This journal is© the Owner Societies 2017 Phys. Chem. Chem. Phys., 2017, 19, 19707--19721 | 19707

Cite this:Phys.Chem.Chem.Phys.,

2017, 19, 19707

Ultrafast Coulomb explosion of a diiodomethane mole-cule induced by an X-ray free-electron laser pulse†

Tsukasa Takanashi, a Kosuke Nakamura,b Edwin Kukk,c Koji Motomura,a

Hironobu Fukuzawa,ad Kiyonobu Nagaya,de Shin-ichi Wada,df Yoshiaki Kumagai,a

Denys Iablonskyi,a Yuta Ito,a Yuta Sakakibara,a Daehyun You,a Toshiyuki Nishiyama,e

Kazuki Asa,e Yuhiro Sato,e Takayuki Umemoto,f Kango Kariyazono,f Kohei Ochiai,b

Manabu Kanno,b Kaoru Yamazaki, gh Kuno Kooser,ci Christophe Nicolas,j

Catalin Miron, jk Theodor Asavei,k Liviu Neagu,k Markus Schoffler,l Gregor Kastirke,l

Xiao-Jing Liu,m Artem Rudenko,n Shigeki Owada,d Tetsuo Katayama,o Tadashi Togashi,o

Kensuke Tono,o Makina Yabashi,d Hirohiko Konob and Kiyoshi Ueda *ad

Coulomb explosion of diiodomethane CH2I2 molecules irradiated by ultrashort and intense X-ray pulses from SACLA,

the Japanese X-ray free electron laser facility, was investigated by multi-ion coincidence measurements and self-

consistent charge density-functional-based tight-binding (SCC-DFTB) simulations. The diiodomethane molecule,

containing two heavy-atom X-ray absorbing sites, exhibits a rather different charge generation and nuclear motion

dynamics compared to iodomethane CH3I with only a single heavy atom, as studied earlier. We focus on charge

creation and distribution in CH2I2 in comparison to CH3I. The release of kinetic energy into atomic ion fragments is

also studied by comparing SCC-DFTB simulations with the experiment. Compared to earlier simulations, several

key enhancements are made, such as the introduction of a bond axis recoil model, where vibrational energy

generated during charge creation processes induces only bond stretching or shrinking. We also propose an

analytical Coulomb energy partition model to extract the essential mechanism of Coulomb explosion of molecules

from the computed and the experimentally measured kinetic energies of fragment atomic ions by partitioning

each pair Coulomb interaction energy into two ions of the pair under the constraint of momentum conservation.

Effective internuclear distances assigned to individual fragment ions at the critical moment of the Coulomb

explosion are then estimated from the average kinetic energies of the ions. We demonstrate, with good agreement

between the experiment and the SCC-DFTB simulation, how the more heavily charged iodine fragments and their

interplay define the characteristic features of the Coulomb explosion of CH2I2. The present study also confirms

earlier findings concerning the magnitude of bond elongation in the ultrashort X-ray pulse duration, showing that

structural damage to all but C–H bonds does not develop to a noticeable degree in the pulse length of B10 fs.

a Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan. E-mail: ueda@tagen.tohoku.ac.jp; Fax: +81-22-217-5380;

Tel: +81-22-217-5381b Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japanc Department of Physics and Astronomy, University of Turku, Turku FI-20014, Finlandd RIKEN SPring-8 Center, Sayo, Hyogo 679-5148, Japane Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japanf Department of Physical Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japang Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japanh Institute for Materials Research, Tohoku University, Sendai 980-8577, Japani Institute of Physics, University of Tartu, 50411 Tartu, Estoniaj Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, FR-91192 Gif-sur-Yvette Cedex, Francek Extreme Light Infrastructure – Nuclear Physics (ELI-NP), ‘‘Horia Hulubei’’ National Institute for Physics and Nuclear Engineering, 30 Reactorului Street,

RO-077125 Magurele, Jud. Ilfov, Romanial Institut fur Kernphysik, J. W. Goethe Universitat, Max-von-Laue-Str. 1, Frankfurt D-60438, Germanym School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, People’s Republic of Chinan J. R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, Kansas 66506, USAo Japan Synchrotron Radiation Research Institute (JASRI), Sayo, Hyogo 679-5198, Japan

† Electronic supplementary information (ESI) available: (1) Electric field effects of the XFEL pulse on electronic and nuclear dynamics, (2) on the accuracy of theSCC-DFTB method, (3) optimal value of the charge build-up time t, (4) total amount of injected kinetic energy in the SCC-DFTB approach, (5) role of the addition ofrepulsive kinetic energy. See DOI: 10.1039/c7cp01669g

Received 15th March 2017,Accepted 28th April 2017

DOI: 10.1039/c7cp01669g

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1 Introduction

The advent of X-ray free-electron lasers (XFELs),1,2 namely LinacCoherent Light Source (LCLS) in the USA and SPring-8 AngstromCompact free electron LAser (SACLA) in Japan, opened newavenues for research fields such as structural determination ofnon-crystallized samples3–5 and of various forms of matter intransient states.6–10 Highly relevant to these two topics is theshort-time behavior of matter exposed to such extreme intensities.X-ray absorption leads to the breakage of chemical bonds,geometrical changes, and distortions of electron distributionsthat manifest the deterioration of the original object. A centralquestion in this context is the time scale on which the originalobject’s structure is preserved. If the structure of the object is tobe determined, it should be determined experimentally beforedistortion occurs.11–13

The new regime of X-ray intensities provided by XFEL pulsesallows us to investigate new research fields, namely the study ofthe interaction between intense X-rays and various forms ofmatter.14–23 Understanding ultrafast reactions induced by an XFELpulse is of fundamental interest as well as of crucial importancefor the use of XFEL pulses for structural determination asdescribed above. These reactions include a complex interplaybetween electronic and nuclear motions. X-ray absorption initiallycreates a core hole at a specific atomic site. Then electronicrelaxations, such as Auger processes, follow. An XFEL pulse is sointense that it can cause multiple, possibly overlapping cycles ofcore-level photoemission and Auger cascades.

To study the coupled motion of electrons and ions inducedby an intense XFEL pulse, a single molecule composed of a smallnumber of atoms is the ideal target, as various levels of theory andexperimental methods are available. Erk et al. investigated ionizationand fragmentation of methylselenol (CH3SeH) molecules by intense(o1017 W cm�2), 5 fs long X-ray pulses of 2 keV energy at theLCLS, using coincident ion momentum spectroscopy.19 We alsoinvestigated the reaction dynamics of iodomethane (CH3I), thesimplest I-substituted hydrocarbon, and 5-iodouracil (C4H3IN2O2,abbreviated as 5-IU), a more complex molecule of biologicalrelevance, irradiated by intense (o1017 W cm�2), 10 fs long X-raypulses of 5.5 keV energy at SACLA, using coincident ion momentumspectroscopy.24–26 We reported that the observed momentumcorrelation maps for both molecules were well reproduced by aclassical Coulomb explosion model including charge evolution(CCE-CE), which accounts for the concerted dynamics of chargebuild-up, charge redistribution and nuclear motion. We haveconcluded that charge build-up takes B10 fs while the charge isredistributed among atoms within only a few fs, based on the CCE-CE model calculations that reproduced our experiments.24,25 We alsoadopted a self-consistent charge density-functional-based tight-binding (SCC-DFTB) method to treat the fragmentation of highlycharged 5-IU ions created by XFEL pulses and found that ourSCC-DFTB modelling, in which the influence of molecular bondsthat were neglected in CCE-CE is taken into account, reproducesthe experimental results better than the CCE-CE method.26

In the present study, we extend the methodology describedabove to diiodomethane (CH2I2), the simplest hydrocarbon

molecule in which two iodine atoms are substituted. We aimat finding the effect of having two X-ray absorption sites on thecharge build-up and charge redistribution, and on the energysharing in the Coulomb explosion processes, i.e., the radiationdamage at the atomic level. We intend to pin down these effectsby comparing the results obtained for CH2I2 with those CH3Iwith the help of the SCC-DFTB calculations.

