predissociation dynamics of i2 b in liquid ccl4 observed...

Predissociation dynamics of I 2„B … in liquid CCl 4 observedthrough femtosecond pump-probe measurements:Electronic caging through solvent symmetry

R. Zadoyan, M. Sterling, M. Ovchinnikov, and V. A. ApkarianDepartment of Chemistry, University of California, Irvine, California 92697-2025

~Received 4 April 1997; accepted 18 August 1997!

Direct observations of the solvent induced electronic predissociation of I2(B) in liquid CCl4 aremade using femtosecond pump–probe measurements in which fluorescence from spin–orbit excitedI* I* pairs, bound by the solvent cage, is used as detection. Data is reported for initial preparationsranging from theB state potential minimum, at 640 nm, to above the dissociation limit, at 490 nm.Analysis is provided through classical simulations, to highlight the role of solvent structure on:recombination, vibrational relaxation, and decay of coherence. The data is consistent with ananisotropic I2(X) – CCl4 potential which, in the first solvent shell, leads to an angular distributionpeaked along the molecular axis. The roles of solvent structure and dynamics on electronicpredissociation are analyzed. The data in liquid CCl4 can be understood in terms of a curve crossingnearv50, at 3.05 Å,Rc,3.8 Å, and the final surface can be narrowed down to 2g or a(1g). Thisnonadiabaticu→g transition is driven by static and dynamic asymmetry in the solvent structure.The role of solvent structure is demonstrated by contrasting the liquid phase predissociationprobabilities with those observed in solid Kr. Despite the twofold increase in density,predissociation probabilities in the solid state are an order of magnitude smaller, due mainly to thehigh symmetry of the solvent cage. The role of solvent dynamics is evidenced in the energydependent measurements. Independent of the kinetic energy content in I2, electronic predissociationin liquid CCl4 proceeds with a time constant equal to the molecular vibrational period. A modifiedLandau–Zener model, in which the effective electronic coupling is taken to be a linear function ofvibrational amplitude fits the data, and suggests that cage distortions driven by the molecule enhanceits predissociation probability. A nearly quantitative reproduction of the observations is possiblewhen using the recently reported off-diagonal DIM surface that couples theB(0u

1) anda(1g) states@Batista and Coker, J. Chem. Phys.105, 4033 ~1996!#. © 1997 American Institute of Physics.@S0021-9606~97!00544-8#

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I. INTRODUCTION

Ever since the first experimental studies of Eisentet al.,1 the solvent induced predissociation of theB(3P0u

1 )electronic state of molecular iodine has become a prototfor investigating nonadiabatic dynamics in condensed meThe literature on this subject is extensive. Here we citselect set of recent developments, noting that extensivetions of the relevant literature are given in thereferences.2–12 With the combination of ultrafast experimentation, and nearly exact numerical methods for treating nodiabatic many-body dynamics,9,11,12 an accurate descriptioof the coupled electronic-nuclear dynamics in this mosystem including all electronic states, now seems a realgoal.

The picosecond era of measurements in the liqphase,2 mostly through transient absorption measuremeconcluded that the predissociation of I2(B) occurs on a timescale shorter than 1 ps.3,4 The fact that electronic predissociation proceeds on a time scale comparable to vibratioperiods, immediately raises doubts about the notion ofscribing the underlying dynamics as a rate process, andcharacterization by a single decay constant.

With a time resolution of 30 fs, Schereret al.studied the

8446 J. Chem. Phys. 107 (20), 22 November 1997 0021-9606/

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predissociation dynamics of I2(B) in the liquid phasethrough careful measurements and analysis of transienchroism and birefringence.5 They prepared the excited stausing short pulses at 580 nm, and monitored the time evtion of the prepared coherence with variable wavelengThey concluded that the decay time of the prepared coence of 230 fs was controlled by predissociation, confirma time scale shorter than the equilibration of nuclear coonates. Moreover, based on probe wavelength dependenthe appearance time of the transient, among the severalsible curve crossings13 ~see Fig. 1!, they concluded that thelikely candidate for the main predissociation channel wasa(1g) surface.5

