolute intensities is

that utilizing the principle of photoionization of a suitable gas. Actually, any gas would

suffice provided its photoionization yield known. The photoionization yield of a gas is

defined as the number of ions produced per photon absorbed by the gas.

We used single ion chamber built in our laboratory to measure the intensity of

VUV light generated by four-wave mixing in Kr gas or Hg vapor. Single ion chamber

current will be monotonically increased by absorption of VUV photons as the pressure

of photoionization gas (NO in He) increases. However, due to distance between

collection electrodes and collimation lens, collected ions reached maximum signal and

then began to decrease as pressure increased. It can be calculated as follows. As VUV

photon passes absorbing gas, the number of photons N (x) will decrease according to

105


2004/01/28 17:41:01

��

Fig. 3.1 The number of photoions by ion chamber currents measured as function

of the pressure of No/He. Voltage between two electrodes in ion chamber is 50 V.


2004/01/28 17:41:01

Beer’s law,

)exp()( 0 xdNxN ε−= (3.6)

where x denotes the position along beam path, d denotes the number density of gas,

and ε denotes absorption coefficient. Fig. 3.1 shows experimental data and its fit. The

maximum ion signal in data is 4.03×109 ions/pulse and the absolute number of VUV

photons ( ) obtained from the curve fit is 9.2×100N 9 photon/pulse.

3.2 Four-Wave Difference Frequency Mixing in Kr Gas

To excite the Kr 5p[1/2]0 – 4p6 transition for VUV generation by four wave

difference mixing, (as shown in Fig. 3.2) the light at 212.5 nm (∼0.5 mJ/pulse) was

generated by frequency tripling of 637.6 nm output of a dye laser (Continuum

ND6000) pumped by the second harmonic of an Nd:YAG laser (Continuum PL8000).

Another dye laser output (420 ∼ 800 nm) pumped by the second or third harmonic of

the second Nd:YAG laser (Continuum Surelite II) was combined with the 212.5 nm

light and loosely focused with a fused silica lens (f = 50 cm) in the Kr cell to generate

the VUV light tunable in the 123 ∼ 142 nm range. A MgF2 lens (f = 25 cm) was placed

at the exit of the Kr cell and the laser beams were aligned off-centered at the lens to

separate the residual light beams (UV and visible) from the VUV light, which was

focused onto the molecular beam. (as shown in Fig. 1.9) The optimized Kr pressure in

the cell was 0.1 ∼ 13 Torr. Its precision was ±0.5 cm-1 in the visible region.

3.3 Four-Wave Sum Frequency Mixing in Hg vapor

VUV in the region of 107 ∼ 127 nm used to measure the spectra of the cations in

the excited states was generated by four-wave sum frequency mixing in Hg. A

schematic diagram of the experimental apparatus is in Fig. 3.4. The UV light (ωUV =

107


2004/01/28 17:41:01

4p6

5p[5/2]2

λ1=212.6nm λ1=202.3nm

5p[1/2]0

λVUV=123 ~ 142nm

λ2=400 ~ 800nm

λVUV=120 ~ 123nm

λ2=573 ~ 630nm

Fig. 3.2 Schematic diagram for four-wave difference frequency mixing in Kr

gas.

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312.8 nm, ∼ 2 mJ/pulse), which excites the Hg 61S0 – 71S0 transition via the two-

photon resonance, was generated by frequency-doubling of an output of a dye laser

(Continuum ND6000) pumped by the second harmonic of an Nd:YAG laser

(Continuum PL8000) with ∼ 7 nsec pulse duration and 10 Hz repetition rates. ωS (2 ∼ 6

mJ/pulse) at 339 ∼ 675 nm was generated by the second dye laser (Lambda Physik

SCANMATE 2E) pumped by the second or third harmonic of another Nd:YAG laser

(Continuum PL8010). The two laser beams were combined with a dichroic mirror and

tightly focused using an achromatic lens (f = 20 cm) onto the Hg vapor. The four-wave

mixing Hg cell was designed similar to that of Hilbig et. al.8 A LiF lens (f = 20 cm)

was placed at the exit of the Hg cell and the laser beams were aligned off-center to

separate the VUV light from the residual UV and visible lights at the interaction region

with the molecular beam. The VUV output in the 107 ∼ 127 nm region was optimized

at the Hg vapor pressure close to 0.9 Torr with Ar buffer (1 ∼ 2 Torr). The spectral

resolution was ∼ 1 cm-1 and 1010 ∼ 1012 photons /pulse were generated. A small portion

of a dye laser output was used to calibrate its frequency based on the optogalvanic

effect in a Fe/Ne hollow cathode lamp. Its precision was ±0.5 cm-1 in the visible region.

3.4 Development of Coherent VUV Source at 104 – 108 nm

Powerful coherent VUV radiation can be obtained by third harmonic generation

and four wave mixing in gaseous nonlinear medium.7,8,18,19 Two tunable outputs from

pulsed dye laser, one in the ultraviolet (ω1) and the other in the visible (ω2), are used in

the latter technique to generate VUV by sum or difference mixing (ωVUV± =2ω1 ±

ω2).7,8 Capability to generate high power VUV radiation which is tunable over a wide

spectral range is the main advantage of this technique. For example, continuously

tunable VUV radiation in the region of 123∼143 nm generated by difference frequency

mixing (FWDM) in Kr and that of 106.6 ~ 125 nm generated by sum frequency mixing

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2004/01/28 17:41:01

61S0

71S061D0

λ1=312.78nm λ1=280.28nm

λ2=320~700nmλ2=405~440nm

λVUV=105~128nm λVUV=104~106nm

Fig. 3.3 Schematic diagram for four-wave sum frequency mixing in Hg vapor.

110


2004/01/28 17:41:01

LiF lens

Achromaticlens

ωUV, ωS

Hg

Heatingblock

Ar/He

Water inWater in

Out Out

ωVUV

Fig. 3.4 Apparatus for VUV generation by four-wave sum frequency mixing in

Hg vapor. The laser beams were aligned off-center of LiF lens to separate the

VUV light from the residual UV and visible lights at the interaction region with

the molecular beam.

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2004/01/28 17:41:01

(FWSM) in Hg have been used in this laboratory for MATI study of molecular ions.

VUV photon flux measured inside the MATI apparatus was 109 photons/pulse or larger

over the above spectral ranges. The low wavelength limit of 106.6 nm is set by the

transmission of the LiF window mounted at the rear end of the Hg cell. To obtain VUV

below this limit, several windowless schemes have been devised, utilizing rotating

pinhole, supersonic jet, or glass capillary array.20-22 For a windowless Hg cell to be

useful as a routine VUV source for ZEKE and MATI spectrometries and especially for

dynamics study using these techniques, its output must be around 5×108 photons/pulse

(1nJ) or higher measured at the interaction region of the main apparatus. In addition,

the device must be free from various troubles such as clogging of flow restrictors,

excessive loss of Hg, etc. such that a prolonged operation (several hours or longer) is

possible. Hardly any contamination of the main apparatus and pumps by Hg is another

important requirement. An improved windowless Hg cell which uses a single capillary

as the flow restrictor has been designed and constructed with the above requirements in

mind. Details of the design and its performance in the 104 ~ 108 nm range will be

presented in this note.


A schematic diagram of the apparatus is shown in Fig. 3.5. The Hg vapor is

generated inside the heating block (2 cm length along the beam path). 14 cm long

water-cooled arms with baffles inside are attached on the front and rear sides of the

heating block to reduce diffusion of the Hg vapor. A cone-type glass capillary (0.8 and

2 mm I.D. with 70 mm length) is installed along the beam path near the rear end of the

cell. The optical transmission through the capillary was larger than 80 %. Conductance

of the buffer gas (He) through the capillary was estimated to be ∼0.4 l/min. A copper

cold trap cooled by liquid nitrogen is installed between the heating block and the

capillary to minimize contamination of the capillary by Hg and also to minimize

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2004/01/28 17:41:01

reabsorption of VUV by Hg.

A differential pumping system has been devised to insure high vacuum in the

monochromator chamber and eventually very high vacuum in the PI chamber. An

intermediate chamber is installed between the Hg cell and the monochromator chamber.

A 40 mm long glass tube with 2.5 mm I.D. connects the intermediate and the

monochromator chambers. The intermediate chamber is evacuated by a mechanical

pump (180 l/min). A copper cold trap is installed in this chamber also to remove

residual Hg and pump oil. The monochromator chamber is evacuated by a

turbomolecular pump (50 l/s). Finally, an aperture (2.5 mm diameter, 3mm length)

separates the monochromator and PI chambers. In a typical operating condition, the Hg

pressure in the cell is ∼1 torr and Ar or He buffer gas with the pressure of several torrs

is introduced to the cell. Then, the pressures in the intermediate, monochromator, and

PI chambers are maintained at ∼3×10-2, ∼5×10-5, and <10-7 torr, respectively. It is to be

mentioned that hardly any trace of Hg is visible in the intermediate chamber after a

prolonged operation.

Two-photon resonant 71S0 - 61S0 or 61D2 - 61S0 transition in Hg has been utilized

for FWSM. The ultraviolet laser (ω1=312.8 or 280.3 nm, respectively, with ~3

mJ/pulse) was generated by frequency-doubling of a dye laser (Continuum ND6000)

output pumped by the second harmonic of an Nd:YAG laser (Continuum PL8000). ω2

at 320 ~ 355 nm (2 ~ 3 mJ/pulse) or 405 ~ 436 nm (3 ~ 6 mJ/pulse) was generated by

another dye laser (Lambda Physik SCANMATE 2E) pumped by the second or third

harmonic of an Nd:YAG laser (Continuum PL8010). Two laser beams were spatially

and temporally overlapped and focused at the center of the Hg cell with an achromatic

lens (f=20 cm).

The home-built monochromator consists of an Al-MgF2 coated concave diffraction

grating (R=0.5 m, 2400 gr/mm, Jobin Yvon) with dispersion of 0.69 nm/mm and an

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2004/01/28 17:41:01

Achromaticlens

ωUV, ωS

m=1

PI chamber

m=0

m=-1

Au plate

Monochromator(pumping with TMP)

Concave gratingR=0.5M

Mechanicalpump

Temperature-controlledpulsed valve

VUV+UV

N2(l)

Hg

Heatingblock

N2(l)Buffer

gas

Water in

Capillary

Aperture(dia.=2.5mm)

Cold finger(Cu)

Hg cell with glass cone type capillary

Fig. 3.5 Schematic diagram of the experimental apparatus including the Hg cell with a cone type glass capillary,

monochromator, and photoionization chamber. 114




Au plate working as a VUV monitor. VUV beam diffracted at m=-1 was introduced to

the PI chamber while the beam at m=1 was monitored by the Au plate. The grating

must be rotated when VUV wavelength is changed significantly (by changing ω2). This

is not needed when the scan range is narrow (< 500 cm-1).

3.4.2 VUV Generation at 104 – 108 nm

The systematic procedure to generate VUV by FWSM in Hg and introduce it to the

main apparatus is as follows. The two-photon resonance frequency, ω1, for transitions

71S0 - 61S0 and 61D2 - 61S0 of Hg was determined by observing the third harmonic

generation at 104.3 and 93.4 nm, respectively, using the Au plate monitor. A third

harmonic spectrum near 104.3 nm is shown in Fig. 3.6(a). Then, ω2 was overlapped

with ω1 observing VUV signal increase in the Au plate monitor. For VUV generation

via 71S0 - 61S0 transition, the spectral profile measured with the monitor is shown in

Fig. 3.6(b). It is to be mentioned that intensity of the ω1 laser was adjusted to suppress

the third harmonic signal. Finally, VUV was introduced to the main apparatus and

ionized benzene in the supersonic beam. The VUV spectrum recorded by measuring

benzene ion signal is shown in Fig. 3.6(c). This is essentially the same as the VUV

spectrum recorded using the Au plate monitor, Fig. 3.6(b). Similar spectra obtained for

VUV generated via 61D2 - 61S0 transition are shown in Fig. 3.7.

Previously, we estimated the number of VUV photons per pulse exiting a Hg cell

with LiF window using a standard photoionization cell with NO.17 Here, we measured

the benzene photoionization signals using VUV at 108 nm from the Hg cell with LiF

window and from the present windowless cell. Combining the above data, the number

of VUV photons per pulse at 108 nm from the windowless cell was estimated.

Correction for the wavelength dependence of the photoionization efficiency of benzene

was not made because variation was less than 15 % in the 104 ~ 108 nm spectral

region.23 Typical VUV power measured were 4×109 photons/pulse (8 nJ/pulse) at

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2004/01/28 17:41:01

104.20 104.22 104.24 104.26 104.28 104.30

(a)In

tens

ity

105 106 107 108

106.24nm

106.68nm(b)

Inte

nsity

105 106 107 108

(c)

Inte

nsity

Wavelength, nm

Fig. 3.6 (a) Spectral profile of VUV generated by frequency tripling in Hg at ω1

~312.8 nm. (b) and (c) show spectral profiles of VUV generated by FWSM via 71S0 -

61S0 transition in Hg recorded using the Au plate monitor and photoionization of

benzene, respectively. PHg ∼ 1 torr and PHe ∼ 2 torr.

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2004/01/28 17:41:01

106.6 nm generated via 71S0 - 61S0 with the He buffer (2 torr) and 6×108 photons/pulse

(1nJ/pulse) at 104.3nm generated via 61D2 - 61S0 with the Ar buffer (0.5 torr). These

are the values at the photoionization region of the main apparatus. The actual power

generated by the Hg cell is thought to be larger by an order of magnitude.

In the 105 ~ 108 nm spectrum of VUV generated via 71S0 - 61S0, Fig. 3.6(c), a dip

appears at around 106.24 nm. This may be the same one as observed by Koudoumas

and Efthimiopoulos at 106.28 nm.24 The latter was attributed to the absorption of the

VUV radiation by Hg+ and Hg2 by the above investigators. The same authors reported

enhanced VUV generation near 106.68 nm, as observed in this work also, which was

attributed to transition to the autoionizing 6p' 3D1 state. A second dip observed near

this wavelength which was attributed to reabsorption by Hg combined with low

conversion efficiency at high Hg pressure does not appear in the present result. Low

conversion efficiency was observed near 107 nm due to the positive ∆k, a phase

mismatch near the resonance as pointed out by Koudoumas and Efthimiopoulos.

In the 104 ~ 106 nm spectrum of VUV generated via 61D2 - 61S0, Fig. 3.7(b), a dip

appears at 104.8 nm which is due to absorption by Ar 4s1[1/2]1 - 3p6 1S0 transition.25

This dip disappeared when He was used as the buffer gas. However, the conversion

efficiency got lower by a factor of 3 ~ 5 than that using the Ar buffer.

In summary, continuously tunable coherent VUV radiation in the 104 ~ 108 nm

region has been generated by four wave sum frequency mixing with a windowless Hg

cell using a cone-type glass capillary as the flow restrictor. Several nJ/pulse of VUV

power was measured at the interaction region of the main apparatus, which seems to be

higher by an order of magnitude at least than previously reported. The device could be

run for a prolonged period without any trouble (such as blocking of the capillary by

Hg) or need for maintenance. In addition, near absence of Hg contamination outside

the cell makes this a useful VUV light source for routine spectroscopic work.

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2004/01/28 17:41:01

104.0 104.5 105.0 105.5 106.0

104.78nm

(a)

Inte

nsity

104.0 104.5 105.0 105.5 106.0

(b)

Inte

nsity

Wavelength, nm

Fig. 3.7 Spectral profiles of VUV generated by FWSM via 61D2 - 61S0 measured

using (a) the Au plate monitor and (b) photoionization of benzene. PHg ∼ 1 torr

and PAr ∼ 0.5 torr.

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2004/01/28 17:41:01

References

1. W. Jamroz and B. P. Stoicheff, in Progress in Optics XX, edited by E. Wolf

(North-Holland Publishing Co., Amsterdam, 1983).

2. S. P. McGlynn, G. L. Findley, and R. H. Huebner, Photophysics and

photochemistry in the vacuum ultraviolet (Kluwer Academic Publishers, 1985).

3. F. J. Wuilleumier, Y. Petroff, and I. Nenner, Vacuum Ultraviolet Radiation

Physics (World Scientific, Singapore, 1992).

4. S. P. McGlynn, G. L. Findley, and R. H. Huebner, Photophysics and

photochemistry in the vacuum ultraviolet (Kluwer Academic Publishers, 1985).

5. U. Becker and D. A. Shirley, VUV and soft X-ray photoionization (Plenum press,

New York, 1996).

6. J. A. R. Samson and D. L. Ederer, Vacuum Ultraviolet Spectroscopy I and II

(Academic Press, San Diego, 1998).

7. R. Hilbig and R. Wallenstein, Appl. Phys. 21, 913 (1982).

8. R. Hilbig and R. Wallenstein, IEEE J. Quantum Electron. QE-19, 1759 (1983).

9. R. Hilbig and R. Wallenstein, IEEE J. Quantum Electron. QE-17, 1566 (1981).

10. D. Cotter, Opt. Commun. 31, 397 (1979).

11. W. Zapka, D.Cotter, and U. Brackman, Opt. Commun. 36, 79 (1981).

12. B. P. Stoicheff, J. R. Banic, P. Herman, W. Jamroz, P. E. Larocque, and R. H.

Lipson, in Proc. Laser Techniques for Extreme Ultraviolet Spectroscopy,

(American Institute of Physics, New York, 1982).

13. S. C. Wallace and G. Zdasiuk, Appl. Phys. Lett. 28, 449 (1976).

14. W. Jamroz, P. E. Larocque, and B. P. Stoicheff, Opt. Lett. 7, 617 (1982).

15. R. Mahon and F. S. Tomkins, IEEE J. Quantum Electron. QE-18, 913 (1982).

119


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16. R. R. Freeman, R. M. Jopson, and J. Bokor, in Proc. Laser Techniques for

Extreme Ultraviolet Spectroscopy, (American Institute of Physics, New York,

1982).

17. J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New

York, 1967).

18. J. C. Miller and R. N. Compton, Phys. Rev. A 25, 2056 (1982).

19. J. P. Marangos, N. Shen, H. Ma, M. H. R. Hutchinson, and J. P. Connerade, J. Opt.

Soc. Am. B 7, 1254 (1990).

20. K. D. Bonin and T. J. Mcllrath, J. Opt. Soc. Am. B 2, 527 (1985).

21. J. Bokor, P. H. Buchsbaum, and P. R. Freeman, Opt. Lett. 8, 217 (1983).

22. P. R. Herman and B. P. Stoicheff, Opt. Lett. 10, 502 (1985).

23. V. H. Dibeler and R. M. Reese, J. Res. Natl. Bur. Std., 68A, 409 (1964).

24. T. Efthimiopoulos and E. Koudoumas, Appl. Phys. B 55, 355 (1992).

25. A. A. Radzig and B. M. Smirnov, Reference Data on Atoms, Molecules, and Ion

(Springer-Verlag, Berlin, Heidelberg, 1985).

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121

Chapter 4

VUV-MATI Spectroscopy of Benzenoid

Molecules

Structure, thermochemical properties, and dynamics of ions are of

fundamental interest in relation to studies of combustion, atmospheric chemistry,

cosmochemistry, etc.1-3 Information on ionic vibrational structures is especially

useful to probe ions in complex mixtures or follow complicated reaction processes.

Nowadays, conventional spectroscopic techniques such as high-resolution

photoelectron or laser-induced fluorescence spectroscopies have been popular in

characterizing polyatomic ions.4,5 However, obtaining vibrational spectra of

polyatomic ions with these techniques is a formidable job because of their limited

capabilities. The resolution of photoelectron spectroscopy (PES), which is

typically 10 meV (80 cm-1), is not good enough to obtain vibrational information

on polyatomic cations, even though PES is useful to investigate electronic states.6

The laser-induced fluorescence spectroscopy, which usually has higher resolution

than PES and can resolve vibrational peaks, is not generally applicable because

most of the excited electronic states of polyatomic cations do not fluoresce.

Zero kinetic energy (ZEKE) photoelectron spectroscopy has a much better

resolution than ordinary PES and hence can obtain even rotational information for

simple molecular ions.7-9 Mass-analyzed threshold ionization (MATI) basically

employs the same principle as ZEKE except for detecting ions instead of electrons

and hence providing mass-selectivity in the spectra.10-11 Generally adopted in the

ZEKE or MATI spectroscopies is a two-color 1+1′ scheme. Namely, excitation to


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a Rydberg state is achieved in two steps via an intermediate state. However, since

the first excited states of most of the molecules are located in the region beyond

commercial dye laser outputs ( > 210 nm) and these states in many cases are either

unbound or relax rapidly, use of this scheme suffers the major limitation of low

transition probability to the Rydberg state. One-photon ZEKE/MATI using tunable

vacuum ultraviolet (VUV) radiation can overcome such difficulties because the

transition occurs directly from the ground state to a Rydberg state, not mediated

by an excited electronic state of the neutral.12-20

One-photon ZEKE scheme has been utilized already to obtain vibrational

spectra of simple cations in the ground and excited states.12-15 The present work

will demonstrate that one-photon MATI scheme can be routinely used to obtain

vibrational spectra of polyatomic cations also once coherent VUV radiation

becomes available over a wide spectral range.

4.1 Determination of Ionization Energies

MATI or ZEKE spectroscopies utilize high Rydberg states of neutrals

conversing to the states of corresponding ions. The energies nlmE of a series of

Rydberg states are described by the Rydberg formula.

2)( l

Mnlm n

REδ−

−= (4.1)

Here n, l, and m are the usual quantum numbers for H-like atoms, RM is the mass-

dependent Rydberg constant (R∞ = 109737 cm-1), and δl is the l-dependent

quantum defect. A Rydberg state with the n quantum number of 200 lies ~3 cm-1

below the corresponding series (ionization) limit. Due to using the pulsed field

ionization, the ionization energy measured by these spectroscopies always gives


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123

the value just below the ionization threshold. Hence, the position of MATI peak

depends on the field strength employed as follows:

FE α=∆ (4.2)

where F is electric field (in V/cm) and theory predicts the adiabatic value of α

to be 6 cm-1 (V/cm)-½. Lowering of the ionization potential due to an electric field

is shown in Fig. 4.1. When molecule is in field-free region, Rydberg electron feels

attraction by ion core and it can be regarded as Coulomb attraction between

positive and negative charge of e’s. When external electric field is applied, it acts

as a perturbation and will distort Coulomb potential, lowering the ionization

energy by E∆ . The perturbed potential energy of electron is

eFzr

eE −πε

−=4

2

(4.3)

where r is distance from the ion core and z is its component along applied

electric field direction. Differentiation of this with respect to z gives the

location of ionization barrier.

eFz

e−

πε= 2

2

40 (4.4)

or,

Fezπε

=4

(4.5)

Then, the lowering of ionization energy from unperturbed value, 0, is given by,

FeF

eeFe

FeE ⋅πε

−=πε

−πε

πε−=∆

42

44

4

32

(4.6)

The coefficient calculated with physical constants are 6.12 cm-1 (V/cm)-½.


2004/01/28 17:41:01

��

Fig. 4.1 Lowering of the ionization potential due to an electric field.


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125

4.2 Selection Rules in One-photon MATI Spectra

Peaks with widely different intensities appeared in one-photon MATI spectra,

which were assigned to the fundamentals, overtones, or combinations. Vibrational

selection rules for one-photon transitions from the neutral ground state to Rydberg

states were helpful for spectral assignment.

• D6h Symmetry Group19,20

The transition dipole moment between the ground and Rydberg states of

neutral is as follows.

Rev

GevGR ΨµΨ=µrr (4.7)

Here GevΨ and R

evΨ are the vibronic wavefunctions of the ground and Rydberg

states, respectively, and µr is the dipole moment operator. RevΨ can be further

separated into the vibronic wavefunction of the ion core, CevΨ , and the

wavefunction of the Rydberg electron, ReΨ . Namely,

Re

Cev

GevGR ΨΨµΨ=µ

rr (4.8)

Electronic and vibrational parts in the ground state and ion core may be further

separated with the Born-Oppenheimer approximation.

Cv

Gv

Re

Ce

GeGR ΨΨΨΨµΨ=µ

rr (4.9)

In the production of the benzene cation in the ground state from the ground state

neutral, GeΨ and C

eΨ belong to a1g and e1g symmetries, respectively. µr in D6h

symmetry has a2u ⊕ e1u species. Rydberg orbitals can be classified in terms of

spherical symmetry, which correlate with the symmetry species in D6h as follows.


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126

s orbital: a1g

p orbitals: a2u (pz); e1u (px,y)

d orbitals: a1g ( 2zd ); e1g (dxz,yz); e2g (dxy, 22 yxd − )

f orbitals: a2u ( )35( 22 rzzf − ); e1u ( )5( 22 rzxf − , )5( 22 rzyf − ); e2u ( )( 22 yxzf − , xyzf );

b1u ⊕ b2u ( )3( 22 yxxf − , )3( 22 yxyf − )

In the ground state benzene, e1g is the highest occupied molecular orbital, which

correlates with a d orbital in spherical symmetry. Then, an electron in e1g can be

promoted to one of the p or f Rydberg orbitals according to the selection rule for

H-like atom (∆l = ± 1). In D6h symmetry, transitions to some of these are electric

dipole-allowed while the others are forbidden. For example, transition to px,y is

allowed because a1g ( GeΨ ) ⊗ a2u (z) ⊗ e1g ( C

eΨ ) ⊗ e1u (px,y) = a1g ⊕ a2g ⊕ e2g.

Since benzene is prepared under the beam condition, it is initially in the zero-

point level, or GvΨ belongs to a1g. Hence, in an electric dipole-allowed transition,

CvΨ must also belong to a1g. Namely, fundamentals and all the overtones of the a1g

modes are allowed while ∆υ = 2, 4, 6, ··· selection rule holds for nontotally

symmetric modes, as have been well established in electronic spectroscopy. Then,

intensity of each vibrational band would be determined by the Franck-Condon

factor.

Fundamentals of nontotally symmetric vibrations which are dipole-forbidden

also appear in MATI spectra, even though weakly. In these cases, vibronic

mechanism must be invoked. For example, let us consider excitation of a b1g

mode by one quantum. Then, GevΨ and C

evΨ belong to a1g and e2g, respectively.

