Isomer-Dependent Fragmentation Dynamics of Inner-Shell PhotoionizedDifluoroiodobenzene

Utuq Ablikim a,b, Cedric Bomme c, Evgeny Savelyev c, Hui Xiong e, Rajesh Kushawaha a, Rebecca Boll c,

Kasra Amini d, Timur Osipov f, David Kilcoyne b, Artem Rudenko a, Nora Berrah e, and Daniel Rolles a,c

a J.R. Macdonald Laboratory, Department of Physics,Kansas State University, Manhattan, KS 66506, USA

b Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USAc Deutsches Elektronen-Synchrotron (DESY), 22607 Hamburg, Germany

d Department of Chemistry, University of Oxford, Oxford OX1 3QZ, United Kingdome Department of Physics, University of Connecticut, Storrs, CT 06269, USA and

f SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA(Dated: September 27, 2018)

The fragmentation dynamics of 2,6- and 3,5-difluoroiodobenzene after iodine 4d inner-shell pho-toionization with soft X-rays are studied using coincident electron and ion momentum imaging.By analyzing the momentum correlation between iodine and fluorine cations in three-fold ion co-incidence events, we can distinguish the two isomers experimentally. Classical Coulomb explosionsimulations are in overall agreement with the experimentally determined fragment ion kinetic en-ergies and momentum correlations and point toward different fragmentation mechanisms and timescales. While most three-body fragmentation channels show clear evidence for sequential fragmenta-tion on a time scale larger than the rotational period of the fragments, the breakup into iodine andfluorine cations and a third charged co-fragment appears to occur within a few hundred femtosec-onds.a time scale larger than the rotational period of the fragments, the breakup in other channelsappears to occur within a few hundred femtoseconds.

INTRODUCTION

The fragmentation or Coulomb explosion of polyatomicmolecules after VUV or X-ray photoionization [1–7],strong-field ionization in intense laser fields [8–14], orelectron and ion impact ionization [15–20] has been in-vestigated extensively in order to understand the dynam-ics of the ionization and fragmentation process as wellas to study the link between the fragmentation patternand the geometric structure of the molecules. Early ex-periments were mostly performed using ion time-of-flightmass spectrometry techniques such as ion-ion coincidencespectroscopy [21, 22]. The development of ion imag-ing techniques [23–25] and, in particular, coincident ionmomentum imaging [26–29] has significantly increasedthe amount of information that can be extracted fromsuch fragmentation studies. Recently, several studieshave focused on the identification of molecular isomers,i.e. molecules with the same chemical formula but dif-ferent geometric structures, from the fragmentation pat-terns. For example, it was demonstrated that it is pos-sible to separate two enantiomers in a racemic mixtureof small chiral molecules by measuring five-fold ion coin-cidences after strong-field ionization [6, 13] or beam-foilinduced Coulomb explosion [30], while three-fold ion co-incidences after inner-shell photoionization were used toidentify the cis and trans geometric isomers of dibro-moethene [31].

Here we report on an experimental study of the frag-mentation dynamics of 2,6- and 3,5-difluoroiodobenzene(C6H3F2I; DFIB; see Fig. 1(b)) after iodine 4d inner-shell photoionization with soft X-rays using coincident

electron and ion momentum imaging. The study aims atextending coincidence momentum imaging investigationsto larger and more complex molecules and, in particular,at determining if, for such complex molecules, it is pos-sible to distinguish between the geometric structure ofdifferent isomers via coincident momentum imaging, andif the fragmentation can still be described by a simple,classical Coulomb explosion model. The choice of theparticular molecules was motivated by previous work onlaser-induced alignment of difluoroiodobenzene molecules[32–36], where both strong-field and soft X-ray inducedCoulomb explosion were used to diagnose the degree ofone- and three-dimensional molecular alignment. Sincethose measurements showed very distinct angular distri-butions of the F+ fragments, we were intrigued to in-vestigate if a coincident momentum imaging experimentthat can determine the angle between the I+ and F+

fragment ion momenta would be able to separate the dif-ferent isomers in a similar way as our previous study ondibromoethene [31].

As we show in the following, the two isomers indeedexhibit characteristically different ion momentum corre-lations and fragmentation patterns that can be linked tothe geometric structure of the molecules and that canbe described adequately in terms of a classical Coulombexplosion model. However, the comparison of the experi-mental data with the Coulomb explosion simulations alsoreveals some distinct differences that we attribute to ul-trafast charge separation across the phenyl ring as well asto a sequential breakup of the triply charged cation on atime scale of several hundred femtoseconds, which seemsto occurs only in the 2,6-DFIB isomer. Other many-body

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fragmentation channels show clear evidence for sequentialfragmentation on a time scale larger than the rotationalperiod of the fragments.

EXPERIMENTAL AND COMPUTATIONALDETAILS

Experimental setup

The experiment was conducted at beamline 10.0.1.3 ofthe Advanced Light Source (ALS) at Lawrence BerkeleyNational Laboratory. 2,6- and 3,5-difluoroiodobenzenewere commercially purchased (Sigma Aldrich, 97% pu-rity). Both samples are liquid at room temperatureand were first outgassed in a freeze-pump-thaw cycle be-fore introducing them into the gas phase via supersonicexpansion through a 30 micron aperture using helium(backing pressure: ≈ 500 mbar) as carrier gas. Afterpassing through a skimmer with a 500 micron diameter,the molecular beam was crossed by a beam of linearly po-larized soft X-ray photons from the ALS (photon energy:107 eV; bandwidth 10 meV) in the interaction center of adouble-sided velocity map imaging (VMI) spectrometer.The setup, which is shown schematically in Fig. 1(a),was identical to the one described in a previous publi-cation [31] and is therefore only summarized in the fol-lowing, along with a brief outline of the data analysisprocedures.