With the advantage of structural order, measurementthe same process in the solid state could provide an ational tool for characterizing this solvent induced intramlecular electron transfer. We reported such studies performin solid Kr, in which we used femtosecond pump–prospectroscopy relying on fluorescence from the molecular ipair states.6 We showed that for very similar initial preparations of the molecule, the solid state predissociation prabilities were nearly an order of magnitude smaller than whad been observed in the liquid phase.6 Given the nearlytwofold increase in local density, an order of magnitude

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8447Zadoyan et al.: Predissociation of I2(B) in liquid CCl4

duction in curve crossing probabilities is not a trivially ovious result. A more direct comparison of observables, usthe same experimental technique, seemed warranted. Inpaper we report single color pump-probe studies in liqCCl4, with initial preparation that spans the full range of tmolecular potential, from minimum to above dissociatilimit. Our liquid phase measurements are in agreement wthose of Schereret al. Indeed predissociation in the solistate is slower than in the liquid state. We will argue that tresult can be understood in terms of the local solvent stture. After narrowing down the main predissociation chanto a(1g) or 2g surfaces, we recognize that the requisitepolar character of the off-diagonal surface that couples thstates undergoes severe cancellation when the local sostructure is highly symmetric. The electronic curve crossis induced by static and dynamic solvent asymmetry, a clective effect which does not simply scale with solvent desity.

Quite relevant to the condensed phase studies arehigh pressure gas phase measurements of Zewailet al.,7,8

who in their most recent work show a strongly nonlinedensity dependence ofT2 and T1 times, whereT1 can beidentified with the predissociation of I2(B).8 These experi-ments help identify the nature of the off-diagonal matrixements that lead to predissociation. Both long rangeshort range interactions are implicated.

On the theoretical front, we mention three important dvelopments. In an ambitious undertaking, Batista and Co~BC!, have presented simulations of I2 first in liquid Xe,9~a!

and more recently in solid Ar and Xe,9~b! in which nonadia-batic transitions among all 23 states that correlate withground I(2P)1I( 2P) have been included. They constructsemiempirical diatomics-in-molecules~DIM ! Hamiltonian

FIG. 1. Relevant potential curves. The pump-probe experiments preparB state, and interrogate the time dependent populations by a varietdipole allowed transitions, as indicated by the up-arrows. FluorescenceI* I*→I* I is used as detection, with a variety of direct and indirect channleading to the population of the upper state. The indicated curves that cthe B state were taken from Ref. 13.

J. Chem. Phys., Vol. 107, N


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matrix for the I2–Rg interactions, and propagate trajectoron the coupled electronic surfaces. A DIM Hamiltonian fI2–Ar was also constructed by Buchachenko and Stepanwho dissected the I2–Ar surfaces and off-diagonal couplinginvolving the B state.10 The reported simulations with thDIM potentials lead to extremely rapid predissociatiothrough a variety of crossings, in qualitative agreement wthe liquid phase results. However, the solid Ar simulatioalso predict ultrafast predissociation, now in discord wexperiment. It would seem that adjustment of the elementthe DIM Hamiltonian are necessary, and at present, eximents are the only viable means to this end.

Ben-Nun and Levine considered the liquid phase predsociation of I2 through simulations that carefully treat thnuclear nonadiabatic dynamics, while assuming a simplifielectrostatic model for the electronic coupling betwestates.11 Their treatment is limited to the consideration of thcrossing betweenB(0u

1) anda(1g) curves, and designed tbe in agreement with the experiments of Schereret al.5 Theyunderscore the strong local density dependence of ratetheir model, which would suggest that predissociation insolid state would be significantly faster than in the liquphase. A more careful treatment of the electrostatic coupwas provided by Roncero, Halberstadt, and Beswick,~RHB!,in their treatment of the predissociation of the I2–Ar van derWaals complex, in which they explicitly indicated the anglar anisotropy of the coupling surface.12 As we elaborate, thisis implicit in the DIM treatment,9,10and key to understandingpredissociation in dense media.

