fermi resonance and coriolis coupling between ν5and 2ν6in ch235clf

JOURNAL OF MOLECULAR SPECTROSCOPY 175, 267–276 (1996)ARTICLE NO. 0032

Fermi Resonance and Coriolis Couplingbetween n5 and 2n6 in CH2

35ClF

Susana Blanco,* Alberto Lesarri,* Juan C. Lopez,* Jose L. Alonso,*,1 and Antonio Guarnieri†

*Departamento de QuıB mica FıB sica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid, Spain; and †Abteilung Chemische Physik,Institut fur Physikalische Chemie, Universitat Kiel, Kiel, Germany

Received: June 20, 1995; in revised form September 18, 1995

The rotational spectra of CH235ClF in the vibrational excited states £5 Å 1 and £6 Å 2 have been observed in the

frequency region 8–250 GHz. From infrared data these states are predicted to be close in energy (2n6 0 n5 Å 10 cm01)and both a Fermi resonance and a third-rank Coriolis resonance between them have been considered in the analysis ofthe rotational spectra. The 35Cl quadrupole coupling constants have been also determined from the analysis of thehyperfine structure for both vibrational states. q 1996 Academic Press, Inc.

INTRODUCTION lated spectrometers with free space cells and point contactdetectors (10) or with an X-band waveguide cell and super-

In a preceding paper (1) we presented a study of the heterodyne detection (11). Experiments were made at 260rotational spectrum of chlorofluoromethane (HCFC-31) in K in the Stark spectrometer and at room temperature in thethe ground state of 35Cl, 37Cl, and 13C isotopomers and in millimeter-wave spectrometers with sample pressures belowthe £6 Å 1 excited state of 35Cl and 37Cl species. We also 30 mTorr. Temperatures of about 230 K and pressures downobserved (1) the spectra of the excited states £5 Å 1 and £6 to 1 mTorr were used in the FT-MW spectrometer. TheÅ 2 for CH2

35ClF, which do not fit into a semirigid rotor accuracy of frequency measurements for resolved quadru-model. pole hyperfine components is estimated to be 10 kHz for

The fundamentals of n6(A*) and n5(A*) vibrations of chlo- FT-MW experiments and 50 kHz for the higher frequencyrofluoromethane (Cs symmetry) have been observed (2–5) spectrometers. In the case of nonresolved splittings the esti-at 385 and 760 cm01, respectively. From these data it is mated accuracy is lower.expected that the states £5 Å 1 and £6 Å 2 are close in energy(2n6 0 n5 Å 10 cm01), giving rise to a situation of third- ASSIGNMENT OF SPECTRArank degeneracy (6). From symmetry arguments it can beshown that a Fermi resonance as well a c-type third-rank Chlorofluoromethane is a near-prolate asymmetric top (kCoriolis resonance are possible. É 00.97) with the electric dipole moment mainly oriented

In this paper we present an analysis of the b-type rotational along the b-inertial axis. The b-type spectrum for the groundspectra of CH2

35ClF in the vibrational states £5 Å 1 and £6 state of the 35Cl isotopomer is very strong (1). The observedÅ 2, showing that both types of resonance interactions intensity for the spectrum of the £6 Å 1 state with an energyshould be considered. of 385 cm01 (2–5) above the ground state indicates that the

excited states £6 Å 2 and £5 Å 1 (Ç760 cm01) should alsoEXPERIMENTAL DETAILS be observed. Initial assignments were made for the Q-branch

transitions J1,J01 R J0,J and for the R-branch transitions J /A commercial sample of CH2ClF was used. Different ex- 10,J/1 R J1,J, with J Å 5 0 14, on the basis of the Stark,

perimental setups were used depending on the frequency intensity, and quadrupole hyperfine structure patterns.range investigated. Initial assignments were made in the fre- Considering the a constants for £6 Å 1 (1) it is expectedquency region between 26 and 72 GHz, using a computer- that in the case of no interaction the £6 Å 2 rotational linescontrolled Stark modulation spectrometer (7, 8). Measure- will appear at frequencies which depend on the rotationalments in the range 8–18 GHz were made using a microwave constants of the ground state corrected by 2a6. ObservationsFourier transform spectrometer (FT-MW) (9). Millimeter- at the corresponding frequencies were not successful. Bywave measurements in the frequency range 80–250 GHz means of survey scans of the spectrum in the appropriatewere carried out using computer-controlled source modu- regions it was possible to identify two vibrational satellites

of about the same intensity which were assigned to the £6 Å2 and £5 Å 1 states. The subsequent analysis of the rotational1 To whom correspondence should be addressed.

