Electronically forbidden ( 5 σ u → k σ u ) photoionization of C S 2 : Mode-specificelectronic-vibrational couplingG. J. Rathbone, E. D. Poliakoff, John D. Bozek, and R. R. Lucchese Citation: The Journal of Chemical Physics 122, 064308 (2005); doi: 10.1063/1.1850474 View online: http://dx.doi.org/10.1063/1.1850474 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/122/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The X+ 2Πg, A+ 2Πu, B+ 2Δu, and a + Σ u − 4 electronic states of Cl 2 + studied by high-resolution photoelectronspectroscopy J. Chem. Phys. 139, 034302 (2013); 10.1063/1.4812376 [1 + 1] photodissociation of CS 2 + ( X ̃ 2 Π g ) via the vibrationally mediated B ̃ 2 Σ u + state: Multichannelsexhibiting and mode specific dynamics J. Chem. Phys. 134, 114309 (2011); 10.1063/1.3567071 Mode-specific photoionization dynamics of a simple asymmetric target: OCS J. Chem. Phys. 130, 044302 (2009); 10.1063/1.3062806 The Jahn–Teller effect in the lower electronic states of benzene cation. III. The ground-state vibrations of C 6 H 6+ and C 6 D 6 + J. Chem. Phys. 120, 8587 (2004); 10.1063/1.1691818 Mode-specific photoelectron scattering effects on CO 2 + (C 2 Σ g + ) vibrations J. Chem. Phys. 120, 612 (2004); 10.1063/1.1630303

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Electronically forbidden „5su\ksu… photoionization of CS 2: Mode-specificelectronic-vibrational coupling

G. J. Rathbonea! and E. D. Poliakoffb!

Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803

John D. BozekAdvanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720

R. R. LuccheseDepartment of Chemistry, Texas A&M University, College Station, Texas 77843

sReceived 28 October 2004; accepted 30 November 2004; published online 26 January 2005d

Vibrationally resolved photoelectron spectroscopy of the CS2+sB 2Su

+d state is used to show hownontotally symmetric vibrations “activate” a forbidden electronic transition in the photoionizationcontinuum, specifically, a 5su→ksu shape resonance, that would be inaccessible in the absence ofa symmetry breaking vibration. This electronic channel is forbidden owing to inversion symmetryselection rules, but it can be accessed when a nonsymmetric vibration is excited, such as bending orantisymmetric stretching. Photoelectron spectra are acquired for photon energies 17øhnø72 eV,and it is observed that the forbidden vibrational transitions are selectively enhanced in the region ofa symmetry-forbidden continuum shape resonance centered athn<42 eV. Schwinger variationalcalculations are performed to analyze the data, and the theoretical analysis demonstrates that theobserved forbidden transitions are due to photoelectron-mediated vibronic coupling, rather thaninterchannel Herzberg–Teller mixing. We observe and explain the counterintuitive result that somevibrational branching ratios vary strongly with energy in the region of the resonance, even thoughthe resonance position and width are not appreciably influenced by geometry changes thatcorrespond to the affected vibrations. In addition, we find that another resonant channel, 5su

→kpg, influences the symmetric stretch branching ratio. All of the observed effects can beunderstood within the framework of the Chase adiabatic approximation, i.e., the Born–Oppenheimerapproximation applied to photoionization. ©2005 American Institute of Physics.fDOI: 10.1063/1.1850474g

I. INTRODUCTION

In this investigation, we show how a photoionizationresonance in CS2 that is symmetry forbidden within theFranck–Condon framework influences the vibrational struc-ture of its photoelectron spectrum, and conversely, how vi-brations make accessible an electronic channel that wouldotherwise be undetectable. This study is part of a larger pro-gram focusing on coupling between electronic and vibra-tional degrees of freedom in photoionization processes, asrevealed by the energy dependence of vibrationally resolvedpartial photoionization cross sections.1–9 In a recent study on5su

−1 photoionization of CS2,5 we reported an unanticipated

result—namely, a symmetry forbiddenksu shape resonancewas “activated” via excitation of the antisymmetric stretch-ing vibration. The results exhibited dramatic mode specific-ity; the branching ratio for the allowed symmetric stretchwas relatively featureless while the symmetry forbidden an-tisymmetric stretch exhibited a branching ratio curve with apronounced peak athn<42 eV. This paper gives a morecomplete account of the phenomenon, including experimen-tal and theoretical results, and discusses the implications.