Selecting px,y (e1u) Rydberg orbital and µx,y (e1u), symmetry of the transition

moment becomes a1g ⊗ e1u ⊗ e2g ⊗ e1u = a1g ⊕ a2g ⊕ 3e2g, making the fundamental


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127

transition of a b1g mode vibronically allowed. It can be shown that all the

fundamentals of nontotally symmetric gerade (g) vibrations of benzene are

vibronically allowed, even though dipole-forbidden, in one-photon excitation to a

Rydberg state and can appear weakly in a MATI spectrum.

If the benzene cation has the center of symmetry, as in D6h or D2h, one would

not expect to observe fundamentals of ungerade (u) modes. However, observation

of the v20 (e2u) fundamental was reported in the previous two-photon ZEKE and

MATI studies. One may invoke magnetic dipole or electric quadrupole

mechanism to account for the appearance of ungerade fundamentals. Such

mechanisms are highly unlike because a g,u-forbidden vibronic transition would

be extremely weak and hence essentially undetectable by ZEKE or MATI. Hence,

appearance of ungerade fundamentals in the two-photon ZEKE or MATI spectra

was attributed to the fact that the intermediate state used in this scheme, A~ 1B2u,

is slightly nonplanar. Such an intermediate state is not involved in the present one-

photon scheme. However, ungerade fundamentals appear, even though very

weakly, in the one-photon spectra as will be shown later. One plausible

mechanism for the very weak appearance of ungerade fundamentals is the l

mixing in the Rydberg states caused by the stray field inside the instrument or by

scrambling field applied.

A guideline for vibrational assignment gained from consideration of the

selection rules can be summarized as follows. Fundamentals and overtones of the

a1g modes may appear prominently in the one-photon MATI spectra of benzene

while nontotally symmetric gerade fundamentals may appear weakly. Ungerade

fundamentals may appear also, even though very weakly.

• C2v Symmetry Group17,18

Rydberg orbitals can be classified in terms of spherical symmetry, which


2004/01/28 17:41:01

128

correlate with the symmetry species in C2v as follows.

s orbital: a1

p orbitals: a1(pz); b1(px); b2(py)

d orbitals: a1( 2zd ); a2(dxy); b1(dxz); b2(dyz); a1( 22 yxd − )

f orbitals: a1( )35( 22 rzzf − ); b1( )5( 22 rzxf − ); b2( )5( 22 rzyf − ); a1( )( 22 yxzf − );

a2( xyzf ); b1( )3( 22 yxxf − ); b2( )3( 22 yxyf − )

Then, the symmetry selection rules for the electric dipole allowed transition

become

1a)()()()( =ΨΓ⊗ΨΓ⊗µΓ⊗ΨΓ Re

Ce

Ge

r . (4.10)

GeΨ belongs to a1 symmetry species for the both phenylacetylene and

benzonitrile. CeΨ is essentially the same as the electronic wavefunction of the

ground state cation and has b1 symmetry in both cases. µr has symmetry species

a1, b1, and b2 in C2v. It can be shown that Rydberg ← ground transition in the

neutral is allowed for various selections of the Rydberg orbital. Most of the

molecules prepared under the supersonic jet condition are in the zero-point

vibrational level which is totally symmetric, a1. Hence, in an electric dipole-

allowed transition, CvΨ should also belong to a1. Then, fundamentals and all the

overtones of a1 modes are allowed while ∆υ = 2, 4, 6, … selection rule holds for

nontotally symmetric modes. Under the Born-Oppenheimer approximation, the

relative intensity of each vibrational peak is determined by the Franck-Condon

factor.

4.3 Franck-Condon Factor Calculations


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129

Assuming that the properties of the ion core in a high Rydberg state be well

approximated by those of the cation, Franck-Condon factors for the Rydberg ←

ground transition were calculated with the above quantum chemical data using the

method of Sharp and Rosenstock.21 A brief account of the method is as follows.

The vibrational wavefunction under harmonic approximation can be written as

ψv(Q) = Nv exp( –21 Q† Γ Q) Hv( Γ1/2 Q ) (4.11)

Here v is the vibrational state vector designating the quantum number for each

mode, Q is the normal coordinate vector, Γ is the diagonal matrix of reduced

frequencies 4π2νi/h, H is the Hermite function, and Nv is the normalization

constant. In the calculation of the Franck-Condon factor for the vC ← vG

component in the Rydberg ( C ) ← ground ( G ) transition.

2CGC ]d)()([q GCGC QQQ vvvv ΨΨ= ∫ (4.12)

Here QC and QG are the normal coordinates in the Rydberg and ground states,

respectively, which can be related by

QG= JQC + K (4.13)

With the common coordinates established, integration in eqn. (4.6) can be carried

out. Analytical expression for the Franck-Condon integral in the harmonic limit

available in the literature,22 which is given as a function of J, K, ΓC, and ΓG. In

addition, the intensities dictate about QC vs. QG, the displacement.

4.4 VUV-MATI Spectroscopy of Monohalobenzenes

MATI spectra of C6H5Cl+• and C6H5Br+•, C6H5I+•, and C6H5F+• in the ground

electronic states and those of C6H5Cl+• and C6H5Br+• in the B~ 2B2 excited states


2004/01/28 17:41:01

��

Fig. 4.2 Illustration of the Franck-Condon principle and intensity distributions

for small and large displacement, respectively.


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131

have been obtained via one-photon excitation. The one-photon MATI scheme has

been found to be especially useful to obtain the cation ground and excited

electronic state spectra because knowledge on the neutral intermediate states is

not required.

4.4.1 Vibrational Spectra in the Ground Electronic States, X~

4.4.1.1 Chlorobenzene Cation

Excitation of chlorobenzene to Rydberg states below the first ionization

threshold followed by PFI produces two isotopomers of the molecular ion,

C6H535Cl+• and C6H5

37Cl+•, in the mass spectrum. By monitoring one of these

isotopomers and scanning the VUV wavelength, MATI spectrum for each

isotopomer was recorded, Figs. 4.3(a) and 4.3(b). Checking the direct ion yield vs.

photon energy, or the photoionization efficiency curve (not shown), the first

intense peaks appearing at ∼73180 cm-1 in these figures were assigned to the 0-0

band. The energy of a 0-0 band appearing in a MATI spectrum is usually smaller

than the true ionization energy. This is because molecules in ZEKE states a few

cm-1 below the threshold can also be ionized due to the high PFI field used. Here,

the position of the 0-0 band was measured using various values of PFI field

without the spoil field and the accurate ionization energy was estimated by

extrapolation to the zero field limit. The ionization energy of C6H535Cl thus

obtained was 73177±5 cm-1, in excellent agreement with 73173±5 cm-1 reported

by Lembach and Brutschy.23 The ionization energy of C6H537Cl obtained similarly

was hardly different from the above. The ionization energies to the ground and

first excited electronic states of halobenzene cations measured in this work are

listed in Table 4.1.

The vibrational frequency of each band was estimated simply as the difference

of its position from that of the 0-0 band. Vibrational frequencies calculated from


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Table 4.1 Ionization energies (IE) to the ground ( X~ 2B1) and B~ 2B2 excited states

of chloro-, bromo-, iodo-, and fluorobenzene cations, in eV.

IE ( X~ 2B1) IE ( B~ 2B2) Ref.

Chlorobenzene 9.0728±0.0006 11.3327±0.0006 This work

9.0723±0.0006 23

9.0720±0.0006 25

9.066±0.008 11.330±0.008 27

Bromobenzene 8.9976±0.0006 10.6406±0.0006 This work

8.991±0.008 10.633±0.008 28

8.98±0.02 26

Iodobenzene 8.7580±0.0006 This work

8.754±0.008 29

8.77±0.02 30

Fluorobenzene 9.2033±0.0006 This work

9.2033±0.0006 31

9.2044±0.0005 32

9.18±0.02 26


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133

73000 74000 75000 76000

6a26b1

8a1121

16b1

41

7a2

6a17a1

6a1121

7a1121

8a1

8b1

6a16b1

6b1

10b1

111 18b1

1118a1

7a1

9a1

19a1

121

6an(a)Io

n Si

gnal

Photon Energy, cm-1

73000 74000 75000 76000

8a1121

6a26b16a16b1

41 7a212

12

6an

0-0

9a111

7a1121

6a17a1

6a11217a1

19a1 8b1

8a118a1

10b1

1216b116b1

111

0-0

(b)

Ion

Sign

al

Photon Energy, cm-1

Fig. 4.3 The ground state one-photon MATI spectra recorded by monitoring

(a) C6H535Cl+• and (b) C6H5

37Cl+•.


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134

Table 4.2 Vibrational frequencies (in cm-1) and their assignments for the ground

state ( X~ 2B1) chlorobenzene cation.

This work Modea (Wilson)

SymmetryNeutrala PESb MPI-PESc MATId ZEKEe C6H5

35Cl+• C6H537Cl+•

1 a1 1003 950 971 975 974 972 4 b1 685 600(?) 600(?) 6a a1 417 427 422 420 422 419 415 6b b2 615 510 526 531 527 530 7a a1 1093 1121 1100 1115 1116 1118 1114 8a a1 1586 1554 1554 8b b2 1598 1593 1592 9a a1 1153 1180 1194 1200 1193 1193

10b b1 741 771 771 11 b1 197 141 139 12 a1 706 720 714 716 713 710 16b b1 467 393 394 482 482 18a a1 1026 960 992 995 991 991 18b b2 287 311 286 19a a1 1482 1429 1411f 1408f

6a2 838 829 6a3 1260 1246 6a4 1677 1661 6a5 2097 2078 7a2 2235 2225

6a16b1 950 950 6a1121 1135 1131 6a26b1 1368 1360 6a111 1394 1392


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135

6a17a1 1533 1527 7a1121 1828 1821 8a1121 2280 2277

a Vibrational assignments in Wilson notation and frequencies for the ground state

neutral taken from ref. 26.

b ref. 27.

c ref. 26.

d ref. 23.

e ref. 25.

f These peaks may be assigned alternatively to 6a118a1.


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136

the MATI peaks in Figs. 4.3(a) and 4.3(b) are summarized and compared with

previous results in Table 4.2. Also listed in the table are the vibrational

frequencies and their assignments (Wilson notation and symmetry)24 of the

ground state C6H5Cl neutral reported by various investigators as summarized by

Walter and coworkers. A more recent report by Wright and coworkers25

interchanged the assignments for the a1-type normal modes 2 and 20a and also for

the b2-type normal modes 3 and 14 of the C6H5Cl neutral. We are not in a position

to judge which of the two assignments are correct. Here we adopt the assignments

by Walter and coworkers26 because the assignments for the C6H5Br and C6H5F

neutrals are also included in that work.

The MATI spectra in Fig. 4.3 recorded by ionization to the ground electronic

state of C6H5Cl+•, or the ground state MATI spectra, are in excellent agreement

with the previous spectra reported by Lembach and Brutschy, even though the

present ones are of higher quality and extend over wider spectral range. The most

striking feature in these MATI spectra is appearance of the prominent 6an

progression. Appearance of these peaks at 419, 838, 1260, 1677, and 2097 cm-1

for C6H535Cl+• (Fig. 4.3(a)) and at 415, 829, 1246, 1661, and 2078 cm-1 for

C6H537Cl+• (Fig. 4.3(b)) clearly shows the presence of the isotope shift for this

substituent–sensitive mode. Wright and coworkers carried out ab initio

calculations for the ground state neutral and cation at the Hartree-Fock (HF) level

with the 6-31G** basis set. It was found that the cation geometry was distorted

from that of the neutral mostly along the direction of the 6a normal mode vector,

in agreement with the appearance of 6an progressions. We also observed the 7a1

and 7a2 progressions in the MATI spectra, 1118 and 2235 cm-1 for C6H535Cl+• and

1114 and 2225cm-1 for C6H537Cl+•. Appearance of these progressions can be

explained as above because the 6a and 7a modes differ only in the phase of atomic

motion.


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137

When transitions start from the ground vibrational state of the neutral, it is

known that the totally symmetric vibrational states of the cation, or the states with

a1 symmetry in the present case, produce prominent ZEKE or MATI peaks.33 In

agreement with this propensity rule, prominent peaks are observed for the a1-type

modes 1, 8a, 9a, 12, 18a, and 19a at 974, 1554, 1193, 713, 991, and 1411 cm-1,

respectively, in addition to the 6an and 7an progressions in the MATI spectrum of

C6H535Cl+•. The b2-type modes such as 6b, 8b, and 18b appear distinctly at 527,

1593, and 286 cm-1, respectively. The b1-type modes also appear, even though less

distinctly, such as 10b and 11 at 771 and 141 cm-1, respectively. In contrast, the

a2-type modes are hardly observable. Various combination bands appear,

especially in the 1600∼2800 cm-1 region. Some of the combination bands, namely

those at 950, 1135, 1533, and 1828 cm-1 have been assigned to the 6a16b1, 6a1121,

6a17a1, and 7a1121 states. For major peaks assigned previously, there is no

difference between the present and previous assignments.

4.4.1.2 Bromobenzene Cation

Vibrational spectra of bromobenzene cation in the X~ 2B1 state were obtained

previously by photoelectron spectroscopy (PES)28 and by MPI-PES.29 Unlike

C6H5Cl+•, no high resolution spectrum utilizing ZEKE or MATI technique has

been reported so far. Ionization of C6H5Br near the threshold to the ground

electronic state of the cation generates two isotopomers, C6H579Br+• and

C6H581Br+•, in the mass spectrum. The ground MATI spectra recorded by

scanning the VUV wavelength and monitoring these ions are shown in Figs.

4.4(a) and 4.4(b). As before, the first peaks appearing at ∼72564 cm-1 in the

spectra were identified as the 0-0 bands based on the photoionization efficiency

curve. The first ionization energy determined by extrapolation was 72570±5 cm-1

(8.9976±0.0006 eV), which compares well with the previous PES results of


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138

8.98±0.0229 and 8.991±0.008 eV.28

Vibrational frequencies of the C6H5Br+• in the X~ 2B1 state estimated as the

difference of each peak position from that of the 0-0 peak are listed in Table 4.3

together with other relevant information. The ground state vibrational spectrum of

C6H5Br+• is similar to that of C6H5Cl+• and can be assigned by referring to the

assignments for the latter. In particular, prominent 6an progression is observed at

331, 659, 987, 1322, and 1653 cm-1. Also, both the fundamental and first overtone

of the 7a mode appear prominently at 1073 and 2142 cm-1. In addition, the a1-type

modes 8a, 12, and 18a appear distinctly at 1577, 678, and 1008 cm-1, respectively.

The peak at 3083 cm-1 can assigned either to the mode 2 or to 20a because both

are the a1-type. Also, distinct are the b2-type modes 6b, 8b, and 18b at 593, 1523,

and 257 cm-1, respectively, while the b1-type modes, 10b at 791 cm-1 and 11 at

126 cm-1, are less distinct. The 6a mode participates heavily to generate various

combination peaks. Readily recognizable is the 6an7a1 progression at 1402, 1734,

and 2061 cm-1. Also distinct are the combination peaks with the 7a participation.

Except for the weak peak at 3083 cm-1, assignments of the vibrational peaks in the

ground state spectrum are rather straightforward. Finally, it is to be mentioned that

the isotope shift in the vibrational spectrum of C6H5Br+• is less than that of

C6H5Cl+•, as expected.

4.4.1.3 Iodobenzene Cation

The vibrational spectrum of iodobenzene cation has not been reported except

for the low resolution PES spectrum where the fundamentals, overtones, and

combination bands of the 6a and 7a modes were identified.29 The ground state

MATI spectrum of C6H5I+• obtained in this work is shown in Fig. 4.5. The first

intense peak at 70633 cm-1 in this spectrum has been identified as the 0-0 band as

before. The accurate first ionization energy determined by extrapolation of its


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139

73000 74000 75000

19a1

10b1

111 21(?)

7a1121

8a1

6a17a28b1 6a18a1

6a28a1

6an7a1

6an

141

9a1

18a17a1

121

6b1

16a118b1

0-0

(b)

Ion

Sign

al

Photon Energy, cm-1

73000 74000 75000

19a1

10b121(?)6a17a2

7a1121

6an

6a28a1

6a18a1

6an7a1

141

18a1

8a1

8b1

0-0

11118b1

16a16b1

121

9a1

7a1

(a)Io

n Si

gnal

Photon Energy, cm-1

Fig. 4.4 The ground state one-photon MATI spectra recorded by monitoring

(a) C6H579Br+• and (b) C6H5

81Br+•.


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140

Table 4.3 Vibrational frequencies (in cm-1) and their assignments for the

ground state ( X~ 2B1) bromobenzene cation.

This work Modea

(Wilson) Symmetry Neutrala PESb MPI-PESc

C6H579Br+• C6H5

81Br+• 1 a1 1001 950 2 a1 3065 3083(?) 3083(?) 6a a1 314 331 320 331 329 6b b2 614 540 593 593 7a a1 1070 1100 1073 1073 8a a1 1578 1530 1577 1577 8b b2 1523 1523 9a a1 1176 1193 1193 9b b2 1158 1180

10b b1 736 791 791 11 b1 181 126 126 12 a1 671 720 678 678 14 b2 1321 1307 1307 16a a2 409 396 394 18a a1 1020 1016 980 1008 1008 18b b2 257 257 19a a1 1472 1466 1466 20a a1 3067 3083(?) 3083(?) 6a2 659 659 6a3 987 986 6a4 1322 1320 6a5 1653 1649

6a16b1 928 6a7a 1402 1399 6a27a 1734 1729 7a12 1754 1750 6a8a 1911 1907 6a37a 2061 2058 6a28a 2241 2239 6a7a2 2474 2471

a Vibrational assignments in Wilson notation and frequencies for the ground state neutral taken from ref. 26. b ref. 28. c ref. 26.


2004/01/28 17:41:01

141

position was 70638±5 cm-1 (8.7580±0.0006 eV). This compares well with the

previous PES results of 8.754±0.00829 and 8.77±0.02 eV.30

The vibrational frequencies obtained from the ground state MATI spectrum

are summarized in Table 4.4 together with relevant information. Vibrational

frequencies of the iodobenzene neutral in the ground electronic state have been

taken from ref. 34. The vibrational assignments in this reference has been changed

by referring to the differences in assignments for C6H5Cl and C6H5Br between

Varsanyi34 and Walter and coworker.26 The general feature of the ground state

MATI spectrum of C6H5I+• is quite similar to those of C6H5Cl+• and C6H5Br+• and

vibrational assignments can be made by referring to those for the latters. Here

again, the 6an progression appears prominently at 284, 567, 848, and 1129 cm-1.

7a1 appears also at 1036 cm-1, but without further progression. Other a1-type

modes appearing distinctly are 8a, 12, and 18a modes at 1575, 661, and 1015 cm-1,

respectively. The b2-type modes 8b and 18b also appear distinctly at 1517 and 242

cm-1, respectively, while the b1-type modes 11 and 16b appear weakly at 127 and

406 cm-1, respectively. More prominent than the non-a1-type modes are the

combination bands involving the 6a mode such as 6a1121, 6a111, 6a118a1, 6a17a1,

and 6a211 at 943, 1269, 1296, 1310, and 1548 cm-1, respectively.

4.4.1.4 Fluorobenzene Cation

The first ionization energy of C6H5F was measured with two-color (1+1′)

ZEKE by Shinohara et al.32 and with two-color (1+1′) MATI by Lembach and

Brutschy.31 The latter work also reported the vibrational frequencies in the X~ 2B1

ground state of C6H5F+• and their assignments. The ground state MATI spectrum

via one-photon VUV absorption obtained in this work is shown in Fig. 4.6. The

dominant peak at 74221 cm-1 in this spectrum was identified as the 0-0 band as

before. The first ionization energy determined from its position was 74229±5 cm-1


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71000 72000 73000

8a1

116b1

16b1

16a1

111

18b1

16a1 16

b1

121 18a1 6a2116a1121

7a1

6a118a1

6a17a111121

6an

0-0

Ion

Sign

al

Photon Energy, cm-1

Fig. 4.5 The ground state one-photon MATI spectrum recorded by

monitoring C6H5I+•.


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Table 4.4 Vibrational frequencies (in cm-1) and their assignments for the ground

state ( X~ 2B1) iodobenzene cation.

Modea

(Wilson) Symmetry Neutrala PESb This work

1 a1 998 990 6a a1 268 282 284 6b b2 612 538 7a a1 1063 1036 8a a1 1575 1575 8b b2 1517 10b b1 729 808 11 b1 167 127 12 a1 654 661 16a a2 398 357 16b b1 421 406 17b b1 903 903 18a a1 1015 1016 1015 18b b2 220 242 6a2 567 6a3 848 6a4 1129

6a1121 943 18b111 1226 6a111 1269

6a118a1 1296 6a17a1 1310 6a211 1548 6a27a1 1594 11121 1648

12118a1 1676 7a1121 1695 6a1121 2256

a Vibrational assignments in Wilson notation and frequencies for the ground

state neutral taken from ref. 34. b ref. 29.


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(9.2033±0.0006 eV). This is in excellent agreement with the two-photon MATI

result of Lembach and Brutschy, 74229±5 cm-1, but deviates somewhat from the

ZEKE result, 74238±4 cm-1.

The vibrational frequencies measured from the spectrum are listed in Table 4.5

together with relevant information. The present results are in excellent agreement

with those reported by Lembach and Brutschy and correlate well with the

vibrational frequencies of the ground state neutral. A noticeable difference from

the two-photon MATI spectrum, and also from the ground state one-photon MATI

spectra of C6H5Cl+• and C6H5Br+• presented above, is the complete absence of 6a

overtones. Other than this, the general spectral feature in the ground state MATI

spectrum of C6H5F+• is similar to those of C6H5Cl+• and C6H5Br+•. The a1-type

modes 6a, 7a, 8a, 9a, and 19a appear prominently at 500, 1274, 1610, 1168, and

1502 cm-1, respectively. The b2-type modes 6b, 9b, 14, and 19b appear distinctly

at 606, 1106, 1339, and 1464 cm-1, respectively, while the b1-type modes 10b and

11 appear weakly at 763 and 182 cm-1, respectively.

4.4.2 Vibrational Spectra in the Excited Electronic State, B~

4.4.2.1 Chlorobenzene Cation

According to the previous high resolution PES study,27 the ionization energy

to the B~ 2B2 state of C6H5Cl+• is 11.330±0.008 eV, or ∼109.4 nm in VUV

wavelength. The VUV-MATI spectrum of C6H535Cl+• obtained in the 107∼109.8

nm spectral region is shown in Fig. 4.7. The dominant first peak in the spectrum

can be identified as the origin. The ionization energy to the B~ state determined

from its peak position is 91404±5 cm-1 (11.3327±0.0006 eV), in excellent

agreement with the above PES result.


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74000 75000 76000 77000

9a2

9b1

6a18a1

9a1121

6a1141

6a19a1

8a1

19a1

19b1

7a11419a1

151

10b1

6b1

16b1

18b1

6a1

121111

0-0

Ion

Sign

al

Photon Energy, cm-1

Fig. 4.6 The ground state one-photon MATI spectrum recorded by

monitoring C6H5F+•.


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ground state ( X~ 2B1) fluorobenzene cation.

Modea

(Wilson) Symmetry Neutrala MPI-PESb MATIc This work

3 b2 1301 1299 6a a1 517 500 500 500 6b b2 615 510 505 606 7a a1 1232 1274 8a a1 1604 1620 1610 8b b2 1597 1574 9a a1 1156 1170 1164 1168 9b b2 1128 1106 10b b1 754 763 11 b1 249 181 182 12 a1 809 810 795 804 14 b2 1326 1339 15 b2 1066 1071 16b b1 498 479 18b b2 400 410 400 402 19a a1 1500 1502 19b b2 1460 1464

6a19a1 1668 6a131 1797 6a1141 1842 6a18a1 2109 9a1121 1968 9a19b1 2282

9a2 2343


state neutral taken from ref. 26. b ref. 26. c ref. 31.


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Unlike in the ground state MATI spectrum, the 0-0 band almost totally

dominates the excited state MATI spectrum, indicating that the equilibrium

geometries of the ground state neutral and the B~ state cation are very similar.

This is in agreement with the previous identification of this state as formed by

removal of an electron from the chlorine nonbonding p orbital parallel to the

benzene ring n(Cl3p‖), or a state with n(Cl3p‖) character.27 In contrast, Anand

and coworkers35 suggested that the B~ state probed in their PIRI study had the σ

character. In the PIRI experiment, the C6H5Cl neutral prepared in a Rydberg state

correlating with the cation ground state by two-photon absorption was further

excited and autoionization or fragmentation in the B~ or higher electronic states

was observed. Similarly, multi-photon absorption mediated by the B~ 2B2←X~ 2B1

resonance was assumed in the REMPD study of the B~ state of C6H5Cl+• by

Ripoche and coworkers.36 One of the problems related to the multi-photon

excitation of the ground state cation (REMPD) or the ion core correlating with the

ionic ground state (PIRI) is that the B~ 2B2←X~ 2B1 transition is electric dipole

forbidden and hence there is no guarantee that the peaks observed reflect the

B~ 2B2←X~ 2B1 resonance. Complication may also arise from the possible presence

of an excited state(s) formed by promotion of an electron in an occupied orbital to

an unoccupied orbital, which is not a hole state observed in PES. Anand and

coworkers argued based on their experimental results that the excited state

observed in their PIRI experiment was the electric dipole allowed 2B1 rather than 2B2. Namely, one can not rule out the possibility that the states probed by PIRI or

REMPD may have been different from the B~ 2B2 state appearing in the PES

spectrum. In contrast, the present one-photon MATI technique probes hole states

only and does not suffer from the complication related to multi-photon absorption.

Hence, it is highly likely that the vibrational structure observed in the 107~109.8


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nm region in this work is that of the B~ 2B2 state with the n(Cl3p‖) character

observed in PES.

Vibrational frequencies measured from the excited state MATI spectrum in

Fig. 4.7 are listed in Table 4.6 together with relevant information. Vibrational

frequencies reported in the REMPD and PIRI works are listed also for comparison.

Considering the n(Cl3p‖) character of the ionic state accessed, one expects good

correlation of ionic vibrational frequencies with those of the ground state neutral.

It is to be noted that the vibrational frequencies measured in this work display

better correlation with the neutral data than the REMPD or PIRI results do.