2670022-2852/96 $18.00

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BLANCO ET AL.268

TABLE 1 infrared data is 10 cm01. Both states are totally symmetricResults of the Fit of the Rotational Spectra of and may interact through a Fermi resonance such as that

£5 Å 1 and £6 Å 2 Vibrational States of CH235ClF which occurs between the same states for the related mole-

up to JÅ 35 to a Two-State Hamiltonian Including cule CH2FBr (4). Rotation about the c axis also belongs toa c-Type Coriolis Resonance (Columns 1 and 2) the totally symmetric species of the Cs group and a third-and the Rotational Parameters for £6 Å 2 (Column rank Coriolis resonance may also occur.3) Calculated from Extrapolation from £6 Å 1 (1)

Both resonances may explain the observed features fromthe first assigned rotational transitions of £5 Å 1 and £6 Å 2states of chlorofluoromethane. The differences between thea constants of the £6 Å 2 and £6 Å 1 states may be mainlyattributed to a Fermi resonance. In the absence of strongrotational crossing effects the Fermi resonance interactioncan be usually taken into account, using effective semirigidrotor Hamiltonians for each state. For this reason the failureof the semirigid rotor model for low Ka values may be causedby a Coriolis interation. The anomalous values observed forthe centrifugal distortion constants could also be attributedto contributions from both resonance interactions.

In order to confirm these hypotheses it was decided totreat the rotational spectra of these states using an effectivetwo-state vibration rotation Hamiltonian including both reso-nances. For the reasons given before only the Coriolis reso-nance was considered initially, in order to fit the observed

TABLE 2Results of the Calculation of the Fermi Resonance Parameters

for the £5 Å 1 and £6 Å 2 Vibrational States of CH235ClF

a Estimated errors in parentheses in units of the lastdigit.

b rms deviation of the fit.c Number of fitted transitions.

spectra of these two states was made using the calculatedunperturbed central frequencies assuming the same quadru-pole coupling constants as found for the ground vibrationalstate (1).

The first identified transitions for both states were fittedto the A-semirigid rotor Hamiltonian of Watson (12) in theIr representation in order to predict and assign new rotationallines. From these semirigid rotor fits the following generalfeatures were observed. The a constants calculated from £6

Å 2 rotational constants differ by 8–18% from those calcu-lated for £6 Å 1. The quartic centrifugal distortion constantsshow large departures from the values observed for the

a Calculated from the ground and £6 Å 1 states of CH235ClFground state. The semirigid rotor model failed for rotational

b Calculated from the relations B£6Å2 / B

£5Å1 Å B9£62 / B*

£5Å1, where thetransitions with values of Ka ú 2–3. These effects evidenceB constants are those given in columns (1) and (2) of Table 1.the contributions to the effective Hamiltonians of a reso- c Standard deviation of the fit to the expressions: B

£6Å2 Å a2 B9£6Å2 / b2

nance between the two levels. B *£5Å1 and B

£5Å1 Å a2 B *£5Å1 / b2 B 9

£6Å2.As indicated above the £5 Å 1 and £6 Å 2 vibrational states d Calculated from: DE Å (d2 / 4W 2

F)1/2, a2 Å (DE / d)/2DE, and b2 Åof chlorofluoromethane are close to a third-rank degeneracy (DE 0 d)/2DE. Estimated error from three times the standard deviation of

a2 and b2 coefficients.situation (6). The energy difference 2n60 n5 calculated from

Copyright q 1996 by Academic Press, Inc.


n5 AND 2n6 COUPLING IN CH235ClF 269

TABLE 3 sible for the more familiar Coriolis resonance interactionsResults of the Fit of the Rotational Spectra of £5 Å 1 and £6 Å and depends primarily on the Coriolis coefficients connect-