The factors responsible for the relative vibrational inten-sities are subtle for CS2 5su

−1 ionization,5 and the currentresults can be understood most clearly when compared toearlier studies on CO2. The underlying physics needed toexplain the CS2 results is the same as used previously in theanalysis of forbidden vibrational excitations observed in CO2

4sg−1 photoionization,2–4 i.e., all of the key aspects of the

process can be understood within a single channel, Born–Oppenheimer framework. This might lead one to supposethat the vibrational enhancement effects are the result of thesame mechanism for both molecules. However, while thetheoretical underpinnings are the same, there is a critical dif-ference in the mechanism that enhances the forbidden vibra-tional excitations.10 Specifically, the resonant electronicchannel for CS2 is forbidden, while it was allowed for CO2.This is verified by inspecting the electronic symmetries in-volved. For both molecules, the electronic symmetry of thetarget state isSg; the shape resonant photoelectron isksu forboth systems studied.4,5 However, the ion hole state for CO2

is C 2Sg+, resulting in a total final electronic symmetry of

Sgsiond ^ susphotoelectrond=Su, for CS2 the ion hole state isB 2Su

+, so the total electronic symmetry for the final state isSusiond ^ susphotoelectrond=Sg. Thus, the CS2 5su→ksu

shape resonance is symmetry-forbidden because the elec-tronic transition isg→g,5,10 while the CO2 4sg→ksu reso-

adPresent address: JILA, University of Colorado, Boulder, CO 80309-0440.bdAuthor to whom correspondence should be addressed; Electronic mail:

epoliak@lsu.edu

THE JOURNAL OF CHEMICAL PHYSICS122, 064308s2005d

0021-9606/2005/122~6!/064308/9/$22.50 © 2005 American Institute of Physics122, 064308-1

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nance is an allowedg→u transition. Another significant dif-ference between the CO2 and CS2 cases is that neither theposition or the width of the CS2 shape resonance is verysensitive to symmetry-breaking distortions of the moleculargeometry.5 In the CS2 case, the dipole amplitude of thephotoionization process is quite sensitive to symmetry break-ing molecular distortions, since the amplitude is zero at theequilibrium geometry and nonzero when the molecule losesits inversion symmetry. This is an aspect which will be ex-plored further here. In the CO2 case, the 4sg→ksu shaperesonance is the typical Franck–Condon breakdown inducedby shape resonances11,12 applied to forbidden transitions,3,4

i.e., the profile of the resonance in the cross section curveshifts and broadens as the geometry is distorted. While wehave shown that the mechanism of forbidden vibrational ex-citation is different for CS2 than for CO2,

3,4 we emphasizethat the excitation of forbidden vibrations for both cases isdue to the photoelectron dynamics,10 rather than beingcaused by an interchannel coupling mechanism, such as in-tensity borrowing caused by interchannel Herzberg–Tellermixing13–16that couples different electronic ionic hole states.This investigation demonstrates the power of high resolutionphotoelectron data with wide spectral coverage as a means todisentangle the details of the photoelectron scattering dy-namics.

The photoelectron spectrum of CS2 is well characterized.There are several examples of vibrationally resolved photo-electron spectra in the literature.17–21 Recently, high-precision zero kinetic energy, pulsed field ionizationsZEKE-PFId electron spectra have refined the assignments anduncovered even weaker vibrational structure.22,23As a resultof this extensive background, the assignments of the featurespertinent to this study are well established. In particular, theobservation of thev+=010sbendingd and 001santisymmetricstretchd vibrations of the CS2

+sB 2Su+d state have been well

characterized in other high resolution studies.19–21 These vi-brational transitions are forbidden because excitation of asingle quantum of a nontotally symmetric vibration is forbid-den in an electronic transition. The appearance of these for-bidden transitions has traditionally been rationalized by in-voking interchannel Herzberg–Teller coupling, i.e., a Born–Oppenheimer breakdown whereby the forbidden vibrationallevel of the CS2

+sB 2Su+d state is mixed with another elec-

tronic state, thereby allowing excitation of the nominally for-bidden level.13,14,21,24 Our more recent studies1–5,10 haveshown that this intensity borrowing, interchannel couplingmechanism is frequentlynot responsible for exciting forbid-den vibrational levels. Rather, such excitations can arise be-cause the electronic transition dipole matrix elements arevarying as the molecule vibrates, and this leads to a Franck–Condon breakdown that permits the excitation of the forbid-den levels. This variation of the transition dipole is a result ofthe sensitivity of the photoelectron ejection dynamics to dis-tortions in the molecular geometry, i.e., the mechanism isintrachannel and photoelectron mediated, as opposed to in-terchannel and ion-core mediated.2–4,10

There have also been extensive efforts geared towardsunderstanding the photoelectron ejection dynamics inCS2,

8,25–32but the earlier photoelectron spectroscopy studies

were performed without vibrational resolution,30–32and typi-cally, at lower photon energies. While these studies havebeen useful in identifying the existence of continuum shaperesonances in CS2, they are not sensitive to the vibrationaleffects that are the focus of the current investigation.