The usual femtosecond pump-probe measurements o2

use the molecular ion-pair states as the terminus forprobe transition.14 Such measurements have not been psible in the liquid phase, due to rapid quenching of the iopair states in such media. To overcome this difficulty oexperiments were designed to use the I* I* surfaces as finastates. All three states that arise from I* (2P1/2)1I* (2P1/2)are repulsive~see Fig. 1! and do not sustain population in thgas phase.15 However, in condensed media, the pair of spexcited atoms can remain in contact per force of the solvcage, with radiation as their main relaxation channel. Atailed spectroscopic analysis of these transitions, andphotodynamics of the doubly spin-excited I* I* states in vari-ous liquids and solid matrices, has already been given.16 Inthe time resolved studies we report here, we useI* I*→I* I emission as detection. Note, in principle boB(0u

1) and a(1g) states can be probed viI* I* (0g

1)←I* I(B(0u1)) and I* I* (1u)←I2(a(1g)) transi-

tions, as indicated in Fig. 1. However, the strongE←B tran-sition, masks the absorption from thea(1g) state, precludingdirect experimental information about its role.

We follow the format of dynamical spectroscopy as pviously outlined.6 The experimental observables, consistiof time dependent resonances, are analyzed with the heclassical simulations. The methods of experiment and simlation are presented in Secs. II and III, respectively. Texperimental observations are summarized in Sec. IV,analyzed in Sec. V. In Sec. VI we discuss the implicatio

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8448 Zadoyan et al.: Predissociation of I2(B) in liquid CCl4

with a critical evaluation of theories. Concluding remarks aprovided in Sec. VII.

II. EXPERIMENT

The experimental setup is illustrated in Fig. 2. The msurements are conducted in a two-window quartz cell ctaining a static solution of I2 in liquid CCl4. The concentra-tion of the solution is adjusted to an optical density of;1 at520 nm. The data are quite insensitive to concentration.

The laser source consists of a femtosecond Ti:Sapposcillator, the 800 nm output of which is stretched, regenetively amplified and recompressed to 55 fs at a repetitionof 1 kHz ~0.7 mJ/pulse!. The amplified output is then used tpump a BBO based three stage optical parametric amplwith 20% conversion efficiency. The OPA output is uconverted using a 0.5 mm thick BBO crystal, either by dobling or by summing with the 800 nm fundamental. Thallows a coverage of the spectral range between 480 andnm. A prism compressor, with a limiting diaphragm befothe folding mirror, is used to maintain near transform limitpulses throughout the tuning range of the OPA with typipulse widths of 50–65 fs. The compressor is adjustedcompensate for group velocity dispersion~GVD! introducedby optical elements in the beam path before it reachessample. The compressed, up-converted output of the OPsplit evenly with a 50% beam splitter in a Michelson-tyinterferometer. After passing through a variable delay liusing a single lens (f l 520 cm), the two beams are recombined at an angle of 5° immediately behind the entrawindow of the cell. The noncollinear geometry of the expement avoids interferometric noise in these single colorperiments at the expense of sacrificing time resolution. Aof recombination angle, with a beam waist of 0.1 mm atcrossing point, the time resolution broadens by;10%. Theexperimental time resolution is verified for each wavelenby measuring the autocorrelation trace when the liquid ce

FIG. 2. Experimental layout.



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replaced with a 0.2 mm thick BBO crystal. The intensitiesboth beams are attenuated by a factor of;2 below the whitelight generation limit in the cell.

Infrared fluorescence from the beam overlap regioncollected at right angle, with a single lens, through a 0.25monochromator, and detected with a liquid nitrogen cooGe detector~response time50.5ms!. The detector output isamplified and integrated with a boxcar while simultaneoumonitoring the OPA output through a second channel ofboxcar integrator. Data is collected when the reference sigfalls within a 2% window of a preset level. Typically, at eacdelay, 1000 selected pulses are acquired and averagedcomputer.