Two broad bands appear in the photoelectron spectrum at 42 and 120 meV (340

and 970 cm-1, respectively) above the 0-0 band of the B~ 2B2 state, which were

assigned to the normal modes 6a and 1, respectively. In the present MATI

spectrum, major peaks other than the 0-0 peak appear at 329, 382, and 961 cm-1. It

is straightforward to assign the peak at 961 cm-1 to the normal mode 1. We will

assign the peak at 382 cm-1 to the normal mode 6a. In addition to better

correlation with the corresponding frequency in the neutral, such an assignment

can explain the appearance of some combination bands and an overtone (Table

4.6). It is not easy to assign the 329 cm-1 peak. We will assign it to the 16a mode

simply based on its proximity to the corresponding frequency in the neutral. Other

peaks display decent correlation with those in the neutral and can be easily

assigned. Here again, majority of the peaks are due to the a1-type modes such as

6a, 12, 1, 18a, 7a, and 9a at 382, 725, 961, 1009, 1080, and 1173 cm-1. Some b2-

type modes (6b, 3, and 14) appear also distinctly at 546, 1279, and 1338 cm-1

while b1-type modes (4, 10b, and 17b) are slightly less distinct. The prominent

16a mode at 329 cm-1 is the only a2-type mode, which casts some doubt on the

validity of its assignment. An alternative assignment may be 18b which is a b2-

type mode.


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500 1000 1500

18b1

18a1 314112110b1 17b19a17a1

11

6b1

6a1

16a1

Ion Energy, cm-1

91000 91500 92000 92500 93000 93500

0-0

Ion

Sign

al

Photon Energy, cm-1

Fig. 4.7 The B~ 2B2 state one-photon MATI spectrum of C6H535Cl+•. The x-

axis of the inset, ion energy, denotes energy scale referred to the position of

the 0-0 band.


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chlorobenzene cation in the B~ 2B2 excited state.

Modea

(Wilson) Symmetry Neutrala PESb REMPDSc PIRId This work

1 a1 1003 970 869 1010 961 3 b2 1271 1279 4 b1 682 667 5 b1 985 730 6a a1 420 340 387 384 382 6b b2 616 562 546 7a a1 1085 943 1131 1080 9a a1 1174 1263 1173 10a a2 830 761 10b b1 740 759e

11 b1 196 153 12 a1 701 636 725 16a a2 400 313 223 329 16b b1 467 218 439 17b b1 902 899 18a a1 1026 866 1009 18b b2 297 260 329 246

6a116a1 709 6b116a1 870


state neutral taken from ref. 26. b ref. 27. c ref. 36. d ref. 35. e This peak may be assigned alternatively to 6a2.


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4.4.2.2 Bromobenzene Cation

Vibrational spectrum of bromobenzene cation in the B~ 2B2 state has been

obtained for the first time in the present MATI work (Fig. 4.8). The strongest peak

in the spectrum is the 0-0 band as in the B~ 2B2 MATI spectrum of C6H5Cl+•. Its

unambiguous assignment also allows accurate determination of the ionization

energy to this state, 85822±5 cm-1 (10.6406±0.0006 eV) as determined through

extrapolation. This is in good agreement with 10.633±0.008 eV determined from

high resolution photoelectron spectrum.28

Vibrational frequencies obtained from the MATI spectrum are listed in Table 4.7

together with relevant information. Vibrational frequencies of C6H5Br+• in the

B~ 2B2 state display good correlation with those of the neutral as expected. By

comparing the frequencies of the substituent-sensitive modes of C6H5Cl+• and

C6H5Br+•, one finds that mass dependences of these frequencies are similar to

those observed for the neutrals. Here again, prominent peaks are mostly a1-type

such as 1, 9a, and 12 modes at 959, 1180, and 622 cm-1. The b2-type modes

appear less prominently such as 3 and 9b at 1251 and 1130 cm-1, respectively. It is

interesting to note that the 6a mode, which has appeared prominently in all the

spectra analyzed so far, is absent in the B~ 2B2 MATI spectrum of C6H5Br+•.

4.4.2.3 Iodobenzene Cation

In a recent high resolution photoelectron spectrum of C6H5I, the B~ 2B2 state

appears overlapped with the A~ 2A2 state.29 Some vibrational bands are observed

but are much broader than those in the X~ 2B1 ground state. We could measure the

MATI signal in the 126.3~127.3 nm region of VUV which is near the ionization

threshold to the B~ 2B2 state. However, the MATI spectrum obtained was a

structureless broad band as seen in Fig. 4.9. This is due to a very short lifetime


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85500 86000 86500 87000 87500

0-0

Ion

Sign

al

Photon Energy, cm-1

500 1000 1500

17b1141 8a1

19a1319a19b1

7a1

18a111

121

6b1

Ion Energy, cm-1

Fig. 4.8 The B~ 2B2 state one-photon MATI spectrum of C6H579Br+•. The x-

axis of the inset, ion energy, denotes energy scale referred to the position of

the 0-0 band.


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bromobenzene cation in the B~ 2B2 excited state.

Modea

(Wilson) Symmetry Neutrala PESb This work

1 a1 1001 970 959

3 b2 1264 1251

6b b2 614 542

7a a1 1070 1015

8a a1 1578 1571

9a a1 1176 1180

9b b2 1158 1130

12 a1 671 620 622

14 b2 1321 1333

17b b1 904 889

18a a1 1020 982

19a a1 1472 1419


state neutral taken from ref. 26.

b ref. 28.


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78600 78800 79000 79200

Ion

Sign

al

Photon Energy, cm-1

Fig. 4.9 The B~ 2B2 state one-photon MATI spectrum of C6H5I+•.


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(<10-13 sec) of the B~ 2B2 state possibly caused by rapid internal conversion to

lower electronic states.

4.4.3 Conclusions

An interesting feature common to the ground state MATI spectra of chloro-,

bromo-, and iodobenzene cations is the presence of strong 6an progression. In

contrast, such a progression is absent for C6H5F+• even though 6a1 appears

prominently. Also, the 0-0 band is especially dominant in the C6H5F+• spectrum

compared to the spectra of the other cations. Through ab initio calculations at the

HF/6-31G** level, Wright and coworkers found that the equilibrium geometry of

C6H5Cl+• in the ground state was distorted from that of the neutral mostly along

the 6a mode eigenvector. To see if the change in molecular geometry upon

ionization can also explain the presence/absence of 6a progression for the

halobenzene cations, similar calculations have been done in this work. Since the

equilibrium geometries of the ground state neutrals and cations are only slightly

different from C2v, results calculated with the C2v symmetry will be presented.

Calculations were done at the Hartree-Fock (HF), the second order Møller-Plesset

perturbation theory (MP2), and the B3LYP density functional theory levels with

various basis sets using GAUSSIAN 98 suite37 of programs. MP2 and B3LYP

calculations gave similar results. Also, the results for bromo- and iodobenzene

were qualitatively similar to those for chlorobenzene. Hence, only the results for

fluoro- and chlorobenzene obtained at the B3LYP/6-311++G** level will be

compared here. Fig. 4.10 shows the equilibrium geometries of fluoro- and

chlorobenzene neutrals and cations in their ground states obtained at this level.

Geometrical changes upon ionization magnified by 20 are drawn as arrows in the

drawings of the neutral geometries. The 6a eigenvectors for the cations are shown,

also as arrows, in the drawings of the cation geometries. As was pointed out by


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��

Fig. 4.10 Equilibrium geometries of (a) C6H5F and C6H5F+• and (b) C6H5Cl

and C6H5Cl+• calculated at the B3LYP/6-311++G** level. Atomic

displacements upon ionization are drawn as broken arrows in the drawings

of the neutrals. The 6a eigenvectors of the cations are drawn as arrows in the

drawings of the cations. Bond lengths in Å and angles in degree.


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Wright and coworkers, the main geometrical change upon ionization of C6H5X

(X=F, Cl) is the contraction of the C-X bond, contraction of the center two C-C

bonds, and elongation of the other C-C bonds. Also, the atomic displacements

upon ionization resemble the 6a eigenvectors as was pointed out by Wright and

coworkers. The 6a eigenvector of the fluorobenzene cation is different from the

others mostly in the significant movement of the C(1) atom where the halogen

atom is attached. Then, the fact that C(1) is displaced only slightly upon

ionization would lead to less overlap between the displacement and the 6a

eigenvector for the fluorobenzene cation. This may be the explanation for the

experimental results that the 6an progression is extensive for the chloro-, bromo-,

and iodobenzene cations and not for C6H5F+•.

In Chapter 2, for charge exchange study of halobenzene cations, the B~ 2B2

states of C6H5Cl+• and C6H5Br+• were found to be long-lived (microseconds or

longer) while those of C6H5I+• and C6H5F+• underwent rapid internal conversion

to lower electronic states.38 Structureless broad band observed for the B~ 2B2

states of C6H5I+• in this work is compatible with the above result. Appearance of

well resolved vibrational peaks in the excited state MATI spectra of C6H5Cl+• and

C6H5Br+• is also compatible with the above charge exchange results. The

vibrational bandwidth of ~10 cm-1 measured under the best experimental

condition in this work corresponds to a lifetime of ~500 fsec. However the

bandwidth seems to be mostly due to factors other than lifetime broadening such

as ionization over a range of Rydberg states in MATI and participation of various

rotational states. For example, the 0-0 bands in the excited state spectra have

essentially the same widths as those in the ground state spectra. Namely, present

MATI spectra alone cannot prove or disprove metastability of C6H5Cl+• and

C6H5Br+• in the B~ 2B2 state. Since the VUV wavelength shorter than the LiF


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cutoff limit was not available, we could not record the MATI spectrum of C6H5F+•

in the B~ 2B2 state. We do not expect to observe a MATI spectrum with

vibrational structure in this case, however, because the corresponding peak looks

broad in the photoelectron spectrum.

4.5 VUV-MATI Spectroscopy of Difluorobenzenes

The structure of p-difluorobenzene cation has been extensively investigated by

analyzing ZEKE and MATI spectra obtained with the two color 1+1' scheme.39-41

Reiser et al. concluded that the ionic ground state has the D2h symmetry just as the

neutral in the ground state.40 On the other hand, Fujii et al. suggested that the

molecular symmetry in the Rydberg state is reduced to C2h based on the fact that p

and f Rydberg series were not observed.42 For o- and m-difluorobenzene cations,

accurate ionization energies, vibrational frequencies, and their structures have not

been reported.

In this section, we present the vibrational spectra of o-, m-, and p-

difluorobenzene cations in the ground electronic states obtained by using the one-

photon VUV-MATI technique. Accurate ionization energies and complete

vibrational assignments are presented. Symmetries of the cations in the ground

electronic states will be discussed based on the spectral features and quantum

chemical results.

4.5.1 Computational

Calculations of equilibrium geometries and vibrational frequencies of o-, m-,

and p-difluorobenzene neutrals and cations in the ground states were performed at

the Hartree-Fock (HF), the second order Møller-Plesset perturbation theory (MP2),

and the B3PW91 and B3LYP density functional theory levels with various basis


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sets using GAUSSIAN 98 suite of programs.37 At all the levels adopted, the

geometrical changes upon ionization look qualitatively the same. Hence, only the

geometrical parameters obtained at the MP2 and B3LYP levels with the highest

basis set used the 6-311+G (df, p), will be tabulated and discussed. For the

calculated vibrational frequencies of difluorobenzene cations, the results obtained

at the B3LYP/6-311+G (df, p) levels will be quoted, which displayed the best

agreement with the experimental frequencies. Frequencies as obtained by

calculation will be presented, namely without scaling.

4.5.2 Molecular Geometry Calculation

As has been mentioned earlier, equilibrium geometries of p-, m-, and o-

difluorobenzene neutrals and cations in the ground electronic states have been

calculated at the HF, MP2, and DFT levels using various basis sets. Regardless of

the levels and basis sets adopted, the point group symmetries of the equilibrium

geometries were the same, namely D2h for the neutral and cation of p-

difluorobenzene and C2v for the neutrals and cations of m- and o-difluorobenzenes.

Symmetries of the neutrals in the ground electronic states, X~ 1A1g for para and

X~ 1A1 for meta and ortho, are in agreement with previous experimental results.34

Among the cations, symmetry is known only for the para isomer in the ground

state ( X~ 2B2g), which is D2h in agreement with the present calculated result.39,40

Structural data obtained at the B3LYP level displayed better agreement with the

experimental results than those at other levels. The B3LYP results obtained with

the largest basis set used, 6-311++G (2df, 2pd), are listed in Tables 4.8 - 4.10. Full

structural data determined by electron diffraction are available for p-

difluorobenzene neutral and partially for the meta isomer.43,44 These are listed in

Tables 4.8 and 4.9 also. It is to be noted that the calculated results are in good

agreement with the experimental data for the para and meta isomers. Similar trend


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was observed for the calculated vibrational frequencies in the case of p-

difluorobenzene cation. Hence, only B3LYP results will be quoted in the

vibrational assignment to be presented later.

4.5.3 Ionization Energies

MATI spectra of p-, m-, and o-difluorobenzenes are shown in Figs. 4.11~4.13.

The intense peaks appearing at the lowest photon energy, namely at around 73853,

75326, and 74994 cm-1 in Figs. 4.11~4.13, respectively, correspond to the 0-0

bands. The position of the 0-0 band in a one photon MATI spectrum is equivalent

to the ionization energy of the molecule. However, the ionization energy thus

measured is usually a little smaller than the correct value because the molecules in

ZEKE states a few cm-1 below the threshold can also be ionized when a high PFI

field is used. To correct for this effect, the 0-0 band position was measured using

various PFI fields and the accurate ionization energy was estimated by

extrapolation to the zero field limit. Spoil field was not used in such

measurements.

The ionization energies to the ground electronic states of p-, m-, and o-

difluorobenzene cations measured from the MATI spectra in this work are listed

in Table 4.11 together with the previous measurements.40,41,46 The ionization

energy of p-difluorobenzene obtained in this work is smaller than the previous

MATI and ZEKE results26,23 by a few cm-1. Our previous measurements17,47 of the

ionization energies of chlorobenzene and iodoethane were in excellent agreement

with the ZEKE results.25,48 Hence, we do not have an explanation for the above

discrepancy at the moment. Accurate ionization energies of m- and o-

difluorobenzenes obtained in this work are in excellent agreement with the

previous data obtained by photoelectron spectroscopy49 and Rydberg

spectroscopy50 which are not as accurate.


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Table 4.8 Geometrical parameters of p-difluorobenzene in the ground state

( X~ 1Ag) and those of the cation in the ground state ( X~ 2B2g) calculated at the

B3LYP/6-311++G (2df, 2pd) level.

B3LYP Exp.a

D2h

X~ 1Ag X~ 2B2g X~ 1Ag

Bond Length (Å)

C1-F1 1.350 1.298 1.354

C1-C2 1.384 1.420 1.388

C2-C4 1.390 1.362 1.400

C2-H2 1.080 1.081 1.088

Bond Angle (º )

C3-C1-C2 122.2 123.6 123.5

C1-C2-H2 119.8 119.2 123.3

a The experimental values by electron diffraction in ref. 43.


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Table 4.9 Geometrical parameters of m-difluorobenzene in the ground state

( X~ 1A1) and those of the cation in the ground state ( X~ 2B1) calculated at the


B3LYP Exp.a

C2v X~ 1A1 X~ 2B1 X~ 1A1

Bond Length (Å)

C2-F2 1.347 1.300 1.351b

C1-C2 1.384 1.380

C2-C4 1.384 1.442

C4-C6 1.390 1.384

C1-H1 1.079 1.080

C4-H4 1.080 1.082

C6-H6 1.081 1.080

Bond Angle (º )

C3-C1-C2 117.0 115.4 116.0

C1-C2-C4 122.7 123.3 123.9

C1-C2-F2 118.3 119.9

C2-C4-C6 118.2 119.4 117.9

C2-C4-H4 119.8 118.1

C4-C6-C5 121.0 119.1 120.4

a The experimental values by electron diffraction in ref. 44. b The experimental values through the combined use of NMR, electron

diffraction, and microwave spectroscopy data in ref. 45.


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Table 4.10 Geometrical parameters of o-difluorobenzene in the ground state

( X~ 1A1) and those of the cation in the ground state ( X~ 2B1) calculated at the


B3LYP C2v

X~ 1A1 X~ 2B1

Bond Length(Å)

C1-F1 1.342 1.295

C1-C2 1.388 1.454

C1-C3 1.382 1.386

C3-C5 1.391 1.378

C5-C6 1.390 1.440

C3-H3 1.081 1.081

C5-H5 1.081 1.081

Bond Angle( º )

C2-C1-C3 120.5 121.1

C2-C1-F1 119.2 117.0

C1-C3-C5 119.3 117.4

C1-C3-H3 118.9 119.8

C3-C5-C6 120.2 121.6

C3-C5-H5 119.5 119.8


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4.5.4 p-Difluorobenzene Cation

Six normal modes of the p-difluorobenzene cation with D2h symmetry are

totally symmetric (ag), the normal modes 1~6 in Mulliken notation. In the MATI

spectrum of p-difluorobenzene, Fig.4.11, many peaks appear prominently in

addition to the 0-0 band, namely at 368, 441, 839, 881, 1152, 1278, 1319, 1379,

1590, 1640, 1816, 2031, 2077, 2470, 2518, 2908, 2968, and 3015 cm-1 in terms of

the vibrational frequencies of the cation. In the beginning, it is assumed that all

these peaks are due to fundamentals, overtones, or combinations of the totally

symmetric modes. Frequencies of the ag modes calculated at the B3LYP level

with various basis sets are shown in Table 4.12. Frequencies calculated with

different basis sets tend to be quite similar, especially with the basis set 6-311+G

(df, p) or larger. Then, by comparing with the calculated frequencies, it is rather

straightforward to find the fundamentals from the prominent peaks mentioned

above, namely peaks at 3015, 1640, 1379, 1152, 839, and 441 cm-1 being

assignable to the modes 1~6, respectively. All the remaining peaks in the above

set except the peak at 368 cm-1 can be easily assigned to the overtones and

combinations of the normal modes 2~6. For example, the peaks at 881(441×2)

and 1319(441×3) are 62 and 63 overtones, respectively, and the peaks at 1590,

2031, 2470, and 2908 cm-1 are the 6n41 combinations. Successful assignments of

the overtones and combinations of the ag modes support the above assignments of

the fundamentals. It is obvious that the distinct peak at 368 cm-1 can not be

assigned to an ag mode and must be assigned to some other symmetry.

The excellent correlation between the frequencies of the ag modes calculated at

the B3LYP level and the experimental results leads one to expect similarly decent

correlation for non-totally symmetric modes also. Complete vibrational

assignments of the peaks in the MATI spectrum of p-difluorobenzene thus made

are listed in Table 4.13. Symmetry of each mode and its Mulliken notation are


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provided in the table together with the Wilson notation. Also listed are vibrational

frequencies of the neutral, frequencies of the cation calculated at the B3LYP/6-

311++G (2df, 2pd) level, and frequencies measured in the previous and present

experiments. It is to be noted that the present assignment is in complete agreement

with the previous ones. This means that the B3LYP/6-311++G (2df, 2pd) results

have been excellent guidelines in the present case.

The most remarkable feature in the MATI spectrum of p-difluorobenzene is

the appearance of the 6n progression and its combinations with other ag modes,

namely 6n21, 6n31, 6n41, and 6n51. This indicates that the molecular geometry

changes along the direction of the mode 6 eigenvector upon ionization. This will

be discussed later. Other than predominance of the fundamentals, overtones, and

combinations of the ag modes, no further symmetry selectivity is observed in the

MATI spectrum. In fact, all the vibrational modes of p-difluorobenzene cation

except 11, 12, 18, 27, and 28 are observable in the MATI spectrum.

The most remarkable feature in the MATI spectrum of p-difluorobenzene is

the appearance of the 6n progression and its combinations with other ag modes,

namely 6n21, 6n31, 6n41, and 6n51. This indicates that the molecular geometry

changes along the direction of the mode 6 eigenvector upon ionization. This will

be discussed later. Other than predominance of the fundamentals, overtones, and

combinations of the ag modes, no further symmetry selectivity is observed in the

MATI spectrum. In fact, all the vibrational modes of p-difluorobenzene cation

except 11, 12, 18, 27, and 28 are observable in the MATI spectrum.

4.5.5 m-Difluorobenzene Cation

A low resolution photoelectron spectrum is the only available spectral

information for the m-difluorobenzene cation.49 Namely, the symmetry and

vibrational frequencies of this ion in the ground electronic state are not known. As


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Table 4.11 Ionization energies (IE) to the ground states of p-, m-, and o-

difluorobenzene cations, in eV.

IE ( X~ ) Ref.

p-difluorobenzene 9.1576±0.0006 This work

9.1590±0.0004 40

9.1589±0.0006 41

9.161±0.002 46

m-difluorobenzene 9.3400±0.0006 This work

9.32±0.02 49

9.34 50

o-difluorobenzene 9.2992±0.0006 This work

9.30±0.02 49

9.30 50


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Table 4.12 Frequencies (in cm-1) of the totally symmetric modes of the p-difluorobenzene cation in the ground

electronic state ( X~ 2B2g) calculated at the B3LYP level with various basis sets.

Modea Symm. Neutrala 4-31G(d,p) 6-31G(d,p) 6-311+G(df,p) 6-311++G(df,pd) 6-311++G(2df,2pd) Exp.b

1[2] ag 3084 3238 3240 3218 3218 3219 3015

2[8a] ag 1617 1697 1694 1679 1681 1680 1640

3[7a] ag 1245 1425 1417 1399 1399 1396 1379

4[9a] ag 1142 1176 1173 1175 1177 1174 1152

5[1] ag 858 855 853 848 848 849 839

6[6a] ag 451 449 447 449 449 449 441

a Vibrational assignments in Mulliken notation (Wilson notation in square bracket) and frequencies for the

ground state neutral taken from ref. 34.

b This work.




168

0 1000 2000 3000

74000 75000 76000 77000

61131

3151

2141

21211

91

261 101

6n21

6n31

6n41

51 41

21

31

61291161291

171

6n

314161

30181

6n51

11

0-0

Ion

Sign

al

Photon Energy, cm-1

Fig. 4.11 One-photon MATI spectrum of p-C6H4F2 recorded by monitoring

p-C6H4F2+• in the ground electronic state. The x-scale at the top of the

figure corresponds to the vibrational frequency scale for the cation. Its

origin is at the 0-0 band position.


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p-difluorobenzene cation in the electronic ground state ( X~ 2B2g).

Modea Symm. Neutrala PESb MATIc ZEKEd Calculated This work 1[2] ag 3084 3219 3015 2[8a] ag 1617 1597 1640 1680 1640 3[7a] ag 1245 1339 1375 1396 1379 4[9a] ag 1142 1113 1150 1149 1174 1152 5[1] ag 858 831 836 836 849 839 6[6a] ag 451 427 439 440 449 441 7[17a] au 943 1001 1015e

8[16a] au 347 359 358 374 368f 9[10a] b1g 800 780 768 10[20a] b1u 3088 3209 3094 11[19a] b1u 1511 1507 12[13] b1u 1212 1317 13[18a] b1u 1012 985 983 14[12] b1u 737 749 743/731g 15[5] b2g 928 1005 1015e

16[4] b2g 692 743 743/731g

17[10b] b2g 375 303 302 306 303 18[20b] b2u 3028 3218 19[19b] b2u 1437 1518 1526 20[14] b2u 1285 1352 1351 21[18b] b2u 1085 1131 1113 22[15] b2u 350 368 368f

23[7b] b3g 3084 3210 3054 24[8b] b3g 1432 1459 25[3] b3g 1285 1277 1278h

26[6b] b3g 635 591 583 27[9b] b3g 434 430 436 28[17b] b3u 833 859 891 29[16b] b3u 504 508 524 515


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30[11] b3u 166 129 127 126 129 124 61301 565 6181 799 803 62 880 881

61291 954 61261 1025

61(141/161) 1169 61(141/161) 1182

6191 1207 6281 1237 1244 5161 1276 1278

63 1319 1319 61131 1419 4161 1589 1590 52 1674 1671

5162 1714 1716 64 1759 1761

3161 1816 1816 62131 1863 6271 1891 4151 1988 1992 4162 2028 2031 2161 2077 2077 5261 2114 2112 5163 2154 2152 3151 2219 3162 2257 2257 42 2302 2302

6371 2329 31131 2362 415161 2426 2431 4163 2471 2470 2162 2517 2518


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5262 2552 2550 5164 2590 3163 2697 21211 2753 2141 2789

415162 2867 4164 2908

314161 2968

a Vibrational assignments in Mulliken notation (Wilson notation in square

bracket) and frequencies for the ground state neutral taken from ref. 34. b ref. 46. c ref. 41. d ref. 40. e This peak may be assigned alternatively to 71 or 151.

f This peak may be assigned alternatively to 81 or 221.

g This peak may be assigned alternatively to 141 or 161. h This peak may be assigned alternatively to 251 or 6151.


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has been mentioned earlier, quantum chemical calculations performed at various

levels in this work suggest that the ground state cation belongs to the C2v point

group. Then, eleven normal modes of the cation, modes 1~11, are totally

symmetric (a1). By comparing the vibrational frequencies of the prominent peaks

in Fig.4.12 with the calculated frequencies, fundamentals, overtones, and

combinations of the a1 modes could be easily identified. Among the a1 modes,

the modes 1~3 which are due to C-H stretching do not appear distinctly in the

MATI spectrum and can not be identified. Among the prominent peaks, those at

379, 885, 909, and 1496 cm-1 could not be assigned to a1 symmetry. By

comparing with the calculated frequencies, these were assigned to 19(b1), 16(b1),

12(a2), and 23(b2), respectively. Complete assignment for the vibrational peaks

in the MATI spectrum of m-difluorobenzene is shown in Table 4.14. A

noticeable feature in the spectrum is the appearance of the 6n and 10n

progressions. If the symmetry of the cation is lowered from C2v, some of the

modes become totally symmetric and may occur prominently in the MATI

spectrum. For example, if the symmetry is lowered from C2v to Cs, b2 symmetry

in C2v becomes a′ which is totally symmetric. There are ten normal modes with

b2 symmetry, modes 21-30, in m-difluorobenzene cation. Among these, only the

mode 23 appears distinctly, as has been mentioned earlier. In fact, the b2 modes

are not particularly more prominent than the a2 and b1 modes. This suggests that

the cation retains the C2v symmetry of the neutral as found in quantum chemical

calculations.

4.5.6 o-Difluorobenzene Cation

Just as for the m-difluorobenzene cation, a low resolution photoelectron

spectrum is the only spectral information available for the o-difluorobenzene

cation.49 C2v symmetry is also found in this case from quantum chemical


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0 1000 2000 3000

76000 77000 78000

4181

51121611116191

161

301201

121

181

61231

5161

51101

231

91101171

101111

131

191

6110n

71 4151

81

111 91

6n

141

10n

0-0

Ion

Sign

al

Photon Energy, cm-1

Fig. 4.12 One-photon MATI spectrum of m-C6H4F2 recorded by

monitoring m-C6H4F2+• in the ground electronic state. The x-scale at the

top of the figure corresponds to the vibrational frequency scale for the

cation. Its origin is at the 0-0 band position.