Sections 2 and 3 describe the experiment and theory, respectively.The experimental and theoretical results are presented in Section 4to reveal the detailed mechanisms of the Coulomb explosion ofCH2I2 and CH3I. Concluding remarks are given in Section 5.

2 Experiment

The experiment was carried out at the experimental hutch 4 (EH4)of beam line 3 (BL3) of SACLA.27,28 The XFEL beam is focused bythe Kirkpatrick–Baez (KB) mirror system29 to a focal size of 0.9 mm(FWHM) in diameter. The photon energy was set at 5.5 keV and thephoton bandwidth was about 20 eV (FWHM). The repetition rate ofthe XFEL pulses was 30 Hz. The pulse length was not measuredbut was estimated to be about 10 fs (FWHM).30 XFEL pulseenergies were measured using a beam position monitor31 locatedupstream of the beam line. The monitor was calibrated using acalorimeter so that output signals from the monitor could betransformed into the absolute value of the pulse energy.32 Themeasured value in this experiment was 5.7 � 102 mJ per pulse onaverage. The shot-to-shot pulse energy fluctuation was about�10% (21% FWHM). Note that the pulse energy is not measuredat the interaction point but upstream, and that losses occur due tobeam transport and diagnostics. The peak fluence at the reactionpoint was 30 mJ mm�2 on average. The absolute value of the peakfluence was calibrated just before the experiment by a well-established calibration procedure using argon.20,33

Diiodomethane (99.7%) was purchased from Nacalai Tesque,Inc. and used without further purification. The gas phase samplewas introduced into the focal point of the XFEL pulses as a pulsedsupersonic gas jet seeded in helium gas. The ions were detectedusing a multi-coincidence recoil ion momentum spectrometer tomeasure three-dimensional momenta for each fragment ion. Themolecular beam was crossed with the focused XFEL beam at thereaction point, and the emitted ions were projected by electric fieldsonto a microchannel plate (MCP) detector, in front of a three-layer-type delay-line anode (HEX80 from Roentdek GmbH).34 We usedvelocity-map-imaging (VMI) electric field conditions.35 Signals fromthe delay-line anode and MCPs were recorded using a digitizer andanalyzed using a software discriminator.36 The arrival time and thearrival position of each ion were determined and allowed us toextract the three-dimensional momentum of each ion. With thevoltage settings of the spectrometer, we could extract all carbon andiodine ions ejected in all directions, while protons with kineticenergies above B80 eV could not be fully collected.

3 Theory

One of the theoretical approaches we developed to simulate thedynamics of Coulomb explosion26,37 is an adaptation of the

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density-functional-based tight-binding (DFTB) method for electronicstructure calculations.38,39 We applied it to on-the-fly classicaltrajectory calculations for the XFEL-induced Coulomb explosion of5-IU molecules while incorporating key physical processes into thetheoretical framework.26 The obtained kinetic energy distributionsand momentum correlations of fragment ions were in goodagreement with the experimental results.26 The DFTB method iscomputationally extremely fast and well reproduces the resultsof the density functional theory (DFT) to describe molecularstructures or chemical bonds. In the DFTB method, the Kohn–Sham total energy is expanded with respect to electron densityfluctuation. We have used the second-order expansion method,called the second-order SCC-DFTB method, where the chargedistribution in a molecule is obtained in an iterative self-consistentmanner by taking into account the charge interactions betweenatoms. The forces on atoms, used for molecular dynamics (MD)simulation of the Coulomb explosion, are calculated by SCC-DFTB.This type of MD simulation is further abbreviated as SCC-DFTB/MD.

In previous experiments by Motomura et al.24 and presentexperiments, a few photons were absorbed within the XFELpulse duration (B10 fs) by the deep atomic inner shells (mainly theL-shell) of iodine atoms. In parallel, and partly also subsequently tothe XFEL pulse, Auger cascades take place to generate multiplecharges, with a large number of decay channels available. Inprevious studies,24,25 the charge multiplication process wasmodeled by assuming that the total charge of a molecule attime t, Qtot(t), increases with time t as

Qtot(t) = Qmax(1 � exp(�t/t)) (1)

where t is a charge build-up time constant and Qmax is the finalcharge of the whole molecule. To incorporate the effects ofionization into the DFTB approach, we have employed a sequentialionization model26,40 where the molecule is vertically ionized fromthe q � 1 charge state to the q charge state when Qtot(t) in eqn (1)reaches an integer q.

In eqn (1), we assume that the Auger processes generatecharges by an exponentially decreasing rate while the chargecreation rate by primary photoabsorption is constant within thepulse. Photoabsorption mainly created iodine L-shell holes,which are filled so rapidly (within a few fs) by the initial stepsof the Auger cascades. Since the valence shell becomes depletedafter the initial cascades, the final steps of the cascades aremuch slower, which results in the final charge build-up wellbeyond the end of the applied XFEL pulse of 10 fs duration. Bycontrast, in a long-pulse (for instance, 100 fs) experiment, thevalue of t is governed by the time span of sequential photo-absorption processes. The build-up time constant t incorporatesin general both pulse duration and Auger lifetimes. A moredetailed explanation about the physical origin of eqn (1) is givenin ref. 24.

Nuclear motion (including Coulomb explosion) competeswith such ultrafast Auger cascades. A molecular system exposedto an XFEL pulse experiences different potential surfaces and isconsequently heated during ionization and subsequent electronicrelaxation processes. Part of the electronic energy is converted intovibrational energy. For instance, in the case of C60, a vibrational

energy of 10–20 eV is generated in the molecule for each coreionization event accompanied by an Auger decay process, i.e.,5–10 eV on average per unit charge increase.41 Taking thesevalues as a reference, we added ‘‘artificially’’ vibrational energyupon each ionization as the kinetic energy of atoms in the SCC-DFTB/MD for 5-IU: the experimental kinetic energy distributions andmomentum correlations of fragment ions were well reproduced.26

The effects of core or valence excitation and subsequentelectronic relaxation cannot be explicitly dealt using the DFTBmethod itself, which exclusively relies on valence orbitals (theone we have used to calculate the energies of valence excitedstates is not a TD-DFTB approach). The above-mentionedprocess of adding vibrational energy is implemented in thepresent DFTB approach as follows. The momentum vector -

pj ofatom j is instantaneously changed from -

pj to -pj0 when the

charge of the molecule switches to the higher one in thesequential ionization model:

-pj0 = -

pj + D-pj (2)

where D-pj is a momentum added according to an assumed

value for the vibrational energy acquired upon each ionization.To determine the direction of the momentum vector D-

pj, wefirst assume that the momentum D-pj that atom j receives is thecomposition of momenta generated parallel to the bond axesbetween atom j and its surrounding atoms, following theexperimental observation that only bond stretching and shrinkingare induced by core ionization.42,43 We proposed a diatom-likemomentum conservation model (bond axis recoil model) whereD-

pj is prepared by treating the two atoms connected by a chemicalbond like in a diatomic molecule; the momenta D-

pA(A–B) andD-pB(A–B) parallel to the axis of the chemical bond between atomsA and B are generated randomly under the constraint ofmomentum conservation, i.e., D-

pA(A–B) + D-pB(A–B) = 0. The

same procedure is applied to all chemical bonds. The resultantmomenta work as a force to stretch or shrink a chemical bond.We chose only the momenta contributing to bond stretchingwhen the Coulomb repulsive energy exceeds the energy associatedwith chemical bonding, i.e., when Qtot(t) exceeds a certain chargenumber (in the present simulations, when Qtot(t) Z 8) where allatoms have considerable positive charges. In this case, all thepotential surfaces should be repulsive.