The remainder of this paper describes measurements andcalculations which complement those discussed in the previ-ous report.5 While the previous study focused solely on thesingle-quantum excitations of the stretches, the current in-vestigation describes effects due to bending vibrations—which are central to the analysis of this vibrationally acti-vated phenomenon—as well as multiple quanta vibrationalexcitations. Also, there are a number of resonant channelsthat are accessible when a 5su electron is ejected, and someof them are also manifested in the vibrational branching ratiocurves, albeit to a lesser extent than the 5su→ksu channel.The central point is that vibrationally resolved electron spec-tra acquired over a range of photoelectron kinetic energiesprovide a window into the coupling between electronic andvibrational degrees of freedom which would otherwise bemasked from view. In so doing, one can understand the re-sponse of resonant channels to selected distortions of themolecular geometry,4,7,29,33,34and thereby property interpretthe relative intensities observed in photoelectron spectra.

II. EXPERIMENTAL AND THEORETICALDETAILS

To generate vibrational branching ratios for 5su−1 photo-

ionization of CS2, we obtain magic angle, vibrationally re-solved photoelectron spectra at photon energies 17øhnø72 eV. The experimental details have been describedpreviously.35 High-resolution photoelectron spectra are ac-quired at the Advanced Light Source at beam line 10.0.1using a Scienta SES-200 analyzer.35 The photon and photo-electron bandwidths are 10 and 5 meV, respectively, result-ing in a net resolution of,11 meV. Doppler broadeningincreases with photoelectron kinetic energy,36 and becomessignificant at higher photoelectron energies.

Due to the different symmetries involved in linear andnonlinear structures of CS2, we have used substantially dif-ferent computational methods to study the excitation ofbending and stretching modes of CS2

+. The calculations forthe excitation of the bending mode of CS2 employed thesame methods as those we have used earlier to study CO2.

3

These calculations utilized an augmented correlation consis-tent polarized valence triple zetasaug-cc-pVTZd basis set37,38

to expand the bound molecular orbitals which were com-puted at the Hartree–FocksHFd level. The scattering calcu-lations were performed with a single-channel frozen-core HFcalculation39 using the methods we have developed forstudying electron scattering from nonlinear molecules.40–42

The calculations are based on single-center expansions of allbound and continuum functions. In the calculations on thenonlinear geometries we included partial waves in the single-center expansions up to,max=50. This is a smaller single-center expansion than we use in the linear geometries dis-cussed below, which results in the calculations at bentgeometries being less well converged than the calculations atthe linear geometries. This smaller expansion was used to

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keep the calculations practical. The calculations were per-formed at five CS2 molecular geometries with/S–C–Sangles of 180°, 175°, 170°, 165°, and 160°, all withRsC–Sd=1.554 Å.43 The vibrational excitation cross sec-tions were then computed by integrating over the bendingvibrational wave functions which were taken to be two-dimensional harmonic oscillator functions with an initialstate frequency of 397 cm−1 sRef. 44d and a final state fre-quency of 356 cm−1.22

To treat the stretching vibrational modes, we used corre-lated initial and ion states. The orbitals were computed usinga valence complete active-space self-consistent fieldsCASSCFd calculation with the same aug-cc-pVTZ basis setas used in the bending calculation. The natural orbitals fromthis calculation were then used in limited configuration inter-action sCId calculations to compute the initial state and ionstates used in the photoionization calculation. The CI calcu-lation for the initial state had all valence electrons active butincluded only up through triple excitations into the valencevirtual orbitals in the description of the initial state andthrough double excitation in the description of the ion states.The scattering calculations were performed using the single-channel Schwinger configuration interaction method.45–47 Inthe linear geometry calculations we included up to,max

=120. In essence, in the single channel calculation the pho-toelectron scatters from the field of the ion where the ion isdescribed by a CI wave function, providing computationalaccuracy while maintaining conceptual simplicity.

The photoionization calculations for the stretching vibra-tional modes were performed on a grid of linear geometrieswithin the fixed-nuclei approximation. The linear geometrieswere defined in terms of normal coordinatesq1 and q3 asRsC–S1d=Re+a1 q1+a3 q3 and RsC–S2d=Re+a1 q1

−a3 q3 where Re=1.554 Å, a1=0.028 33 Å, a3

=0.046 67 Å so thatqi = ±1 corresponded to the classicalturning points in the ground vibrational state of the neutralmolecule. The grid of points were then obtained usingq1=−2, −1, 0, 1, 2, andq3=0.5, 1.5, and 2.5. This led to a totalof 15 unique geometries. The value of the photoionizationmatrix elements at geometries corresponding to negative val-ues ofq3 were obtained by symmetry. The vibrational wavefunctions were assumed to be two-dimensional harmonic os-cillator states. In the neutral initial state the vibrational wavefunctions hadResC–Sd=1.554 Å sRef. 43d and the vibra-tional frequencies were taken to be 657 and 1532 cm−1.44 IntheB 2Su

+ ion state we usedResC–Sd=1.564 ÅsRef. 48d andvibrational frequencies of 602 and 1318 cm−1.21

In the fixed nuclei approximation used to compute thephotoelectron dynamics, the ionization potential was then afunction of the geometry at which a particular calculationwas performed. We then computed the vibrationally resolvedphotoionization cross section in the adiabatic nucleiapproximation49 where the cross section is obtained as anintegral over a series of fixed nuclei calculations. For a givenfinal scattering state with a specific asymptotic photoelectronkinetic energy, the integral was performed over the differentfixed nuclei calculations with the photoelectron kinetic en-ergy corresponding to the desired final asymptotic value. Forthe CS2

+sB 2Su+d state, this final kinetic energy was deter-

mined assuming an ionization potential of 14.49 eV whichwas the computed vertical ionization potential in the linearmolecule calculation. With all of the desired matrix elementscomputed, it was then necessary to interpolate these matrixelements to intermediate geometries to allow for the compu-tation of the required vibrational integrals. For both linearand nonlinear calculations this was done using polynomialinterpolation.