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Table 4.14 Vibrational frequencies (in cm-1) and their assignments for the m-

difluorobenzene cation in the ground electronic state ( X~ 2B1).

Modea Symm. Neutrala Calculated This work 1[20a] a1 3222 2[2] a1 3087 3223 3[7a] a1 3049 3206 4[8a] a1 1605 1572 1605 5[19a] a1 1449 1538 1559 6[13] a1 1277 1374 1355 7[18a] a1 1066 1111 1092 8[12] a1 1008 997 987 9[1] a1 735 740 728

10[6a] a1 524 519 505 11[9a] a1 331 346 343

12[17a] a2 879 933 909 13[16a] a2 599 622 614 14[10a] a2 251 204 199 15[5] b1 978 1006

16[17b] b1 850 904 885 17[11] b1 769 802 784 18[4] b1 672 599 587

19[16b] b1 458 399 379 20[10b] b1 230 190 190 21[20b] b2 3096 3209 22[8b] b2 1613 1432 1429 23[19b] b2 1490 1523 1496 24[3] b2 1337 1279 25[14] b2 1260 1399 1377 26[9b] b2 1158 1119 27[18b] b2 1120 1228 1258 28[7b] b2 954 928 923 29[6b] b2 514 489 467 30[15] b2 478 421 418

142 393


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111141 543 112 686

111301 759 111291 806 101111 846

102 1008 101111141 1047

811201 1175 91101 1231 101171 1289 91181 1316 81111 1330 103 1513

61111 1694 8191 1713 91102 61191

1734

102171 1794 61101 1859 101251 1876 101231 1999 51101 2060 6191 2085 61102 2363 51121 2465 4181 2585 62 2706

61231 2848 61103 2864 5161 2910


bracket) and frequencies for the ground state neutral taken from ref. 34.


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0 1000 2000 3000

75000 76000 77000 78000

41111

251

271

10n111

171 28

1

301

151

201291

71 101

41101

3110121

6171 41 3181

91

11n

161

61101

10n

0-0

Ion

Sign

al

Photon Energy, cm-1

200 400 600 800

141

111301

112291

191

151

301161

201

Ion Energy, cm-1

Fig. 4.13 One-photon MATI spectrum of o-C6H4F2 recorded by

monitoring o-C6H4F2+• in the ground electronic state. The x-scale at the top

of the figure corresponds to the vibrational frequency scale for the cation.

Its origin is at the 0-0 band position. Spectrum in the 100~800 cm-1 region

magnified by 30 is shown as an inset to demonstrate the quality of the

MATI spectra obtained in this work.


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Table 4.15 Vibrational frequencies (in cm-1) and their assignments for the o-

difluorobenzene cation in the ground electronic state ( X~ 2B1).

Modea Symm. Neutrala Calculated This work 1[2] a1 3081 3221 3089

2[20b] a1 3045 3210 3032 3[8a] a1 1605 1575 1548

4[19b] a1 1514 1516 1487 5[14] a1 1292 1399 1397b 6[7a] a1 1272 1364 1342c 7[9a] a1 1152 1196 1171

8[18b] a1 1025 979 966 9[1] a1 762 762 749

10[6a] a1 568 572 553 11[15] a1 287 297 294 12[5] a2 970 1012

13[17a] a2 840 883 887d 14[4] a2 703 746 704

15[16a] a2 588 423 413 16[10b] a2 196 150 148 17[17b] b1 929 992 994 18[11] b1 749 782 799

19[16b] b1 450 456 442e 20[10a] b1 275 262 254 21[7b] b2 3218 22[20a] b2 3060 3203 23[8b] b2 1618 1534 1523 24[19a] b2 1472 1346 1342c 25[3] b2 1253 1206 1202 26[13] b2 1206 1473 1435 27[18a] b2 1103 1124 1065 28[12] b2 857 856 29[6b] b2 546 533 505 30[9b] b2 440 394 382 111161 442


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112 588 111301 677 101111 848 291301 887

101301 930 101291 1051

102 1104 81111 1261

102111 1397

103 1658 71101 1723

101251 1755 41111 1778 171281 1842 61101 1896 51101 1949 41101 2039 41101 2099 7181 2138 4191 2237 71102 2278 6181 2308 4181 2452 6171 2509 41102 2591


bracket) and frequencies for the ground state neutral taken from ref. 34. b This peak may be assigned alternatively to 102111.

c This peak may be assigned alternatively to 61 or 241. d This peak may be assigned alternatively to 291301. e This peak may be assigned alternatively to 111161.


2004/01/28 17:41:01

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calculations. All the a1 vibrational modes except for the modes 1 and 2 which are

due to C-H stretching appear prominently in the MATI spectrum. Experimental

and calculated vibrational frequencies and assignments are listed in Table 4.15.

In this case overtones and combinations do not appear as abundantly and

intensely as in the case of para and meta isomers, even though 10n and 11n

progressions are observed. Frequency of the peak at 848 cm-1 is close to the

calculated frequency of the mode 28(b2). Then, it becomes the only b2 mode

with prominent intensity. Considering appearance the 10n and 11n progressions,

however, we would rather assign it to the combination 101111. Then, none of the

b2 modes which become totally symmetric upon symmetry reduction to Cs

appear prominently in the MATI spectrum of o-difluorobenzene. This suggests

that the C2v symmetry of the neutral is retained in the cation.

4.5.7 Geometrical Change upon Ionization and Vibrational

Progressions

A remarkable feature common to the MATI spectra of three isomers of

difluorobenzene is the appearance of strong overtone progressions of some

totally symmetric modes. These are 6n for the para, 6n and 10n for the meta, and

10n and 11n for the ortho isomers. Progressions of combinations involving these

overtones are observed abundantly also. Appearance of overtones of a particular

totally symmetric mode, or large Franck-Condon factors for such overtones,

indicates that the geometrical change upon ionization is well overlapped with the

eigenvector of the mode involved. As an example, atomic displacements upon

ionization of p-difluorobenzene evaluated from the quantum chemical results in

Table 4.8 are compared with the eigenvector of the mode 6 of the cation in

Fig.4.14. Similarity of the two vectors is apparent in the figure. As a more

quantitative measure of the overlap, the atomic displacement vector was mass-


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Fig. 4.14 Equilibrium geometries of (a) neutral and (b) cation of p-C6H4F2.

Arrows in (a) indicate atomic displacements upon ionization magnified by

10. Arrows in (b) indicate the eigenvector of the mode 6 of the cation.


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weighted and its projection on the eigenvector of each totally symmetric mode

was calculated. In the case of the para isomer, the absolute values of the

projection were 0.001(1), 0.13(2), 0.13(3), 0.12(4), 0.11(5), and 0.42(6) with the

numbers in the parentheses indicating the normal mode number. Large

projection along the mode 6 is in agreement with the prominent 6n progression

observed in the MATI spectrum. In the case of the meta isomer, these were

0.001(1), 0.001(2), 0.002(3), 0.12(4), 0.04(5), 0.15(6), 0.03(7), 0.10(8), 0.09(9),

0.32(10), and 0.12(11). Appearance of strong fundamentals of the modes 10 and

6 and their overtones and combinations is in good agreement with the

projections calculated. For the ortho isomer, the calculated absolute projections

of 0.000(1), 0.001(2), 0.13(3), 0.10(4), 0.08(5), 0.06(6), 0.08(7), 0.06(8), 0.08(9),

0.29(10), and 0.20(11) are in agreement with the strong fundamentals, overtones,

and combinations of the modes 10 and 11. Successful explanation of the above

spectral features indicates reliability of the results from the B3LYP/6-311++G

(2df, 2pd) calculation in the present cases.

4.5.8 Conclusions

VUV-MATI spectra of o-, m-, and p-difluorobenzene cations have been

obtained and vibrational frequencies have been assigned by comparing to those

calculated at B3LYP/6-311+G (df, p) level. Even though the structure and

vibrational frequencies of p-difluorobenzene cation have been completely

analyzed by ZEKE-PES spectroscopy using two color 1+1' scheme, one-photon

MATI spectra in our present work would have provided much more information

on vibrations of the fundamentals, their combinations and overtones. By

comparing the measured vibrational frequencies to the calculated, it is concluded

that the symmetries of the o-, m-, and p-difluorobenzene cations belong to the

point group of C2v, C2v, and D2h, respectively, same as those of neutrals. The 6an


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progressions prominently appear as p-C6H4F2+• >m-C6H4F2

+• >o-C6H4F2+• in the

MATI spectra. Considering the geometrical change upon ionization from

calculations, it has been found that the overlaps between the atomic

displacements upon ionization and eigenvectors of the 6a mode are expected to

be substantial and decrease in turn p-C6H4F2+•, m-C6H4F2

+•, and o-C6H4F2+•. In

addition, the most common feature in the structure of all difluorobenzene cations

studied in the ground state is the contraction of the C-F bonds upon ionization

resulting from removal of a π electron in benzene ring.

4.6 UV-MATI Spectroscopy of Phenylacetylene and

Benzonitrile

One-photon MATI spectra of halobenzenes reported recently by this

laboratory showed well-resolved vibrational peaks of the corresponding cations,

which consisted mostly of fundamentals with proper symmetries. Vibrational

assignments were made by referring to the previous results, comparing with

calculated frequencies, and invoking the selection rule for one-photon process.

Difference in the geometry between the neutral and cation, or geometric change

upon ionization, was calculated quantum chemically and used to explain the

prominent overtones of some vibrational modes and combinations involving

these. As a more rigorous attempt to utilize spectral intensity information for

vibrational assignment, Franck-Condon factors were calculated from the

quantum chemical results in our recent study of an aliphatic halide.51 Theoretical

prediction of the intensities for transitions to all the totally symmetric vibrational

states was found to be extremely useful for reliable assignment.

In this section, we report the vibrational spectra of phenylacetylene and

benzonitrile cations obtained by one-photon MATI spectroscopy. Successful


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vibrational assignments made based on the above strategy, namely by utilizing

the calculated frequencies and Franck-Condon factors and symmetry selection

rule, will be presented also.

4.6.1 Quantum Chemical Calculations

Calculations of equilibrium geometries and vibrational frequencies of

phenylacetylene and benzonitrile and their cations in the ground states were

performed at the density functional theory (DFT) levels, B3LYP, B3PW91, and

BP86, with various basis sets using GAUSSIAN 98 suite of programs. Size of

the basis set was systematically increased until the basis set dependence

disappeared. Hence, only those obtained with the largest basis set used, the 6-

311++G (2df, 2pd), will be listed and discussed. For the vibrational frequencies,

the results obtained at the BP86/6-311++G (2df, 2pd) level showed the best

agreement with the experimental data. Frequencies obtained by these

calculations are presented without scaling in Tables 4.16 and 4.17. At all the

levels used in the calculation, equilibrium geometries of the phenylacetylene and

benzonitrile neutrals and cations belong to the C2v symmetry. Invoking the

symmetry selection rule, prominent peaks in the MATI spectra must be mostly

due to transitions to the a1 vibrational states. The Franck-Condon factors for

such transitions, either fundamentals, overtones, or combinations, calculated at

three density functional theory (DFT) levels, B3LYP, B3PW91, and BP86 using

the 6-311++G (2df, 2pd) basis set were rather similar. The Franck-Condon

factors calculated at the BP86/6-311++G (2df, 2pd) level and normalized to that

of the 0-0 transition are listed in Tables 4.19 and 4.20 also. Comparing the

experimental and calculated frequencies and Franck-Condon factors was helpful

to identify a1 peaks. The remaining weak peaks in one-photon MATI spectra

must be due to electric dipole-forbidden but vibronically allowed transitions.


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184

Only the calculated frequencies, not intensities, can be used to assign these

nontotally symmetric transitions.


MATI spectra of phenylacetylene and benzonitrile recorded by monitoring

C6H5C≡CH+ and C6H5C≡N+ in the ground electronic states are shown in Figs.

4.15 and 4.16, respectively. The spectra magnified by 15 are also shown as

insets in the figures. The intense peaks appearing at the lowest photon energy,

namely at 71127 and 78461 cm-1 in Figs. 4.15 and 4.16, respectively, correspond

to the 0-0 bands. The position of the 0-0 band in a one-photon MATI spectrum is

equivalent to the ionization energy of the molecule. However, the ionization

energy thus measured is usually a little smaller than the correct value because

the molecules in ZEKE states9 some cm-1 below the threshold can also be

ionized when a high PFI field is applied. To correct for this effect, the 0-0 band

position was measured using various PFI fields and the accurate ionization

energy was estimated by extrapolation to the zero field limit. Spoil field was not

used in such measurements. The ionization energies to the ground electronic

states of phenylacetylene and benzonitrile cations measured in this work are

listed in Table 4.18 together with previous results.52-55 There has been no

previous report on the accurate ionization energy of phenylacetylene measured

by ZEKE or MATI. The ionization energy of phenylacetylene determined in this

work, 8.8195 ± 0.0006 eV, is a little different form 8.825 ± 0.001 eV measured

by threshold photoelectron spectroscopy (TPES).52 More annoying is that the

ionization energy of benzonitrile obtained in this work, 9.7288 ± 0.0006 eV, is

smaller than a previous ZEKE result54 by ∼ 20 cm-1. My experience is that the

present MATI technique which uses high voltage electronics tends to under-

estimate ionization energies by 0 ∼ 5 cm-1.52,53 We do not have an explanation


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Table 4.16. Vibrational frequencies (in cm-1) of phenylacetylene neutral and

cation in the ground electronic states calculated at the B3LYP, B3PW91, and

BP86 levels with the 6-311++G (2df, 2pd) basis set and experimental data for

the neutral.

Neutral Cation Mode Symm.Exp.a B3LYP B3PW91 BP86 B3LYP B3PW91 BP86

1 a1 763 777 781 756 766 767 746 2 a1 3064 3202 3210 3125 3221 3228 3144 3 b2 1283 1310 1325 1290 1298 1304 1257 4 b1 691 708 707 683 741 738 699 5 b1 986 1014 1011 968 1045 1040 999 6a a1 467 474 471 459 470 467 455 6b b2 619 638 648 616 581 578 560 7a a1 3035 3172 3179 3094 3196 3201 3119 7b b2 3198 3206 3121 3219 3226 3142 8a a1 1598 1640 1651 1587 1643 1652 1592 8b b2 1573 1609 1621 1558 1536 1538 1483 9a a1 1178 1202 1198 1163 1210 1206 1172 9b b2 1158 1185 1180 1149 1175 1174 1139 10a a2 842 860 859 825 827 824 789 10b b1 165 142 142 136 120 118 115 11 b1 756 782 777 752 817 815 787 12 a1 1000 1018 1017 987 998 999 971 13 a1 1192 1223 1228 1193 1266 1271 1228 14 b2 1331 1358 1357 1325 1387 1393 1348 15 b2 161 159 152 153 151 145 16a a2 418 413 409 395 363 358 345 16b b1 531 558 558 536 481 479 457 17a a2 971 998 996 953 1027 1024 982 17b b1 918 946 944 904 991 988 949


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18a a1 1028 1050 1053 1020 1009 1011 981 18b b2 1071 1102 1103 1069 1113 1115 1081 19a a1 1489 1526 1525 1474 1486 1483 1435 19b b2 1444 1478 1477 1429 1436 1442 1399 20a a1 3083 3191 3198 3113 3210 3216 3133 20b b2 3058 3180 3188 3103 3208 3214 3130 βCC b2 516 539 538 517 531 528 507 βCH b2 653 689 690 635 694 695 645 vCC a1 2118 2202 2209 2131 2107 2108 2053 vCH a1 3291 3468 3472 3393 3409 3412 3334 γCC b1 352 371 369 354 324 322 311 γCH b1 610 645 633 588 645 642 621

a Ref. 34.

Table 4.17. Vibrational frequencies (in cm-1) of benzonitrile neutral and cation

in the ground electronic states calculated at the B3LYP, B3PW91, and BP86

levels with the 6-311++G (2df, 2pd) basis set and experimental data for the

neutral.

Neutral Cation Mode Symm. Exp.a B3LYP B3PW91 BP86 B3LYP B3PW91 BP86

1 a1 769 774 774 752 755 756 736 2 a1 3071 3196 3215 3130 3210 3228 3143 3 b2 1289 1319 1334 1298 1416 1426 1382 4 b1 686 706 704 682 631 628 607 5 b1 987 1021 1016 974 1042 1035 994 6a a1 461 467 465 452 459 456 445 6b b2 629 641 637 619 504 500 483 7a a1 3042 3178 3185 3100 3196 3201 3118


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7b b2 3027 3204 3212 3127 3219 3225 3141 8a a1 1599 1641 1654 1588 1660 1669 1603 8b b2 1584 1615 1627 1563 1275 1279 1235 9a a1 1178 1203 1200 1165 1210 1207 1172 9b b2 1163 1188 1184 1153 1148 1150 1110 10a a2 848 863 862 828 814 811 775 10b b1 172 147 146 140 118 116 111 11 b1 758 781 780 751 815 813 784 12 a1 1001 1019 1019 989 1001 1000 971 13 a1 1191 1220 1226 1188 1252 1256 1215 14 b2 1337 1361 1361 1329 1392 1389 1344 15 b2 162 169 166 160 157 155 148 16a a2 401 410 406 392 353 347 335 16b b1 548 573 574 552 449 442 413 17a a2 978 1002 1000 957 1029 1025 983 17b b1 925 954 952 912 990 985 947 18a a1 1027 1050 1053 1021 984 988 962 18b b2 1071 1105 1106 1073 1088 1093 1054 19a a1 1492 1528 1527 1475 1474 1469 1425 19b b2 1448 1481 1480 1431 1528 1529 1475 20a a1 3080 3207 3203 3118 3221 3216 3132 20b b2 3039 3188 3195 3110 3209 3214 3131 βCN b2 551 570 570 549 568 570 548 vCN a1 2232 2332 2341 2236 2192 2196 2124 γCN b1 381 392 390 375 317 312 298

a Ref. 34.


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Table 4.18. Ionization energies (IE) of phenylacetylene and benzonitrile, in eV.

IE ( X~ ) Ref.

Phenylacetylene 8.8195 ± 0.0006 This work

8.825 ± 0.001 TPES52

8.82 ± 0.02 PES53

Benzonitrile 9.7288 ± 0.0006 This work

9.7315 ± 0.0002 ZEKE54

9.71 ± 0.01 PI55

for the above discrepancy at the moment even though we would like to point out

that quality of the present MATI spectrum is superior to the previous ZEKE

spectrum54. Assuming that the shift of a vibrational peak in a MATI spectrum

due to the applied electric fields is similar to that of the 0-0 band, the vibrational

frequency corresponding to each peak can be determined simply by taking the

difference of its position from that of the 0-0 band. Vibrational frequency scales

with origins at the 0-0 band positions are also drawn in Figs. 4.15 and 4.16.

Vibrational frequencies of C6H5C≡CH+ and C6H5C≡N+ in the ground electronic

state calculated at the BP86/6-311++G (2df, 2pd) level are compared with the

experimental data in Tables 16 and 17, respectively. Also listed in the tables are

intensities of each peak in the MATI spectra normalized to that of the 0-0 band.

Frequencies of some vibrations measured previously by TPES52 and ZEKE54 are

also included in the tables.

4.6.3 Phenylacetylene Cation


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The phenylacetylene cation with C2v symmetry has 36 nondegenerate normal

modes, thirteen of which belong to the a1 symmetry species, three to a2, eight to

b1, and twelve to b2. Among the a1 type modes, 2, 7a, 20a, and νCH in Wilson

notation33 are due to CH stretching and have frequencies of ∼ 3000 cm-1.

According to our previous study on the CH stretching modes, they are not

expected to appear distinctly in the one-photon MATI spectrum. Then,

prominent peaks in the spectral region 0 ∼ 1700 cm-1 and near ∼ 2000 cm-1 can

mostly be assigned to the fundamentals of the remaining a1 modes, 1, 6a, 8a, 9a,

12, 13, 18a, 19a, and vCC, as well as their overtones and combinations. Among

these, the calculated Franck-Condon factors are especially significant for the

fundamentals of 6a, 1, 12, 9a, 8a, and vCC whose calculated frequencies at the

BP86 level are 455, 746, 971, 1172, 1592, and 2053 cm-1, respectively. Hence,

the prominent peaks at 458, 747, 979, 1185, 1604, and 2040 cm-1 in the MATI

spectrum of phenylacetylene can readily be assigned to 6a1, 11, 121, 9a1, 8a1, and

vCC1, respectively. Even though the fundamental of v13, which is another a1-type

mode, is expected to be weak according to its calculated Franck-Condon factor,

it appears distinctly near its calculated frequency, at 1249 cm-1. 19a1 appears

rather distinctly at 1435 cm-1 even though its calculated Franck-Condon is only

0.004. We would rather assign this to a composite of 19a1 and 6a1121 based on

the calculated frequencies and Franck-Condon factors. A weak shoulder peak at

989 cm-1 is close to 981 cm-1 calculated for 18a1. We are reluctant to make such

an assignment because the calculated Franck-Condon factor for this transition is

extremely small, 0.0002. It is to be mentioned that the harmonic frequencies

calculated at the BP86 level are usually a little smaller than the experimental

ones while those at the B3LYP and B3PW91 levels are larger. The same trend

holds for most of the fundamentals of the phenylacetylene and benzonitrile


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Fig. 4.15 One-photon MATI spectrum of C6H5C≡CH recorded by

monitoring C6H5C≡CH+ in the ground electronic state. The x-scale at the

top of the figure corresponds to the vibrational frequency scale for the

cation whose origin is at the 0-0 band position. Spectrum in the 50 ∼ 2500

cm-1 region magnified by 15 is shown as an inset to demonstrate the

quality of the MATI spectrum obtained in this work.


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Table 4.19 Vibrational frequencies (in cm-1) and their assignments for

phenylacetylene cation in the ground electronic state ( X~ 2B1).

Calculatedc This work Modea Symm. TPESb

Frequency Intensityd Frequency Intensityd

Fundamentals 1 a1 759 746 0.131 747 0.076 2 a1 3144 5×10-6 3 b2 1257 0 1287 0.007 4 b1 699 0 706 0.017 5 b1 999 0 996 0.008 6a a1 460 455 0.353 458 0.438 6b b2 560 0 561 0.008 7a a1 3119 3×10-6 7b b2 3142 0 8a a1 1592 0.096 1604 0.073 8b b2 1483 0 1505 0.006 9a a1 1172 0.081 1185 0.102 9b b2 1139 0 1158 0.018 10a a2 789 0 795e 0.015 10b b1 115 0 110 0.008 11 b1 787 0 795e 0.015 12 a1 971 0.069 979 0.066 13 a1 1228 0.010 1249 0.087 14 b2 1348 0 15 b2 145 0 143 0.005 16a a2 345 0 346 0.011 16b b1 457 0 17a a2 982 0 989 0.006 17b b1 949 0


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18a a1 981 0.0002 18b b2 1081 0 1076 0.007 19a a1 1435 0.004 1435f 0.044 19b b2 1399 0 20a a1 3133 0.0003 20b b2 3130 0 βCC b2 504 507 0 499 0.012 βCH b2 645 0 658 0.008 vCC a1 2053 0.101 2040 0.042 vCH a1 3334 0.0001 γCC b1 311 0 303 0.010 γCH b1 621 0 622 0.010

Overtones and Combinations 10b2 a1 230 0.002 221 0.010 152 a1 290 0.0002 286 0.007

10b1γCC1 a1 426 0.002 409 0.034 6a110b1γCC1 a1 881 0.0007 865 0.006

6a2 a1 910 0.065 914 0.063 41γCC1 a1 1010 0.0003 1009 0.012 6b1βCC1 a1 1067 0.0004 1064 0.005 6a111 a1 1201 0.045 1205 0.082 6a3 a1 1365 0.008 1370 0.022 42 a1 1398 0.008 1407 0.028 6a1121 a1 1426 0.026 1435f 0.044 6a117a1 a2 1437 0 1448 0.009 121βCC1 b2 1478 0 1465 0.007 6a19a1 a1 1627 0.029 1643 0.017 6a1131 a1 1683 0.004 1706 0.025 1117a1 a2 1728 0 1739 0.010 6a119a1 a1 1890 0.002 1895 0.017


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6a18a1 a1 2047 0.035 2058 0.017 9a1121 a1 2143 0.005 2164 0.017 121131 a1 2199 0.001 2228 0.013 118a1 a1 2338 0.011 2356 0.016 6a1vCC1 a1 2508 0.038 2496 0.027 8a1121 a1 2563 0.005 2582 0.012 11vCC1 a1 2764 0.008 8a19a1 a1 2799 0.012

2789 0.016

19a119b1 b2 2834 0 2837 0.007 6a2vCC1 a1 2963 0.007 2953 0.011 121vCC1 a1 3024 0.008 3022 0.010

6a18a1121 a1 3018 0.002 3032 0.008 8a2 a1 3184 0.006 3206 0.014 9a1vCC1 a1 3224 0.010 3227 0.011 131vCC1 a1 3281 0.002 3292 0.010

a Wilson notation. b Ref. 52. c BP86/6-311++G (2df, 2pd) level. d Normalized to the intensity of the 0-0 band. e A composite of 10a1 and 111. f A composite of 19a1 and 6a1121.


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neutrals as can be seen in Tables 4.16 and 4.17. Even though the results must

rise from different error cancellations at these levels,56 the correlation can be

used advantageously in the peak assignments.

The fact that 6a1 appeared most prominently in the one-photon MATI

spectrum indicates that the geometrical change upon ionization occurs mostly

along the 6a eigenvector. This has been confirmed by calculation, even though

not shown here, by projecting the geometrical change vector on the 6a

eigenvector. This also suggests that 6an overtones and combinations of 6a and

other a1 modes would appear prominently in the one-photon MATI spectrum.

Accordingly, the prominent peaks at 914 and 1370 cm-1 can be assigned to 6a2

and 6a3, respectively. Also, the distinct peaks at 1205, 1435, 1643, 1706, 2058,

and 2496 can be assigned to 6a combinations, 6a111, 6a1121, 6a19a1, 6a1131,

6a18a1, and 6a1vCC1, respectively, from the calculated frequencies and Franck-

Condon factors. The peak at 1435 cm-1 can be alternatively assigned to 19a1 as

has been mentioned earlier. Other combinations of the a1 modes, 1118a1, 9a1121,

and 118a1 appeared distinctly also at 1739, 2164, and 2356 cm-1, respectively.