In order to detect electrons and ions in coincidenceand to record both position and time information forthe charged fragments, which is necessary to determinetheir three-dimensional momentum vectors, the double-sided VMI was equipped with microchannel plate (MCP)detectors with multi-hit delay-line anodes (RoentDekDLD80 for the electrons and RoentDek HEX80 for theions). The analog MCP and delay line signals were am-plified, processed by a constant fraction discriminator(CFD), and then recorded by the data acquisition systemconsisting of two Roentdek TDC8HP 8-channel multi-hittime-to-digital converters (TDC). The TDCs have a res-olution of ¡100 ps and a multi-hit dead-time of ¡10 ns.They were triggered by the detection of the first elec-tron (which could be either a photoelectron or Augerelectron), which typically arrived at the detector aftera flight time of approximately 5 nanoseconds. The ex-periment was performed during the standard ALS multi-bunch top-off mode of operation, which has an electronbunch spacing in the storage ring of 2 ns. Since this isnot sufficient to link the detected photo- or Auger elec-tron to a specific soft X-ray pulse, the time of flight ofthe ions was measured with respect to the arrival timeof the first detected electron rather than with respect tothe ALS bunch marker.

The lens voltages of the VMI spectrometer were cho-sen to allow for the collection of electrons up to 120 eV,

FIG. 1. (a) Schematic of the experimental setup includinga supersonic molecular beam and a double-sided VMI spec-trometer with time- and position-sensitive delay-line detec-tors for coincident detection of photo-/Auger electrons andfragment ions. (b) Geometric structures of 3,5- and 2,6-difluoroiodobenzene.

singly charged ions up to 18 eV, and doubly charged ionsup to 35 eV over the full solid angle. This was achievedby applying +500 and 0 V to the two inner-most extrac-tor/repeller electrodes, +1000 and -500 V to the two ad-ditional focusing lenses, and +/-3300 V to the two drifttubes. Since the electric field in a VMI spectrometer isnot homogeneous, one cannot derive analytical formulasto reconstruct the ion momenta from the measured timeof flight and hit positions of each ion. Instead, we use theSIMION 8.1 software package to simulate the expectedtime of flight and hit positions for ions starting in the in-teraction region with different kinetic energies and emis-sion angles. Using this procedure, the three-dimensionalmomentum vectors for each detected ion can be recon-structed and used to calculate the emission angles of thefragments as well as their kinetic energies. To verify theenergy calibration, the kinetic energy release spectrum ofN2 molecules was measured, which agreed with literaturevalues [37].

As mentioned above, the time between two consecutivelight pulses in the ALS multi-bunch operation is too shortto unambiguously determine the time of flight of the elec-trons in order to determine their three-dimensional mo-menta, so only the two-dimensional projection of theirmomentum distribution contained in the electron hit po-sitions is measured. The three-dimensional momentum

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distribution of the integrated electron image can then bereconstructed using standard VMI imaging reconstruc-tion methods [38–41]. For the electron spectra shown inthis paper, a modified Onion Peeling method [42] wasused to invert the VMI images and reconstruct the elec-tron spectra.

When analyzing electron-ion-ion or electron-ion-ion-ion coincidences, only those events were considered wherethe component-wise momentum sum of all ionic frag-ments falls within a narrow peak around zero witha FWHM of 15 a.u., which imposes momentum con-servation and therefore rejects most false coincidences,i.e. events where the fragments do not originate from thesame parent molecule.

Coulomb explosion calculations

In order to compare the experimentally determinedfragment ion kinetic energies and momentum vector cor-relations with the expectations from a classical Coulombexplosion model, we have performed numerical simu-lations assuming purely Coulombic repulsion betweenpoint charges. As a starting point, we placed the chargesat the center of mass of each fragment and assumed in-stantaneous creation of the charges followed by explosionfrom the equilibrium geometry of the neutral molecule,as determined by the Gaussian 09 software package [43].By numerically solving the classical equations of motionsfor all the fragment ions in their combined Coulomb fieldusing a 4th order Runge-Kutta method, the momentumvectors and kinetic energies of all fragments were ob-tained for an ideal Coulomb explosion model. In or-der to account for possible ultrafast migration of chargesinside the molecule, the calculations were repeated forother possible locations of the charges, where appropri-ate (see section ). Furthermore, in order to account forlong Auger lifetimes and/or sequential bond breaking, aversion of the code was implemented that allowed an in-crease in the charge of one of the fragments and/or thebreaking of a second bond inside the molecule after agiven time delay τ (see section ). In that case, we simplyinterrupt the numerical propagation at time step τ anduse the particle’s positions and velocities at that momentas starting values for a new simulation with the final frag-ment masses and charges.