The experiments to be reported consist of single copump–probe measurements. Accordingly, the transieshould in principle be strictly symmetric in time. A systematic linear deviation from such a symmetry, of;50 fs over ascan of 1 ps is observed experimentally. Using interferefringes from a He:Ne laser we have verified that this is nthe result of nonlinearity in the mechanical drive, and ascrit to a combination of beam walk-off in the unconstrainvolume of the solution, and spatial chirp in the pulses. Athough the effect is noticeable, we do not correct the datathis systematic error.

III. SIMULATIONS

The classical molecular dynamics simulations usedthe interpretation of the data to be presented are carriedby standard methods. A cell of 108 particles subject to podic boundary conditions is considered, and the equationmotion for the microcanonical ensemble are propagateding the Verlet algorithm. With the pair potentials defined, tcell dimensions are adjusted such that the pressure ofsimulated system fluctuates aboutP50, while the tempera-ture fluctuates aboutT5300 K. This corresponds to a reduced density ofr* 50.7 in the present simulation of CCl4

under room temperature and pressure conditions. The C4

molecules are represented by single particles with pairwadditive Lennard-Jones intermolecular potentials,17 for pa-rameters see Table I. Two different potential constructsused to describe the I2–CCl4 interaction in the groundX(1Sg

1) state of the molecule. The first, to which we referisotropic potentials, consists of pairwise additive atom–atpotentials, in which the I–CCl4 potential is treated asLennard-Jones, with parameters suitable for Xe–CCl4 inter-action~see Table I!. The second, to which we refer as anistropic potentials, is a three body potential constructed as

V~ I2~X!– CCl4!5 (i 51,2

cos2~u i !VS~r i !

1sin2~u i !VP~r i ! ~1!

in which the indices 1 and 2 refer to the I atoms,u is mea-sured from the I–I axis,VS andVP are expressed as Morsfunctions, derived from known I–Rg potentials,18 and scaledby the rules appropriate for nonbonded interactions

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in which De , r e , andb are the Morse parameters, ands ande are the Lennard-Jones parameters for Rg–RgCCl4–CCl4 interactions. Note, in the form given in Eq.~1!,VS is responsible for the linear well on theI–I–CCl4 surface.It can be shown, quite generally for rare gas–molecular hgen interactions, that the linear well arises from the admture of ionic character in the ground surface.19 Accordingly,in polarizable media in which the ionic excited statesstrongly solvated, it can be expected that the linear minwill be even deeper. The ground state potential determstructure of the solvent from where the excitation is initiateand will accordingly effect coherences, recombination aenergy dissipation. In the excitedB(3P0u

1 ) state, the I–CCl4

potentials are treated as isotropic. The justification for usan anisotropic ground state and isotropic excited state atoatom potentials has been given before.19–21

The simulations are started by Monte Carlo samplinginitial conditions from a file thermalized on the ground staThe excited state potentials are then used to propagateequations of motion. In accord with the Franck–Condprinciple for vertical excitations, the initial I–I coordinatdistribution is chosen to match the reflection of the laspectral distribution from the difference potential of ttransition.22 The pump-probe signal can then be generafrom an ensemble ofN trajectories by temporal and spectrconvolution of the probe laser with the many-body diffeence potential

TABLE I. Potential parameters used in simulations.

Lennard-Jones:V54e@(s/r )122(s/r )6#

s(Å) e(cm21)

CCl4–CCl4 5.881 227I(B) – CCl4 ~Xe–CCl4! 4.968 190Xe–Xe 4.055 159

Morse:V5De@12exp(2b(r2re))#2

De(cm21) r e(Å) b(Å 21)

VS (I–CCl4) 336 4.96 1.12VP (I–CCl4) 147.5 5.71 1.16I2(B) 4503.6 3.016 1.85I* I(1g) 240 6.2 0.46

Exponential:V5C11C2 exp(2r/C3)

C1(cm21) C2(cm21) C3(Å)

I2(a) 11928 6.343107 0.33



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in which the indicesn and m refer to the initial and finalelectronic states of the probe transition, and at a time deltbetween pump and probe pulses, the probe laser intensicharacterized spectrally and temporally by the window fution, W(hnprobe,t).