2 Vibrational States of CH235ClF to a Two-State Hamiltonian ing different vibrational modes. H30 depends on the cubic

Including Both Fermi and Coriolis Resonance Terms [(a) Fit Using potential energy terms and is responsible for the Fermi reso-the Unperturbed Rotational Constants Given in Table 2 for £6 Å nance effects where third-rank near-degeneracies occur. In2 as Initial Values with a Priori Errors of 0.1 MHz; (b) Fit Using the case of the £5 Å 1 and £6 Å 2 vibrational states ofthe Parameters Obtained from Fit (a) as Initial Values with No

chlorofluoromethane where a c-type interaction may occur,Restriction on the Variation of the Determinable Parameters]the c-axis corresponds to the y-axis when using the Ir repre-sentation. The H31 term includes only the Jy angular momen-tum operator (6) and in the harmonic oscillator–symmetricrotor basis set has matrix elements connecting K of £5 Å 1with K { 1 of £6 Å 2:

»£5 Å 1, £6 Å 0, J, KÉHO 31É£5 Å 0, £6 Å 2, J, K { 1…

Å Wc12 [J(J / 1) 0 K(K { 1)]1/2.

[1]

The coupling operator has the same form as the H21 Cori-olis resonance term but in this case Wc is an effective Coriolisparameter. This parameter includes the contribution from theH31 term and from the perturbation product between H21

and H30. This implies that Wc has a dependence on Corioliscoupling coefficients and cubic potential constants connect-ing the different modes of the molecule (14).

Using the approximate rotational parameters for £5 Å 1and £6 Å 2 obtained from the first assigned rotational linesand the calculated energy difference of 10 cm01 betweenthem, it can be easily predicted that rotational level crossingsoccur for Ka Å 5 of £5 Å 1 and Ka Å 4 of £6 Å 2. Then itcan be expected that rotational transitions involving levelsclose to these values of Ka will show the strongest effectsof this Coriolis interation.

Having these considerations in mind the assignment andanalysis of the spectrum was continued using the programCALPGM of Pickett (15) with an effective two-state Hamil-tonian

H Å ZHR(£5 Å 1) Hc

Hc HR(£6 Å 2) / DEZ , [2]

spectrum and to assign new lines with increasing values ofJ and Ka. A further reason to treat only the Coriolis resonanceinitially is that this procedure also permits the determination where HR is the A-reduced semirigid rotor Hamiltonian ofof the perturbed energy difference between the states. This Watson (12) in the Ir representation for each state, DE isenergy difference may be used together with the rotational the energy difference between rotational levels, and Hc isconstant values to calculate the Fermi resonance parame- the Coriolis operatorters (13).

Hc Å iWcJy, [3]CORIOLIS COUPLING ANALYSIS

When using an effective vibration–rotation Hamiltonian giving rise to matrix elements of the form given in Eq. [1].This Hamiltonian, which included only quartic centrifugalto treat both near-degenerate vibrational states, the trans-

formed third-rank Coriolis resonance term H31 includes con- distortion terms, proved to fit the observed spectra very welland allow new assignments of rotational lines up to valuestributions from the untransformed H31 term and from the

perturbation product between H21 and H30 (6). H21 is respon- of J Å 25. When lines with higher J values and with Ka



BLANCO ET AL.270

TABLE 4A Selection of the Observed Central Line Frequencies for the £5Å 1 Vibrational

State of CH235ClF and Their Differences with Those Calculated from the Rota-

tional Parameters Given in Table 3 (a)

values of 4 and 5 were included, then higher order correcting difference between vibrational levels are well determined.The sextic centrifugal distortion constants FJ and fK for £6terms from H33 had to be considered in Hc

Å 2 are not determinable with this set of rotational transitionsand were fixed to zero. The calculated energy difference is

Hc Å i(Wc / W *cJ2 / W 9cJ

2z)Jy. [4] very close to the calculated value of 10 cm01.