The Franck-Condon factors for 11vCC1 and 8a19a1 calculated at the BP86 level

are 0.012 and 0.008, respectively. Hence, the peak at 2789 cm-1, which can be

assigned either to 11vCC1 or to 8a19a1 based on the frequencies may better be

assigned to a composite of the two transitions, 11vCC1/8a19a1. The calculated

Franck-Condon factors for the fundamentals of the CH stretching modes 2, 7a,

20a, and νCH are negligible. This is understandable because the lengths of all

the CH bonds hardly change upon ionization. Extremely weak peaks appeared in

the 3000 ∼ 3200 cm-1 region of the present MATI spectrum (Fig. 4.16). We are

reluctant to assign them to 21, 7a1, 20a1, or νCH1 because their calculated

Franck-Condon factors are very small. Instead, it is more likely that they are

overtones or combinations. Thus, the very weak peaks at 3022, 3206, and 3292


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were assigned to 121vCC1, 8a2, and 131vCC1, respectively. Some distinct peaks

may be assigned to combinations of nontotally symmetric modes with a1 overall

symmetry. Hence, the distinct peaks at 221, 286, 409, 1009, and 1407 were

assigned to 10b2, 152, 10b1γCC1, 41γCC1, and 42, respectively.

The fundamentals of nontotally symmetric modes do not appear in the

simulated spectrum because the Franck-Condon factors calculated under the

Born-Oppenheimer approximation are zero for these transitions. They still

appeared in the actual spectrum, even though very weakly, through vibronic

mechanism. Hence, very weak peaks at 303, 346, 499, 561, 622, 706, and 795

cm-1 can be assigned to γCC1, 16a1, βCC1, 6b1, γCH1, 41 and 10a1/111 by

comparing with the calculated frequencies of 311, 345, 507, 560, 621, 699, and

789/787 cm-1, respectively. A very weak 16b1 is expected at ~457 cm-1 but must

have been buried in the strong 6a1 transition. Similarly, 17a1 and 17b1 expected

at 950~980 cm-1 may have been buried as shoulders of 121. The weak shoulder

peak at 989 cm-1 mentioned previously may be 17a1 rather than 18a1.

4.6.4 Benzonitrile Cation

Kimura and coworkers reported 1+1' ZEKE spectrum of benzonitrile in the 0

~ 1200 cm-1 vibrational energy region.54 Tentative assignments were made by

comparing with results from PM3 semi-empirical calculations. They adopted

Mulliken notation for vibration modes, with some minor errors. We reinterpreted

their assignments using the DFT frequencies calculated in this work and listed

them in Table 4.20.

A spectrum with much higher quality than the above was obtained in the 0 ~

2500 cm-1 region (78200 ~ 81000 cm-1 in photon energy) by one-photon MATI

in this work. The 81000 ~ 81500 cm-1 region could not be recorded due to a dip

in VUV output. According to our experience in MATI of phenylacetylene in this


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work and halobenzenes in previous studies, this region is not expected to be

important because the CH stretching fundamentals would not be observed

anyway. Symmetry selection rule and frequencies and Franck-Condon factors

calculated at the DFT levels will be utilized to assign the observed vibrational

peaks as has been done for phenylacetylene.

Quantum chemical calculations performed at various levels for this molecule

suggest that the cation belongs to the C2v point group in the ground electronic

state. Twelve normal modes are a1-type as listed in Table 4.17. Among these, 2,

7a, and 20a are high frequency vibrations with CH stretching character and can

be neglected in this work. Among the a1-type vibrations, the fundamental of 6a

displays the largest Franck-Condon factor and is readily identified as the peak at

438 cm-1. Franck-Condon factors are significant for 11, 18a1, 121, 9a1, 8a1, and

vCN1 with the calculated frequencies of 736, 962, 971, 1172, 1603, and 2124

cm-1, respectively. The prominent peaks at 737, 959, 968, 1168, 1612, and 2136

cm-1 in the MATI spectrum correspond to these transitions. The remaining a1-

type fundamentals are 131 and 19a1 with the calculated frequencies of 1215 and

1425 cm-1, respectively, and the calculated Franck-Condon factors of only 0.001

for each. Even though one might assign the peak at 1413 cm-1 to 19a1 based on

the frequency, 6a1121 seems to be a better assignment when the intensity is

considered also. For 131, the peak at 1223 cm-1 is the only candidate even though

the calculated and observed intensities show a substantial discrepancy. For the

peak at 1223 cm-1, no alternative assignment is possible, either to a fundamental,

overtone, or combination. Namely, its assignment to 131 is unavoidable and its

small Franck-Condon factor must be attributed to inaccuracy in the calculation.

It is to be noted from Table 4.20 that the Franck-Condon factor for the same

transition in phenylacetylene is also much smaller than the experimental

intensity, even though not as dramatically as in benzonitrile. It is to be


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Fig. 4.16 One-photon MATI spectrum of C6H5C≡N recorded by

monitoring C6H5C≡N+ in the ground electronic state. The x-scale at the top

of the figure corresponds to the vibrational frequency scale for the cation

whose origin is at the 0-0 band position. Spectrum in the 50 ∼ 2200 cm-1

region magnified by 15 is shown as an inset to demonstrate the quality of

the MATI spectrum obtained in this work.


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Table 4.20 Vibrational frequencies (in cm-1) and their assignments for

benzonitrile cation in the ground electronic state ( X~ 2B1).

Calculatedc This work Modea Symm. ZEKEb

Frequency Intensityd Frequency Intensityd

Fundamentals 1 a1 736 0.213 737 0.098 2 a1 3143 0.0001 3 b2 1382 0 1386 0.011 4 b1 607 0 606 0.022 5 b1 1036 994 0 1034 0.047 6a a1 447 445 0.295 438 0.376 6b b2 559 483 0 7a a1 3118 2×10-7 7b b2 3141 0 8a a1 1603 0.143 1612 0.032 8b b2 1235 0 9a a1 1172 0.098 1168 0.072 9b b2 1110 0 1111 0.025 10a a2 854 775 0 771e 0.017 10b b1 110 111 0 111 0.016 11 b1 784 0 771e 0.019 12 a1 971 0.036 968 0.039 13 a1 1215 0.001 1223 0.024 14 b2 1344 0 1353 0.020 15 b2 144 148 0 143 0.011 16a a2 332 335 0 336 0.011 16b b1 405 413 0 412 0.022 17a a2 1005 983 0 984 0.011 17b b1 920 947 0 922f 0.025 18a a1 962 0.081 959 0.047 18b b2 1054 0 19a a1 1425 0.001 1413g 0.017


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19b b2 1475 0 1470h 0.011 20a a1 3132 1×10-5 20b b2 3131 0 βCN b2 537 548 0 536 0.015 vCN a1 2124 0.055 2136 0.037 γCN b1 298 0 291 0.018

Overtones and Combinations 10b2 a1 219 222 0.005 223 0.015 10b2151 b2 370 0 361 0.037 6a110b2 a1 667 0.002 662 0.011 4110b1 a1 718 0.001 712 0.022 16b2 a1 826 0.017 6a2 a1 890 0.045

854 0.091

6b2 a1 966 0.009 922f 0.023 42 a1 1214 0.0004 1212 0.015 6a1121 a1 1416 0.012 1413g 0.017 12 a1 1472 0.020 1470h 0.011 6a1131 a1 1660 0.0003 1647 0.008 1118a1 a1 1698 0.017 11121 a1 1707 0.006

1724 0.034

119b1 b2 1846 0 1841 0.011 119a1 a1 1908 0.018 1903 0.013 13 a1 2208 0.001 2205 0.036

a Wilson notation. b Ref. 55. c BP86/6-311++G (2df, 2pd) level. d Normalized to the intensity of the 0-0 band. Intensity of the peaks above 1700 cm-1 is not accurate due to very weak VUV power. e A composite of 10a1 and 111. f A composite of 17b1 and 6b2. g A composite of 19a1 and 6a1121. h A composite of 19b1 and 12.


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mentioned that Kimura and coworkers did not identify the a1-type fundamentals,

except for 6a1, in their 1+1' ZEKE work.54

Strong fundamental of the 6a mode suggests that its overtones and

combinations, especially with other prominent a1-type modes 1, 8a, 9a, 12, 13,

18a, and vCN, would appear distinctly in the one-photon MATI spectrum. 6a2

and 6a3 overtones are expected to appear at somewhat lower than 876 and 1314

cm-1. Their calculated Franck-Condon factors are 0.045 and 0.005, respectively.

They are not easy to identify, however, because of the presence of strong

spectral features nearly. The strong peak at 854 cm-1 can not be matched with the

calculated frequency of any fundamental. It may be a composite consisting of

6a2 and 16b2. I do not attempt to identify 6a3 because of its small Franck-Condon

factor. a1-type combinations involving 6a1, namely 6a1121 and 6a1131, are

identified at 1413 and 1647 cm-1, respectively. The mode 1 which has substantial

fundamental intensity also shows an overtone 12 at 1470 cm-1. The a1-type

overtones and combinations involving nontotally symmetric modes are also

observed even though with weaker intensities than the a1 fundamentals. These

are 10b2, 6a110b2, 4110b1, and 42 at 223, 662, 712, and 1212 cm-1, respectively.

Fundamentals of some nontotally symmetric modes also appear probably

through vibronic mechanism. The most noticeable among these are the

fundamental, overtone, and combinations of the 10b mode, namely 10b1, 10b2,

10b2151, 6a110b2, and 4110b1. 10b1 appeared very prominently in the 1+1' ZEKE

spectrum reported by Kimura and coworkers.54 It is not as prominent in the

present one-photon MATI spectrum. The fact that the initial electronic states

involved in the transition moment integral are different in the two processes

must be responsible for the above difference. The remaining distinct feature in

the MATI spectrum is the peak at 1034 cm-1. Comparing with the frequencies

calculated at the three DFT levels, it seems to be logical to assign this to 51, in


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agreement with the assignment by Kimura and coworkers. Even though

6b1βCN1 may be an alternative based on the frequency alone, very small Franck-

Condon factor calculated for the latter, 0.001, is incompatible with the

observation.

4.6.5 Conclusions

For a molecule with a large number of vibrational degrees of freedom such as

C6H5C≡CH+ and C6H5C≡N+, assigning its vibrational spectrum can be a

formidable job, especially when no additional information is available in the

literature. In the case of two-photon ZEKE/MATI, further information can often

be obtained through intermediate state selection. This is not the case in the one-

photon scheme, even though the fact that excitation via an intermediate is not

needed is its clear advantage in experimental terms. It was demonstrated that use

of the selection rule and calculated frequencies and Franck-Condon factors,

especially those at the DFT levels, led to nearly complete vibrational

assignments for the cations of phenylacetylene and benzonitrile. It is to be

emphasized that the frequencies obtained at the DFT levels, especially BP86,

provided nearly quantitative fit to the experimental data even though harmonic

approximations were adopted for all the vibrations. Cancellation of various

errors must have acted favorably to result in such good fits.


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Chapter 5

The Jahn-Teller Effect in Benzenoid Cations

The Jahn-Teller effect,1 which distorts the symmetry of a nonlinear molecule

in a degenerate electronic state through vibronic interaction, has been a subject

of great interest in spectroscopy and chemistry. Polyatomic cations have been

actively studied in this regard because removal of an electron from a degenerate

orbital in a neutral results in the cation in the orbitally degenerate electronic state.

In fact, the cations of benzene and hexafluorobenzene have been prototypes in

the study of the Jahn-Teller effect.

5.1 General Descriptions

Acquisition of a vibrationally resolved spectrum is a prerequisite for the

Jahn-Teller investigation. Even though the photoelectron spectroscopy may be

used for the Jahn-Teller study in the cations, detailed vibrational data are not

often available because of its poor resolution. More often than not, optical

spectroscopic techniques are not useful either because most of the polyatomic

cations in excited electronic states relax nonradiatively very fast. In the case of

the benzene cation, even though the first excited state ( B~ 2E2g) is very long-lived,

the vibrational spectra in the first excited and the ground ( X~ 2E1g) states can not

still be recorded by optical spectroscopy because the B~ ↔ X~ transition is

optically forbidden. Recently developed zero kinetic energy (ZEKE)

photoelectron spectroscopy, mass-analyzed threshold ionization (MATI)

spectroscopy, and photo-induced Rydberg ionization spectroscopy have been


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useful to obtain vibrational spectra in the X~ and B~ states of C6H6+. In the

case of the hexafluorobenzene cation (C6F6+), B~ 2A2u ↔ X~ 2E1g is allowed and

emission is observed. Early investigation on the Jahn-Teller effect in the ground

state of C6F6+ reported by Leach and coworkers2 utilized this emission spectrum

measured in the discharge medium. Subsequently, spectra with much better

quality were reported by Miller and coworkers,3 which were obtained by

measuring dispersed fluorescence induced by laser for C6F6+ trapped in inert gas

matrices. Similar spectrum for the gas phase cation was also reported. However,

its quality was rather poor compared to the matrix spectra.

Early theoretical developments to elucidate the Jahn-Teller effect can be

accessed through excellent reviews. One of the recent efforts was to evaluate the

spectroscopic Jahn-Teller parameters from topographical features of the

potential energy surface obtained by quantum chemical calculations.4,5 Then, the

energies of various vibronic states calculated with these parameters were utilized

for spectral assignment. Since the Jahn-Teller effect lifts the electronic

degeneracy in the ground states of C6H6+ and C6F6

+, its proper treatment requires

the use of a multiconfiguration treatment. Barckholtz and Miller4 suggested to

calculate the average of the two Jahn-Teller surfaces by using a complete active

space self-consistent field (CASSCF) wavefunction. Various difficulties are

involved in this approach such as the inaccuracy of energy obtained at moderate

CASSCF levels and difficulty in evaluating reliable normal mode eigenvectors.

Johnson5 suggested to obtain the topographical parameters through the single

configuration density functional theory (DFT) calculation and to use the

eigenvectors at the global energy minimum. A decent agreement with the

experimental results for C6H6+ in the X~ 2E1g state was reported. Influence of the

spin-orbit coupling was ignored in the two approaches. The quantum mechanical

method to calculate the vibronic energy levels in the presence of the Jahn-Teller

effect and the spin-orbit coupling has been developed also and a software


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package (SOCJT) is available from Miller’s laboratory.6

5.2 Computation

The Jahn-Teller effect distorts the equilibrium geometry of C6F6+ (or C6H6

+)

in the ground electronic state ( X~ 2E1g) from D6h to D2h symmetry and splits the

electronic state into B2g and B3g. The optimized geometries and energies in these

states were calculated at the B3LYP density functional theory level using the

GAUSSIAN 98 suite of programs. Size of the basis set was systematically

increased until the basis set dependence became insignificant. All the results

reported in this paper were obtained with the 6-311++G (2df) basis set. The

vibrational frequencies and eigenvectors were obtained at the global minimum

also. To follow the Johnson’s method,5 the geometry and energy of the

undistorted structure are needed, which correspond to those of the conical

intersection, or D6h cusp, in the Jahn-Teller potential energy surface. Its

geometry was optimized at the B3LYP/6-311++G (2df) level enforcing the D6h

symmetry.

5.2.1 The Jahn-Teller Potential Energy Surfaces and Coupling Constants

The linear Jahn-Teller effect lifts the electronic degeneracy and results in the

potential energy surface (PES) looking like a ‘Mexican hat’ along the normal

coordinate involved. A circularly symmetric moat may describe the shape of the

PES near the equilibrium geometry. The depth of the moat along the ith mode,

εi(1), is the stabilization energy due to the linear Jahn-Teller effect by this

vibration and is related to the linear coupling constant, Di, as follows.

εi(1) = Diωe,i (5.1)


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Here ωe,i is the harmonic frequency of this mode. The quadratic Jahn-Teller

effect breaks the circular symmetry of the moat, resulting in a maximum and a

minimum in the moat. A half of the energy difference between the two

corresponds to the additional stabilization energy due to the quadratic effect, εi(2),

and is related to the quadratic coupling constant, Ki, as follows.

εi(2) = Diωe,i Ki (5.2)

The total Jahn-Teller stabilization energy, εT, can be evaluated as the energy

difference between the D6h cusp (2E1g) and the global minimum (2B3g).

εT = E (2E1g) - E (2B3g) (5.3)

It is not possible to apportion this into each Jahn-Teller active mode because the

geometry at the global minimum does not necessarily correspond to

simultaneous minima along all the Jahn-Teller active modes. The usual approach

to evaluate εi(1) and εi

(2) is to start from the undistorted geometry, the energy

minimum in D6h or the Jahn-Teller cusp, and calculate the potential energy along

each Jahn-Teller active normal coordinate. Following Johnson,5 the eigenvector

of the ag component of the Jahn-Teller active e2g mode obtained at the global

minimum (2B3g) was used in the calculation. Energies at twenty points each in

the positive and negative directions along the eigenvector were calculated by

B3LYP/6-311++G(2df) and fit quadratically such that the two potential energy

curves meet at the cusp. εi(1) and εi

(2) were evaluated from the energies at the

cusp and two minima. Sum of the stabilization energy along each Jahn-Teller

active mode would correspond to the total stabilization energy under the ideal

situation.

εT ≈ ∑∑==

+=+p

iiiei

p

iii KDεε

1,

1

)2()1( )1(ω)( (5.4)


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5.2.2 Jahn-Teller Parameters and Vibronic Energies

The Jahn-Teller splitting is frequently described in terms of the vibronic

angular momentum quantum number j defined below.7

j = l + 1/2 Λ (5.5)

Here l is the vibrational angular momentum and Λ is the quantum number

designated to differentiate the two components of the degenerate electronic state.

Four e2g normal modes in X~ 2E1g, namely v15 ~ v18 (to be explained), are

linear Jahn-Teller active, which results in the splitting of each singly excited

level into j = ± 1/2 and ± 3/2 states. The quadratic effect further mixes j = 3/2

and -3/2 states and lifts the degeneracy. It is usual to use the ii l,,υΛ bases.

Then, the matrix elements for the Jahn-Teller Hamiltonian are given in terms of

ωe,i, Di, and Ki. Even when mode-mode coupling is not incorporated explicitly,

the Jahn-Teller active modes are coupled through the zero-point level, which

necessitates a simultaneous multimode calculation. In the multimode case, l

represents the total vibrational angular momentum ∑i

il . The multimode

package available from Miller’s laboratory, SOCJT,6 was used in this work.

Spin-orbit coupling was ignored.

Initially, single mode calculation was performed for each linear Jahn-Teller

active mode to get rough estimates of its vibronic energy levels. Then, two-mode

calculation was done for two linear Jahn-Teller active modes, v17 and v18, which

determine the spectral pattern in the low energy region. Finally, all the four

linear Jahn-Teller modes were included to get the complete vibronic levels. The

maximum j was set at 9/2 and the maximum vibrational quantum number used in

the four-mode calculation were 3, 3, 5, and 8 for v15, v16, v17, and v18,

respectively. The number of the bases for each j was 37841 in the four-mode


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calculation, leading to 37841×37841 Hamiltonian matrix. The multimode results

were compared with the experimental data for the final assignments. Then, the

assigned vibronic peak positions were fed into SOCJT to evaluate the Jahn-

Teller parameters for the linearly active modes through nonlinear regression

under the same multimode condition as above.

5.3 C6H6+ and C6D6

+ in the X~ State

Benzene cation has been the focus of intensive research effort, both

experimental8-17 and theoretical,18-25 over the years. Interest in this system arises

mainly from the fact that it is a prototype molecular system displaying Jahn-

Teller distortion because its ground electronic state, X~ 2E1g, is orbitally

degenerate.

Unlike the symmetrically substituted halobenzene cations such as 1,3,5-

C6H3F3+ and C6F6

+, the benzene cation in the gas phase does not have sufficient

quantum yield of fluorescence.26-29 Hence, emission spectroscopy and laser-

induced fluorescence which were used to study various benzene derivative

cations could not be performed for the benzene cation. Even though

photoelectron spectroscopy was used to study the benzene cation, the technique

is not generally adequate to resolve vibrational structures embedded in the

spectrum.8,10 By improving spectral resolution with the use of one color ‘1+1’

laser photoelectron spectroscopy, however, Reilly and coworkers1 could observe

the vibrational splitting of a Jahn-Teller active mode ν18 (Mulliken notation,30 to

be used in this paper) in C6H6+ and C6D6

+ and suggested that the ground

electronic state of the benzene cation is 2E1g belonging to the D6h point group. At

nearly the same time, Iwasaki and coworkers31 performed the electron spin

resonance study of the benzene cation trapped in 4.2 K freon matrix. Evidence

was observed that the orbital degeneracy of the X~ 2E1g state was lifted due to


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static distortion for the trapped benzene cation and the unpaired electron

occupied the b2g orbital with D2h symmetry. Even though the experimental data

were not sufficient, a number of theoretical calculations were performed.18-20

Stabilization energy and linear and quadratic Jahn-Teller coupling constants

were obtained by quantum chemical calculations at various levels to investigate

the extent of Jahn-Teller distortion to the equilibrium geometry. Even though

higher resolution spectral data have become available recently,11-15 theoretical

endeavor is still continuing because analysis of the complicated spectral data is a

formidable task.25

Zero kinetic energy (ZEKE) photoelectron spectroscopy and mass-analyzed

threshold ionization (MATI) spectroscopy which detects ions rather than

electrons in ZEKE are useful techniques to study structure and dynamics of

molecular cations. Considering the theoretical importance of the benzene cation,

it is not surprising that this system has been the focus of many ZEKE and MATI

investigations. Müller-Dethlefs and coworkers12 obtained rotationally resolved

photoelectron spectrum of benzene by ZEKE and concluded that the benzene

cation in the ground electronic state has the D6h symmetry. The vibrational peaks

arising from the Jahn-Teller active mode 18 (e2g) were identified and analyzed.

D6h symmetry was confirmed at a time scale of pseudorotation, even though the

structure in the ground state would be fluxional and dynamically coupled to the

two D2h structures.13 Krause and Neusser14 recorded MATI spectra and found

evidence for the quadratic Jahn-Teller effect, namely splitting of j = ± 3/2

vibronic states of the mode 18. Johnson and coworkers15 recently measured

MATI spectra of C6H6 and C6D6 and analyzed them considering the linear Jahn-

Teller effect in the mode 18 and the quadratic effect in the mode 20 (e2u). In

addition to ZEKE and MATI, infrared (IR) absorption spectroscopy was also

attempted by measuring IR-induced photodissociation of van der Waals

complexes between the benzene cation and rare gas atoms.32,33 The observed


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spectra appeared very similar to the IR spectra expected for the bare benzene

cations, with little deviation in peak positions (~1%), according to Meijer and

coworkers. Most of these spectral data have been utilized in a recent theoretical

investigation of the Jahn-Teller effect in the benzene cation in the ground

electronic state by Applegate and Miller.25

In all the ZEKE and MATI studies of the ground state benzene cation made

so far, two-color ‘1+1’ scheme was used. The first photon in this scheme

prepares neutral benzene in the 181 vibrational state of the excited electronic

state A~ 1B2u, which is further excited to a high Rydberg state by the second

photon. It is widely acknowledged that capability to select a particular

vibrational state of the intermediate electronic state in the two-photon scheme is

helpful to assign the ZEKE or MATI spectra. A general drawback of this scheme

is the difficulty to find an appropriate intermediate state which is accessible with

a commercial dye laser output (> 200 nm) and displays well-resolved peaks upon

transition from the ground state. In the case of benzene, ν18 is the vibrational

mode which shows serious Jahn-Teller distortion and splitting in the ground

state of the cation. ZEKE and MATI intermediated by the 181 vibrational state of

A~ 1B2u result in various overtone, combination, and difference excitations

involving the ν18 mode which is Jahn-Teller active. The resulting spectra are

very complicated and hence difficult to assign. This is one of the reasons why

the vibrational assignment for and the elucidation of the Jahn-Teller effect in the

benzene cation are still an outstanding problem even after tremendous efforts

made over the years.


One-photon MATI spectra of C6H6 and C6D6 are shown in Figs. 5.1 and 5.2.

The intense peaks appearing at the lowest photon energy, namely at around

74545 and 74568 cm-1 in Figs. 5.1 and 5.2, respectively, correspond to the 0-0


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bands. The position of the 0-0 band in a one- photon MATI spectrum is

equivalent to the ionization energy of the molecule. However, the ionization

energy thus measured is usually a little smaller than the correct value because

the molecules in ZEKE states at several cm-1 below the ionization threshold can

also be ionized when a high PFI field is applied. To correct this effect, the 0-0

band positions were measured using various PFI fields and the accurate

ionization energy was estimated by extrapolation to the zero-field limit. The

spoil field was not used in such measurements.

The ionization energies to the ground electronic states of C6H6+ and C6D6

+

measured from the one-photon MATI spectra in this work are listed in Table 5.1

together with the previous measurements. Ionization energies of C6H6 and C6D6

obtained in this work tend to be slightly lower than the previous data obtained by

ZEKE9,35 and MATI11,15 techniques using the two-photon scheme even though

the differences, ~0.0005 eV, are not serious considering the random errors in the

measurement. Presence of tiny stray field in the apparatus may be responsible

for such differences.

5.3.2 Jahn-Teller Effect and Vibronic Splitting

Benzene cation in the ground electronic state X~ 2E1g with D6h symmetry

possesses a1g (1, 2), a2g (3), a2u (4), b1u (5, 6), b2g (7, 8), b2u (9, 10), e1g (11), e1u

(12, 13, 14), e2g (15, 16, 17, 18), and e2u (19, 20) modes. Numbers in the

parentheses indicate the mode number designated by Mulliken notation. Among

these, e2g modes, four in total, are active under linear and quadratic Jahn-Teller

coupling while e1g, e1u, and e2u modes are active under quadratic coupling only.

With a single vibrational excitation in the X~ 2E1g state, an e2 mode splits into b1,

b2, and e1 vibronic species while an e1 mode into a1, a2, and e2. The linear Jahn-

Teller coupling in a singly excited e2g mode results in splitting into j = ± 1/2 and


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215

Table 5.1 Ionization energies (IE) to the ground states of C6H6+ and C6D6

+, in eV.

IE ( X~ ) Ref.