The maximum electric field strength of the applied XFELpulse was extremely high, estimated to be as high as 1.5 �1012 V m�1. The optical cycle-averaged potentials for nuclearmotion,40,44 which are time-dependent, may be significantlydistorted even by the highly oscillating field. Here we considerthe effect of field-induced potential distortion to be virtuallyincluded in the process of adding kinetic energy. See thediscussion in Section S1 in the ESI.†

The magnitudes of D-pj are then scaled by a factor so that the

total kinetic energy of atoms increases by an average vibrationalenergy ei for the ith ionization step. The total kinetic energyadded up to the final charge state Qmax is expressed as

DE ¼XQmax

i¼1ei (3)

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In other words, we assume that the vibrational energy depositedin the molecule increases as Qmax increases. If the bond distancedAB between atoms A and B becomes much larger than itsequilibrium distance Re, we infer that the correspondingchemical bond is broken and no extra momentum is generatedalong the A–B bond axis (because one of the atoms is far fromthe interaction region). In the present treatment, we use thecriterion of dAB 4 3Re. The vibrational energy actually added forthe ith ionization step is thus given by

ei = e(Ni/NCB) (4)

where e is the initially assumed energy to be added per ionization,NCB is the number of chemical bonds of the neutral molecule,and Ni is the number of chemical bonds that survive at the ithionization step. If the acquired vibrational energy DE is largerthan the atomization energy DHa of the neutral molecule, themolecule is immediately decomposed into individual atoms. AsDE approaches DHa, all atoms are separated so that vibrationalenergy is no longer accumulated upon further ionization. Theupper limit of DE is hence BDHa. The final results of thenumerical simulation do not depend on the value of e severelyas long as DE reaches BDHa. In the present study, we have usede = 6 eV.

In the DFTB approach, charge redistribution in real time isignored and it is assumed that the electronic state instantaneouslyrelaxes to the ground electronic state or an electronic statedistribution characterized by the electronic temperature Te, whichrepresents the width of the Fermi–Dirac distribution. The chargedistribution is thus in the ground electronic state or the relaxedelectronic state distribution of the instantaneous molecularstructure. The value of Te should be in the range from a feweV to several eV, as high as the energies of excited states, toinclude the effects of populated excited states on the chargedistribution. The optimal value of Te for 5-IU was B6 eV.26 Inthe present simulations, Te is set to be 6 eV for all charge states.

In the present study, we carried out all DFTB calculations byusing the DFTB+ program package (ver. 1.2.2).45 The adoptedSlater–Koster parameter sets for two-center integrals werehalorg-0-146 and mio-1-1.38 The initial positions and velocitiesof the atoms in the neutral molecule just before interactionwith the XFEL pulse are taken from an equilibrium ensemblesampled from SCC-DFTB/MD trajectories at a given temperatureT. Here we set T = 300 K. The kinetic energy distributions offragment ions for each charge state of CH2I2 and CH3I areaverages over 1000 trajectories. The time step Dt for SCC-DFTB/MD was 0.1 fs.

4 Results and discussion4.1 Charge distributions

Let us first review the fragmentation pattern of multiplecharged CH2I2. Fig. 1(a) depicts the ion time-of-flight (TOF)spectrum of CH2I2 where we can see that atomic fragments H+,Cl+ (l = 1–4) and Im+ (m = 1–8) dominate, while only a smallnumber of the molecular fragments CH2

+ and CH2I+ are present

together with the parent ion. It is not clear from this spectrumwhether charge states higher than I7+ are present, since I8+ andI9+ overlap with the peaks of possible impurity ions O+ and ofmolecular fragment ions CH2

+, respectively. I10+ may also beembedded in a large peak of C+. We can however extract triplecoincidence events of carbon and two iodine ions from all ionsrecorded in the coincidence mode with the help of momentumfiltering.24 The TOF spectrum of ions in all triple coincidenceevents is shown in Fig. 1(b). In this filtered spectrum, molecularfragment ions and residual gas ions are absent and we can nowsee that I8+ charge states are present while ions charged higherthan +9 are absent; the number of triple-coincidence events thatinvolve highly charged iodine ions (m Z +9) is at the statisticalnoise level if there are any events.

From the coincidence data set, charge distributions can beextracted at various levels of detail. At first we consider the finaltotal charge Qfin of the molecule, comparing it with the resultsof CH3I.24 In the following, the experimental data set for CH3Ifrom ref. 24 is used for comparison. Before making thesecomparisons, let us outline the general assumptions. Firstly,the XFEL field conditions for the experiments with the twosamples were very similar in terms of peak fluence and beamfocusing (small differences will be accounted for below). Secondly,the X-ray absorption cross-section of CH2I2 is expected to beroughly the double of the cross-section of CH3I at 5.5 keV, atwhich energy I 2p ionization is the dominant photoprocess.Thirdly, it would create a formidable experimental challenge toinclude all ions in a coincident set and therefore we do notexplicitly measure the charge carried by the hydrogen fragments.We thus resort to the assumption that at sufficiently high finalcharge states, all hydrogen atoms always become charged,of which charge can then be implicitly added as such to the

Fig. 1 Ion time-of-flight (TOF) spectra of CH2I2 recorded at 5.5 keV ofXFEL photon energy, plotted on a log scale. (a) Non-coincident ionspectrum; (b) spectrum reconstructed of three atomic ions Cl+, Im+ andIn+ recorded in coincidence.

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measured charge in the triple (in CH2I2) or double (in CH3I) ioncoincidences. This assumption is expected to be reasonable forQfin Z 8, according to the present DFTB calculations. Theprevious experimental results for CH3I24 also suggest that thisis a suitable assumption when the combined charge of thecarbon and iodine ions exceeds +4.

In Fig. 2(a) total counts of the coincidence events are plottedas a function of the finally generated charge Qfin of themolecule. For CH2I2, the ions explicitly included are from triplecoincidences of Cl+, Im+ and In+, and for CH3I they are fromdouble coincidences of Cl+ and Im+. The final total molecularcharge Qfin (i.e., Qmax of eqn (1) in DFTB/MD) reached viamultiple ionization (as described below) is given on theabscissa as l + m + n + 2 for CH2I2 and l + m + 3 for CH3I,therefore assuming that all hydrogen fragments carry unitcharge. At lower final charges, however, the fraction of neutralhydrogen fragments becomes significant. The actual finalcharge for the point at Qfin = 5, for example, is close to +4 forboth CH2I2 and CH3I, according to the present DFTB estimates.In such situations, a direct comparison of the lowest data pointsof the two molecules in Fig. 2 might not be valid.

Let us now concentrate on the coincident yield curves forfinal charges Qfin Z 8, at which value the curves are alsonormalized to equal count. We can see that starting fromQfin C 10 the yields in the CH2I2 sample become increasinglyhigher, a tendency better quantified by taking the ratio of theion yields. In Fig. 2(b), the ratio of the CH2I2 to CH3I coincidentyields is plotted (and it is unity at the normalization point ofQfin = 8). The point of interest here is to relate this divergencein the charge production in the two molecules to different

multiphoton absorption characteristics. In a previous experiment,20

we carried out the charge distribution measurement for xenonatoms under similar experimental conditions. From the ion yieldrecorded as a function of the peak fluence, we found that chargestates as high as Xe8+ are still created predominantly by singlephoton absorption. At the same photon energy of 5.5 keV, the 2psubshell of xenon has the highest photoionization cross-section.Then the L2,3MM Auger decay can occur followed by the MNN andNOO Auger decay. Such Auger cascades can multiply the initialsingle charge up to Xe8+. We expect such Auger cascades to takeplace also in the iodine absorption sites of CH3I and CH2I2, sincethe only difference between the electronic structures of iodine andxenon is one 5p electron less in the former. Thus, the followinganalysis of CH3I and CH2I2 is based on the premise that final chargestates of up to +8 are created mainly by single photon absorption.