The total Coulomb energy Etot (in units of eV ) of amolecules dissociating into N charged fragments can alsobe calculated analytically as

Etot [eV ] = 14.49

N∑i 6=j

qiqj|ri − rj |

, (1)

where qi and qj are the charges of the ith and jth fragmentand |ri − rj | is the distance between the two charges (inunits of A) prior to the fragmentation. If no energy is

stored in internal degrees of freedom, e.g. as vibrationalor rotational energy of the fragments, this formula can beused to calculate the total kinetic energy release (KER),i.e. the sum of all fragment kinetic energies. For the caseof a simple two-body fragmentation, i.e. a break-up ofthe molecule into two fragments that, when combined,contain all of the atoms of the original parent molecule,the KER is partitioned, due to momentum conservation,as

E1 =m2

m1 +m2KER, E2 =

m1

m1 +m2KER, (2)

where E1 and E2 are the kinetic energies of the two frag-ments with masses m1 and m2.

RESULTS AND DISCUSSION

Fig. 2(a) shows the ion time-of-flight mass spectra of2,6- and 3,5-difluroiodobenzene recorded at 107 eV pho-ton energy. At this photon energy, which is approxi-mately 50 eV above the iodine 4d ionization thresholdbut below the iodine 4p ionization thresholds in DFIB, asingle photon can ionize any of the molecular valence andinner-valence shells as well as the iodine 4d shell. Whilevalence ionization predominantly leads to singly chargedfinal states that either remain bound or fragment into oneionic and one or several neutral fragments, emission of anI(4d) inner-shell photoelectron is typically followed byrapid Auger decay into doubly or triply charged cationicstates. As a reference, the typical Auger lifetimes of a 4d-ionized Xe atom, which is electronically similar to iodine,are 6 fs for the first Auger decay and 23 fs for the secondAuger step [44], and we expect these values to be a goodestimate for the order of magnitude of the lifetimes ofthe dominant atomic-like Auger channels in DFIB. Af-ter Auger decay, the di-cationic and tri-cationic states inDFIB generally fragment into two or three charged frag-ments that are emitted with relatively high kinetic ener-gies due to the Coulomb repulsion of the positive charges(hence, this process is referred to as Coulomb explosion).Additionally, further neutral fragments may be produced,which are not detected in this experiment. The breakupinto several charged fragments can be represented in aphotoion-photoion coincidence (PIPICO) plot, as shownin Fig. 3, where the ion yield is shown as a function of thetime of flight of the first and second detected ion. ThePIPICO plots for both isomers show that the moleculescan break up in a large number of different channels, pro-ducing almost every charged fragment that is stoichio-metrically possible. In particular, narrow diagonal linesin the PIPICO plot correspond to two-body fragmenta-tion channel or channels where the remaining fragment(s)carry negligible momentum, while broader features corre-spond to breakup into three or more heavy and energeticfragments. If the molecules breaks up into three ionic

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FIG. 2. (a) Ion time-of-flight mass spectra generated by photoionization of 2,6- and 3,5-difluroiodobenzene at 107 eV photonenergy. Peaks from residual gas are labeled in red. The spectrum of 3,5-DFIB was scaled to have the same maximum valueof the I+ peaks as the spectrum of 2,6-DFIB. (b) Normalized difference (TOF2,6−DFIB − TOF3,5−DFIB)/(TOF2,6−DFIB +TOF3,5−DFIB) between the two ion mass spectra shown in the panel above.

fragments, one can construct a PIPIPICO (i.e. triple ioncoincidence) plot, as shown in Fig. 4, where the ion yieldis plotted as a function of the time of flight of one ofthe fragments and the sum of the times of flight of twoother fragments that were detected in a given coincidenceevent. Again, narrow diagonal lines correspond to events,where the momenta of the three ionic fragments add tozero, while broader features correspond to breakup intomore than three heavy and energetic fragments.

While the ion time-of-flight mass spectraand PIPICO/PIPIPICO plots of 2,6- and 3,5-difluroiodobenzene look rather similar at first sight,some differences, especially in the yield of F+, C2H+

2 andfluorine containing fragments such as C2HF+, as well asof heavy fluorine and iodine containing fragments, suchas IF+ and C2FI+, are visible upon closer inspection.This can also be seen in Fig. 2(b), where the normalizeddifference between the ion time-of-flight mass spectraof 2,6- and 3,5-DFIB is shown. The generation of F+

ions from both 2,6 and 3,5-difluroiodobenzene is veryrare due to the large electronegativity of fluorine, ascan be seen from Fig. 2(a), but it is significantly higherin 3,5-DFIB than in 2,6-DFIB. Many of the otherdifferences in the fragment ion yield can be explainedwhen considering the geometry of the molecule, whichfavors certain fragments in one isomer as compared tothe other. This is particularly evident for the C2FI+

fragment, for example, which is only formed from2,6-DFIB, since a C2FI group does not exist in the3,5-DFIB molecule. In this context, it is interesting to

point out the IF+ fragment, which is only producedfrom 2,6-DFIB. Formation of this fragment requires thebreaking of two bonds, C−F and C−I, and the formationof a new bond between the iodine and fluorine atoms.As one may intuitively expect, this bond formation onlyoccurs in 2,6-DFIB, where iodine and fluorine are boundto neighboring carbons.