22 In practice, since the many-body eletronic surfaces are not knowna priori, the interpretation ofobserved transients is greatly simplified by an effective odimensional inversion of the trajectory data, under thesumption that the probe difference potential is mainly goerned by the I–I coordinate,R. For a fixed probe resonancethis also allows the neglect of the coordinate dependent tsition dipole. Thus

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3d@R2Ri~ t8!# ~4!

in which the one-dimensional resonance condition is usetransform the probe laser spectral distribution to coordinspace, where it is further approximated that the windfunction is a Gaussian in space and time, which is centereR* along the I–I coordinate with a spatial width ofD.22

Note, DV(R) is the difference between a pair of solvateiodine states. While educated guesses can be made abosolvated potentials, for configurations reached in ultrafpump–probe studies there usually is no independent inmation. In practice, the inversion is made with an ensemof trajectories for the I2 internal coordinate, withD andR*as adjustable parameters. A faithful reproduction of theserved transients is then taken as a consistency check ininterpretation of the underlying dynamics and the effectsolvated potentials.

All of the data to be reported here are single copump–probe measurements, where att50 each of the laserpulses serve as both pump and probe. Accordingly,S(t) issymmetric with respect to the time origin. This consideratiis most conveniently accommodated by first reflectingtrajectory ensemble aboutt50, and then carrying out theconvolution of Eq.~4!, using the experimentally measureauto correlation width of the laser ford.

The classical simulations are carried out on a single etronic surface, theB state potential of I2. Yet, we expectsignificant predissociation in the liquid phase. In the effetive one dimensional treatment of transients, the LandaZener model for curve crossings is the natural framework

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use.23 Accordingly, for population prepared and probedthe B state, the signal may be fitted by weighting the trajetories based on the number of crossings they undergo bereaching the probe window

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whereP12 is the Landau–Zener probability of remaining othe initial surface

P12~vc!5expS 24p2^V12&

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huvc~]V2 /]R2]V1 /]R!uR5RcD . ~7!

While consistent with the method used for the inversiontrajectories, this one dimensional curve crossing probabis only an approximation of the many-body problem at haNevertheless, as in the case of the reduction of the mabody resonances using an effective solvated potential,expect this treatment of predissociation to be useful inderstanding the transients, with the caveat that the coupmatrix elements,V12&, that are extracted must be regardaseffective matrix elements between solvated potentialseraged over solute–solvent configurations.

IV. EXPERIMENTAL RESULTS

A. Pump–probe transients in CCl 4

Two-photon excitation of I2 in room temperature liquidsolutions leads to near infrared emission from the thermequilibrated 0g

1 , 0u2 , and 1u surfaces that arise from th

interaction of a pair of spin–orbit excited iodine atoms16

The liquid phase single color pump–probe studies whichreport here, rely exclusively on this fluorescence as detion. In Fig. 3 we show pump–probe transients obtainedwavelengths ranging from 640 to 480 nm, i.e., for prepation of the molecule in itsB state, from the potential minimum to above the dissociation limit. The transients dewithin 200 fs,t,700 fs, after showing a few oscillations. Iall cases there is a contribution to the signal att50, thereforea probe resonance near the inner branch of theB potential.As the wavelength is shortened, a dip develops att50, dueto a delayed resonance which occurs at a time less thanthe vibrational period. This would indicate that a secoprobe window opens for stretched geometries of the mecule. The relative contribution from the outer window dcreases progressively as the excitation energy is lowesuch that at 580 nm, only the inner window contributes tosignal. Also noticeable is the distinctly different appearanof the transients at wavelengths ranging from 600 to 640Here, after thet50 signal, the packet returns to the inn



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turning point in a vibrational period, yet it no longer showany oscillations. We will fix the locations of the windowwith the aid of simulations, then rationalize the implied resnances. What is clear at the onset is that since theB state isinitially prepared, the rapid decay of the signal results fropopulation loss, the result of predissociation. Reliable detimes can be extracted from the data, as we describe beInspection is, however, sufficient to conclude that the higthe initial preparation energy in theB state, the longer is theelectronic lifetime: the observed predissociation is domnated by a crossing near the potential minimum.