The abrupt increase in the coincident ion yield ratio aboveQfin Z 12 can hence be attributed to the different characteristicsof sequential multiphoton absorption in the two molecules.While the single-photon absorption probability p1 dependslinearly on the absorption cross section s and on the X-rayfluence I (p1 p s � I), multiphoton absorption probabilities arenonlinear: pN B (s � I)N, where N is the number of photonsabsorbed. According to our initial assumptions, s(CH2I2) E2s(CH3I). The average peak fluences of the XFEL pulses in theCH2I2 and CH3I experiments were 30 mJ mm�2 and 26 mJ mm�2,respectively. Taking into account these differences in s and I,the ratio of single-photon absorption probabilities is expected tobe p1(CH2I2)/p1(CH3I) = 2.3 (= 2 � 30/26), for two-photonprobabilities p2(CH2I2)/p2(CH3I) = 5.3 (= 2.32) and for three-photon probabilities p3(CH2I2)/p3(CH3I) = 12 (= 2.33). Since theratio curve in Fig. 2(b) is normalized to unity at a single-photonabsorption point, its value in the two-photon absorption regimeis expected to be 2.3 and, in the three-photon absorptionregime, 5.3.

The above-obtained yield ratio values, characteristic of a pure1-, 2- or 3-photon regime, are marked in Fig. 2(b) by horizontaldashed lines. Although in the actual curve these regimes are, ofcourse, partly overlapping, the lines still serve as a guideindicating where the transitions to higher-order multiphotonprocesses occur. This comparison of charge generation inmolecules with one and two X-ray absorption sites is a differentand alternative approach to scrutinizing the multitude of chargegenerating relaxation pathways in ref. 16, 20, e.g. xenon atoms.

The observed effect of the roughly doubled cross-section inCH2I2 is then, expectedly, that a larger fraction of dissociationevents is induced by multiphoton, rather than single photonabsorption. At the used fluences, such an effect does not yethave profound consequences on the dissociation dynamics andon the rate at which structural damage takes place, but witheven higher XFEL fluences of future sources, the change in thedynamics could be dramatic, when, for example, a differentnumber of hydrogen atoms in organic molecules are substitutedwith heavy elements.

After studying the final total charge distributions, we nowinvestigate the charge partitioning between the iodine atomicfragments as well as between the carbon and the iodine fragments.

Fig. 2 (a) Total triple coincidence counts of Cl+, Im+ and In+ recorded forCH2I2 and total double coincidence counts of Cl+ and Im+ for CH3I, as afunction of the final total charge, Qfin, estimated as l + m + n + 2 for CH2I2and l + m + 3 for CH3I. (b) Ratio in the total coincidence counts of CH2I2 tothose of CH3I normalized at Qfin = +8. Error bars represent statisticaluncertainties given by standard deviation. The experimental values forCH3I are cited from Fig. 2 of ref. 24.

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Fig. 3(a) presents a summary of the C3+, Im+, In+ ion pairs found inthe triple coincidence events of CH2I2. One can see that the highestpair counts do not occur with equal charge partitioning. This,however, should not be taken to mean that there is a fundamentalreason favoring the uneven partitioning. Rather, the reason isstatistical: there are two permutations, for example, for creatingan I4+–I6+ ion pair, while only one possibility exists for an I5+–I5+

ion pair. Fig. 3(a) in fact depicts relatively symmetric chargedistributions demonstrating a rather efficient equalization ofcharge. Such efficient charge redistribution in a molecule mustmean strong electronic interaction, such as in the form ofmolecular orbital formation that are then involved in the laterstages of the Auger cascades. But it is also clear from the figurethat charge equalization is not always complete – it can beinterrupted by the concurrent dissociation process, as discussedlater. Fig. 3(b) shows the coincident yield of carbon ions as afunction of the combined charge of the two iodine atoms inCH2I2. It also shows the average combined charge values m + nof the iodine ions detected together with differently chargedcarbon ions. Charge sharing among carbon and iodine atomsmay be better seen by comparing, in all triple coincidenceevents with a final charge Qfin = m + n + l + 2 for CH2I2, the

average charges of iodine and carbon ions. Such a comparisonis given in Fig. 4, plotting the average charge of iodine versusthat of carbon, with individual data points corresponding tovarious values of Qfin. Some values of Qfin are also marked at thecorresponding data points. The figure shows also an analogouscurve for CH3I, as well as the results from the DFTB/MDsimulations for both molecules. The charge distribution thatthe SCC-DFTB approach affords is an averaged fractional oneover the electronic temperature Te but almost unique afterCoulomb explosion. Any special procedures to round off thefractional charges of fragments to integers were not employed inthis study. The appearance of fractional charges is partly due tothe introduction of electronic temperature. However, Te E 0does not provide a charge distribution like in the experiment.Even if the fragment charges are integers, only one chargecombination is allowed in the present approach.

The experimental curves show, for Qfin Z 8, a close-to-lineardependence and also, that the iodine/carbon charge ratio islower in CH2I2 than in CH3I. This is again expected if oneconsiders single-photon ionization: in CH2I2 the final chargegenerated by the ‘‘absorber’’ iodine is gradually transferred tothe ‘‘spectator’’ iodine, thus lowering the average charge periodine atom.

The theoretical values in Fig. 4 are considerably lower thanthe experimental ones for both molecules. The reason why thetheoretical charges of the iodine ions are lower may stem fromthe fact that the DFTB method allows only the valence electronsto be ionized. The maximum charge of an iodine ion is then +7,while that of a carbon ion is +4. In the experiment, we couldclearly identify iodine ions with the charge up to +15 for CH3Iand +8 for CH2I2, while the highest observed charge of a carbonion is +4 for both CH3I and CH2I2. In the theoretical calculations,the charge of iodine ions is thus underestimated more withincreasing final charge.

Another observation from Fig. 4 is that the theoretical chargeratio between an iodine ion and a carbon ion for CH2I2 is nearlyidentical to that for CH3I. This can be explained as follows: in thepresent DFTB treatment the electronic state of a molecule isdescribed as a stationary state in quantum mechanics. The chargesof two iodine atoms in CH2I2 are those in an ‘‘equilibrium’’ stateand thus the iodine charges become exactly the same as themolecule expands. The ratios of the charges between the iodineand the carbon ions are determined mostly by the electronicconfigurations of these two atoms and thus they are almost thesame for CH2I2 and CH3I, irrespective of the number of iodineatoms. In the experiment, on the contrary, two iodine ions do notalways have the same charge but a broad distribution of chargepartitioning is observed (Fig. 2) instead. As discussed in ref. 24 and25, the charge builds up first at one iodine site and then spreadsout over the entire molecule, e.g., via molecular Auger transitionsthat occur in the later stages of the Auger cascades. These chargebuild-up and redistribution processes compete with fast dis-sociation via repulsive Coulomb forces between highly chargedions. Because of the time lag of charge redistribution, the chargeof the second iodine ion in CH2I2 may not reach the level of thefirst one, or the level determined by the iodine atomic nature.

Fig. 3 (a) Triple coincidence counts of C3+ and two iodine ions Im+ andIn+ stemming from a CH2I2 molecule. (b) Distributions for the charge summ + n of two iodine ions Im+ and In+ recorded in coincidence with Cl+

with l = 1, 2, 3 and 4. A colored vertical arrow with a number indicatesthe average value of m + n for the distribution represented by the samecolor line. Error bars represent statistical uncertainties given by standarddeviation.

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In the present theoretical model, the charge redistribution isassumed to be instantaneous (i.e., no time lag), though thecharge build-up is taken into account empirically (see eqn (1)).The time lag of the charge redistribution to the second iodineion may result in a lower charge than that of the first one andexplains why the average charges of iodine ions are lower forCH2I2 than for CH3I.