In the following, we will concentrate our discussion onthe kinetic energies and momentum correlations observedin particular coincidence channels, and on the conclusionsabout the fragmentation dynamics that we can draw fromthis information.

C6H3F2+ + I+ and C6H3F2

++ + I+ two-bodyfragmentation channels

As briefly mentioned in section , the conceptually eas-iest fragmentation channels are ”complete” two-bodyfragmentations, where the molecule breaks into twocharged fragments, which, when combined, contain allatoms that were in the original molecule. In these cases,the two fragments are emitted strictly back-to-back dueto momentum conservation, and they share all of theavailable Coulomb energy. The strongest two-body frag-mentation channel of this type is the C6H3F2

+ + I+

channel, which is predominantly produced by I(4d) inner-shell ionization followed by ultrafast Auger decay, asproven by the electron spectrum measured in coinci-dence with this fragmentation channel, which is shown in

5

FIG. 3. Photoion-photoion coincidence (PIPICO) plots for 2,6-DFIB (left) and 3,5-DFIB (right). The ion yield is shown on alogarithmic color scale.

FIG. 4. Triple-ion coincidence (PIPIPICO) plots for 2,6-DFIB (left) and 3,5-DFIB (right). The ion yield is shown on alogarithmic color scale.

Fig. 5(c). The I(4d) photoelectrons have a kinetic energyof 50 eV, while a distinct Auger peak appears at around29 eV kinetic energy, which is similar to the energy of themost energetic Auger lines observed after I(4d) ionizationof CH3I [45, 46]. Note that there is also a smaller peakbetween 70 and 80 eV kinetic energy, which we attributeto valence double ionization, which also produces a dou-bly charged final state that can fragment into C6H3F2

+

+ I+.

The electron spectrum for the triply chargedC6H3F2

+++I+ final state shown in Fig. 5(d) also con-

tains the I(4d) photoelectron peak, but instead of theAuger peak at around 29 eV kinetic energy, the spec-trum contains a broader Auger feature with a maximumslightly above 10 eV, which is reminiscent of the lower-energetic Auger group observed in CH3I [45]. Althoughthe electron spectra are only shown for one photon en-ergy, we have also recorded the spectra at other photonenergies to confirm that the photoelectrons indeed changetheir kinetic energy, while the Auger electrons remain ata fixed kinetic energy, as expected.

The kinetic energy distributions of the C6H3F2+ and

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FIG. 5. Velocity map electron images and kinetic energy spec-tra measured in coincidence with the C6H3F2

++I+ (a, c) andthe C6H3F2

+++I+ (b, d) fragment ion channels in DFIB.Panels (a) and (b) show the raw (right) and inverted (left)electron images for 2,6-DFIB, while the kinetic energy spec-tra in (c) and (d) are shown for both isomers.

the I+ fragments in the C6H3F2+ + I+ coincidence chan-

nel as well as the total kinetic energy release (KER)for 2,6-DFIB and 3,5-DFIB are shown in Fig. 6(a) andFig. 6(b), respectively. In both isomers, the KER ispeaked at around 3.1 eV, with each fragment carryingabout half of the energy since they have almost the samemass (the peaks of the experimental kinetic energy distri-butions are at 1.65 eV for C6H3F2

+ and 1.45 eV for I+).Assuming that the two charged fragments can be approx-imated as point charges and that the molecule breaks upon a purely Coulombic potential energy curve after bothcharges are created, we can calculate the Coulomb energyof the system for different locations of the two charges, asdescribed in section . The dashed lines in Fig. 6 show thevalue of this Coulomb energy if one of the two chargesis localized on the iodine fragment, while the other oneis located at three different positions on the phenyl ring:(A) on the carbon atom furthest away to the iodine, (B)at the center of the ring, and (C) on the carbon atomclosest to the iodine. Case (A) agrees almost perfectlywith the maximum of the measured KER distribution,case (B) lies in the high energy ”shoulder” of the KERdistribution, while case (C) clearly overestimate the en-ergy significantly. From this, we can conclude that either(i) the fragmentation does not occur along a Coulombicpotential curve and a significant fraction of the Coulombenergy is transformed into internal energy, e.g. in elec-tronic, vibrational or rotational excitations, (ii) the C−Ibond has stretched significantly before the second chargewas created, or (iii) the second charge has localized at thefar end of the phenyl ring before the Coulomb explosionoccured.

FIG. 6. Kinetic energy release (black squares) of theC6H3F2

++I+ (left) and C6H3F2+++I+ (right) two-body

fragmentation channel for 2,6-DFIB (top) and 3,5-DFIB (bot-tom) along with the kinetic energies of the C6H3F2

+ orC6H3F2

++ (green) and I+ (blue) fragments. The KER val-ues obtained from a classical Coulomb explosion simulationfor three different locations of the charge(s) on the C6H3F2

+

or C6H3F2++ fragments, respectively, as depicted in the in-

sets, are shown as dashed lines. The simulated fragment ionkinetic energies for case (A) are 1.38 eV for I+ and 1.54 eVfor C6H3F2

+.