Table 1 also presents in column (3) the values for theThese terms can be obtained by a formal expansion of the rotational parameters of £6 Å 2 calculated from extrapolationCoriolis operator H31 in J2 and J2

z and might be comparable of those for £6 Å 1 (1). The differences between the observedwith the distorsion effects caused by the reduction of the and extrapolated values of the rotational parameters for £6

effective Hamiltonian (16). Applying W*c and W9c and Å 2 are strong evidence of a Fermi-type resonance betweenallowing sextic centrifugal distortion constants to vary led the vibrational levels. Further evidence is the fact that theto a very good fit of the P-, Q-, and R-branch lines observed average values of the centrifugal distortion constants for £5

up to J Å 35. The results of that fit are shown in Table 1. It Å 1 and £6 Å 2 are close to the observed values for theground and £6 Å 1 states of CH2

35ClF (1).can be observed that the Coriolis parameters and the energy




TABLE 5 resonance term is a scalar connecting both vibrational statesA Selection of the Observed Central Line Frequencies for the £6 which do not include any angular momentum operators ifÅ 2 Vibrational State of CH2

35ClF and Their Differences with no higher order correction terms are included. In our caseThose Calculated from the Rotational Parameters Given in Ta- such terms were included in order to fit the transitions withble 3 (a) higher J values. The final form of the Fermi operator used

was (16–18).

F£5Å1, £6Å2 Å WF / W *FJ 2 / W 9F(J

2x 0 J 2

y). [5]

A correction term in J2z was also tested but it was found

to be not determinable from the rotational transitions mea-sured.

This model fits the spectra of the £5 Å 1 and £6 Å 2 statesof CH2

35ClF very well and allowed the assignment of P-, Q-, and R-branch lines up to J Å 60. However, because of themutual high correlations due to the inclusion of the Fermiresonance term, some of the parameters were fixed to theprecalculated values in the first fits made for predicting thespectra. As can be expected, these correlations are particularlyhigh between the rotational constants, the energy difference,d, and the Fermi parameter, WF. For £6 Å 2 the rotationalconstants were fixed to the calculated values of A9, B9, andC9 (shown in Table 2) and the sextic centrifugal constants tothe extrapolated values (see Table 1, column 3). For £5 Å 1only the sextic rotational constants were fixed to the groundstate values. As soon as lines with J values in the range 40–60 were included, some variation in the rotational constantsof £6 Å 2 was allowed by giving them a priori errors of 0.1MHz whereas estimated errors of 800 and 400 MHz weregiven for d and WF, respectively. The sextic centrifugal con-stants were set free, except for the FJK, fJK, and fK constantsWhen higher J-value transitions were included in the fitof £6 Å 2 and the fJK and fK constants of £5 Å 1, whicha progressive decrease in the quality of the fit was found.could not be determined and were put fixed to extrapolatedThe inclusion of octic centrifugal distortion terms in theor ground state values, respectively. Table 3 presents in col-rotational Hamiltonians HR yielded fits of a similar quality

as before. However, instead of continuing to add new termsin this vibration–rotation Hamiltonian, it was decided to

TABLE 6include the Fermi resonance term.Principal Inertial Axis Quadrupole Cou-

pling Constants for £5 Å 1 and £6 Å 2 Vi-FERMI RESONANCE ANALYSIS brational States of CH2

35ClF

The Fermi interaction parameters were first calculated fromthe observed rotational constants of Table 1, from the a con-stants for £6 Å 1, and from the observed energy differenceDE, which was considered the difference between the per-turbed levels (13). The results for the vibration–rotation inter-action parameters, a, the Fermi resonance parameter, WF, thenonperturbed energy difference between states, d, and themixing coefficients a2 and b2 are collected in Table 2.