4.2 Ion kinetic energy distributions

From the triple coincidence data of CH2I2 for the events ofdifferent final charges Qfin, we can also extract the kinetic energydistributions of individual ions, as well as the distributions ofkinetic energy sum for these ions. As typical examples wepresent the results for the final charges Qfin = 9 and 14 inFig. 5. The final charge for the experimental data is an expectedone given by l + m + n + 2 for CH2I2. It is worth noting that thevalues of l + m + n from theory are not necessarily integer, sincetheoretical calculations are performed for integer numbers offinal total charges for the whole molecules (Qfin = Qmax).

Let us first focus on the distributions of the total kineticenergies of the carbon and the two iodine ions (Fig. 5(a) and(c)). The center and the width of the distribution increase withthe increase in the final charge, while the shape of the dis-tribution remains nearly the same irrespective of the finalcharge. These observed behaviors are reproduced well byDFTB/MD, illustrating the validity of the present theoreticalapproach. To evaluate the accuracy of the SCC-DFTB method,we performed electronic structure calculations for the potential

surfaces of CH2I2 (and CH3I). The agreement between the SCC-DFTB and B3LYP/6-311G(d,p) methods is satisfactory, consideringthe large kinetic energies of fragment ions, which range over afew hundred eV. For comparison between the two methods, thedissociation energies calculated for C–I stretching and C–Hstretching are given in Section S2 in the ESI.†

We now turn to examine the kinetic energy distributions ofindividual ion species. The peak energies of the experimentalkinetic energy distributions of carbon ions are roughly twice aslarge as those of iodine ions. The centers and widths of bothcarbon and iodine ions gradually increase with increasing finalcharge, while the shapes of these distributions remain nearlythe same. The kinetic energies of the ions are roughly propor-tional to the square of the final charge. These behaviors arepractically the same as for the sum of ion kinetic energies. Thekinetic energy distributions of iodine ions in the DFTB/MDresults are, however, slightly shifted to lower energies compared tothe experimental distributions, whereas the theoretical energiesfor carbon ions are slightly higher than the experimental ones. Thedisagreement may stem from the fact that the theoretical ratiosbetween carbon and iodine charges do not agree well with the

Fig. 4 Charge sharing between carbon and iodine ions for CH2I2 andCH3I. The average charges of an iodine ion are correlated with those of acarbon ion. The final charges of corresponding parent molecular ions areindicated with arrows. The charge ratios of an iodine ion to a carbon ion inthe theoretical calculations are lower than the experimental ones. Theexperimental ratios for CH3I are higher than those for CH2I2 whereas theyare nearly equal to each other in the DFTB/MD approach. The experimentalratios for CH3I are constructed from Fig. 2 of ref. 24.

Fig. 5 (a and c) Distributions of kinetic energy sum of carbon (Cl+) andtwo iodine (Im+ and In+) ions of CH2I2; (b and d) kinetic energy distributionsof individual carbon and iodine ions. The final charges Qfin = l + m + n + 2are +9 for (a) and (b) and +14 for (c) and (d). In (a) and (c), theexperimentally measured distributions are denoted by red solid lines andthe theoretical ones are denoted by blue dashed lines. In (b) and (d), redsolid lines indicate the experimental distributions for iodine ions, blue linesindicate those for carbon ions; pink dashed lines indicate the distributionsfor iodine ions obtained by DFTB/MD and navy dashed lines indicate thosefor carbon ions. Vertical lines indicate the kinetic energies of individual ionsobtained by using the classical Coulomb explosion model combined withthe sequential ionization model. Orange dashed vertical lines indicate thekinetic energies of an iodine ion or carbon ion when the point charges ofions are taken from the experimentally determined average charges.Green dashed vertical lines indicate the kinetic energies of an iodine ionor carbon ion when the point charges of ions are taken from the finalcharges of fragment ions in the DFTB/MD simulations.

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experimental ratios as discussed above (see Fig. 4). To examine thishypothesis we carried out also classical MD calculations, whereonly Coulomb interactions between the ions are treated as point-charge interaction. In the calculations, the sequential ionizationmodel is adopted and the charge build-up time is assumed to be10 fs,24,25 as employed in the DFTB/MD approach. As indicated inFig. 5(b) and (d), the kinetic energies obtained by classical MDsimulations agree fairly well with the centers of the experimentaldistributions when the point charges of individual ions areassumed to be the same as the experimentally measured ones,whereas they provide reasonable agreement with those of theDFTB/MD distributions when the point charges of individual ionsare assumed to be the same as the theoretical ones.

For comparison, we present in Fig. 6 the kinetic energydistributions of CH3I for different final charges: l + m + 3 = 9and 14. The dependences of the experimental and theoreticalion kinetic energy distributions of CH3I on the final charge aresimilar to those of CH2I2. The centers of the kinetic energysums for CH2I2 (Fig. 5(a) and (c)) are larger in energy than thosefor CH3I (Fig. 6(a) and (c)). The difference is the kinetic energyof an iodine ion of CH2I2. A careful inspection reveals that thecenters of the iodine kinetic energy distributions for CH2I2

(Fig. 5(b) and (d)) are nearly three times higher in energy thanthose for CH3I (Fig. 6(b) and (d)), while the carbon kineticenergies for CH2I2 are only slightly higher than those for CH3I.

The present SCC-DFTB simulation is carried out in theframework of eqn (1)–(4). We examined how the calculatedkinetic energies of fragment ions depend on the charge build-upconstant t. As t becomes larger, the kinetic energy distributionof each fragment ion is shifted toward the lower energy side,which reflects the Coulomb explosion at a more expandedstructure. By carrying out SCC-DFTB/MD simulations at differentt, we found that the deviations from the experimental kineticenergy distributions of fragment ions are minimized aroundt = 10 fs for both CH2I2 and CH3I. See the details in Section S3in the ESI.† This value is in accordance with the optimal one of tobtained in ref. 24, which well reproduces experimental results suchas the charge state distributions of carbon and iodine ions for Cl+–Im+ coincidences. The optimal value of t E 10 fs for eqn (1) meansthat in the XFEL pulse duration of 10 fs the molecule does not reachthe final charge state. The charge of the molecule at the end of the10 fs pulse is about 2/3 of its final charge, indicating that the presentexperiment lies in the intermediate regime where the time scale ofinternal Auger decays takes part in the determination of t, as well asthe time span of sequential photoabsorption processes.

We have confirmed that the vibrational energy deposited inthe molecule is almost proportional to the final charge of themolecule. See Section S4 in the ESI.† We examined the role ofthe extra addition of repulsive kinetic energy for Qtot(t) Z 8 bycomparing the two cases with and without adding artificialkinetic energies for the final charges Qmax Z 8. From thediscussion in Section S5 in the ESI,† we concluded that theaddition of extra kinetic energy for Qtot(t) Z 8 changes thekinetic energy distributions only slightly.

The SCC-DFTB/MD kinetic energy distributions presentedin Fig. 5 and 6 are those obtained at a propagation time Tend

of 400 fs. By making the propagation time longer up to 4 ps atQmax = 6, 10 and 14, we checked the convergence of the kineticenergies of fragments. The kinetic energy distributions of ionswere shifted to the higher energy side. The difference betweenthe converged kinetic energy and that obtained at Tend = 400 fsincreases with decreasing Qmax. The kinetic energy distributionsof carbon ions were almost converged at Tend = 400 fs. Forexample, for Qmax = 6, the average kinetic energy at Tend = 4 ps islarger than that at Tend = 400 fs only by B4%; these two kineticenergy distributions almost overlap with each other. For thekinetic energy distributions of iodine ions, the increases were15%, 8% and 6% at Qmax = 6, 10, 14, respectively, when Tend ischanged from 400 fs to 4 ps. The kinetic energy distributions atTend = 4 ps are a little closer to the experimental ones.