Since we cannot distinguish between these possibil-ities without detailed quantum chemistry calculations,we turn to another two-body fragmentation channel toobtain further information. Fig. 6(c) and (d) show themeasured fragment ion kinetic energy distributions andKER for the C6H3F2

++ + I+ channel in both 2,6- and3,5-DFIB, compared to the calculated Coulomb energiesfor the three scenarios described above. Again, the sit-uation where both charges on the C6H3F2

++ fragmentare located at the far end of the phenyl ring gives almostperfect agreement with the experimental data. Since it isunlikely that the amount of internal energy in the molec-ular fragment, which would have to be 6 eV to explainthe difference, would have increased so drastically in thiscase as compared to the doubly charged fragmentationchannel, we conclude that ultrafast charge localization isthe most likely scenario: After photoionization removesan I(4d) electron, the inner-shell vacancy in the iodineatom is filled by a valence or inner-valence electron viaan Auger process that ejects a second and sometimes athird valence electron. This leaves the system with twoor three holes in the valence shell. Charge migrationalong the phenyl ring, driven by the Coulomb repulsionbetween the holes, could lead to a situation where theholes are located at opposite ends of the molecule beforethe molecule fragments.

Similar ultrafast charge migration after inner-shell ion-ization of a benzene compound was recently suggested ina theoretical study of nitrosobenzene molecules [47]. In

7

this study, the authors investigated charge migration inthe valence shell driven solely by electron correlation andelectron relaxation. The calculations show that in core-ionized nitrosobenzene, charge migration occurs withinless than 1 femtosecond and, in particular, even fasterthan the Auger decay. From the present experimentaldata, we do not have direct evidence for such a chargemigration effect in DFIB nor can we draw any conclu-sions about the mechanism for charge localization, butwe note that this process would explain the experimen-tally observed fragment energies.

The differences in the yield of F+ ions seen in Fig. 2,which we pointed out earlier, may further support thishypothesis: If charge migration leads to a positive chargeat the end of the ring opposite to the iodine, i.e. close tothe fluorine atoms in 3,5-DFIB, a lack of electrons inthe vicinity of the fluorines might make it more likely toproduce F+ ions than in the case of 2,6-DFIB, where thepositive charge on the phenyl ring is located further awayfrom the fluorine atoms.

Sequential breaking of C−I and C−C bonds

While the majority of DFIB molecules are in a dou-bly ionized final state after I(4d) inner-shell ionizationand subsequent Auger decay, a significant fraction ofthe molecules end up in a triply charged final state, asdemonstrated by Fig. 4. This can happen via directdouble ionization, most likely via a shake-off process,in the first ionization step followed by a single Augerprocess, or via emission of a single photoelectron fol-lowed by emission of two Auger electrons, either simulta-neously (double-Auger) or sequentially (Auger cascade)[48, 49]. For the triply charged C6H3F2

+++I+ final state,the electron spectrum in Fig. 5(d) clearly shows thatthis state is reached via single photoelectron emission,since direct double photoionization would not yield awell-defined photoline at 50 eV kinetic energy. This firststep is followed, most likely, by a sequential Auger cas-cade, since ”double-Auger” emission would also producea more continuous electron kinetic energy distributionthan what is observed here.

Since the triply charged DFIB parent ion is not sta-ble, it breaks up in two or three charged fragments and,possibly, further neutral fragments. The events wherethe molecule breaks into three charged fragments areshown in the triple-ion coincidence maps in Fig. 4. Thestrongest contributions are from fragmentation channelswhere an I+ ion and two fragments from the phenyl ringare produced. Here we concentrate on three exemplarytriple coincidence channels, namely CF++C5H3F++I+,C2HF++C4H2F++I+, and C3HF++C3H2F++I+. Theircoincident electron spectra are qualitatively similar tothose of the C6H3F2

+++I+ final state shown in Fig. 5(d),but the statistics and kinetic energy resolution of our

FIG. 7. Kinetic energies of individual ionic fragments and to-tal kinetic energy release for the CF++C5H3F++I+ (top),C2HF++C4H2F++I+ (middle), and C3HF++C3H2F++I+

(bottom) channels in 2,6-DFIB (left) and 3,5-DFIB (right).

data are not sufficient to observe possible subtle differ-ences in the Auger electron spectrum.

After obtaining the three-dimensional momenta of allionic fragments in these coincidence channels, the indi-vidual fragment ion kinetic energies and the KERs arecalculated and are shown in Fig. 7. For all three frag-mentation channels, the kinetic energies are very similarin both isomers, 2,6- and 3,5-DFIB. Furthermore, it isinteresting to note that the narrow kinetic energy distri-butions of the iodine ions are almost identical to those inC6H3F2

+++I+ two body Coulomb explosion channel.

In order to gain further insight into the fragmentationmechanism leading to these three-body channels, Newtonplots are shown in Fig. 8, where the momenta of the twocarbon-containing fragments are plotted with respect tothe momentum of the iodine ion, which is represented bya black arrow. The curved, semi-circular structures thatappear in these Newton plots are a strong indication fora sequential fragmentation [19], with a delay between thebreaking of the C−I bond and the subsequent breakingof the C−C bonds longer than the rotational period ofthe C6H3F2

++ fragment, which is on the order of 100ps in the rotational ground state. We can thus hypothe-size that the process leading to these three-body channelsproceeds as follows: Inner-shell photoionization followedby emission of two Auger electrons leaves the moleculein a triply charged state, which undergoes Coulomb ex-plosion into C6H3F2