In the final step of the assignment and analysis of thespectra of £6 Å 2 and £5 Å 1, a two-state Hamiltonian includ-ing Fermi and Coriolis resonance terms was used. The Cori-olis term was the same as that given in Eq. [4]. The Fermi



BLANCO ET AL.272

TABLE 7Observed Quadrupole Hyperfine Components for the £5 Å 1 Vibrational State of CH2

35ClF Used to Determinethe Quadrupole Coupling Constants Given in Table 6

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TABLE 8Observed Quadrupole Hyperfine Components for the £6 Å 2 Vibrational State of CH2

35ClF Used to Determinethe Quadrupole Coupling Constants Given in Table 6

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BLANCO ET AL.274

TABLE 9A Selection of the Observed Central Line Frequencies for £5 Å 1 and £6 Å 2 Vibrational

States of CH235ClF, their Differences with Those Calculated from the Rotational Parameters

Given in Table 3 (a) and the Contributions to the Observed Frequencies from the Coriolis (nC)and Fermi (nF) Resonance Terms

umn (a) the results of fitting in this way all observed lines. (15). Only resolved components have been included in thefinal fit in order to determine the principal axis quadrupoleA selection of the observed central line frequencies for £5 Å

1 and £6 Å 2 is presented in Tables 4 and 5, respectively. coupling tensor elements. The observed transitions withhigher values of J consist of pairs of blended componentsor nonresolved single lines which fit this model very wellQUADRUPOLE COUPLING ANALYSISbut which do not contribute further to the determination of

The 35Cl nuclear quadrupole hyperfine structure observed the quadrupole coupling constants.for the £5 Å 1 and £6 Å 2 states of CH2

35ClF has been fitted Because lines with medium J values were included in theby incorporating the nuclear quadrupole coupling Hamilto- final fit, which made it impossible to vary all the parameters,nian into the model used to treat the Coriolis and Fermi it was decided to fix suitable parameters to the values of fitresonance interactions. The observed components were ana- (a) in Table 3 and to fit only the quadrupole coupling con-lyzed by direct diagonalization of the Hamiltonian using the stants. Parallel fits using alternatively all the observed com-

ponents, including nonresolved splittings up to J Å 40 orbasis sets implemented in the CALPGM Pickett program




the corresponding center line frequencies, give the same CH235ClF. It can be observed from this table that Coriolis

contributions are larger than 1 GHz for those transitionsresults for the rotational, Fermi, and Coriolis resonance pa-rameters. in which levels with Ka Å 5 of £5 Å 1 and Ka Å 4 of

£6 Å 2 are involved whereas the rest of the lines haveThe quadrupole coupling parameters obtained in this wayfor £5 Å 1 and £6 Å 2 are collected in Table 6. The observed lower values. The Fermi resonance contributions are rela-

tively high in almost all the lines and for the most partquadrupole coupling components are listed in Table 7 for £5

Å 1 and in Table 8 for £6Å 2. The elements of the quadrupole they can be accounted for by using effective semirigidrotational Hamiltonians for each separate state. In thiscoupling tensor have values close to those found for the

ground and £6 Å 1 states (1), thus justifying the initial as- way some reasonable limit should be set for the variationof the rotational parameters in the fit of the spectra forsumption of taking ground state values to calculate the center

line frequencies for £5 Å 1 and £6 Å 2. both interacting states when the Fermi resonance term isincluded.

Fits (a) and (b) (see Table 3) give slightly different valuesDISCUSSIONfor the energy difference, d, and for the Fermi resonanceparameter, WF. Due to the high correlations found in theseAs we mentioned before, the inclusion of the Fermi

resonance term originates mutual correlations which are fits some care should be taken when considering the errors.The values of these parameters expressed in wavenumbersclose to unity for elements connecting the sets of rota-

tional parameters of both states, the energy difference d, are coincident in fits (a) and (b) up to the second digit andthis might be the upper error limit. Within this limit theand the Fermi parameter WF. This is the reason for the

great difficulty in determining the Fermi resonance term parameters have the same values as those calculated in Table2 and together with the determined Coriolis coupling con-from the rotational spectra. For low J and Ka values the

only way to fit the rotational spectra of the interacting stant Wc may provide valuable information about the forcefield of CH2