C6H6+ 9.2432±0.0006 This work

9.24365±0.00005 9

9.24371±0.00006 11

9.24381±0.0001 15

9.243841±0.000006 35

C6D6

+ 9.2466±0.0006 This work

9.24732±0.0001 15

9.247181±0.000006 35

± 3/2 states. The quadratic effect further splits j = 3/2 and –3/2 states. It is

important to note that neither the vibrational quantum number v nor l is a good

quantum number while j is a good quantum number when only the linear Jahn-

Teller effect is considered. Also to be noted is that the Jahn-Teller active modes

are coupled through the zero-point level, which make complete analysis

extremely difficult.

5.3.3 Vibrational Analysis

Even though benzene was used as a prototype molecule in the development

of ZEKE, and subsequently MATI, comprehensive analysis of the cation

vibration has not been attempted until recently. In one of the early MATI studies

of benzene, Krause and Neusser11 reported tentative assignment of MATI peaks,

even though only up to 1325 cm-1 in vibrational energy. The most recent IR


2004/01/28 17:41:01

��

Fig. 5.1 One-photon MATI spectrum of C6H6 recorded by monitoring

C6H6+ in the ground electronic state. The x-scale at the top of the figure



30 is shown as an inset to demonstrate the quality of the MATI spectrum

obtained in this work. Relative intensity of the peak marked by asterisk (*)

changed with the beam expansion condition.


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217

Table 5.2 Vibrational frequencies (in cm-1) and assignments for C6H6+ in the

ground electronic state ( X~ 2E1g).

Modea Symm. Neutralb PESc MATId Millere This work 1[2] a1g 3073 3082 2[1] a1g 993 976 967 969 967 3[3] a2g 1350 1393 4[11] a2u 673 659 660 5[13] b1u 3057 3022 6[12] b1u 1010 883 878 7[5] b2g 990 934 8[4] b2g 707 415 416 418 420 9[14] b2u 1309 1351 1357 10[15] b2u 1146 1180 1183f

11[10] a2g(1g) 983 986g

11[10] e2g 846 843 843

11[10] a1g(2g) 724 724

12[20] e1u 3064 3109 13[19] e1u 1482 1420 1420 14[18] e1u 1037 948

15(1/2)[7] e1g 3056 3062 15(±3/2) b2g(1g) 2848

16(1/2)[8] e1g 1599 1573 1648 16(±3/2) b2g(1g) 1563 16(±3/2) b1g(2g) 1522 1519

17(1/2)[9] e1g 1178 1234 1228 1257 1255 17(±3/2) b2g(1g) 1183f

17(±3/2) b1g(2g) 1157 18(1/2)[6] e1g 606 673 674 677 18(± 3/2) b2g(1g) 363 367 363 18(± 3/2) b1g(2g) 355 343 347 350

19[17] e2u 967 994 986g

20[16] b2u(1u) 328 327


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218

20[16] e1u 398 319 303 306 305 20[16] b1u(2u) 285 289 296

202 586/608 596 (1/2,3) 763 761 (1/2,4) 1073 1072 191201 1283 21181 1328 1322 101201 1475

21181201 1613 21111 1786 112 1825

111171 1881 22 1934

161181 1999 161181 2007

21111181 2046 21111201 2085

22201 2238 111161 2365 217181 2445 21112 2508 21161 2524 21161 2621 31171 2639

23 2903 a Vibrational modes in Mulliken notation (Wilson notation in square bracket). b From ref. 34. c From ref. 8. d Peak assignments for the two-photon MATI spectrum reported in ref. 4. Similar

assignments were also reported in ref. 15. e Assignment of the two-photon ZEKE13 and IR-induced photodissociation33

spectra reported by Applegate and Miller in ref. 25. f This peak may be assigned alternatively to 101 or 171(±3/2). g This peak may be assigned alternatively to 111 or 191.


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219

photodissociation study of benzene-Ne, Ar reported by Meijer and coworkers33

showed vibrational peaks up to 1470 cm-1 and a peak at 3097 cm-1 but only the

peaks below 1000 cm-1 were assigned. Applegate and Miller25 used all these data

and some unpublished results and reported assignment up to 1815 cm-1 by

comparing with their own calculated results. It is to be mentioned that there are

far more peaks in the original ZEKE spectrum, for example in the 1000 ~ 1500

cm-1 region, than assigned by these investigators. Namely, not all the ZEKE

peaks were assigned. The number of peaks in the present one-photon MATI

spectra is much less than that in ZEKE as has been mentioned earlier. Complete

vibrational assignment, even though tentative, up to the C-H stretching region

(~3000 cm-1) is attempted in this work. Assignments by Applegate and Miller

have been adhered to when available. Also taken into account were the positions

of some Jahn-Teller components predicted by these investigators through

calculation. For the peaks without any previous information, assignments have

been attempted by referring to the mode frequencies in neutral benzene. In

particular, the ratio of the frequency of a particular mode in C6D6 to that in C6H6,

namely the isotope ratio, was calculated for the neutral and cation. Similar

isotope ratios in the neutral and cation were taken as an evidence for successful

assignment. This is based on the assumption that the force fields in the benzene

neutral and cation are rather similar. Finally, it is to be mentioned that effort was

made to identify the hot bands, especially in the region of low vibrational

frequency, by changing the beam condition drastically. Relative intensity of the

very weak peak at 463 cm-1 marked by an asterisk in the inset of Fig. 5.1

changed with the beam condition. Assignments for the peaks in the one-photon

MATI spectra, Figs. 5.1 and 5.2, are listed in Tables 5.2 and 5.3, respectively,

together with the previous spectral data.

In the one-photon MATI spectrum of C6H6, Fig. 5.1, the most intense peak

other than the 0-0 peak appears at 967 cm-1, the v2 (a1g) fundamental according

to previous assignments.8,11,13 Two peaks at 1934 and 2903 cm-1 can be assigned


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220

readily to its overtones, 22 and 23, respectively. Corresponding peaks are

observed at 926, 1849, and 2772 cm-1 in the MATI spectrum of C6D6, Fig. 5.2.

The isotope ratio of this mode, 926/967=0.96, is in excellent agreement with

0.95 for the neutral.34 Appearance of the strong 2n progression suggests that the

geometrical change upon ionization of neutral benzene occurs mostly along this

normal mode. This is a part of the proof for the preservation of D6h symmetry in

the cation. Fundamentals of the other a1g mode, v1, are observed at 3082 and

2350 cm-1 for C6H6 and C6D6, respectively, not much different from 3073 and

2303 cm-1 observed in the neutral.

The other nondegenerate gerade modes are v3 (a2g), v7 (b2g), and v8 (b2g).

Among these, v8 can be readily identified by referring to the previous

assignments, namely peaks at 420 and 343 cm-1 for C6H6 and C6D6, respectively.

Applegate and Miller identified the peaks at 934 and 754 cm-1 in the ZEKE

spectra of C6H6 and C6D6 as the v7 fundamentals. A weak peak was found at 750

cm-1 for C6D6 accordingly, even though the corresponding peak for C6H6 could

not be seen due to the presence of an intense peak nearby. The v3 fundamentals

have not been assigned before. We assign them to the peaks at 1393 and 1061

cm-1 in the one-photon spectra of C6H6 and C6D6, respectively, based on their

proximity to those in the neutrals, 1350 and 1059 cm-1, and the adequate isotope

ratio.

The remaining gerade modes are v11 (e1g) which shows quadratic Jahn-Teller

effect and v15 ~ v18 (e2g) for which linear coupling is present and mode mixing

can be important also. Applegate and Miller25 assigned the peaks at 724, 843,

and 983 cm-1 in the ZEKE spectrum of C6H6 to v11. The first two peaks are found

at the same positions in the present one-photon MATI spectrum. The third may

correspond to a shoulder peak at ~986 cm-1. Even though Applegate and Miller

assigned 562 and 673 cm-1 to v11 of C6D6+, it is difficult to find them in Fig. 5.2

due to the presence of broad bands. They may be buried in the asymmetric tails


2004/01/28 17:41:01

��

Fig. 5.2 One-photon MATI spectrum of C6D6 recorded by monitoring

C6D6+ in the ground electronic state. The x-scale at the top of the figure



40 is shown as an inset to demonstrate the quality of the MATI spectrum

obtained in this work.


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222

Table 5.3 Vibrational frequencies (in cm-1) and assignments for C6D6+ in the

ground electronic state ( X~ 2E1g).

Modea Symm. Neutralb PESc MATId Millere This work 1[2] a1g 2303 2350 2[1] a1g 945 928 926 926 3[3] a2g 1059 1061 4[11] a2u 496 488 488 491 5[13] b1u 2285 6[12] b1u 970 877 840f

7[5] b2g 829 754 750 8[4] b2g 599 351 344 343 9[14] b2u 1282 1327 10[15] b2u 824 833 840f

11[10] a2g(1g) 11[10] e2g 660 673 658(?) 11[10] a1g(2g) 562 550(?) 12[20] e1u 2288 2331 13[19] e1u 1333 1229 1230 14[18] e1u 814 773 766

15(1/2)[7] e1g 2274 2292 15(±3/2) b2g(1g) 2168

16(1/2)[8] e1g 1558 1552 16(±3/2) b2g(1g) 1453 16(±3/2) b1g(2g) 1409

17(1/2)[9] e1g 869 877 17(±3/2) b2g(1g) 821

17(±3/2) b1g(2g) 802g

18(1/2)[6] e1g 579 637 634 636 18(± 3/2) b2g(1g) 356 357 18(± 3/2) b1g(2g) 343 335 338 334

19[17] e2u 787 810 802g

20[16] b2u(1u) 285 289 289 20[16] e1u 345 278 262 265 263 20[16] b1u(2u) 245 249 252


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223

202 509 202 550(?) 82 681

4181 820 821 111201 975

191201, (1/2,5) 1058 1061 (3/2,5) 1119 1117 (1/2,6) 1154

81171, (1/2,7) 1164 1161 21201 1189

2181, (1/2,8) 1266 1267 21202 1431 21111 1581 2171 1663

21141 1691 21171 1708 21171 1744 21171 1795

22 1849 21171201 2006 21171201 2033

22201 2109 2281 2196

21161 2468 22171 2653 22171 2717

23 2772 a Vibrational modes in Mulliken notation (Wilson notation in square bracket). b From ref. 34. c From ref. 8. d Peak assignments for the two-photon MATI spectrum reported in ref. 15. e Assignment of the two-photon ZEKE13 and IR-induced photodissociation33

spectra reported by Applegate and Miller in ref. 15. f This peak may be assigned alternatively to 61 or 101. g This peak may be assigned alternatively to 171(±3/2) or 191.


2004/01/28 17:41:01

224

of these bands. In all the previous two-photon ZEKE and MATI investigations

of C6H6, vibronic peaks correlated to v18 (e2g, v6 in Wilson notation35) appeared

prominently at 347, 367, and 677 cm-1 and were the focus of the study of the

linear and quadratic Jahn-Teller effect in C6H6+. In the present one-photon

MATI spectrum, no peak can be found near 677 cm-1 which can be assigned to

181 (1/2). Peaks are observed at 350 and 363 cm-1, even though weakly, which

can be attributed to 181 (± 3/2). Dramatic difference in the intensities of the 181

vibronic bands between the one- and two-photon spectra is not unexpected

because the two-photon scheme involves excitation of this mode in the neutral

intermediate state. More surprising is the fact that observations made in the

photoelectron spectrum16 are opposite to the present results. Namely, the j = 1/2

peak appears prominently in the photoelectron spectrum while the j = ± 3/2

peaks are missing. We do not have an explanation for these results at the

moment. We will just mention that this spectral region in the one-photon MATI

spectrum has been reproduced and checked several times to assure that the

results are not due to some artifacts. In addition to the above peaks, Applegate

and Miller assigned ten e2g vibronic peaks up to 1522 cm-1. Among these, six

were correlated to prominent peaks in the two-photon ZEKE spectrum, namely

at 763, 1073, 1245, 1257, 1408, and 1435 cm-1. Assignment of each peak to a

particular normal mode was not made probably because of severe mode coupling.

Only the j quantum number for each peak was given. Since the v18 mode has a

resonance frequency which is much lower than those of the other e2g modes,

some of the aboves must have main contribution from the v18 overtones and

could appear prominently in the two-photon spectrum intermediated by 181

excitation. Then, the fact that many of these are not prominent in the one-photon

spectrum is not surprising. A prominent peak at 1255 cm-1 in the one-photon

spectrum can be correlated to the peak at 1257 cm-1 in the two-photon spectrum

which was assigned to a j = 1/2 peak by Applegate and Miller. Considering the

harmonic frequencies calculated by these investigators, this peak can be assigned


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to 171 (1/2). Two peaks were observed in the two-photon ZEKE of C6D6, namely

at 868 and 877 cm-1, which were assigned to 171 (1/2) and 61 by Applegate and

Miller. Considering that the peak at 877 cm-1 appears very prominently and that

v6 is an ungerade mode, assignment to 171 (1/2) would be more appropriate for

this peak. Then, the isotope ratio for this mode becomes 0.70 (=877/1255) which

is not too different from 0.74 (=869/1178) in the neutral. There are two choices

for the 171 (±3/2) pair in C6H6+, 1052 and 1072 or 1157 and 1183 cm-1 pairs.

Considering appearance of a pair at 802 and 821 cm-1 in the one-photon

spectrum of C6D6, We would prefer the second pair, 1157 and 1183 cm-1, which

result in the isotope ratio of 0.69.

Since the previous ZEKE and MATI studies of benzene were not performed

above 1500 cm-1, there was no report on the assignment of v16. Reilly and

coworkers8 suggested 161 (1/2) as the transition responsible for the peak at

around 195 meV (1570 cm-1) in the laser photoelectron spectrum. This mode has

the frequencies 1599 and 1558 cm-1 in neutral C6H6 and C6D6 with the isotope

ratio 0.97. Strong peaks at 1648 and 1552 cm-1 in the one-photon spectra of C6H6

and C6D6, respectively, with the isotope ratio 0.94 can be assigned to this

transition. Doublets appearing at 1519 and 1563 cm-1 for C6H6 and at 1409 and

1453 cm-1 for C6D6 can be similarly assigned to 161 (±3/2). It is to be mentioned

that such assignments are in agreement with the prediction made by Applegate

and Miller through theoretical calculations. The peaks at 3062 and 2292 cm-1 in

the one-photon spectra of C6H6 and C6D6, respectively, may be assigned to

151(1/2) by referring to the corresponding frequencies in the neutrals, 3056 and

2274 cm-1. Then, assignment of the peaks at 2848 and 2168 cm-1 in the one-

photon MATI spectra of C6H6 and C6D6, respectively, to 151(±3/2) completes

the assignment for the gerade modes.

Among the ten ungerade modes four vibrations are IR active under the D6h

symmetry, namely v4 belonging to a2u and v12 ~ v14 belonging to e1u.


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Fundamentals of these modes appear prominently in the IR-induced

photodissociation spectra33 of C6H6+-rare gas complexes. Some combination

peaks also appeared prominently in the above spectra aided by Fermi resonance.

For example, two strongest peaks at 629 and 697 cm-1 in the IR-induced

photodissociation spectrum of C6H6+-Ne were attributed to 181201 components

with the e1u symmetry which are in Fermi resonance with 41. In addition, some

prominent peaks were assigned to the fundamentals and combinations belonging

to other vibrational symmetries by invoking vibronic symmetry. It looks a little

strange to note, however, that 81141 belonging to e2u is more intense in the IR

spectrum than 131 which is vibrationally allowed (e1u). Peaks belonging to b1u

and b2u which are vibronically forbidden were also observed. In addition, some

gerade modes, 181 and 202 were also reported to have been observed. All these

seem to suggest the importance the symmetry breaking effect arising from the

attachment of a rare gas atom. Some prominent peaks in the two-photon ZEKE

spectrum13 were assigned to the fundamentals of the ungerade modes. For

example, peaks at 306, 660, and 994 cm-1 assigned to 201 (e2u), 41 (a2u), and 191

(e2u), respectively, have intensities nearly comparable to the strongest two-

photon ZEKE peaks. Whether C6H6+ has the D6h symmetry or is slightly

perturbed to D2h, the center of symmetry is maintained in the present one-photon

MATI scheme. Accordingly, the ungerade fundamentals appear very weakly in

the one-photon spectrum, the strongest among which is the weak 201

fundamental at 305 and 263 cm-1 in C6H6 and C6D6, respectively. Plausible

mechanisms for the appearance of the ungerade fundamentals have been

presented already.

Among the nondegenerate ungerade fundamentals, 61 and 91 can be assigned

to peaks at 878 and 1357 cm-1 in Fig.5.1 by referring to the previous

assignments.18 41 which appeared prominently at 660 cm-1 in the two-photon

spectrum and the IR-induced photodissociation spectrum does not appear at all,


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even though a very weak feature at around 491 cm-1 in the one-photon spectrum

of C6D6 can be correlated to the peak at 488 cm-1 in the two-photon spectrum.

The peak at 1183 cm-1 which has been assigned to 171 (±3/2) above can be

alternatively assigned to 101. Among the fundamentals of three e1u modes, 131

can be assigned to the peaks at 1420 and 1230 cm-1 in the C6H6 and C6D6 spectra.

141 can be found for C6D6 only at 766 cm-1 while 121 can be assigned to the

peaks at 3109 and 2331 cm-1 in the C6H6 and C6D6 spectra, respectively. Distinct

peaks at 305 and 327 cm-1 and a shoulder peak at 296 cm-1 in the one-photon

spectrum of C6H6 can be assigned to 201 by referring to the previous

assignments. Similarly, very weak shoulder peaks at 986 and 802 cm-1 in the

one-photon spectra of C6H6 and C6D6 can be assigned to 191. It is to be

mentioned that assignments for the ungerade fundamentals are in excellent

agreement with those by Applegate and Miller.

With almost all the fundamentals assigned, an attempt has been made to

assign the remaining peaks to overtones and combinations. The prominent peaks

at 1283 and 1061 cm-1 in the one-photon spectra of C6H6 and C6D6, respectively,

can be attributed to 191201 which contains a1g species. Even though the weak

peak at 1475 cm-1 is close to the strong peak at 1470 cm-1 in the IR-induced

photodissociation spectrum, we would rather assign the former to a 101201

component belonging to a1g. Distinct peaks at 1786, 1881, 1999, 2238, 2365, and

2524 cm-1 in the C6H6 spectrum and those at 1708, 1795, and 2006 cm-1 in the

C6D6 spectrum have been assigned as combinations also. Even though these

assignments are tentative only, the data are presented here as an aid for future

theoretical study. Even after the above effort, there still remain some peaks, even

though extremely weak, which are left unassigned. These are the peaks at 1052,

2569, 2738, and 2754 cm-1 in the C6H6 spectrum and at 411, 1306, 1360, 1626,

2399, and 2623 cm-1 in the C6D6 spectrum. It is to be noted that all the peaks

below 1700 cm-1 in the one-photon MATI spectrum of C6H6 except the peak at


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1052 cm-1 have been reasonably assigned in this work. In contrast, only around

60 % of the peaks appearing below 1500 cm-1 and around 30 % in the 1000 ~

1500 cm-1 region in the two-photon ZEKE spectrum were assigned.18

5.3.4 Conclusions

One-photon MATI spectra of C6H6 and C6D6 have been obtained by using

tunable and coherent VUV radiation generated by four-wave difference

frequency mixing in Kr. The spectra were simple compared to the two-photon

ZEKE and MATI spectra reported previously. Vibrational data for the neutral

benzene and the previous assignment for the cation made by utilizing two-

photon ZEKE peaks, IR-induced photodissociation peaks, and calculated results

were useful to assign the peaks in the one-photon spectra. Also useful was the

selection rule for Rydberg transition which classifies the transitions into three

groups in terms of intensity, electric dipole-allowed, vibronically allowed, and

g,u-forbidden vibronic transitions. Exceptions to this selection rule have been

found to be rare in the one-photon spectra while surprises were encountered

frequently in the two-photon ZEKE or MATI and IR-induced photodissociation

spectra. Compared to the two-photon spectra obtained via transition to the 181

vibrational state of A~ 1B2u of the neutral, the one-photon spectra were simpler

and hence easier to analyze. In particular, almost all the peaks below 1700 cm-1

in the one-photon spectrum of C6H6 could be assigned while around 70 % of the

peaks in the 1000 ~ 1500 cm-1 region of the two-photon spectrum are left

unassigned. This suggests that analysis of the one-photon spectrum, rather than

two-photon spectrum, can be the useful first step in the vibrational study of a

polyatomic cation especially when complications are involved such as those

arising from the Jahn-Teller effect.

Even though the peaks in the one-photon spectra could be assigned extremely

well by referring to the previous assignments, some changes had to be made.


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More fundamentals have been assigned than before, some of which being to

vibronic levels arising from Jahn-Teller splitting. Incorporation of the results in

the theoretical study is expected to lead to a better understanding of the Jahn-

Teller effect in the benzene cation.

5.4 C6H6+ and C6D6

+ in the B~ State

Considering only the three highest energy occupied orbitals, electron

configuration of the neutral benzene in the ground electronic state ( X~ 1A1g) is

(1a2u)2(3e2g)4(1e1g)4. Removing an electron from these orbitals results in the hole

states of the cation X~ 2E1g, B~ 2E2g, and C~ 2A2u. Ionization energies to the first

two states are 9.243 and 11.488 eV, respectively, according to a recent PES

study16 of C6H6. The C~ band appears broad and overlapped with the B~ band

in the photoelectron spectrum. The C~ state onset is thought to lie a few tenths

of an eV above that of the B~ state.

Benzene cation in the ground electronic state has been heavily investigated

over the years because the orbital degeneracy makes it a prototypical system for

the Jahn-Teller (JT) effect. Situation for the first excited state, B~ 2E2g, is even

more interesting because of its proximity to the C~ 2A2u state. Namely, in

addition to the usual intrastate JT interaction, the pseudo Jahn-Teller (pseudo-

JT) interaction between B~ 2E2g and C~ 2A2u is also possible.15,36,37

Another interesting feature in the benzene cation system is that no emission

is observed at all even when many excited hole states are populated by electron

ionization or photoionization. This is in contrast with the observation of strong

emission from the B~ state of various benzene derivative cations. For benzene

cation with D6h symmetry, B~ 2E2g→ X~ 2E1g transition is electric dipole-


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forbidden. A general consensus has been that the same transition occurring

nonradiatively, namely via internal conversion, is very efficient such that the

radiative transition is almost completely quenched. Köppel and coworkers

carried out extensive quantum chemical and dynamical calculations on the

benzene cation system.36,37 Many conical intersections were found

computationally, including those between B~ and X~ . Since the latters are

located somewhat above the zero-point level of the B~ state, however, there is a

possibility that some of the benzene cations prepared in this state do not undergo

rapid internal conversion. In fact, we found through charge exchange and other

mass spectrometric experiments that some of the benzene cations in the B~ state

have a very long lifetime, 10 microsecond or possibly much longer. Then, lack

of emission from the B~ state indicates extremely poor probability for the B~ -

X~ radiative transition, which has been a serious obstacle to the use of

conventional spectroscopic techniques for the study of the benzene cation system.

A dipole-forbidden transition such as B~ ←X~ can occur vibronically, even

though very weakly. However, absence of emission from the B~ state means

that one needs a method, other than the measurement of emission, to confirm the

absorption of a photon. Schlag and coworkers obtained the first optical spectrum

for the B~ ← X~ transition by measuring C6H5+ generated by resonance-

enhanced multiphoton dissociation (REMPD) of the benzene cation in the

ground state.38 Resonance-enhanced multiphoton ionization was used to

selectively generate the ground state ion. Initial state selection was further

improved by Johnson and coworkers by introducing photoinduced Rydberg

ionization (PIRI) spectroscopy.15 Here neutral benzene was selectively prepared

in some vibrational states of a high Rydberg state converging to the ionic ground

state via two-photon excitation. Then ion core of the Rydberg state was further

excited by the third photon and C6H6+ formed by autoionization or its fragment


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were detected. Since gerade vibrational states of the Rydberg state could be

populated efficiently, PIRI spectra recording ungerade vibrations in the ionic B~

state were obtained with high quality. This was useful to investigate pseudo-JT

interaction induced by e2u vibrations. Gerade vibrations were also recorded,

which are needed to study the intrastate JT interaction. The spectral quality was

not as good as those for the ungerade modes, however.

Complications due to multiphoton effect can be present in the above REMPD

and PIRI schemes because a high power laser is used to induce dipole-forbidden

B~ ←X~ transition. A better scheme to investigate the B~ state is to excite the

neutral to a Rydberg state converging to this state and record ZEKE or MATI

spectra, namely without going through the ionic (or ion core) ground state. With

the usual two-photon ZEKE or MATI scheme, this involves exciting an electron

in the e2g orbital to an unoccupied orbital. No spectroscopic information is

available for such neutral states. In practical terms, such states would lie high

above the ground state and not be accessible with a commercial dye laser.

5.4.1 Jahn-Teller Effect and Vibronic Splitting

If the benzene cation in the B~ 2E2g electronic state has D6h symmetry, its

vibrational modes can be classified into a1g (1, 2), a2g (3), a2u (4), b1u (5, 6), b2g

(7, 8), b2u (9, 10), e1g (11), e1u (12, 13, 14), e2g (15, 16, 17, 18), and e2u (19, 20)

modes. Numbers in the parentheses indicate the mode number designated by

Mulliken notation. For e-type degenerate electronic states in D6h, e2g modes are

active under linear and quadratic JT coupling while e1g, e1u, and e2u modes are

active under quadratic coupling only. A singly excited e2 mode in B~ 2E2g splits

into a1, a2, and e2 vibronic species while an e1mode into b1, b2, and e1 species.

An alternative description of vibronic species is to designate the vibronic angular

momentum quantum number j which is the sum of the vibrational (l) and


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electronic (Λ) parts. There has been some controversy concerning the definition

of Λ. Goode et al. suggested Λ = ± 2 for the B~ 2E2g state and predicted weak

intrastate JT effect.15 Recent theoretical work reported by the same laboratory

found evidence for very strong JT effect in this state, however. We will follow

Miller6 and put Λ = ± 1. Then, j becomes

Λ+= 21lj (5.6)

Since l = ± 1 for a singly excited (v = 1) degenerate mode, j becomes ± 1/2 and ±

3/2. Linear JT interaction splits j = ± 3/2 from ±1/2 states. Quadratic JT further

splits j =3/2 and –3/2. The above is only a simplified picture because v is not a

good quantum number in the presence of JT coupling and interaction among

zero-order states with different υ cannot be neglected. Mode coupling further

complicates the situation and makes vibrational analysis extremely difficult. e2u

modes were reported to be active in pseudo-JT interaction between B~ 2E2g and

C~ 2A2u. Pseudo-JT effect will not be considered here, however, because the

peaks observed in the one-photon MATI spectra are mostly gerade fundamentals.