In order to assess the magnitudes of Coulomb interactionsin CH3I and CH2I2, we plotted in Fig. 7 the average total kineticenergy K of carbon and iodine ions for the experimental andDFTB/MD results as a function of the final charge, Qfin = l + m +n + 2 for CH2I2 and Qfin = l + m + 3 for CH3I. The kinetic energiesof hydrogen ions are not included. The four curves increasequadratically with Qfin resulting in the slope of two in thelogarithmic plots. The data points for Qfin r 7 are not shown inthe figure because the estimates Qfin = l + m + n + 2 for CH2I2 andQfin = l + m + 3 for CH3I are no more valid and Qfin is closer to l +m + n + 1 for CH2I2 and Qfin = l + m + 2 for CH3I for Qfin r 7. ForQfin Z 8, agreement between theory and experiment is fairlygood. The kinetic energies of individual ions are also nearlyproportional to the square of the final charge, as in the case ofkinetic energy sums. For more details, see the next section.

To illustrate the general dependence of ion kinetic energieson the final charge and also to pin down the origin of the

Fig. 6 (a and c) Distributions of kinetic energy sum of carbon (Cl+) andiodine (Im+) ions of CH3I; (b and d) kinetic energy distributions of individualcarbon and iodine ions. The final charges Qfin = l + m + 3 are +9 for (a) and(b) and +14 for (c) and (d). The other notations are the same as in Fig. 5. Thedata used to generate the experimental distributions are the same as thoseanalyzed in ref. 24.

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difference in kinetic energy generation between the two molecules,we analyze the kinetic energy distributions of fragment ionsusing a simple Coulomb energy partition model described inthe next subsection, where the analysis is based on the datapoints of Qfin Z 8.

4.3 Coulomb energy partition model

Since the dependence of the kinetic energy sum K on the finalcharge is dominated by a quadratic term Qfin

2 we fitted K to afunction of Qfin

2. The increases in K are expressed in units of eVas follows: for CH3I, K = �22.3 + 0.82Qfin

2 (experiment) andK = �5.68 + 0.65Qfin

2 (DFTB/MD); for CH2I2, K = �16.5 +0.91Qfin

2 (experiment) and K = 8.42 + 0.77Qfin2 (DFTB/MD).

This expansion also works for the kinetic energy of eachion. For example, the kinetic energy of an iodine ion, KI, isexpressed as KI = �2.67 + 0.11Qfin

2 for CH3I and KI = �6.32 +0.30Qfin

2 for CH2I2 (experiment); KI = �1.22 + 0.08Qfin2 for CH3I

and KI = �6.32 + 0.23Qfin2 for CH2I2 (DFTB/MD). KI is about

three times larger for CH2I2 than for CH3I. We conclude thatthe Coulomb interaction is dominant in the generation ofkinetic energy and exceeds the energy of chemical bonds asthe molecule reaches the final charge state. We have confirmedin the DFTB/MD results that the total kinetic energy of the ionsincluding protons, Ktot, can also be approximated by a quadraticform: Ktot = 47.9 + 1.26Qfin

2 for CH3I and by Ktot = 54.4 +1.29Qfin

2 for CH2I2. The total kinetic energy of CH2I2 is onlyslightly higher than that of CH3I. The accuracy of the quadratic

fitting with Qfin justifies the use of simple models, such as theCCE-CE model, that contain only the Coulomb energy to simulatethe dynamical processes of XFEL-induced Coulomb explosion.

Here we propose a simple Coulomb explosion model toextract the essential mechanism of Coulomb explosion of CH3Iand CH2I2 from the experimentally measured kinetic energies offragment atomic ions. In the case of CH3I, there are 10 Coulombinteractions between five ions: QCQI/hRC–Ii, 3QCQH/hRC–Hi,3QIQH/hRI–Hi and 3QHQH/hRH–Hi, where hRC–Ii, hRC–Hi, hRI–Hiand hRH–Hi are the average distances between ions at the momentof Coulomb explosion (for instance, hRC–Ii is the distancebetween the carbon and iodine ions), that is, when the moleculeacquires the final charges QC, QI and QH of carbon, iodine andhydrogen ions or when it is about to Coulomb explode into ions.

We merely partition each pair Coulomb energy into two ionsof the interaction pair under the constraint of momentumconservation, in line with the diatomic-like momentum con-servation model. For instance, the kinetic energies that thecarbon and iodine ions receive from QCQI/hRC–Ii are mI/(mI +mC) � QCQI/hRC–Ii and mC/(mI + mC) � QCQI/hRC–Ii, respectively,where mC is the mass of the carbon ion and mI is the mass ofthe iodine ion. These individual pair interactions, of which thesum is the overall Coulomb repulsion energy, can be groupedinto the Coulomb repulsion energies EC, EI and EH associatedwith carbon, iodine and hydrogen ions:

EC ¼mI

mC þmI

QCQI

RC�Ih i þ3mH

mC þmH

QCQH

RC�Hh i (5)

EI ¼mC

mC þmI

QCQI

RC�Ih i þ3mH

mI þmH

QIQH

RI�Hh i (6)

EH ¼mC

mC þmH

QCQH

RC�Hh i þmI

mI þmH

QIQH

RI�Hh i þ2mH

mH þmH

QHQH

RH�Hh i(7)

The Coulomb repulsion energies EC, EI and EH in eqn (5)–(7) areexpected to be correlated with the final kinetic energies KC, KI

and KH of carbon, iodine and hydrogen ions, though thepresent splitting of Coulomb energy into ions does not reflectthe detailed structural information of the molecule, such as thedirections of bond axes. We found in the DFTB/MD results thatEC, EI and EH in eqn (5)–(7) are nearly proportional to KC, KI andKH, respectively (Ej B Kj/2 for an ion j). We presume that theproportionality between the Coulomb repulsion energy Ej andkinetic energy Kj of an ion j holds in the experimental results aswell. In the following treatment, we set Ej B Kj to make thediscussion as simple as possible, though Ej o Kj. The experi-mental values of KC, KI and KH can be determined from theaverage kinetic energies of the ions in the kinetic energydistributions of individual ions or the observed peak values.The final charges QC, QI and QH are also theoretically andexperimentally available.

The average distances hRC–Ii, hRC–Hi, hRI–Hi and hRH–Hi areexperimentally unknown but may be determined as parametersthat satisfy eqn (5)–(7). In this paper, on one hand, we employ asimple approach where hRC–Ii and hRC–Hi in eqn (5) are replaced

Fig. 7 Charge dependence of the total kinetic energy K of carbon andiodine ions for CH3I and CH2I2: for CH3I, K is the sum of the kineticenergies of a carbon ion and an iodine ion; for CH2I2, the sum of the kineticenergies of a carbon ion and two iodine ions. The value of K is the averagevalue obtained from the distribution function of the total kinetic energy forCH3I or CH2I2. The final charge Qfin is defined as follows: Qmax for theDFTB/MD results whereas, for the experimental results, l + m + 3 for CH3Iand l + m + n + 2 for CH2I2. The data for CH3I used to generate theexperimental distributions are the same as those analyzed in ref. 24.

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by an effective internuclear distance hRCi that is close to theaverage of hRC–Ii and hRC–Hi. Similarly, hRC–Ii and hRI–Hi ineqn (6) are replaced by hRIi, and the distances hRC–Hi, hRI–Hi andhRH–Hi in eqn (7) by hRHi. Following this simplification, we canrecast EC, EI and EH as

EC = hQCQi/hRCi (8)

EI = hQIQi/hRIi (9)

EH = hQHQi/hRHi (10)

where the charge products hQCQi, hQIQi and hQHQi are given by

QCQh i ¼ mI

mC þmIQCQI þ

3mH

mC þmHQCQH (11)

QIQh i ¼ mC

mC þmIQCQI þ

3mH

mI þmHQIQH (12)

QHQh i ¼ mC

mC þmHQCQH þ

mI

mI þmHQIQH þ

2mH

mH þmHQHQH

(13)

These charge products are known quantities. The effectiveinternuclear distances hRCi, hRIi and hRHi in this simplifiedapproach can be roughly estimated from the experimentallydetermined kinetic energies KC, KI and KH alone. It shouldhowever be noted that the effective internuclear distancesdetermined this way are relative ones (to determine themexactly from the experimental results alone, one has to find amethod for evaluating the ratio EC/KC experimentally).