35ClF.states is to fix some parameters to precalculated values orto give them low a priori errors (19). Only when lines A test of the consistency for the analysis of the spectra

also comes from the rotational and centrifugal distortionwith high J and Ka values are fitted do rotational crossingeffects allow the determination of the Fermi resonance constants obtained for each state. The centrifugal distor-

tion constants for £5 Å 1 are reasonable and of the sameparameters. In the set of rotational transitions measuredin this work this condition is not completely fullfilled and order as those obtained for the ground state. The same

happens for £6 Å 2 but in this case the rotational parame-a reasonable result is obtained from a fit without restric-tions only when the initial parameters are not so far from ters are very close to those shown on Table 1 column (3),

calculated by extrapolation from £6 Å 1.the expected minimum. This was the procedure followedin fit (b) of Table 3 for which the results of fit (a) wereused as initial values and the determinable parameters

ACKNOWLEDGMENTSwere set free. It can be observed that the quoted errorsare relatively high by comparison to fit (a) due to the

This work has been supported by the Direccion General de Investigacionmutual high correlation coefficients. CientıB fica y Tecnica (DGICYT, Grant PB90-0345) and by the European

The rms’s of fits (a) and (b) are of the same order as Program Human Capital and Mobility (Network SCAMP, ContractERBCHRXCT930157). S.B. gratefully acknowledges an FPI grant fromthat reported in Table 1 with transitions up to J Å 35the DGICYT. A.G. thanks the DFG, the Land Schleswig-Holstein and thewhere only the Coriolis interaction is being considered.Fond der Chemische Industrie for research funds. The colleagues of theHowever, in the fit of Table 1 there are no correlationChemical Physics Department, University of Kiel, are thanked for helpful

coefficients larger than 0.9 with the exception of DJ/FJ discussions. Finally, we thank the Workshop of the Institute of Physicalof the £5 Å 1 state and those connecting the Coriolis pa- Chemistry of University of Kiel for setting up many mechanical parts of

the spectrometers.rameters Wc, W*c, and W9c. The correlation coefficients be-tween the Coriolis parameters and the rest are very lowand the same situation is found in fits (a) and (b) of Table REFERENCES3. The Coriolis parameters have the same values in allthree fits and it can be concluded that they are well deter- 1. S. Blanco, A. Lesarri, J. C. Lopez, J. L. Alonso, and A. Guarnieri, J.mined in the limit of the assumptions. Mol. Spectrosc. 174, 397–416 (1995).

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(1951).to the observed line frequencies. These contributions are4. M. Z. El-Sabban, A. Danti, and B. J. Zwolinsk, J. Chem. Phys. 44,

listed for a set of selected transitions in Table 9, which, 1770–1779 (1966).together with Tables 4, 5, 7, and 8, contains all the ob- 5. A. I. Jaman and R. N. Nandi, Z. Naturforsch A 34, 954–956 (1979).

6. M. R. Aliev and J. K. G. Watson, in ‘‘Molecular Spectroscopy: Modernserved transitions for both £5 Å 1 and £6 Å 2 states of



BLANCO ET AL.276

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8. A. G. Lesarri, J. C. Lopez, and J. L. Alonso, J. Mol. Struct. 273, 123– 16. S. Urban, J. Behrend, K. M. T. Yamada, and G. Winnewisser, J. Mol.Spectrosc. 161, 511–541 (1993).131 (1992).

9. J. L. Alonso et al., to be published. 17. S. Maes, Cah. Phys. 14, 125–208 (1960).18. A. Perrin, V. Jouen, A. Valentin, J. M. Flaud, and C. Camy-Peyret, J.10. J. L. Alonso, A. G. Lesarri, L. A. Leal, and J. C. Lopez, J. Mol.

Spectrosc. 162, 4–19 (1993). Mol. Spectrosc. 157, 112–121 (1993).19. D. L. Albriton, A. L. Schmeltekopf, and R. N. Zare in ‘‘Molecular11. J. C. Lopez et al., to be published.

12. J. K. G. Watson, in ‘‘Vibrational Spectroscopy and Structure’’ (J. R. Spectroscopy: Modern Research’’ (K. Narahari Rao, Ed.), Vol. 2 Chap.1, pp. 1–65, Academic Press, London, 1976.Durig, Ed.), Vol. 6, pp. 1–89, Elsevier, Amsterdam, 1977.



fermi resonance and coriolis coupling between ν5and 2ν6in ch235clf

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