According to a recent quantum chemical study by Johnson,4 the calculated

linear JT coupling parameters were very large for the e2g modes v16 and v18 while

those for v15 and v17 were rather small. With a substantial JT effect along a

normal coordinate, electronic degeneracy is essentially lifted and energy

minimum moves along this coordinate, resulting in symmetry reduction to D2h.

Then, an e2g mode in B~ 2E2g splits into ag ⊕ b3g, which result in (ag ⊕ b3g) ⊗ (ag

⊕ b3g) = 2ag ⊕ 2b3g vibronic species. Namely, a1g vibronic species in D6h is

converted to ag in D2h, a2g to b3g, and e2g to ag ⊕ b3g.

5.4.2 Selection Rule

The selection rule for one-photon MATI from supersonically cooled benzene


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neutral (zero-point level in X~ 1A1g) to X~ 2E1g of the cation was described in

previous section. Following the same procedure, identical selection rule is

obtained for one-photon MATI to B~ 2E2g of the cation. Results can be

summarized as follows. Vibronic transitions appearing in one-photon MATI can

be classified into three categories, electric dipole-allowed, vibronically allowed,

and g,u - forbidden vibronic transitions. A1g fundamentals can appear

prominently because the transition involved is dipole-allowed. Fundamentals of

all the other gerade modes may appear less prominently via dipole-forbidden

vibronic transitions. Even though ungerade fundamentals are not expected when

the center of symmetry is present in the cation, instrumental imperfection or high

order effect may allow the processes, even though very weakly, as was found in

one-photon MATI to X~ 2E1g. According to the previous quantum chemical

calculations,4 the geometrical change upon B~ 2E2g ← X~ 1A1g ionization is not

significant. Hence overtones and combinations are not expected to appear

prominently in one-photon MATI. This is in contrast with the PIRI spectra of

gerade states reported previously, in which the transitions started from the

201(e2u) vibrational state of X~ 2E1g. Accordingly, most of the prominent peaks in

the PIRI spectra were assigned to the overtones and combinations involving v20.

Finally, it may be helpful to study the changes in symmetry selection rule

when D6h→D2h symmetry reduction occurs. In this case, the normal modes of

interest are a1g and e2g vibrations in D6h, which generate the totally symmetric ag

vibrations in D2h. Namely, e2g vibrations may occur prominently upon symmetry

reduction in addition to a1g vibrations.


One-photon MATI spectra of C6D6 and C6H6 measured by exciting the

neutrals to the high Rydberg states converging to the ionic B~ 2E2g state are


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shown in Figs. 5.4 and 5.5, respectively. Magnified spectra are shown as insets

to demonstrate the quality of the spectra. A dip at ~ 94110 cm-1 appears in both

spectra, which is due to the dip in VUV power (Fig. 5.3). Quality of these

spectra looks much better than the corresponding PIRI spectra for the gerade

states reported by Johnson and coworkers.15 The 0-0 bands appearing at around

92938 and 92664 cm-1 in Figs. 5.4 and 5.5, respectively, are the most intense

peaks in each spectrum while the corresponding peaks were relatively weak in

the PIRI spectra. X~ 2E1g and B~ 2E2g cation states are generated by removal of a

bonding e1g or antibonding e2g electron, respectively, from the neutral ground

state X~ 1A1g. Hence, the geometrical change in B~ 2E2g ← X~ 2E1g would be

larger than that in B~ 2E2g ← X~ 1A1g. In addition, the zero vibrational states in

the PIRI spectra were accessed via an excited vibrational state (201) in X~ 2E1g

such that the fundamental and overtones of v20 would be favored. The aboves

may explain the remarkable difference in the relative intensities of the zero

vibrational bands between the one-photon MATI and three-photon PIRI spectra.

5.4.3.1 Ionization Energies

Table 5.4 Ionization energies (IE) to the excited states of C6H6+ and C6D6

+, in eV.

IE ( B~ ) Ref.

C6H6+ 11.4897±0.0006 This work

11.4900±0.0001 15

11.488±0.003 16

C6D6

+ 11.5235±0.0006 This work

11.5240±0.0001 15


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The position of the 0-0 band in one-photon MATI spectrum is equivalent to

the ionization energy to the ionic state which the Rydberg states accessed by

VUV are converging into. The 0-0 band position appearing in a spectrum is

usually a little smaller than the correct ionization energy because molecules in

ZEKE states several cm-1 below the threshold can also be ionized when a high

PFI field is used. To correct for this effect, the 0-0 band position was measured

using various PFI fields and the results were extrapolated to the zero field limit.

Spoil field was not used in such measurements. The ionization energies to

B~ 2E2g of C6H6+ and C6D6

+ thus obtained are listed in Table 5.4 together with the

previous PIRI15 and PES16 measurements.

5.4.3.2 Vibrational Assignment

Vibrational patterns of the one-photon MATI spectra obtained in this work

are quite different from the gerade state PIRI spectra. The main reason may be

that overtones and combinations involving v20 (e2u) are prevalent in the PIRI

spectra because transitions start from 201 in X~ 2E1g while peaks in the one-

photon MATI spectra are expected to be fundamentals mostly. The guidelines

adopted to assign the one-photon MATI peaks are as follows.

Vibrational frequencies in B~ 2E2g were calculated by time-dependent density

functional theory (TDDFT) at the B3LYP/6-311G(2d, p) level by Johnson

recently.15 For modes other than e2g, calculated frequencies appeared reasonable

and resembled the corresponding values for the neutral. Calculated frequencies

for these modes will be utilized for assignments as much as possible. Among the

e2g modes, v15 lies outside the spectral range covered in this work. Since the

calculated linear JT coupling constant for v17 was very small, the fundamental

may be searched in the vicinity of the calculated frequency. These leave the e2g

modes v16 and v18. Very large calculated linear JT coupling constants for these

modes indicate that their assignments will be a formidable job. The second


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93000 93500 94000 94500

Sign

al

Photon Energy, cm-1

Fig. 5.3 Photoionization spectrum of C6H6 measured as a function of the

VUV photon energy (in cm-1).


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��

Fig. 5.4 One-photon MATI spectrum of C6D6 recorded by monitoring

C6D6+ in the excited electronic state B

~ 2E2g. The x-scale at the top of the

figure corresponds to the vibrational frequency scale for the cation, or the

ion internal energy. Its origin is at the 0-0 band position. Spectrum in the

0~1900 cm-1 region magnified by 10 is shown as an inset to demonstrate

the quality of the MATI spectrum obtained in this work.


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Table 5.5 Vibrational frequencies (in cm-1) and assignments for C6D6+ in the

excited electronic state ( B~ 2E2g).

Assignmentc Observed Neutrala PIRIb

Empiricald JT fite

154 201 |3/2, 1⟩ 373 366 181(±3/2) 481 486 181(±3/2) |1/2, 2⟩

574 599 596 81 597 579 181(±1/2) |1/2, 3⟩ 729 728 171(±3/2) |3/2, 3⟩ 745 171(±3/2) |3/2, 4⟩

780 787 776 191

849 869 742 171(±1/2) |1/2, 6⟩ 934 945 21

1206 |3/2, 10⟩ 1222 171181 |3/2, 11⟩ 1293 |3/2, 12⟩

1373 181191 1443 171181 |3/2, 15⟩

1493 |1/2, 16⟩

1580 |1/2, 19⟩

a From ref. 34. b From ref. 39. c Vibrational modes in Mulliken notation. d Assignment made by referring to the calculated frequencies in ref. 4. Small

D18 assumed for v18. e Three-mode (v16, v17, v18) JT fit assuming large D16 and D18. See text for

details.


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guideline adopted was the selection rule. Peaks were assigned to gerade

vibrations as much as possible, except for some very weak peaks. For a very

prominent peak, assignment to an a1g or e2g mode was regarded as a higher

priority. Finally, the fact that the calculated frequency of each non-e2g mode in

B~ 2E2g is similar to the corresponding frequency in the neutral suggests that the

force fields in the cation B~ 2E2g and in the neutral X~ 1A1g are rather similar.

Hence, a pair of peaks in the one-photon MATI spectra of C6H6 and C6D6 was

chosen such that the isotope ratio (C6D6/C6H6 frequency ratio) in the cations was

similar to that in the neutral.34 The results of the vibrational assignments for

C6D6+ and C6H6

+ are listed in Tables 5.5 and 5.6, respectively.

Of the two a1g modes, v1 fundamental is outside the spectral range covered in

this work. v2 fundamental for C6D6+ can be readily identified to the strong peak

at 934 cm-1 in excellent agreement with the calculated frequency and the

frequency in the neutral. Since its isotope ratio in the neutral is 0.95 (945/993),

the corresponding fundamental in C6H6+ is expected at ~ 980 cm-1. Two weak

peaks appear in this region of Fig. 5.5, namely at 971 and 1034 cm-1. The former

is apparently a better candidate even though its intensity seems to be very weak

as an a1g fundamental.

The next strongest in the C6D6 MATI spectrum are the peak at 849 cm-1 and

the doublet at 729 and 745 cm-1. Among the gerade fundamentals, 171 (e2g) and

111 (e1g) are expected in this region. 111 (e1g) for C6D6+ is expected at 700 ~ 750

cm-1 according to the calculation while the corresponding frequencies for C6H6+

are expected at 860 ~ 960 cm-1. Having assigned the peak at 971 cm-1 in the

C6H6 spectrum to 21 already, only an extremely weak peak at 915 cm-1 remains

in this region. Considering the intensities of the above peaks, it seems to be more

appropriate to assign the peak at 849 cm-1 in the C6D6 MATI spectrum to 171

(±1/2) and the doublet at 729 and 745 cm-1 to 171 (±3/2). Then, corresponding

peaks are expected at ~1150, ~980, and ~1010 cm-1 in the C6H6 spectrum when


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the isotope ratio (0.74) in the neutral is used. The peak at 1226 cm-1 and the

doublet at 1034 and 1065 cm-1 are assigned to 171 accordingly. Isotope ratios are

0.69 for the 849 and 1226 cm-1 pair, 0.70 for 745 and 1065 cm-1, and 0.70 for

725 and 1034 cm-1. Assignment of the intense peak at 1290 cm-1 in the C6H6

spectrum to 171 (±1/2) would have resulted in the isotope ratio of 0.66 which is

quite different from those for the doublets.

The remaining strong peak in the C6D6 spectrum appears at 597 cm-1. A very

weak peak appeared at 596 cm-1 in the gerade PIRI spectrum of C6D6+. Johnson

assigned this and a tiny feature at 656 cm-1 in the spectrum of C6H6+ to 81 (b2g)

because the frequencies observed were in excellent agreement with the

calculated values.39 A peak corresponding to the latter appears at 654 cm-1 in the

one-photon MATI spectrum of C6H6. In fact, this is the most intense band other

than the 0-0 band in this spectrum. The same peak appearing at 0.0808 eV (652

cm-1) above the 0-0 band of B~ 2E2g was the most intense fundamental in the

photoelectron spectrum of C6H6 and was assigned to 181 (e2g).16 Even though the

calculated frequencies for this strongly JT-active mode are not expected to be

dependable, its higher frequency components are expected at ~630 and ~590 cm-

1 for C6H6+ and C6D6

+, respectively. For neutrals, 181 appears at 606 and 579 cm-

1, respectively. Then, considering the intensities of the peaks at 597 and 654 cm-1

in the one-photon MATI spectra of C6D6+ and C6H6

+, respectively, their

assignment to 181 (±1/2) rather than to 81 may be more appropriate. Weak peaks

are embedded as lower frequency tails of these peaks, at ~574 and ~626 cm-1 in

Figs. 5.4 and 5.5, respectively, which may be assigned to 81.

Left unassigned in the low frequency region of the one-photon MATI

spectrum of C6D6 are two weak peaks at 373 and 481 cm-1. Referring to the

mode frequencies calculated by Johnson, these cannot be assigned to

nondegenerate fundamentals, either gerade or ungerade. Two peaks appeared

close to the above positions in the gerade PIRI spectrum, at 366 and 458 cm-1,


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241

which were assigned to 202 by Johnson. The above two peaks in the one-photon

MATI spectrum might be assigned similarly. In the case of the gerade PIRI

spectrum, the B~ 2E2g ← X~ 2E1g transition started from the 201 vibrational state

in X~ 2E1g. Hence, the 20n overtone band is not unexpected. In the one-photon

MATI, B~ 2E2g ← X~ 1A1g, planar symmetry of the ion core is maintained

whether B~ 2E2g belongs to D6h or D2h. On the other hand, v20 (e2u) is an out-of-

plane ring deformation. Hence, it is highly unlikely that 20n overtones are

observed in the present one-photon MATI.

Having eliminated 202, there are some possible assignments for the peaks at

373 and 481 cm-1 in the one-photon MATI spectrum of C6D6. One is to assign

them to the j = ± 3/2 components of 181 already. It is to be noted that the peak at

597 cm-1 in the same spectrum has been assigned to the j = ± 1/2 components of

181. The linear JT coupling constant for v18, D18, expected from such

assignments would not be as large as was predicted quantum chemically (D18 =

0.663). Another possibility is that these are the JT components of v16 (e2g), for

which the calculated linear JT coupling constant was very large, D16 = 1.11.

There are several weak but distinct peaks at the 1200 ~ 1600 cm-1 region in

the one-photon MATI spectrum of C6D6, namely at 1222, 1293, 1443, 1493, and

1580 cm-1. Referring to the calculated frequencies again, these cannot be

assigned to nondegenerate gerade fundamentals or overtones. The peaks at 1222

and 1443 cm-1 may be assigned to combination bands, 849 + 373 or 745 + 481

and 849 + 597, respectively. It is more likely, however, that most of the peaks in

this region are due to the JT components of the linearly and quadratically active

modes.

Left unassigned below 600 cm-1 in the one-photon spectrum of C6H6 is the

doublet consisting of two peaks at 511 and 535 cm-1, which may be assigned to

the j = ± 3/2 components of 181 as in C6D6+ if the linear JT coupling constant is


2004/01/28 17:41:01

��

Fig. 5.5 One-photon MATI spectrum of C6H6 recorded by monitoring

C6H6+ in the excited electronic state B

~ 2E2g. The x-scale at the top of the

figure corresponds to the vibrational frequency scale for the cation, or the

ion internal energy. Its origin is at the 0-0 band position. Spectrum in the

0~1900 cm-1 region magnified by 10 is shown as an inset to demonstrate

the quality of the MATI spectrum obtained in this work.


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243

Table 5.6 Vibrational frequencies (in cm-1) and assignments for C6H6+ in the

excited electronic state ( B~ 2E2g).

Assignmentd

Observed Neutrala PESb PIRIc

Empiricale JT fitf

229 234 225 201 |3/2, 1⟩

511 202 181(±3/2) 535 256 181(±3/2) |1/2, 2⟩

626 707 656 81

654 606 652 181(±1/2) |1/2, 3⟩ 971 993 976 21

1034 171(±3/2) |3/2, 5⟩ 1065 171(±3/2) |3/2, 6⟩

1115 |3/2, 7⟩ 1226 1178 171(±1/2) |1/2, 7⟩

1267 171201 |3/2, 9⟩ 1290 171201 |1/2, 9⟩ 1414 |3/2, 10⟩ 1483 21181 |1/2, 11⟩

1570 171181 |3/2, 12⟩

a From ref. 34. b From ref. 16. c From ref. 39. d Vibrational modes in Mulliken notation. e Assignment made by referring to the calculated frequencies in ref. 4. Small D18

assumed for v18. f Three-mode (v16, v17, v18) JT fit assuming large D16 and D18. See text for details.


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244

small. Above 1200 cm-1, the peaks at 1290, 1483, and 1570 cm-1 are distinct.

Even though, the v3 (a2g) and v7 (b2g) fundamental are expected in this region,

assignments to the JT components of the degenerate gerade modes are more

likely when the situation in C6D6+ is taking into account. Finally, we attempted

multi-mode JT calculations for e2g modes (v16, v17, and v18) to see if the peaks in

question could be assigned to the JT components. The SOCJT package

developed by Miller was used in the calculation.6 Initial guesses for the

unperturbed harmonic frequencies, ωi were made by referring to the calculated

frequencies for the cations and the neutral frequencies. Similarly, the linear JT

coupling constants, Di, calculated by Johnson were used initially. Small

quadratic JT coupling constants, Ki, were added for initial fit. These were all

optimized until the experimental peak positions could be reproduced by

calculation. Decent fits could be found for the MATI peaks of C6D6 and C6H6

which are suspected to be the JT components. For C6D6+, peaks at 481, 597, 729,

745, 849, 1206, 1222, 1293, 1443, and 1493 cm-1 could be reproduced at 471,

584, 728, 742, 868, 1203, 1211, 1318, 1452, and 1486 cm-1, respectively. The

optimized (ωi, Di, Ki) values were (1347, 1.07, -0.07) for v16, (741, 0.02, 0.02)

for v17, and (536, 1.22, -0.06) for v18. ωi is in cm-1 while Di and Ki are unitless.

Similarly, the C6H6 MATI peaks at 535, 654, 1034, 1065, 1226, 1267, 1290,

1414, 1483, and 1570 cm-1 could be reproduced by calculation at 531, 648, 1033,

1066, 1225, 1271, 1291, 1413, 1483, and 1572 cm-1, respectively. The optimized

(ωi, Di, Ki) values in this case were (1467, 1.09, 0.097) for v16, (1044, 0.002,

0.263) for v17, and (561, 0.991, -0.141) for v18. Then, the isotope ratios for the

unperturbed harmonic frequencies are 0.92, 0.71, and 0.96 for v16, v17, and v18,

respectively. These compare rather well with 0.97, 0.74, and 0.96 for the neutrals.

The assignments based on these calculations are listed as jn,j in Tables 5.5

and 5.6. nj means nj th value when the frequency eigenvalues are listed in the

order of increasing frequency.


2004/01/28 17:41:01

245

We also attempted the fit using the linear JT coupling constants much

smaller than the calculated values. Decent fits were possible with various

combinations of (ωi, Di, Ki), which then changed the assignments. Hence, it is to

be emphasized that the tentative assignments for the JT components presented

above can be meaningful only if the calculated linear JT coupling constants are

reliable. Even though the results from the TDDFT calculations at the B3LYP/6-

311G (2d, p) level by Johnson have been very helpful in the present work, it is

not clear whether the results are accurate enough for the fine details of the

excited state potential energy surfaces. Calculations at the configuration

interaction levels seem to be needed to confirm the results from the TDDFT

/B3LYP/6-311G (2d, p) calculations. Reliable JT calculations and hence

improved assignments would be possible thereafter. Calculations of the excited

state potential energy surface at such high levels would require tremendous

computational effort and are beyond the scope of the present work.

5.4.4 Radiationless B~ 2E2g → X~ 2E1g Transition

The widths of the 0-0 bands in the one-photon MATI spectra of C6H6 and

C6D6 are 21 cm-1, which is nearly the same as those observed in MATI to the

ground electronic state of the benzene cation. Insufficient rotational cooling and

use of high PFI voltage seem to be the main reasons for the rather poor spectral

resolution. More importantly, essentially the same width for the 0-0 bands in

MATI to X~ 2E1g and B~ 2E2g suggests that the benzene cation in the zero-point

level of B~ 2E2g does not undergo rapid relaxation to X~ 2E1g. This is in

agreement with the previous finding that some benzene cations prepared in the

B~ 2E2g state have very long lifetime, 10 microseconds or much longer.

Widths of some vibrational peaks recorded up to ~ 1600 cm-1 (0.2 eV) look a

little broader. However, it is more likely that these are due to the presence of


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246

overlapping peaks rather than inherently broader width. For example, width of

the peak at 1570 cm-1 in the one-photon MATI spectrum of C6H6 is ~ 22 cm-1,

comparable to that of the 0-0 band. This indicates that the B~ 2E2g →X~ 2E1g

radiationless transition is not very rapid up to 0.2 eV vibrational energy in the

B~ 2E2g state. The spectral resolution in this work is not good enough to estimate

the natural lifetime at this vibrational energy. Even though the lower limit

estimated from the peak widths is ~ 1psec, actual lifetime may be much longer.

Köppel and coworkers carried out extensive ab initio calculations on the

potential energy surfaces of the benzene cation in various electronic states.23 The

outer valence Greens function (OVGF) and equation-of-motion ionization

potential coupled clusters singles and doubles (EOMIP-CCSD) methods were

used with the DZ+P or TZ2P basis set. It was found that the lowest conical

intersection between X~ and B~ lied a few tenths of an eV above the B~ state

minimum. This is in agreement with the present observation that the benzene

cation in the B~ state with vibrational energy less than 0.2 eV does not seem to

undergo very rapid relaxation to the ground state. Also performed by the same

research team was the quantum dynamics calculation for the C~ →B~ →X~ and

E~→D~ →B~ internal conversions.24 In the case of the former, the C~ →B~ and

B~ →X~ decays were found to occur on the time scales of ~ 20 and ~ 50 fsec,

respectively. The C~ state onset is thought to lie a few tenths of an eV above the

zero-point level of the B~ state, which is close to the upper limit of the internal

energy probed in this work. Hence we are not in a position to judge the

reliability of quantum dynamics results of Köppel and coworkers even though 50

fsec lifetime for the B~ →X~ decay seems to be much shorter than the 1 psec

lower limit set in this work. Quantum dynamics calculation starting from the B~

state with internal energy just below the C~ sate onset would be very interesting


2004/01/28 17:41:01

247

in this regard.

5.4.5 Conclusions

One-photon MATI spectra of C6D6 and C6H6 converging to the ionic excited

state B~ 2E2g have been obtained by using coherent VUV radiation generated by

four-wave sum frequency mixing in Hg vapor. These are essentially the

vibrational spectra of the B~ 2E2g state. It is thought that the present one-photon

spectra are free from various complications such as those arising from multi-

photon effects. Quality of the spectra was much better than the gerade PIRI

spectra for the same state reported previously.15 Spectral patterns in the one-

photon MATI were different from those in the gerade PIRI which utilized three

sequential excitations by powerful lasers. The main reason for the difference

may be traced to the fact that an excited vibrational state of the ion core was

used in the gerade PIRI while the one-photon MATI started from the ground

state neutral.

By comparing with the calculated results, assignments have been possible for

some nondegenerate modes and degenerate modes which are not expected to be

affected much by the JT effect. To assign the JT components arising from the e2g

modes, multimode JT calculations have been carried out. Even though good fits

have been possible, we do not take the results as reliable because of the

arbitraries involved. High level calculations of the JT coupling constants in the

B~ 2E2g state of the benzene cation are called for in this regard.

5.5 C6F6+ in the X~ State

As has been mentioned already, a high quality dispersed fluorescence

spectrum for the B~ 2A2u → X~ 2E1g transition is not available for the gas phase

C6F6+ cation. A useful alternative is to record a ZEKE or MATI spectrum, which


2004/01/28 17:41:01

248

often provides more decisive and trouble-free information than the emission

spectrum. No ZEKE or MATI spectrum has been reported for the ground state

C6F6+ cation yet, possibly due to some experimental difficulties involved in the

use of the usual two-photon scheme. In this section, a MATI spectrum for the

ground state C6F6+ cation measured with one-photon scheme utilizing coherent

vacuum ultraviolet radiation generated by four-wave difference frequency

mixing in Kr will be reported. Also reported will be the calculation of the

vibronic energy levels from the DFT results following the Johnson’s method5

and determination of the Jahn-Teller parameters through nonlinear regression of

the experimental results.

5.5.1 MATI Spectrum and Ionization Energy

The one-photon MATI spectrum of hexafluorobenzene recorded by

monitoring C6F6+ in the ground electronic state is shown in Fig. 5.6. The

spectrum in the 50 ~ 1900 cm-1 range magnified by 20 is also shown in the

figure as an inset to demonstrate the quality of the spectrum obtained in this

work. Quality of this spectrum is substantially better than any gas phase

spectrum reported so far2,40 and is comparable to or better than the dispersed

fluorescence spectrum recorded for C6F6+ trapped in the inert gas matrix. The

fact that the gas phase spectrum is free from environmental perturbation which

often plagues the matrix spectrum and that the vibrational peaks observed are

definitely due to C6F6+ as guaranteed by the mass selectivity of MATI are the

main advantage of the present approach. The fact that the electronic states

involved in the one-photon MATI are different from those in the emission in the

matrix provides a means to check the validity of the spectra obtained by the

latter. Also, one may expect to obtain structural information unavailable in the

matrix spectrum because the principles governing the two techniques are

different.


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249

79800 80300 80800 81300 81800

378

1798

1727

1650

119

160

958

1048

1108 12

1612

48

1408

1498

835

651/

671

632

362

1565

1260

183115

48

600/

615

734

759

1345

553

51847

5

909689

493

786

406

321/

333

145

214

233

266 389

283

Sign

al

Photon energy, cm-1

0 500 1000 1500

500 1000 1500

Ion energy, cm-1

Fig. 5.6 One-photon MATI spectrum of C6F6 recorded by monitoring

C6F6+ in the ground electronic state. The x-scale at the top of the figure

corresponds to the vibrational frequency scale for the cation whose origin

is at the 0-0 band position. Spectrum in the 50 ~ 1900 cm-1 region

magnified by 20 is shown as an inset to demonstrate the quality of the

MATI spectrum obtained in this work.


2004/01/28 17:41:01

250

The intense peak appearing at the lowest photon energy, namely at ~79931

cm-1 in Fig.5.6, corresponds to the 0-0 band. The position of the 0-0 band in a

one-photon MATI spectrum is usually a little smaller than the correct ionization

energy because the molecules in ZEKE states some cm-1 below the threshold can

also be ionized when high PFI field is applied. To correct this effect, the 0-0

band position was measured with various values of the PFI field and the accurate

ionization energy was estimated by extrapolation to the zero field limit. Spoil

field was not used in such measurements. The ionization energy to the ground

electronic state of C6F6+ measured in this work is listed in Table 5.7 together

with the previous results. Even though the random error in the measurement of

the ionization energy with the present MATI technique is ± 0.0001 ~ 0.0002 eV,

a larger error (± 0.0006 eV) is quoted here from our experience in the previous

measurements on other samples. There has been no report on the accurate

ionization energy measured by ZEKE or MATI. The present result, 9.9108 ±

0.0006 eV, agrees with the ionization energy measured by the threshold

photoelectron spectroscopy (TPES), 9.930 ± 0.045 eV, within the error limits.