+++I+, leading to a singly charged

8

FIG. 8. Newton plots of the CF++C5H3F++I+,C2HF++C4H2F++I+, and C3HF++C3H2F++I+ coincidencechannels in 2,6-DFIB (left) and 3,5-DFIB (right). The mo-mentum of the I+ fragment is plotted as a unit vector (blackarrow), while the momenta of the two other ionic fragmentsrelative to the I+ momentum are plotted in the upper andlower half, respectively. The shift between the upper andlower semi-circular structures in the asymmetric break-upchannels is caused by the large mass difference between thefragments, which results in very unequal sharing of the center-of-mass momentum from the first fragmentation step.

iodine ion with about 3 eV final kinetic energy and ametastable C6H3F2

++ di-cation with about 3.5 eV ki-netic energy, both repelled in opposite directions. At thesame time, the C6H3F2

++ fragment seems to have re-ceived some angular momentum during the C−I bondbreaking (e.g. as the result of C−I bending vibrations),resulting in a rotation around its center of mass. Aftera delay longer than its rotational period, the metastableC6H3F2

++ di-cation breaks up into two singly chargedfragments, each containing a fluorine atom and differentnumbers of carbons atoms. At that time, the distance tothe iodine ion is large enough that the Coulomb force onthe I+ ion is negligible, as demonstrated by the narrow I+

kinetic energy distribution, which is independent of thesecondary fragmentation. Under this assumption, we canretrieve the kinetics of the second-step fragmentation bysubtracting the center-of-mass velocity of the C6H3F2

++

FIG. 9. Kinetic energies of individual fragments and totalkinetic energy release for the second fragmentation step in thethree-body fragmentation channels shown in Fig. 7 and 8 for2,6-DFIB (left) and 3,5-DFIB (right). The kinetic energiesobtained from a classical Coulomb explosion simulation areshown as dashed lines.

di-cation, which can be calculated from the measuredI+ momentum because of momentum conservation, fromeach of the other fragment velocities, thus retrieving thekinetic energy spectrum of the second Coulomb explosionstep, which is shown in Fig. 9. Again, our classical modelsimulation, shown as dashed lines, are in good agree-ment with the experimental data, suggesting that thesecond-step decay also occurs along Coulombic potentialcurves. To obtain the best match with the experimentalkinetic energies, we placed the two charges in the secondCoulomb explosion step on the fluorine atom in one ofthe fragments and on the carbon atom in the second frag-ment that is furthest away from the first fluorine atom.This yields very good agreement in the two asymmetricfragmentation channels but overestimates the kinetic en-ergies in the symmetric C3HF++C3H2F++I+ fragmen-tation, suggesting an intermediate geometry where thetwo charges are even further apart in that case, possiblydue to a deformed geometry of the metastable di-cation.

9

FIG. 10. Newton plots of the F+ + C6HF+ + I+ fragmen-tation channel for (a) 2,6-DFIB and (b) 3,5-DFIB. The mo-mentum vectors of F+ and C6HF+ are normalized to the sizeof the momentum vector of I+.

Identification of molecular isomers via fragment ionmomentum correlations in three-body fragmentation

channels

As we have shown previously for the case of dibro-moethene [31], the momentum correlations in certainthree-body fragmentation channels can be used to iden-tify geometric isomers, in that case by determining theangle between the momentum vectors of the two Br+ ionsthat are emitted in coincidence with a C2H+

2 fragment.In the case of DFIB, one might expect that the angle be-tween I+ and F+ fragments could be used to distinguishbetween 2,6- and 3,5-DFIB, if the fragmentation happensfast enough to preserve the angular correlation betweenthese two fragments. We first concentrate on the F+

+ C6HF+ + I+ fragmentation channel, in which all theheavy atoms are accounted for in the ionic fragments, andonly two hydrogen atoms are missing. They were mostlikely emitted as neutral fragments, since the momentumsum of the three ionic fragments is very narrow aroundzero (FWHM=±7.5 a.u). Fig. 10 shows the Newton plotsfor this fragmentation channel in both 2,6- and 3,5-DFIB.The first observation from these Newton plots, where themomenta of two fragments (F+ and C6HF+) are plottedin the frame of the momentum of the third fragment (I+),is that they show well-defined peaks rather than smearedout circular structures, suggesting that both bond breaksbetween the charged fragments happen on a time scalefaster than the molecular rotation. Furthermore, thereis a clear difference in the fragmentation patterns of thetwo isomers, with smaller relative momenta of the F+ andC6HF+ fragments in the case of 3,5-DFIB and a largerangle between I+ and F+ fragments as compared to 2,6-DFIB. The difference in the fragmentation patterns forthe two isomers is also very apparent in Fig. 11, wherethe KER and the fragment ion kinetic energies for thischannel are shown for both isomers, along with the an-gle θ between the momentum vectors of the F+, I+, andC6HF+ fragments detected in coincidence. The KERand F+ kinetic energies are rather similar in 2,6- and

FIG. 11. Total kinetic energy release, kinetic energies of theindividual ionic fragments, and angle θ between the momen-tum vectors of the F+, I+, and C6HF+ fragments for the F+

+ C6HF+ + I+ fragmentation channel in 2,6-DFIB (top) and3,5-DFIB (bottom). The kinetic energies and angles obtainedfrom a classical Coulomb explosion simulation are shown asdashed lines.