For CH2I2, the charge products in eqn (8)–(10) arereplaced by

QCQh i ¼ 2mI

mC þmIQCQI þ

2mH

mC þmHQCQH (14)

QIQh i ¼ mC

mC þmIQCQI þ

mI

mI þmIQIQI þ

2mH

mI þmHQIQH

(15)

QHQh i ¼ mC

mC þmHQCQH þ

2mI

mI þmHQIQH þ

mH

mH þmHQHQH

(16)

The presence of QIQI � mI/(mI + mI) in eqn (15) is the majordifference from CH3I. We will show that the Coulomb inter-action between the two iodine ions is persistent and plays adecisive role in the acquisition of higher kinetic energy by theiodine ions.

In order to assess the validity of the above simplifiedCoulomb partition model, we now apply it to the results ofthe DFTB/MD simulations. We are now in a position to examinethe relation between the kinetic energy Ej and the charge producthQjQi for each fragment ion j. Fig. 8(a) and (b) are the results forCH3I and CH2I2, respectively. The results obtained by linearfitting are as follows: in the units of eV, KC = 3.70 � hQCQi +8.75, KI = 5.76 � hQIQi + 0.71 and KH = 4.42 � hQHQi + 4.82 forCH3I; KC = 3.91 � hQCQi + 19.11, KI = 3.31 � hQIQi + 1.09 andKH = 3.99 � hQHQi + 8.87 for CH2I2. The relations between Ej

and the charge product hQjQi are nearly linear and the slopesare, roughly speaking, almost independent of the ion species.These features are expected if hRCi, hRIi and hRHi depend onlyweakly on Qmax. The deviation from linearity and the differencein slope are attributed to the nuclear motion occurring in CH3Ior CH2I2.

We have also applied the same procedure to the kineticenergies KC and KI experimentally determined for carbon andiodine ions. The linearity holds well. The following relations areobtained by linear fitting: in the units of eV, KC = 5.15 � hQCQi� 0.47 and KI = 8.21 � hQIQi + 0.08 for CH3I; KC = 4.97 � hQCQi+ 1.65 and KI = 3.97 � hQIQi + 2.14 for CH2I2. These slopes are alittle larger than the corresponding DFTB/MD values.

To extract the nuclear motion from the DFTB/MD results, weevaluated hRCi, hRIi and hRHi as a function of the final chargeQfin = Qmax from the equation hRji = hQjQi/Ej (see eqn (8)–(10)).Ej therein are replaced by Kj � bj, where bj are the interceptswhen Kj are expressed as Kj = ajhQjQi + bj (see the above twoparagraphs). We regard the offset energies bj as non-Coulombicenergies. The evaluated values for CH3I and CH2I2 are indicatedby open symbols in Fig. 9(a) and (b), respectively, which shows

Fig. 8 Kinetic energies of carbon, iodine and hydrogen ions obtained byDFTB/MD as functions of charge products hQCQi, hQIQi and hQHQi ineqn (14)–(16): (a) CH3I; (b) CH2I2. The kinetic energy of an ion increasesnearly linearly with its charge product and the slope is almost independentof ion species. The slope does not change largely between CH3I and CH2I2.

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that hRCi, hRIi and hRHi are almost constant with Qmax. We havealso obtained the effective internuclear distances hRCi and hRIifrom the kinetic energies KC and KI experimentally determinedfor carbon and iodine ions and the charge products hQCQi andhQIQi. We used eqn (8) and (9) and simply replaced EC in eqn (8)by KC � bC and EI in eqn (9) by KI � bI. The obtained effectiveinternuclear distances for CH3I and CH2I2 are shown by closedsymbols in Fig. 9(a) and (b), respectively.

The bond distances at the equilibrium structure of CH3I areas follows: RC–I = 2.136 Å and RC–H = 1.084 Å.47 Although theeffective internuclear distances hRCi, hRIi and hRHi cannot beregarded as the absolute values of internuclear distances,definite correlations between hRIi and hrC–Ii and between hRHiand hrC–Hi are found in the DFTB/MD results for CH3I, wherehrC–Ii and hrC–Hi are trajectory averages of the C–I and C–Hbond distances, respectively. The DFTB/MD effective distancehRIi B 2.5 Å in Fig. 9(a) corresponds to hrC–Ii at t B 13 fs; andhRHiB 3.3 Å corresponds to hrC–Hi at t B 10 fs. The DFTB/MDvalue of hRCi B 3.8 Å is however much longer than hRIi andhRHi (hrC–Ii and hrC–Hi). The reason why hRCic hRIi is ascribedto the tetrahedral structure that the carbon ion is surroundedby four ions. The momenta that the carbon ion receives fromthe surrounding ions are canceled with each other to someextent. The kinetic energy that the carbon ion takes away issmall, compared to the magnitude of the Coulomb repulsionsbetween the carbon ion and its surroundings. The effectivedistance hRCi is thus longer than the actual internucleardistances. On one hand, the dangling heavy iodine ion receivesrecoil from the other four ions almost in one direction oppositeto the carbon atom. This contributes to the generation ofrelatively large kinetic energy of the iodine ion, which makeshRIi shorter. These two factors enhance the difference betweenhRCi and hRIi in CH3I. Although both hRCi and hRIi are intimatelyassociated with the same C–I bond distance, these two effective

distances reflect different physical processes of the Coulombexplosion.

The relation that hRCic hRIi holds in the experimental caseof CH3I as well. The major difference between theory andexperiment is that hRCi and hRIi are rather shorter than theDFTB/MD values. One of the reasons for the faster motion orexplosion in the DFTB/MD simulation is the introduction of theelectronic temperature, which increases the speed of bonddissociation in the early stage. The value of hRIi obtained fromthe experiment is even shorter than the equilibrium C–I distance.This suggests that the nature of the directional recoil of theiodine ion is more distinct in the experiment than in theDFTB/MD simulation.

We next discuss the effective bond distances for CH2I2 areshown in Fig. 9(b). The DFTB/MD effective distance hRIiB 4.3 Åin Fig. 9(b) is much longer than the value in Fig. 9(a). Weattribute this to the I–I repulsion, because this value corre-sponds to hrI–Ii at t B 20 fs. This large shift in hRIi from CH3I toCH2I2 demonstrates that the dominant interaction with aniodine ion or iodine ions drastically changes from C–I repulsionto I–I repulsion. A large shift in hRIi is also observed for theexperimental results, which experimentally reveals that the I–ICoulomb repulsion is dominant over I–C and I–H Coulombrepulsions. The dominance of the I–I Coulomb repulsion is dueto the second term on the rhs of eqn (15), which originates fromthe interaction energy mI/(mI + mI) � QIQI/hRI–Ii assigned to aniodine ion.

The DFTB/MD value of hRHiB 3.5 Å in Fig. 9(b) correspondsto hrC–Hi at t E 9–12 fs; hRCi B 3.5 Å corresponds to hrC–Ii att B 17 fs. The effective distances hRCi and hRHi do not changesignificantly between CH3I and CH2I2. The experimental hRCifor CH2I2 are also almost equal to those for CH3I. In summary,hRCic hRIi for CH3I and hRIic hRCi for CH2I2; only hRIi shiftsto larger values on going from CH3I to CH2I2.

4.4 Time evolution of internuclear distances

From the results of the present theoretical calculations, we canextract time evolution of the internuclear distances duringthe Coulomb explosion process. The trajectory-averaged bonddistances for CH2I2 are shown in Fig. 10 while those for CH3Iare shown in Fig. 11. The C–H distance of CH2I2 is the averagelength of the two C–H bonds and the C–H distance of CH3I isthe average of the three C–H bonds. At first glance, we noticethat the speed of each bond elongation is surprisingly similar,even quantitatively, for these two molecules of the same finalcharge. C–H bonds elongate much faster than C–I bonds whilethe I–I distance in CH2I2 elongates much more slowly.