Assuming that the shift of a vibrational peak in a MATI spectrum due to the

applied fields is similar to that of the 0-0 band, the vibrational frequency

corresponding to each peak can be determined as its distance from the 0-0 band

position. The vibrational frequency scale with the origin at the 0-0 band position

is also drawn in Fig. 5.6. The vibrational frequencies of each peak are listed in

Table 5.8 together with the previous dispersed fluorescence results.

5.5.2 Calculated Results

For C6F6+ in the ground electronic state, X~ 2E1g, with the D6h symmetry, the

vibrational modes can be classified into a1g (1, 2), a2g (3), a2u (4), b1u (5, 6), b2g

(7, 8), b2u (9, 10), e1g (11), e1u (12, 13, 14), e2g (15, 16, 17, 18), and e2u (19, 20).

Numbers in the parentheses indicate the mode number designated by Mulliken


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251

notation. In X~ 2E1g, the e2g modes are active both in the linear and quadratic

Jahn-Teller effect while the e1g, e1u, and e2u modes are only quadratically active.

A singly excited e2g,u mode in X~ 2E1g splits into b1g,u, b2g,u, and e1g,u vibronic

species while an e1g,u mode into a1g,u, a2g,u, and e2g,u species. Only the Jahn-Teller

distortion due to the four e2g vibrations has been considered in this work.

Table 5.7 Ionization energies (IE) of hexafluorobenzene, in eV.

IE ( X~ ) Ref.

9.9108 ± 0.0006 This work

9.930 ± 0.045 TPES41

9.906 PES42

The optimized geometries for the 2E1g (D6h), 2B2g (D2h), and 2B3g (D2h) states

obtained by the method explained in the previous section are drawn in Fig. 5.7.

Energies at the 2B2g (D2h) and 2B3g (D2h) geometries referred to the D6h cusp

(2E1g) are -1011 and -1032 cm-1, respectively. The 2B3g minimum corresponds to

the global minimum under the overall Jahn-Teller effect. The 2B2g geometry

corresponds to a saddle point in the moat and has one negative eigenvalue.

The Jahn-Teller PESs along each normal coordinate of v15 ~ v18 calculated

following the method described in the previous section are shown in Fig. 5.8.

Only the portions in the 2B3g side are drawn. The 2B2g sides of PESs are virtually

the y-reflections of those in the figure except for the v18 mode, even though the

energies at the minima are slightly different from those in the 2B3g side. The

difference was more noticeable for v18 because both the linear and quadratic

parameters were significant. It is to be emphasized that the geometry which can


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252

1.307Å

1.291Å1.448Å

1.389Å

117.6º121.2º

(b)

B2g(D2h)

1.407(1.388)Å

1.296(1.330)Å

120.0º

(a)

E1g(D6h)

1.302Å

1.286Å

1.370Å

1.427Å

122.4º118.8º

(c)

B3g(D2h)

Fig. 5.7 The optimized geometries for the (a) 2E1g (D6h), (b) 2B2g (D2h), and (c) 2B3g (D2h) states of C6F6+

calculated at the B3LYP/6-311++G (2df) level. Values in parentheses in (a) are the bond lengths in the neutral.




253

Table 5.8 Vibrational frequencies (in cm-1) of hexafluorobenzene cation in the

ground electronic state ( X~ 2E1g) measured by the one-photon MATI and their

assignments.

Jahn-Teller fitdObserved LIFa Calc.b Main characterc

Eigenvalue Eigenstate 0 0-0 0 |1/2, 1⟩

119 123 201 145 181(3/2) 145 |3/2, 1⟩

160 155

181(-3/2) 160 |3/2, 2⟩ 214 219 41 233 247 202 266 281 101 283 289 181(1/2) 277 |1/2, 2⟩ 321 326 171(3/2) 327 |3/2, 3⟩

333 335 182(-5/2)/171(-3/2) 333/340 |1/2, 3⟩/|3/2, 4⟩ 362 111 378 367 111 389 111 406 171(3/2)181(-1/2) 407 |1/2, 4⟩ 475 448 81 493 417 17υ(1/2)(υ=1~ 4) 494 |1/2, 5⟩ 518 498/508 183(7/2) 511/515 |1/2, 6⟩/|1/2, 7⟩ 553 554 560 21 600 609 61 / 171(3/2)181(1/2) 602 |3/2, 7⟩ 615 171(-3/2)181(1/2) 611 |3/2, 8⟩ 632 ? 651 ? 671 172(-5/2) 669 |1/2, 9⟩ 689 699 171(-3/2)182(3/2) 684 |1/2, 11⟩ 734 782 71 759 172(5/2)181(-1/2) 760 |3/2, 12⟩ 786 797 172(1/2)182(1/2) 788 |1/2, 13⟩


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254

835 843 21181 909 172(1/2)182(5/2) 904 |1/2, 17⟩

958 21171181 / 172(-5/2)182(-1/2) 964 |1/2, 21⟩

1048 1052 21171 / 173(7/2)181(3/2) 1047 |3/2, 23⟩

1108 1107 1120 22 / 171(3/2)182(5/2) 1108 |1/2, 28⟩ 1216 161(±3/2) 1219 |3/2, 32⟩ 1248 1226 161(1/2) 1247 |1/2, 36⟩ 1260 161(±3/2) 1260 |3/2, 35⟩ 1345 1357 91 / 186(9/2) 1349 |3/2, 42⟩ 1408 1416 51 / 183(-5/2) 1409 |1/2, 46⟩ 1498 1466 121 / 188(1/2) 1494 |1/2, 48⟩ 1548 1554 11 / 151(±3/2) 1534 |3/2, 48⟩ 1565 173(-7/2)182(5/2) 1590 |3/2, 49⟩ 1650 172(-1/2)183(1/2) 1624 |1/2, 49⟩ 1727 174(9/2)184(-7/2) 1725 |1/2, 50⟩ 1798 21161(1/2) 1831 11181(1/2)

a Refs. 27 and 43.

b Vibrational frequencies at the global minimum (2B3g (D2h)) calculated at

the B3LYP/ 6-311++G (2df) level for modes other than v15 ~ v18. c Mulliken notation30 was used for the vibrational modes. For the four

linear Jahn-Teller active modes, the main characters were determined by

checking the decoupled states making the largest contribution in the four-

mode SOCJT output. Slashes ( / ) indicate two alternative assignments.

Further details for the Jahn-Teller components are listed in the next

columns. d Outputs from the four-mode SOCJT calculation after the best fit to the

experimental data. The eigenstate denotes | j, nj ⟩.


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255

be specified by the coordinates at the minima of PESs in Fig. 5.8 does not

coincide with the geometry at the global minimum because each PES represents

a cut along each normal coordinate. The Jahn-Teller stabilization energies due to

the linear (εi(1)) and quadratic (εi

(2)) coupling in each mode are listed in Table 5.8

together with the coupling constants calculated therefrom and compared with the

previous results by Miller and coworkers. The linear coupling constants

calculated here are not much different from the calculated and experimental data

by Miller and coworkers, which suggests that their assignment can be a useful

guideline for the present attempt. As was pointed out by Johnson, the magnitude

of the calculated quadratic coupling constants, and even their sign, can be in

serious error because of various approximations made such as in the choice of

the eigenvectors. These are used only as qualitative guidelines in this work.


Almost all the major vibrational peaks observed in the dispersed fluorescence

spectrum of C6F6+ in solid Ne were assigned to the Jahn-Teller states arising

from the fundamentals, overtones, and combinations of v15 ~ v18 by Bondybey

and Miller.27 Most of these, especially the ones in the low frequency region, find

their counterparts in the present one-photon MATI spectrum. Some additional

peaks appear in the latter, which are probably due to other vibrations.

The vibrational selection rule in the transition from the ground electronic

state of C6F6, X~ 1A1g, to Rydberg states converging to the ionic ground state,

X~ 2E1g, must be the same as that in the corresponding process in benzene

prepared under the beam condition. To summarize, fundamentals and all the

overtones of the a1g modes are allowed while ∆υ=2, 4, 6, … selection rule holds

for nontotally symmetric modes. Fundamentals of nontotally symmetric,

nondegenerate, and gerade vibrations which are dipole-forbidden can appear in a

MATI spectrum via vibronic mechanism, even though weakly. The vibrational


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256

selection rule involving Jahn-Teller states in electronic transition between a 2A1

state and a 2E state was described in details by Barckholtz and Miller.6 Even

though the transition intensity to the overtones of degenerate modes is zero

under the harmonic oscillator potentials, Jahn-Teller coupling produces intensity.

The observable Jahn-Teller levels in the 2E state are those with | j | ≤ | ∑υ′′+i

i2/1 |.

When the transitions start from the vibrationless ground state, only 2/1±=j

levels are accessible. When quadratic Jahn-Teller coupling is introduced, the

2/1±=j levels are mixed with the 2/5m=j levels, rendering some intensity

to the transitions to the levels which are predominantly 2/5±=j . The fact that

the equilibrium geometries of the neutral ( X~ 1A1g) and the cation ( X~ 2E1g) are

substantially different especially along the eigenvectors of the Jahn-Teller active

modes also leads to the appearance of strong peaks associated with the

fundamentals, overtones, and combinations of the Jahn-Teller active vibrations.

Here we will first attempt to assign peaks arising from the e2g modes, v15 ~ v18,

which are linearly and quadratically Jahn-Teller active. The remaining modes

will be assigned thereafter.

The Jahn-Teller peaks were assigned by an iterative calculation-assignment-

fitting procedure as follows. The procedure started with the low frequency v17

and v18 modes which had large linear coupling constants in the calculation.

Using the linear and quadratic Jahn-Teller coupling constants for these modes

obtained by the quantum chemical calculation, we performed the two-mode

Jahn-Teller calculation with SOCJT. Similar calculation was done with Miller

and coworker’s parameters25 also. The results from the two calculations were

similar even though the former provided more fits to the experimental peak

positions than the latter. The major low frequency MATI peaks at 283, 406, 493,

and 518 cm-1 could be readily identified with the calculated Jahn-Teller

eigenvalues of 280, 424, 491, and 529 cm-1, respectively. Designating the Jahn-


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257

Teller eigenstates as | j, nj ⟩, in which nj indicates the njth state with j in terms of

increasing energy, the aboves corresponded to |1/2, 2⟩, |1/2, 4⟩, |1/2, 5⟩, and |1/2,

6⟩, respectively, the 0-0 band being |1/2, 1⟩. From the coefficients in the linear

combination of decoupled states i∏ | υi, li ⟩, the main characters of these states

were identified. These were used to trace the evolution of the Jahn-Teller states

as the calculation got more complicated with the inclusion of v15 and v16. There

were some peaks in the low frequency region which could not be assigned to any

of the Jahn-Teller inactive fundamental such as those at 145 and 160 cm-1. These

two are close to the broad peak centered at ~ 155 cm-1 in the dispersed

fluorescence spectrum of C6F6+ in the gas phase by Sears et al.,43 which was

assigned to the 2/3=j state arising from 181, or 181(3/2). In the two-mode

calculation described above, a pair of states at 145 and 160 cm-1 were predicted

with the main character of 181(±3/2). Similarly, the pair at 321/333 cm-1 is close

the 171(3/2) pair at 326/335 cm-1 reported by Sears et al.43, while the present

two-mode calculation generated the 171(±3/2) pair at 313/317 cm-1. It is

surprising to note that the 2/3±=j states are observed in the one-photon

MATI spectrum, even though forbidden. Compared to the 145/160 cm-1, the

intensity of the 321/333 cm-1 pair is significant. It must contain a contribution

from the transition to |1/2, 3⟩ which has not been assigned yet. Using all the

above peaks, the linear and quadratic Jahn-Teller parameters for v17 and v18 were

calculated via nonlinear regression. The results were used to identify peaks up to

~ 1000 cm-1. Then, the Jahn-Teller parameters for v15 and v16 obtained from the

quantum chemical calculations were added and the four-mode calculation was

performed. Changes in the positions of the above peaks were checked. The main

character of each peak was useful for this. Other peaks with the v17 / v18 character

were identified. Since the linear Jahn-Teller parameter of v16 is very small, its

fundamental is expected to appear near the calculated frequency of 1248 cm-1. In


2004/01/28 17:41:01

258

fact, a broad peak at ~ 1226 cm-1 in the dispersed fluorescence spectrum of C6F6+

in solid Ne was assigned to 161(1/2) by Bondybey and Miller.27 This was split

into three peaks at 1216, 1248, and 1260 cm-1 in the one-photon MATI spectrum.

According to the above four-mode calculation, the best assignments were

161(1/2) for the peak at 1248 cm-1 and 161(±3/2) for those at 1216 and 1260 cm-1.

It was difficult to identify peaks assignable to the fundamental of v15 because its

linear Jahn-Teller parameter was large and because mixing of the decoupled

states was rather extensive in the spectral region above 1500 cm-1. Finally,

eighteen peaks which were positively assigned to the Jahn-Teller states, namely

at 145, 160, 283, 321, 333, 406, 493, 518, 689, 786, 909, 1216, 1248, 1260, 1548,

1565, 1650, and 1727 cm-1, were fed into SOCJT to determine the Jahn-Teller

parameters by the four-mode fit. The parameters thus determined are compared

with those calculated by Applegate and Miller,25 those determined from the

experimental data by Sears and coworkers,43 and those obtained by the quantum

chemical calculation in this work in Table 5.9. The parameters determined from

the experimental data in this work are in reasonable agreement with those from

others. The eigenvalues of the Jahn-Teller states identified are listed in Table 5.8

together with the | j, nj ⟩ state designations and the main characters. The present

assignments are in good agreement with those by Sears and coworkers even

though there are some differences in specifying the main character of each peak.

For example, we designated the main characters of 171(3/2)181(-1/2) and

17υ(1/2)(υ=1 ~ 4) to the peaks at 406 and 493 cm-1, respectively. On the other

hand, 171(1/2) was designated to the peak at 417 cm-1 by Sears and coworkers,43

which can be better correlated to the peak at 406 cm-1 than at 493 cm-1 in the

MATI spectrum. Since a main character is simply determined by checking the

decoupled state making the most important contribution to a particular Jahn-

Teller state as found through the calculation, we do not have an explanation for

the above differences. It is to be emphasized that the designation of main


2004/01/28 17:41:01

259

0.0 0.1 0.2

-600

-300

0

300

600

o

v17v15 v18v16

Displacement along each mode, A

Pote

ntia

l ene

rgy,

cm

-1

Fig. 5.8 The Jahn-Teller potential energy surfaces along each normal

coordinate of the four e2g modes of C6F6+ in the ground electronic state.

Only the portions in the 2B3g side are drawn.


2004/01/28 17:41:01

260

Table 5.9. Calculated and experimental Jahn-Teller coupling parameters for the

four e2g vibrational modes of C6F6+.

Miller This work Mode Calc.a Exp.b

Calc.c Exp.d

15 ωi 1629 1610 1704 1702 Di 0.34 0.23 0.261 0.246 Ki -0.0018 - -0.006 0.010 εi

(1)e 554 370 445 418 εi

(2)f -1 - -3

16 ωi 1210 1215 1248 1252 Di 0.032 0.05 0.017 0.011 Ki 0.075 - -0.321 -0.275 εi

(1) 39 61 21 13 εi

(2) 3 - -7

17 ωi 418 425 434 433 Di 0.72 0.68 0.805 0.751 Ki -0.019 ±0.006 0.017 0.030 εi

(1) 301 289 349 325 εi

(2) -6 ±1.7 6

18 ωi 256 265 265 256 Di 0.45 0.38 0.270 0.462 Ki 0.0096 - 0.057 0.057 εi

(1) 115 101 72 118 εi

(2) 1 - 4

εT 1019g 821 888g 875 a Ref. 25. b Ref. 43. c Determined from the B3LYP/6-311++G (2df) results. d Determined by the four-mode fit to the experimental data. e Stabilization energy due to the linear Jahn-Teller effect. f Stabilization energy due to the quadratic Jahn-Teller effect. g Total stabilization energy calculated by eqn. (4).


2004/01/28 17:41:01

261

does not affect the Jahn-Teller fitting and analysis in practical terms. In fact,

such a designation is meaningless when the Jahn-Teller interaction is

significant,25 except in very low frequency region.

With all the significant Jahn-Teller peaks assigned, we set out to assign the

remaining vibrations. The most important among these are a1g vibrations, v1 and

v2. The v2 fundamental, 21, could be readily assigned to the strong peak at 553

cm-1, close to the calculated frequency of 560 cm-1. Its overtone, 22, appeared at

1108 cm-1. These are in agreement with the assignments for the strong peaks at

554 and 1107 cm-1 by Bondybey and Miller.27 The prominent peak at 1548 cm-1

was assigned to 11 based on its calculated frequency of 1554 cm-1, even though

the peak may contain contribution from Jahn-Teller states such as 151(±3/2). It is

interesting to note that the same type vibration of the benzene cation in X~ 2E1g,

namely the totally symmetric C-H stretching, appeared very weakly. This was

attributed to the fact that the C-H bond length changed less than 0.001 Å upon

ionization and presumably led to a very small Franck-Condon factor. Much

larger change in the C-F bond length, 0.034 Å in Fig. 5.7(a), in the present case

is compatible with the prominent 11. Among the remaining nondegenerate

fundamentals, 41 ~ 101 appeared near their calculated frequencies, even though

very weakly. Excellent agreement between the experimental and calculated

frequencies of the Jahn-Teller inactive vibrations shows that the potential energy

surface of C6F6+ calculated at the D2h global minimum is the excellent

representation of its structure in the ground electronic state. An interesting aspect

in the above assignments is that the fundamentals of the ungerade modes 4, 5, 6,

9, and 10 appear in the one-photon MATI spectrum even though they are doubly

forbidden. Similar transitions were observed in our previous one-photon MATI

study of benzene. The l mixing in the Rydberg states caused by the stray field

inside the instrument or by scrambling field applied was mentioned as a possible

mechanism.44


2004/01/28 17:41:01

262

The vibrations which are Jahn-Teller active only quadratically are left

unassigned. The lowest frequency peak at 119 cm-1 can be assigned to 201 (e2u)

which has the calculated harmonic frequency of 123 cm-1. Obviously, no

alternative assignment can be found. Appearance of the more prominent

overtone, 202, at 233 cm-1 supports such an assignment. Similarly, the peaks at

362, 378, and 389 cm-1 are probably due to 111. Some peaks are left unassigned,

such as those at 632 and 651 cm-1, because there are various possibilities which

can not be confirmed.

As has been mentioned already, all the major peaks in the low frequency

range, namely those at 289, 417, 508, and 554 cm-1, observed in the dispersed

fluorescence spectrum of C6F6+ in the Ne matrix reported by Bondybey and

Miller27 find their counterparts in the one-photon MATI spectrum. This is not

always the case for the minor peaks appearing at the higher frequency range. For

example, even though the peak at 972 cm-1 is prominent in the matrix spectrum,

its counterpart can not be found in the MATI spectrum. Also, the MATI

spectrum shows more peaks than those observed in the matrix spectrum. It is to

be emphasized that most of these new peaks, even though weak, could be

identified properly by comparing with the calculated results. Most importantly,

the present data have been obtained mass selectively in the gas phase and hence

are free from the environmental effect caused by the matrix.

5.5.4 Conclusions

Quantum chemical calculation of the Jahn-Teller parameters from

topographical features of the potential energy surface requires evaluation of the

energy at the crossing point of two Jahn-Teller split states. This, in turn, requires

multiconfiguration calculations as suggested by Miller and coworkers,5 which

can be extremely time consuming for a polyatomic molecule as large as C6F6+,

especially when a large basis set is used to achieve good energy accuracy. It has


2004/01/28 17:41:01

263

been found that a single configuration calculation at the B3LYP level, as

suggested by Johnson,4 with a rather extensive basis set is an adequate

alternative in the C6F6+ case.

The Jahn-Teller parameters obtained from the calculation were the starting

point in the assignments of vibrational peaks appearing in the one-photon MATI

spectrum. These were improved progressively until an excellent agreement

between the experimental data and the results from the four-mode Jahn-Teller

calculation was achieved. Compared to the previous vibrational analysis for the

same system by Bondybey and Miller,27 which utilized the spectral data obtained

in the matrix mostly, the number of modes assigned is larger and the frequencies

are expected to be more accurate. To say the least, the present results provide

experimental data useful for further theoretical study of the Jahn-Teller effect in

this system.


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264

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19. M. Huang and S. Lunell, J. Chem. Phys. 92, 6081 (1990).

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Phys. 117, 2657 (2002).

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2004/01/28 17:41:01

국문 초록

전하교환 이온화 질량분석법과 광분해 반응속도론을 통해 벤젠분자

양이온의 수명이 긴 들뜬 전자상태를 발견하였다. 이런 전자상태는 그

수명이 수십 마이크로초정도이며 에너지론과 대칭 선택규칙에 의해 첫

번째 들뜬 전자상태로 예측된다. 다른 분자양이온 경우 수명이 긴 들뜬

전자상태를 효과적으로 탐색하기 위해 역배치 이중집중 질량분석계의

이온원 밖에 전하교환 이온화를 위한 충돌실을 설치하였다. 이는

이온원과 전하교환 이온화의 충돌실을 공간적으로 분리함으로써

이온/분자 회합반응을 피하고 대상 이온의 재결합 에너지를 전하교환

반응의 발열성 규칙에 근거하여 측정함으로써 수명이 긴 들뜬

전자상태의 분자 양이온을 발견하기 위함이다. 이렇게 개발된 방법을

이용하여 벤젠 분자양이온의 수명이 긴 들뜬 전자상태의 존재를

검증하고 염화벤젠, 브롬화벤젠, 시아노벤젠, 페닐아세틸렌 양이온들의

수명이 긴 들뜬 전자상태를 발견하였다. 이들 전자상태는 같은 평면의

각 할로겐원자의 비결합 p 오비탈이나 삼중결합의 π 오비탈로부터

전자를 제거해서 생긴 전자상태들로 바닥 전자상태의 π 오비탈과 서로

수직관계에 있음이 그 이유로 제안되었다.

들뜬 전자상태 벤젠족 양이온들의 분광학적 연구를 위해 수은

증기에서 사파장 혼합 방법으로 104-125nm 영역에서 수 백 nJ 세기의

가변 진공자외선 광원을 개발했다. 여기에 단광자 질량분석문턱이온화

방법을 접목하여 바닥 전자상태뿐만 아니라 들뜬 전자상태의 벤젠족

양이온들의 주로 특정 대칭모드들로 구성되는 진동스펙트럼들을 얻었다.

그 진동배정은 문헌값과 양자계산값을 참조하고 전이 선택성 규칙을

267


2004/01/28 17:41:01

도입함으로써 이루어지며 양자화학계산으로 이온화시 기하구조 변화를

비교하여 진동구조 특징을 설명할 수 있다. 나아가 각 대칭진동모드의

세기 정보를 제공하는 Franck-Condon 인자 계산은 특히 진동배정에

효과적이다.

한편 바닥 전자상태의 Jahn-Teller 벤젠족 양이온(벤젠과 헥사불화

벤젠 양이온)들의 스펨트럼 분석을 위해 네 e2g 모드들의 위치에너지

표면을 양자화학계산을 통해 구축하고 그들 형태로부터 이론적인 Jahn-

Teller 요소들을 결정하였다. 이들을 Jahn-Teller 상태 에너지 계산에

이용해서 다중모드 회귀분석을 수행함으로써 실험과 이론 진동수들의

좋은 일치를 이루었다. 나머지 진동모드들은 양자화학계산을 통해 잘

배정하였다.

● 주요어 : 벤젠족 양이온, 수명이 긴 들뜬 전자상태, Jahn-Teller,

진동 스펙트라, 진공자외선, 질량분석문턱이온화 분광법, 전하 교환

이온화 질량분석법, 광분해 반응속도론, 양자화학계산, Franck-Condon

인자, 위치에너지 표면.

● 학번 : 99305-802

268


2004/01/28 17:41:01

감사의 글

오늘의 성과를 이루기까지 지난 학위과정동안 끊임없는 관심과 질타로

헌신적인 지도를 아끼지 않으셨던 김명수 교수님께 깊이 감사 드립니다.

선생님께서 보여주신 진정한 과학자로서의 자세와 가르침은 저를 일깨웠

을 뿐 아니라 제가 나아갈 인생의 중요한 길잡이가 될 것입니다. 아낌없는

조언과 용기를 주신 김홍래, 최중철 교수님께 감사 드립니다. 또한 바쁘신

중에도 저의 부족한 논문을 읽고 심사해주신 이순보, 장두전, 신석민 교수

님께 감사 드립니다.

힘들고 때로는 좌절도 했던 긴 연구기간동안 그래도 재미와 보람을 느

꼈던 것은 많은 선배님, 동료, 그리고 후배들 덕분입니다. 항상 따뜻한 말

씀으로 용기를 주신 영환 형, 성태 형, 영진 형, 연구에 매진할 수 있도록

도와 준 완구, 상태, 상현, 두영에게 깊이 감사 드립니다. 그리고 오랫동

안 실험실 생활을 함께 한 정희, ZAB-E 고치며 많은 밤 함께 고생한 동신

과 연호, 많은 도움을 주지도 못했는데 늘 열심히 따라 준 주연, 태훈, 오

규, 봉준, 승환, 지원, 효영, Long-lived ion 탐지법을 물려받아 마음 고생

많이 한 미진과 여영, MATI 팀을 이끌 미나, 그리고 함께 했던 다른 모든

후배들에게도 감사의 뜻을 전합니다.

이제 또 한 번의 과정을 마치고 새로운 시작을 하면서 너무나 아쉽고

부족했음을 알기에 앞으로 나아가는 길의 교훈으로 삼고자 합니다. 이런

저를 계속 지켜보고 관심을 가져주시면 큰 힘이 되리라 생각합니다.

마지막으로 지금까지 부족한 자식이었던 저를 항상 헌신적인 지지와 변

함없는 믿음으로 대해 주신 아버지, 어머니, 빙장, 빙모님, 그리고 다른

가족 모두에게 진심으로 깊이 감사 드립니다. 그리고 끊임 없는 애정으로

고락을 함께 해온 사랑하는 아내 명원과 딸 미주에게 이 영광을 돌립니다.

269


2004/01/28 17:41:01

spectroscopy and mass spectrometry of state-selected...

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