B. Pump–probe transient in solid Kr

The rapid predissociation observed in liquid CCl4 is tobe contrasted with what is observed in solid Kr. Sincepreviously reported data in Kr were obtained by two-comeasurements,6 to ensure that the comparison is direct, hewe provide a single color measurement. In Fig. 4 we shotransient from solid Kr, using 556 nm to pump and to probwith the E(0g) ion-pair state acting as the upper state in tprobe transition. This transient is nearly identical to whwas previously reported in the two-color experiments,6 andyields itself to the same interpretation presented there. Adtionally, the one-color experiment clearly marks the origintime, and uniquely identifies the probe window locationthe outer turning point of theB potential. It is unambiguousthat the observed transient is in the initially accessed stthe B state, and not the result of trapping in the lower eletronic manifold after predissociation, as assumed by Batand Coker in their interpretation of our published data.9~b!

FIG. 3. Single color pump–probe transients in liquid CCl4.

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V. ANALYSIS

Gross features of the liquid phaseB state dynamics canbe directly read from the experimental transients in Fig.The data indicate that:~a! predissociation of theB state oc-curs on a time scale of;0.5 ps;~b! when prepared near thmiddle of the potential, at 580 nm, predissociation procewith complete retention of vibrational coherence;~c! whenprepared in the anharmonic part of theB state, near its dis-sociation limit or above, nuclear coherence is lost on the tscale of predissociation;~d! predissociation is most rapid athe bottom of the potential. Furthermore, by comparison wthe data in Fig. 4, it is possible to conclude that predissotion in solid Kr is an order of magnitude slower thanliquid CCl4. To further characterize the system parameteris necessary to quantify energy dissipation from I2 to thesolvent, and to locate the curves responsible for predissotion. This information is more subtly encoded in the expements, and requires scrutiny through simulations. We bewith a discussion of the anticipated resonances, prior tosection of the pump–probe transients.

A. Excitation resonances

If we restrict ourselves toDV50 transitions andu↔gselection rules, in the spectral range of the experiments, ttransitions probe the B state: a8(0g

1)←B(0u1),

I* I* (0g1)←B(0u

1) andE(0g1)←B(0u

1). The latter only be-comes accessible due to solvation of the ion-pair states indielectric of the medium, the extent of which may be esmated from the Onsager cavity model24

Es58m2

d3

~e21!

~2e11!'

e2

r e

~n221!

~2n211!~8!

in which the cavity diameter is approximated asd52r e ,where r e53.6 Å, is the equilibrium bondlength of the ionpair state.25 Using the index of refraction of CCl4, n51.46, avertical electronic solvation of;7000 cm21 can be antici-pated. This estimate is quite sensitive to the choice of ca

FIG. 4. Single color pump–probe transients in solid Kr, obtained at 556and using ion-pair state fluorescence for detection.



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radius, which is an ill-defined quantity. A vertical shift o;6000 cm21 is more consistent with the resonances etracted from the dynamical simulations, as will be elaborabelow, and well within the uncertainty in the cavity modeWe have used this shift in Fig. 5 to show the predictedE–Bdifference potential, which is double valued for all probwavelengths.

The only resonance that is accessible after predissotion, from states that correlate with I(2P1/2)1I( 2P1/2), is theI* I* (1u)←I2(a(1g)) transition. This difference potentiavalid after the crossing point,Rc53.16 Å,26 is single valuedas shown in Fig. 5. Since at large internuclear distancestransition corresponds to a double spin–flip, it can bepected to be rather weak. While selection rules allowconnection of all states correlating with the ground stateoms to ion-pair states, none of these resonances lie inwavelength range of our studies.