3,5-DFIB, with the main difference being a lower I+ andhigher C6HF+ kinetic energy in 2,6-DFIB as compare to3,5-DFIB, where both fragments have almost identicalkinetic energies. The angles show large differences be-tween the two isomers, with the angle between F+ andI+ fragments peaking around around 84 ◦ (cos θ = 0.1)for 2,6-DFIB as opposed to 120 ◦ (cos θ = −0.6) for 3,5-DFIB.

While these plots show that the momentum correlationbetween the F+ and I+ fragments can indeed be used toseparate and identify the two isomers, the experimentallyobserved angles are surprising for 2,6-DFIB, where onemay have naively expected a smaller angle between F+

and I+ since the angle between the F and I atoms in theequilibrium geometry of the neutral 2,6-DFIB moleculeis 61 ◦. The Coulomb explosion simulation for the three-body fragmentation shows that this naive expectationis not justified, since the charged fragments repel eachother in a way that the angles between the detected ionmomenta are not necessarily equal or even close to thebond angles in the molecule. While the Coulomb explo-sion simulations, shown as dashed lines in Fig. 11, are ingood agreement with the experimentally observed kineticenergies and angles in 3,5-DFIB, they do not reproducethe observed angles for 2,6-DFIB. In this simulation, onecharge is placed at the position of the iodine atom, thesecond at the position of the fluorine atom, and the thirdone in the center of the ring. Both the C−I and the C−Fbond are assumed to break simultaneously, a scenariocommonly referred to as concerted fragmentation. For2,6-DFIB, concerted fragmentation for any charge config-uration yields angles between the fragments that do not

10

match the experimentally determined angles at all. Wehave tried various other possible positions of the chargeon the C6HF+ and found that none of them can repro-duce the experimentally observed energies and/or angles.In particular, they all yield too large of an angle betweenthe F+ and I+ fragments. Interestingly, for some chargeconfigurations, concerted fragmentation of 2,6-DFIB caneven lead to F+-I+ angles that are very similar to thoseobserved in 3,5-DFIB, suggesting that the seemingly ”ob-vious” link between the molecular geometry and the frag-ment angle correlations should be considered with cau-tion and on a case-by-case basis, rather than as a generalrule.

One scenario that would lead to a smaller angle be-tween F+ and I+ fragments would be a step-wise ioniza-tion and/or fragmentation, where the I−C bond is brokenfirst, e.g. after the first Auger decay, and the the remain-ing C6HxF2

+ remains in an excited state that decays, viaa second Auger decay, after a few hundred femtoseconds,when the distance to the iodine has already increasedconsiderably due to the first Coulomb explosion step. Afurther indication for such as delay of the second-stepAuger decay is the kinetic energy of the I+ fragment,which is significantly lower than any concerted fragmen-tation scenario would allow.

As described in section 2.1, we can model a delayedionization and fragmentation by introducing a time τ ,after which the charge of a specific fragment is increasedand/or a specific bond is broken. Fig. 12 shows the re-sult of these calculations for step-wise fragmentation of2,6-DFIB for the case that the two charges, in the firststep, are located at the position of the iodine atom andthe carbon atom that is furthest away from it, and fortwo different locations of the charges in the second step,as a function of the delay τ between the two steps. Whenassuming that the charge on the C6HF2

+ fragment in thesecond step is located in the vicinity of the F+ fragment,we can reproduce all of the experimentally observed ki-netic energies and angles, within reasonable accuracy, ata delay τ around 400 fs, as shown in Fig. 12(e) and (f).Note that this delay is still significantly shorter than therotational period of the C6HF2

+ fragment, such that no”smearing out” of the angles can be seen in the New-ton plot in Fig. 10(a). Any other scenario (includingmany more that we have tried but that are not shownhere) yields significant deviations in at least one observ-able. Without having a direct proof for this hypothesisbeyond the agreement between the Coulomb explosionsimulation and the experimental data, we tentatively ex-plain our observation as follows: After the initial Augerdecay following the creation of a I(4d) vacancy, there isa certain probability that the molecule fragments into anI+ and an electronically excited C6HxF2

+∗ fragment. Ifthe electronic energy in the C6HxF2

+∗ is sufficient, e.g. ifit has an inner-valence hole, this fragment can decay fur-ther into a multitude of tri-cationic channels that can be

FIG. 12. Fragment ion kinetic energies and angles betweenthe momentum vectors obtained from the Coulomb explosionsimulation of a two-step fragmentation of 2,6-DFIB with avariable time delay τ between the two fragmentation steps(see text) and for different locations of the charge on theC6HF+ fragment, as shown in the sketch above. In (a) and(b), one of the charges in the second-step Coulomb explosionis placed on the carbon furthest away from the iodine (labeledA), in (c) and (d), it is placed in the center of the phenyl ring(labeled B), and in (e) and (f), it is placed close to the fluorineatom at the position labeled X. The second charge is alwayson the fluorine atom. The experimentally observed kineticenergies and angles are shown as shaded areas. The verti-cal black dashed lines in the bottom panels mark the delayτ , at which the simulations agree best with the experimentalvalues.