In additional to the full SCSCI calculation, we also per-formed calculations using the adiabatic static model-exchangesASMEd potential. This approach has been previ-ously used to visualize resonant states in electron-moleculescattering50 and molecular photoionization.40 These calcula-tions directly yield resonant wave functions and the energyand width of the resonant states for a local model potential.The resonance parameters from the model potential calcula-tion have been found to be fairly close to those found frommore accurate calculations, thus supporting the use of thecorresponding wave functions to interpret the qualitative fea-tures of the resonance.

III. RESULTS

Representative photoelectron spectra are shown in Fig.1. All three vibrational modes are observed with single-quantum excitation. In addition, the two-quanta excitations

FIG. 1. Photoelectron spectra of CS2+sB 2Su

+d state at selected energies. Notethe large enhancement in thev+=s010d and s001d peaks in thehn=40 eVspectrum.

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are observed for the bending and symmetric stretching vibra-tions. Most of the vibrations are resolved, although some ofthe peaks become blended owing to increasing Dopplerbroadening with increasing energy.36 For the overlappings100d ands020d peaks, as well as thes001d ands200d peaks,the individual intensities are obtained via fitting to a sum ofGaussians. The spectra are consistent with established pho-toelectron spectra.20,22The peak to the higher binding energyside of thes001d peak is not assigned to CS2, and is probablydue to an impurity. What is apparent from these spectra arethe dramatic intensity enhancements for the single-quantumbending excitations010d and the single-quantum antisym-metric stretching excitations001d in the 40 eV spectrum. Incontrast, the relative intensities of the other peaks are com-paratively constant.

Figure 2 shows the vibrational branching ratios for all ofthe observed peaks in the photoelectron spectra over the en-ergy range 17øhnø72 eV. Both theory and experiment areshown, and the qualitative agreement is generally good, andin some cases there is nearly quantative agreement. Thesingle-quantum stretch data were discussed previously,5 andit is now instructive to take a broader view of the completedata set. The most striking feature is that the curves exhibit-

ing a large resonant enhancement athn<42 eV are those forvibrations forbidden by inversion symmetry, namely,v+

=s001d and s010d. The other three curves,v+=s100d, s200d,and s020d, are relatively featureless, although there are no-ticeable weak oscillations about a constant value in thes100dand s200d curves.

The theoretical curves reproduce the main features of theexperiment very well for the single-quantum stretchingbranching ratios, as reported previously.5 There is goodqualitative agreement even for the smaller oscillations in thes100d / s000d curve with the magnitude of the theoreticalcurve being about 50% too large. There are larger discrepan-cies between experiment and theory for the other curves.First, the peak predicted by theory for thes020d / s000dcurves is not evident in the experimental data. This is remi-niscent of the CO2 4sg

−1 study.3,4 Second, the experimentalnonresonant contribution to thes020d / s000d curve is muchlarger than predicted by theory. Third, the peak position ofthe s010d / s000d theory curve is shifted from the experimen-tal result. Fourth, the magnitude of the predicted cross sec-tion for v+=s200d is lower than the measured values. Thesediscrepancies can be understood, and are discussed furtherbelow.

Calculations using the ASME potential reveal the pres-ence of five resonant scattering states occurring over a rangeof energies, and contour maps of the resonant wave functionsare shown in Fig. 3. Note that the energy positions denotedin this figure are expected to be shifted from the actual reso-nant positions. These shifts arise because the potentials usedin to calculate the contour maps differ from those used togenerate the cross sections, as discussed elsewhere.51 We em-phasize that resonances of bothgeradeand ungeradesym-metry are predicted. The ungerade resonances are not dipoleaccessible at any geometry with inversion symmetry, butthey are activated by symmetry-breaking vibrations, as dis-cussed previously.5

In the earlier investigation,5 it was determined that thelarge excursion observed in the antisymmetric stretchingbranching ratiofs001d / s000d, cf. Fig. 2g resulted from the5su→ksu symmetry-forbidden shape resonance. Figure 4shows the results of calculations on that channel in the righthand frames. Specifically, the lower right-hand frame showsthe dipole strength for only theksu channel, and this is donefor three different geometries: the symmetric equilibrium ge-ometry, the molecule distorted by 1.5 times the classicalturning point for the antisymmetric stretching vibrationsq3