The presence of a peak at the time origin of all transieshown in Fig. 3, suggests the presence of a probe windowthe repulsive wall of theB state throughout the wavelengtrange 640–490 nm. Thea8←B transition can act as suchresonance, as illustrated in Fig. 5. The requirement forfluorescence channel is that the excitation terminate abthe crossing betweena8 and I* I* surfaces~see Fig. 1!. Also,at the short internuclear distances corresponding to inturning points of theB state,L–S coupling will prevail, andstrict Hund’s case~c! considerations are no longer valid. Under case~a! we can find a variety of transitions that coupthe repulsive wall of theB state to the repulsive potentiathat arise from both I1I and I*1I limits, above their cross-ing with the I*1I* potentials. The inner resonances leadito a signal at time origin can be rationalized, however,curves at these short internuclear distances are poknown, and the difference potentials in Fig. 5 are only usas guidance. Quite clearly, multiple probe windows will

,

FIG. 5. Difference potentials that serve as probe transitions. In the leg** refers to I* I* . The probe window locations extracted from the simutions of the data are shown as open circles.

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active in the detected signals, and should be taken into csideration in the interpretation of data.

B. The 580 nm transient, coherent predissociationand vibrational relaxation

The 580 nm transient shows the most regular oscitions, with evidence of only one active probe window. Aexpansion of the transient, shown in Fig. 6, resolves a dithe signal att50. This would signify a time delay betweelaunching the wave packet on theB surface and its arrival tothe probe window. With the help of trajectories shownFig. 6~b!, this delay allows an accurate location of the prowindow atR* 53.05 Å, ~see vertical arrow in Fig. 6!. Sincethe temporal width of the probe window is fixed by the mesured auto correlation of the laser pulse as 95 fs, onlyvariables remain to simulate the signal: the spatial widththe probe window,D, and the predissociation probability. Aadequate reproduction is obtained, as shown in Fig. 6~a!,when usingD50.075 Å, and assuming predissociation v

FIG. 6. Analysis of the 580 nm transient using molecular dynamics silation. The experimental data points are shown as open circles in thepanel. The simulated signal is shown as the continuous line~based on 360trajectories!. In the lower panel, a set of representative trajectories, foldet50, is shown. The dip att50 in the data helps to fix the probe windowlocation with accuracy. A delay in the appearance of the resonanc;50 fs~vertical line!, locates the probe window at 3.05 Å~horizontal line inlower panel!.



n-

-

in

e

-of

a(1g) with an effective coupling matrix elementu^VB2a&u5175 cm21 ~Rc53.16 Å, and DudV/dRu513 200 cm21

Å1!.While the predissociation probability per crossing is w

determined by the above analysis, the assumed parametethe one dimensional Landau–Zener model are not indepdently determined. However, with respect to the locationthe crossing,Rc , the analysis firmly establishes that it muoccur at an internuclear distance greater than the probedow, i.e., Rc.R* 53.05 Å. Had this not been the case,very different intensity ratio would have been observedthe first two resonances, as illustrated in Fig. 7. The diffence between these two conditions arises from the factthe first resonances is due to the outgoing packet alone, wthe subsequent resonances consist of both outgoing anward moving packets@see Fig. 6~b!#. The first resonance corresponds to a half-period sampling of the potential, whilesecond is a full-period sampling. Thus the relative ratiothe first resonance to latter resonances will dependwhetherRc occurs before or after the first observation of tpacket atR* . Only the latter case is consistent with the da

We may safely conclude that:~a! the predissociation occurs at Rc.3.05 Å, and therefore cannot be due to tB9(1u) surface@see Fig. 1#; ~b! the parameters used yield thcorrect magnitude of predissociation,;60% per period.

Vibrational energy relaxation is an integral part of thobserved signals and their interpretation. Since CCl4 istreated as structureless, it may be expected that the vitional energy transfer to the solvent is underestimated. Tcould affect the interpretation of predissociation parameextracted from fits, since the LZ probabilities are determinby instantaneous velocities atRc , which in turn are deter-mined by the instantaneous vibrational energy content inmolecule. The time dependence of the period between olations of the signal contains this information, and can,this case, be extracted from an analytical fit to the expment. Taking into account the inverse velocity dependeof the signal intensity,22 and an exponential decay of popu