Let us examine the details focusing on the bond elongationsin the first 10 fs. Note that the time zero (t = 0) corresponds tothe starting point of the charge build-up. Since the chargebuild-up time is 10 fs and the XFEL pulse width is also B10 fs,the first period of 10 fs corresponds to the duration of chargebuild-up under XFEL radiation. The initial C–H, C–I and I–Idistances in CH2I2 are 1.09 Å, 2.20 Å and 3.71 Å, respectively.The C–H, C–I and I–I distances change to 3.0 Å, 2.3 Å and 3.8 Å,respectively, at t E 10 fs. These values are nearly independent

Fig. 9 Effective internuclear distances hRCi, hRIi and hRHi as a function ofthe final charge Qfin of the molecule: (a) CH3I; (b) CH2I2. The final chargeQfin indicates Qmax for the DFTB/MD results and, for the experimentalresults, l + m + 3 for CH3I and l + m + n + 2 for CH2I2. The effectiveinternuclear distances hRji are evaluated by using eqn (8)–(10); theCoulomb repulsion energies Ej are replaced by Kj � bj, where bj are theintercepts of the linear fits of Kj against hQjQi. The experimental values aredenoted by closed symbols and the DFTB/MD values are denoted by opensymbols. The data for CH3I used to generate the experimental distributionsare the same as those analyzed in ref. 24.

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of the final charge Qfin = l + m + n + 2. The C–I and I–I distancesare elongated only by B0.1 Å for all final charges (r14) within10 fs of XFEL irradiation; then, dissociation starts rapidly dueto charge build-up. The C–H bonds, on the other hand, arestretched nearly three times at t E 10 fs, compared to the initialC–H distance. The quantitative features of bond elongation forCH3I are practically the same as those for CH2I2. These findings

suggest that the bond elongations, that is, the structural damage,may be negligible, except for the fact that the hydrogen atoms flyaway, in the context of the X-ray structure determination in theXFEL pulse of B10 fs. A unique point for CH2I2 may be that thetwo iodine atoms stay close together for long time, as pointed outin the analysis using the Coulomb energy partition model. Underthese circumstances, an interatomic electronic decay processbetween the two iodine sites might occur. In the present ionyield measurements, however, we could not identify suchprocesses. A time-resolved study, which is currently under progress,has potential to reveal such decay processes.

5 Conclusions

The Coulomb explosion process of CH2I2 induced by ultrashort,intense X-ray free-electron laser pulses was investigated by ioncoincidence measurements and SCC-DFTB simulations. Whilethe SCC-DFTB approach can deal with the reaction dynamicsunder the existence of chemical bonds and Coulomb repulsion,it cannot treat inner ionization and Auger decay on the basis ofthe first principles. These processes are phenomenologicallyintroduced in the present simulation as the charge build-upmodel described by eqn (1): the competition between Coulombexplosion and Auger decay is thus integrated in the theoreticalframework. The kinetic energy distributions calculated by theSCC-DFTB approach reflect the expansion process of the moleculeduring the generation of multiple charges. The efficient SCC-DFTBapproach we developed has successfully captured the dynamicalaspect of the induced Coulomb explosion, thus reproducing theexperimental kinetic energy distributions of fragment ions.

Through the comparison of the results obtained for CH2I2

and CH3I, and by analyzing the kinetic energy distributions onthe basis of the Coulomb energy partition model, we revealedthe characteristic features of the ionization and Coulomb explosionprocesses of CH2I2 originating from two iodine atoms contained inCH2I2. Since the two iodine atoms act as X-ray absorbers, thetriggering process of the Coulomb explosion i.e. multiphotonprocess occurs more effectively. This structural difference alsoinfluences the dynamical aspect. Further analysis of the experi-mental and theoretical results by the Coulomb energy partitionmodel clarified the distinctive difference in the Coulomb explosiondynamics between CH2I2 and CH3I. The effective internucleardistance obtained for an iodine ion in this model is much longerin CH2I2 than in CH3I, which evidences that the dominant Coulombinteraction for an iodine ion in CH2I2 is switched from the C–Irepulsion to the I–I repulsion. The Coulomb energy partition modelis useful to grasp the essence of the Coulomb explosion processes asa result of charge and energy distribution in a molecule. Thus, theexperimental and theoretical approaches integrated in the presentreport provide a new method to explore the mechanism of radiationdamage at the molecular scale.

Author contributions

K. U. conceived the research. T. Ta., E. K., K. M., H. F., K. Nag.,S. W., Y. K., D. I., Y. I., Y. Sak., D. Y., T. N., K. A., Y. Sat., T. U.,

Fig. 10 Time evolution of internuclear distances of C–H, C–I and I–I forCH2I2 for two final charges of Qfin = +9 and +14. The distances are theaverages over DFTB/MD trajectories.

Fig. 11 Time evolution of internuclear distances of C–H and C–I for CH3Ifor two total charges of Qfin = +9 and +14.

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K. Ka., K. Ko., C. N., T. A., L. N., M. S., G. K., X.-J. L. and K. U.prepared and performed the experiment. T. Ta., E. K. andK. M. analyzed the data. K. Nak., K. O., M. K., K. Y. andH. K. developed the simulation method. K. Nak., K. O. andH. K. formulated the Coulomb energy partition model andperformed numerical simulations. S. O., T. K., T. To., K. T.and M. Y. are responsible for SACLA and the SACLA beamline.T. Ta., E. K., H. F., C. M., H. K. and K. U. prepared themanuscript. All authors discussed the results and commentedon the manuscript.

Acknowledgements

The XFEL experiments were performed at the BL3 of SACLAwith the approval of the Japan Synchrotron Radiation ResearchInstitute (JASRI) and the program review committee (no. 2015B8057).This study was supported by the X-ray Free Electron Laser UtilizationResearch Project and the X-ray Free Electron Laser Priority StrategyProgram of the Ministry of Education, Culture, Sports, Science andTechnology of Japan (MEXT), by the Proposal Program of SACLAExperimental Instruments of RIKEN, by the Japan Society for thePromotion of Science (JSPS) KAKENHI Grant Number 15K17487,by the Cooperative Research Program of ‘‘Network Joint ResearchCenter for Materials and Devices: Dynamic Alliance for OpenInnovation Bridging Human, Environment and Materials’’, andby the IMRAM project. T. Ta. gratefully acknowledges support bythe JSPS KAKENHI Grant Number JP 16J02270, E. K. the financialsupport by the Academy of Finland and H. K. Grant-in-Aid forScientific Research by MEXT (no. 16H04091). Part of calculationswas carried out by using supercomputing resources at CyberscienceCenter, Tohoku University and at the Research Center forComputational Science, Okazaki, Japan. K. Nak. is supportedby Research Fellowships of Institute for Quantum ChemicalExploration for Young Scientists. D. Y. acknowledges support aGrant-in-Aid of Tohoku University Institute for Promoting GraduateDegree Programs Division for Interdisciplinary Advanced Researchand Education. G. K. and M. S. acknowledge financial support bythe Federal Ministry of Education and Research (BMBF). A. R. wassupported by the Chemical Sciences, Geosciences, and BiosciencesDivision of the Office of Basic Energy Sciences, Office of Science,U.S. Department of Energy under contract No. DE-FG02-86ER1349.K. Ko. acknowledges the financial support provided by the EstonianResearch Council (grant no. PUT735) and from the Vaisala Founda-tion of the Finnish Academy of Science and Letters. K. Y. is gratefulfor the financial supports from Building of Consortia for theDevelopment of Human Resources in Science and Technology,MEXT. H. K. would like to thank S. Koseki for valuable discussionson the charge transfer in CH2I2.

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