=1.5d, and the molecule further distorted toq3=2.5. Theq3

=0 curve is identically zero, as expected for this forbiddentransition, while theq3=1.5 and theq3=2.5 curves havesimilar shapes, albeit with different magnitudes. This simi-larity is reinforced in the upper right hand frame of Fig. 4,which shows the ratio of theq3=2.5 andq3=1.5 curves, andthe result is nearly a constant. In other words, the profile ofthe shape resonance is insensitive to this type of geometrychange,5 which is the atypical behavior discussed in the In-troduction. The 4sg→ksu shape resonance in CO2 behavesvery differently, as shown in the left-hand frames of Fig. 4for comparison. Here, analogous calculations of dipolestrengths for the 4sg→ksu channel of CO2 have been per-

FIG. 2. Measured and theoretical vibrational branching ratios for theCS2

+sB 2Su+d state.

064308-4 Rathbone et al. J. Chem. Phys. 122, 064308 ~2005!

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formed at the same three geometries. The position andwidths of the CO2 resonant feature have a significant depen-dence on the extent of the distortion, and the ratio of thesecurves is not constant as a result.

We note that the CS2 5su→ksu resonance is also rela-tively insensitive to the bending vibration, i.e., the shape andwidth of the resonance is unchanged, but the amplitude ofthe cross section curve increases as the molecule is bent.This is illustrated by the calculatedksu dipole strengthcurves for bending distortions shown in Fig. 5, where theratio of curves is nearly constant. Note that the predictedresonance peak position for the bent moleculeslower frame,Fig. 5d is at higher energy than for the antisymmetricallystretched moleculescf. lower right frame of Fig. 4d. Thisdifference is due mainly to differences in the bending andstretching calculations mentioned above, i.e., the stretchingcalculation included correlated targets whereas the bendingcalculations had only Hartree–Fock targets. This differencebetween stretching and bending calculations is also evidentin the branching ratio curves in Fig. 2.

IV. DISCUSSION

A. Single-quantum bend

The previous study5 of the single-quantum stretching vi-brations had conclusions that are pertinent here. First, theresonant electronic excitation channel is forbidden, but isactivated by a symmetry breaking vibration. Second, this5su→ksu shape resonance is insensitive to changes in ge-ometry in the mode which activate the resonance. Each ofthese conclusions has implications for thes010d / s000d curve

FIG. 3. Contour maps of resonant continuum photoelectron wave functionscalculated at the energies indicated with the indicated widthsG. In thesediagrams, the C atom is located at the origin and the S atoms are located atz= ±2.94 a.u. The 47 eVksu resonance is responsible for the large excur-sion observed in Fig. 2. Thekpg resonances are also observable experimen-tally, as discussed in the text.

FIG. 4. The bottom frames compare the dipole strengths for CS2 5su

→ksu and CO2 4sg→ksu ionization channels. Calculations are done foreach molecule distorted along the antisymmetric stretching coordinate withdifferent amplitudes. Note that the curves are of comparable intensity forCO2, but that the intensities are radically different for the three CS2 curves.With respect to the shapes of the curves, the CO2 curves are shifting andbroadening as the distortion is increasing, while the profiles of the CS2

curves are nearly identical. Only their magnitude changes with the ampli-tude of the vibration. These comparisons are summarized graphically in thetop frames, which show the ratios of theq3=2.5 andq3=1.5 curves from thebottom frames.

FIG. 5. Same as Fig. 4, except for the bending coordinate for CS2 5su

→ksu ionization. Note that the energy range is slightly larger in order todisplay the whole resonance.

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scf. Fig. 2d. First, because this resonance is activated by theantisymmetric stretching vibration that breaks the inversionsymmetry, then it follows that the resonance should also beactivated by the bending vibration, and hence visible in thebending branching ratio,s010d / s000d. Indeed, Fig. 2 showsthat this is the case. There is a more quantitative implication,as well. Because the profile of this resonance is insensitive togeometry changes, one would expect that the branching ratiocurve would closely track that of the antisymmetric stretch-ing branching ratio curve. A cursory glance at Fig. 2 suggeststhat this is the case, and the comparison is revealed moreclearly in Fig. 6, which overlays the branching ratio curvesfor the antisymmetric stretch and bending vibrations. Theyare nearly superimposable, giving credence to the predictionthat this 5su→ksu resonance is insensitive to geometrychanges in the symmetry breaking modes.

B. Single- and multiple-quantum stretches

The comparison between the single-quantum stretchingbranching ratio curves has been discussed previously,5 andfurther implications are described here. The antisymmetricstretch curve has a pronounced peak, while the symmetricstretch curve shows only a slight deviation from being con-stant with energy. The results in Fig. 2 show that we obtainnearly quantitative agreement between theory and experi-ment in the s001d / s000d branching ratio whereas in thes100d / s000d ratio there is a 50% discrepancy in the magni-tude of these curves. We cannot at this time definitively statethe source of this difference, however, it could be due toerrors in the harmonic approximation used in these calcula-tions which may be different in these two cases. We empha-size that the shapes of the experimental and theoreticalcurves are very similar.