seen in Fig. 4. Most of these secondary Auger decays willoccur much faster than the ≈400 fs lifetime that we de-rive from our simulation, leading, e.g., to the three-bodyfragmentation channels discussed in section 3.2. How-ever, since the fragmentation into F+ + C6HF+ + I+

is a rather weak channel, it is conceivable that it onlyoccurs after an initial Auger decay into a rather long-lived state with an inner-valence vacancy with a lifetimeon the order of ≈ 400 fs. Furthermore, since fluorinehas a very high electronegativity, it is very unlikely todissociate into a F+ fragment, unless the inner-valencevacancy in the C6HxF2

+ is located in an orbital that

11

has significant overlap with one of the near-atomic flu-orine orbitals. Even without further calculations, it istherefore conceivable that the different geometry of 2,6-and 3,5-DFIB and, in particular, the different location ofthe fluorine atoms with respect to the iodine atom, maylead to significantly different lifetimes of the intermediatestates that lead to this particular fragmentation channel.

Of course, the classical Coulomb explosion model isunable to test or predict any of these detailed electronicdynamics, but it seems to be clear that a step-wise frag-mentation model needs to be considered in order to ob-tain satisfying agreement with the experimental data for2,6-DFIB. We further note that there is not only an ambi-guity in the exact positioning of the charge in the model,but also in the geometry of the intermediate state. Thisleads to an uncertainty of the delay, for which we canachieve satisfactory agreement of the simulated kineticenergies and angles with the experimental data. We havenot attempted to perform a multi-parameter least-squarefitting procedure to obtain a more accurate number forthe delay τ , since the classical Coulomb explosion modelis not suitable to draw such precise and quantitative con-clusions. Nevertheless, it yields, at least, an estimate forthe lifetime of the second-step Auger process, if the as-sumption of a two-step Auger process is correct.

FIG. 13. Total kinetic energy release, kinetic energies of theindividual ionic fragments, and angle between the momentumvectors of the F+, I+, and C6H2

+ fragments for the F+ +C6H2

+ + I+ fragmentation channel.

Finally, we investigate how general the above findingsare for other channels involving F+ production. Fig. 13shows the kinetic energy and momentum angle distribu-tions for the strongest three-body fragmentation channelcontaining F+, namely F+ + C6H+

2 + I+, where the miss-ing fluorine and hydrogen atoms are emitted as one ortwo neutral fragment(s). For 3,5-DFIB, the distributionsare very similar to the F+ + C6HF+ + I+ fragmenta-tion channel, with the angular distributions for F+ +C6H+

2 + I+ being slightly broader. For 2,6-DFIB, bothkinetic energy and angular distributions are significantly

FIG. 14. Momentum vector correlation between F+ and I+

fragments in 2,6-DFIB (black solid symbols) and 3,5-DFIB(red open symbols) for fragmentation channels where F+ isthe first and I+ is the third detected fragment.

broadened, while the peak positions are still close thethe former case. Furthermore, Fig. 14 shows the I+-F+

angle for all events where F+ is detected as the first frag-ment and I+ as the last fragment, thus integrating overall possible partner fragments. Again, the I+-F+ anglesare very similar to the F+ + C6HF+ + I+ fragmentationchannel discussed above, suggesting that the sequentialbreakup with a delay of approximately 400 fs is commonto all triply charged final states that involve F+ produc-tion in 2,6-DFIB, while a concerted fragmentation is wellsuited to describe the breakup in 3,5-DFIB.

CONCLUSIONS

We have presented a detailed study of the photoion-ization and fragmentation dynamics of inner-shell ion-ized 2,6- and 3,5-DFIB isomers using coincident electron-ion moment imaging. Our results demonstrate that thecoincident electron-ion momentum imaging technique isa powerful method to study even such rather complexmolecules consisting of twelve atoms. Fragment ion ki-netic energies and angular correlations contain detailedinformation on the fragmentation dynamics, which canbe interpreted using classical Coulomb explosion models.By comparing these model calculations with the exper-imental observations, we can distinguish different elec-tronic decay dynamics and fragmentation mechanisms.In particular, we conclude that charges on the di- and tri-cation separate on an ultrafast timescale, and that somefragmentation channels of the tri-cation involve step-wisefragmentation with a delay between the two steps rang-ing from a few hundred femtoseconds to tens or hun-dreds of picoseconds or longer. Finally, our experimen-

12

tal observations show that the angle between F+ and I+

fragments in three-body fragmentation channels can beused to identify and separate the 2,6- and 3,5-DFIB iso-mers. However, such a direct link between the moleculargeometry and the fragmentation pattern should not betaken for granted since the Coulomb repulsion betweenthe fragments and the exact fragmentation dynamics caneasily betray naive expectations. Nevertheless, our studydemonstrates how sensitive coincident (ion) momentumimaging is to the molecular geometry and dynamics, thusmaking it a very promising technique for time-resolvedexperiments, even on polyatomic targets containing tenor more atoms per molecule.

ACKNOWLEDGEMENTS

This work is supported by the Chemical Sciences, Geo-sciences, and Biosciences Division, Office of Basic EnergySciences, Office of Science, U.S. Department of Energy,Grant No. DE-FG02-86ER13491 (Kansas group) and de-sc0012376 (U Conn group). D.R. also acknowledges sup-port through the Helmholtz Young Investigator programfor the DESY group. We thank the staff of the AdvancedLight Source for their hospitality and their help duringthe beamtime.

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