As discussed in the Introduction, the effects influencingthe current CS2 5su

−1 branching ratio curvesfparticularlys001d / s000d and s100d / s000dg are qualitatively differentfrom those causing the behavior observed for CO2 4sg

−1

photoionization. The calculations shown in Fig. 4 highlightthe differences. For CO2, the symmetry forbidden vibrations

are induced by variations of dipole amplitudes with changesin molecular geometry, and, in particular, due to the shifts inthe position and widths of resonances.2,3 Indeed, the CO2cross section curves for theksu channel in the lower leftframe of Fig. 4 are evolving as the molecule is deformedalong theq3 coordinate. However, the CS2 mode specificityreported here is evidence for a shape resonant ionizationchannelwhich would not occur in the absence of the forbid-den vibration. The resonant contribution to the cross sectionfor CS2 scf. bottom right frame, Fig. 4d is identically zero forthis channel, and the curve becomes amplified as the mol-ecule is distorted along theq3 coordinate. However, theshape of the curve does not change as the molecule distorts,as it does for CO2.

There are additional lessons to be gleaned from thes100d / s000d curve. This curvescf. Fig. 2d is not constant as afunction of energy, even though it is more nearly constantthan thes001d / s000d curve. This is significant, because thecross section for the symmetry forbidden resonant channelshould be zero in any symmetric geometry. This is an indi-cation that the deviations in thes100d / s000d curve arenotdue to the 5su→ksu resonance. The excursion observed forthis curve occurs at relatively high energys,40 eVd, sug-gesting that the source of the non-Franck–Condon behavioris the result of the 5su→kpg shape resonancescf. Fig. 3dthat occurs in this range. This illustrates that there can beseveral resonant channels available to an exiting photoelec-tron, and they can have qualitatively different sensitivities toalternative vibrational motions. Second, the resonance re-sponsible for the deviations in the symmetric stretch haskpg

symmetry, so this result also demonstrates that continuumelectrons localized away from the bonding axes can coupleto molecular vibration. This is the first instance of such anobservation.

Additional calculations were performed to check theconclusion that the 5su→kpg shape resonance is responsiblefor the energy dependence of thes100d / s000d branching ra-tio. Specifically, the calculations for thes100d / s000d branch-ing ratio curve in Fig. 2 include the zero point motion of theantisymmetric stretch. Thus, one might speculate that the en-ergy dependence is the result of the 5su→ksu resonancerather than thekpg resonance, and the zero-point motion ofthe antisymmetric stretch is responsible for accessing thesymmetry-forbidden resonance. In order to test this, the cal-culation was performed without any zero-point motions ex-cept for the symmetric stretching vibration, and it was deter-mined that the results of calculation were indistinguishablefrom those obtained when the zero-point motion was in-cluded. This is definitive evidence that the 5su→ksu reso-nance is not responsible for the energy dependence of thes100d / s000d curve. The effects of thekpg resonance had ac-tually been observed in the multiple scattering calculationsof Carlson, Krause, and Grimm31 although they did identifythe feature as being due to a shape resonance. In order toverify that the kpg resonances shown in Fig. 3 were notartifacts of the ASME model calculations, we have also com-puted the eigenphase sum for scattering in the 5su→kpg

continuum using the SCSCI model. The eigenphase sum,

FIG. 6. Comparison of vibrational branching ratio energy dependence forthe two forbidden vibrations in CS2. They track each other very closely, andthis is a strong indication that the resonance is vibrationally driven, and thatthe 5su→ksu resonance isinsensitiveto changes in the molecular geometry.

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shown in Fig. 7, clearly shows rises indicative of resonantstates, near bothkpg resonance energiess20 and 44 eVdgiven in Fig. 3.

Given the evidence for the newkpg symmetry shaperesonant channel observed in thes100d / s000d curve, it isreasonable to assume that it might even be more apparent inthe s200d / s000d curve and the results shown in Fig. 2 cor-roborate this reasoning. Thes200d / s000d curve exhibits apronounced maximum athn<40 eV, and the profile of thetheoretical curve matches the experimental data nicely. How-ever, there is a significant discrepancy for the magnitude ofthe peak. Similar discrepancies were observed in 4sg

−1 photo-ionization of CO2, and we have learned that the theoreticalpredictions are strongly influenced by the ion vibrational fre-quency and degree of anharmonicity used in the calculations.However, in preliminary calculations, these effects do notresolve the disagreement between experiment and theory forthe s200d / s000d results.

Finally, it is interesting to consider the sensitivity of theposition of theksu shape resonance as a function of thesymmetric stretching modeq1. As discussed previously,5 thischannel is rigorously forbidden when the molecule has inver-sion symmetry. So in order to interrogate the response of theksu resonance to theq1 mode, the molecule must first bedistorted from its symmetric equilibrium geometry. Whilethis is not feasible experimentally, it is possible theoretically,and is shown in Fig. 8, where we plot theksu contribution tothe photoionization cross section for different values ofq1 ata nonsymmetric geometry, i.e., withq3=2.5. The position ofthe ksu shape resonance is seen to shift by,7.3 eV asq1

varies from −2 to 2. This shift shows that the shape reso-nance is sensitive to symmetric stretching, in contrast to theantisymmetric vibrational modesscf. Figs. 4 and 5d. Forcomparison, we also give the corresponding result for CO2

with q3=0. In that case, the shift in the resonance position is,9.5 eV asq1 varies over the same range. We note that theclassical turning points are nearly the same for the symmetricmodes in these two molecules witha1=0.02790 Å for CO2

anda1=0.028 33 Å for CS2 as noted above. Thus the com-parison given in Fig. 8 for the same values ofq1 correspondto nearly the same changes in bond lengths in CO2 and CS2.One can estimate the expected changes in the position of theresonance based on a particle-in-a-box model using the O–Oand S–S distances as the box length in the two systems. Sucha model predicts thatDEsCO2d /DEsCS2d<1.35, which isvery close to the value of 1.30 obtained from the data givenabove. The results shown in Fig. 8 for CS2 are noteworthybecause they demonstrate that the 5su→ksu resonanceissensitive to the symmetric stretching vibration, but that thissensitivity is not evident unless the inversion symmetry ofthe molecule is broken.

C. „020… / „000… results

The experimentals020d / s000d branching ratio curvedoes not agree well with theory. In the previous CO2 study,4

there was an analogous enhancement predicted for thes020d / s000d ratio, and that enhancement was not observedexperimentally either. In that case, the discrepancy was at-tributed to a Fermi resonance between thes020d and s100dlevels. It is likely that the same effect arises here, as well,given the proximity of thes020d ands100d levels. Vibrationalclose-coupling calculations are planned to address these is-sues, since they appear to be widespread. In addition to thedisagreements with respect to the resonant cross section,there is also a discrepancy with respect to the magnitude ofthe nonresonant cross section for thes020d level. As men-tioned for thes200d excitation, such discrepancies probablyarise from the sensitivity of the cross section to the vibra-tional frequencies and anharmonicities used in the calcula-tions.

There are additional symmetry considerations regardingexcitation of thes020d level. Thes020d vibrational state haseither Sg or Dg symmetry. In the computed cross sections,the dominant contribution comes from theSg vibrationalstate. Thus the vibrational symmetry is the same as for the

FIG. 7. Eigenphase sum for CS2 in the 5su→kpg channel computed withthe SCSCI method.

FIG. 8. Partial cross section for the CS2 5su→ksu andCO2 4sg→ksu ionization channels. Calculations aredone for each molecule distorted along the symmetricstretching coordinate with five different amplitudesq1

=−2, −1, 0, 1, 2, and with a displaced antisymmetriccoordinate ofq3=2.5 in CS2 and in the symmetric ge-ometry,q3=0 in CO2.

064308-7 Photoionization of CS2: Mode specificity J. Chem. Phys. 122, 064308 ~2005!

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process leading to thes000d state. In both cases, the con-tinuum electron can only havesg or pg symmetry. However,at bent geometries, even an electron that leaves in thesg

continuum has a perturbed cross section due to coupling tothe resonantsu continuum. We therefore conclude that thepredicted resonant change in thes020d / s000d branching ratioarises because the vibrational integral for thes020d state em-phasizes the bent angles more than the vibrational integralfor s000d. This is why the predicteds020d cross section isinfluenced more by theksu shape resonance than is thes000dcross section.

D. Comparisons with vibrational sensitivityin other molecules

Note that the mode selectivity observed in the presentwork contrasts sharply with what has been seen in the fewprevious vibrationally resolved studies of polyatomic mol-ecules available for comparison.7,34,52To illustrate the differ-ences, consider the cases of CO2 sRefs. 1–4d and N2O.7,34,52

As already noted regarding CO2 4sg−1 photoionizationscf.

Fig. 4d,3,4 both the position and the width of theksu shaperesonance depends strongly on bending, antisymmetricstretching, and symmetric stretching distortions. For the cur-rent CS2 case, theksu resonance is not sensitive to any ofthese motions at the equilibrium geometry. Second, the CS2

5su→ksu resonance also differs from that of the valenceisoelectronic CO2 3su→ksu shape resonance.1,2 A dispersedfluorescence study on the CO2 3su→ksu resonance demon-strated that that resonance was sensitive to the bending vi-bration. Thirdly, in another study53 on a high energy 7s→ks shape resonance in N2O, both the antisymmetricstretch and the bending vibrations influenced the resonantionization dynamics. Note that N2O does not have a center ofsymmetry so that its two stretching modes are not strictly“symmetric” and “antisymmetric.” However the two stretch-ing vibrational motions in N2O are very similar to the corre-sponding symmetric and antisymmetric modes in CO2 andCS2. The behavior observed in the current CS2 study istherefore by no means typical.

It is also instructive to compare the current trends withthose observed for a near-threshold N2O 7s→ks shaperesonance.7,34,52In that case, the results were the opposite ofwhat is observed here, i.e., the symmetric stretch branchingratio varied dramatically while the antisymmetric stretch wasvery nearly constant. The stretching vibration branching ra-tios are compared for that N2O case and the current CS2 datain Fig. 9, and the differences are readily apparent. In an oddway, the underlying sensitivity of the resonant scattering dy-namics to molecular geometry for this N2O resonance andthe CS2 5su→ksu resonance are quite similar, even thoughthe observed branching ratio trends are not. In the N2O 7s−1

case, it was observed that the shape resonant trapping de-pended on the overall length of the molecule, and that is whythere was sensitivity to symmetric stretching, but not anti-symmetric stretching, as the antisymmetric stretch does notalter the end-to-end length of molecule appreciably. For thecurrent CS2 5su→ksu case, neither the shape or width of theresonance is sensitive to the antisymmetric stretch, and this

is true for the near-threshold N2O 7s→ks resonance, aswell. The difference arises because the resonance is onlyactivated when the symmetry breaking vibration occurs forthe CS2 case, whereas it occurs even in the absence of vibra-tion in the N2O case. In other words, the contrasting behav-ior in the stretching branching ratios illustrated in Fig. 9 isthe result of symmetry considerations rather than a funda-mental change in ionization dynamics.

V. CONCLUSIONS

In summary, we have shown that 5su−1 photoionization

of CS2 has a shape resonance in theksu continuum that isaccessed via symmetry breaking vibrations. As a result, theresonance is readily apparent in vibrational branching ratiosfor symmetry-forbidden vibrations, but not for the symmetricstretch. The electronic resonance and the coupling to forbid-den vibrations can be understood very well by treating thecontinuum electron at the independent particle level, i.e.,without invoking interchannel coupling between alternativehole states of the ion.13,24,54,55In addition to theksu reso-nance, there is clear evidence of a weaker 5su→kpg reso-nance in the same energy range, and this is apparent in thevibrational branching ratio for the symmetric stretchfs100d / s000dg.

Even though the effects of the 5su→ksu shape reso-nance appear similar to those observed for CO2 4sg

−1 photo-ionization, the underlying photoionization dynamics arequite different, as is the nature of the electronic/vibrationalcoupling. While this photoelectron-mediated mechanism hasbeen shown to be operative in exciting forbidden vibrationalexcitations in several recent studies,1–5,10caution is requiredin making assumptions as to the source of symmetry-

FIG. 9. Comparison of vibrational branching ratios for CS2 and N2O. ForCS2, the antisymmetric stretch is very sensitive to the continuum resonancewhile the symmetric stretch is not. The situation is reversed for N2O. Theexperimental and theoretical N2O results are from Refs. 7 and 34,respectively.

064308-8 Rathbone et al. J. Chem. Phys. 122, 064308 ~2005!

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forbidden vibrational excitations. It is possible and evenlikely that the more traditionally cited interchannel mecha-nism might be responsible in some cases—or even possibly,a combination of the interchannel and intrachannel mecha-nisms might be responsible. With that said, it is fortunate thatthe photoelectron mediated mechanism appears to be rathercommon. This is because when the photoelectron-mediatedmechanism is operative, studies of the resonance sensitivityto alternative geometries become straightforward, as shownin several recent studies1–5,10 as well as the current report.Normally, one assumes that shape resonances—whether pro-duced via valence shell ionization11,12 or observable in x-rayappearance near-edge structure spectra56–58—are affected bygeometry changes and this sensitivity to geometry leads tonon-Franck–Condon behavior. Here we see that the modesthat are active do not shift the resonance but gain intensitythrough symmetry breaking. These observations reinforcethe general strategy of using state-resolved measurements toprobe the response of the photoionization dynamics to se-lected changes in molecular geometry. Polyatomic systemsprovide different opportunities, as there are many classes oflocalization phenomena which may occur, and the nature ofthe continuum localization can be interrogated in complexpolyatomic systems using the increased vibrational degreesof freedom available in complex systems.

ACKNOWLEDGMENTS

The authors acknowledge the support of the ChemicalSciences, Geosciences and Biosciences Division, Office ofBasic Energy Sciences, Office of Science, U.S. Departmentof Energy, R.R.L. also acknowledges the support of the Rob-ert A. Welch FoundationsHouston, Texasd under Grant No.A-1020, and the support of the Texas A&M University Su-percomputing Facility. J.D.B. and the Advanced LightSource are supported by the Director, Office of Science, Of-fice of Basic Energy Sciences, of the U.S. Department ofEnergy under Contract No. DE-AC03-76SF00098.

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