-op

t

of

FIG. 7. Expected signals for curve crossing before arriving to the prwindow ~solid line! and after passing through the probe window~dashedline!.

o. 20, 22 November 1997


b

wnsalt

the

rgt

rg

n

De

e

notisa-

0

epul-

m-ell

ase,

henentof

on-

be

of

for

hisne

. 5,

mlso

beiodomon.aysys,thee

ely.as-

. 5.ol-


lation due to predissociation, the oscillatory signal canrepresented as

S~ t !5e2t/tLZ

AE~ t !2V*@11 f ~ t !sin~v~ t !t1w!# ~9!

in which V* is the value of the potential at the probe windolocation, R* ; f (t) describes the decay of the modulatiodepth due to decay of coherence among the trajectoriephase space; andE(t) describes the dissipation of vibrationenergy. For a given function ofE(t), the time dependenangular frequency is obtained for the Morse oscillator as

v~ t !

2pc5ve22vexen~ t !

5vexe

1A~ve2vexe!224vexe@E~ t !2ve/22vexe/4#.

~10!

The 580 nm data can be well fit by this expression underassumptions of complete coherence and exponential endecay

f ~ t !51, and E~ t !5E0 exp~2t/tv!. ~11!

With a vibrational energy relaxation time oftv510 ps, apredissociation time constanttLZ5320 fs ~and w51.4 rad!,the experimental data can be well described~see Fig. 8!. Thefunctional fit enables the simultaneous extraction of enedissipation and predissociation rates, without resortingsimulations. The extracted value oftLZ5320 fs correspondsto the vibrational period oftn5313 fs of the initially pre-pared vibration~n513 prepared at 580 nm!, therefore con-sistent with the predissociation probability of;60% per pe-riod derived above. The data is not sensitive to the enedissipation rate as long astv /tLZ.10; i.e., energy relaxationis insignificant within the electronic predissociation time. Aequally good fit to the data is obtained when using forE(t) afunctional fit to the energy loss curve obtained from the Msimulations, which is better described as a double expontial decay~see below!. In short, the vibrational energy in th

FIG. 8. Fit of the 580 nm transient to the analytic form of Eq.~9! in the text.



e

in

ergy

yo

y

n-

B state, and therefore the instantaneous velocities atRc , arereliably treated in the simulations. The experiment doesdeterminetv with any accuracy since the observation timelimited by predissociation, which is much faster than vibrtional relaxation.

Finally, the analysis fixes the probe window atR*53.05 Å for a probe wavelength of 580 nm (17256250 cm21). To rationalize this window location it wasnecessary to assume a somewhat steeper curve for the rsive I* I* (0g

1) potential in Fig. 5 than Mulliken’s originalguess.15

C. The 556 nm transient, coherent dynamics in solidKr

The solid state data is included here to make direct coparisons. We simulate the signal in this case using the wdetermined parameters of the probe window,R* 53.7 Å andthe same curve crossing parameters as in the liquid cexcept for the effective coupling element,u^V12&u. Now, theexperimental transient is reproduced as shown in Fig. 4 wu^V12&u565 cm21 is used. The parameters used in the presare similar to those previously extracted in the analysispredissociation in Kr, where the measurements were cducted using a uv probe laser tuned to thef (0g) ion-pairstate.6 In the present single color measurement the proaccesses the minimum ofE(0g) ion-pair state. In our priortreatment we assumed exponential decay of theB state popu-lation due to predissociation, and extracted a valueu^V12&u55467 cm21. Here, we explicitly treat the curvecrossing during the simulations.

D. The 515 and 490 nm transients, loss of coherence

Similar transients are observed at 490 and 515 nm,initial preparations above theB state dissociation limit andnear it, respectively. In both cases a sharp peak att50 isobserved, followed by a broader peak att5130– 160 fs, i.e.,at a time delay shorter than half the vibrational period. Twould imply the presence of at least two probe windows, oon the repulsive wall and one on the attractive wall of theBpotential. Based on the difference potentials shown in Figif we ascribe the outer resonance to theE←B transition, thenthis window further splits into two, necessitating a minimuof three probe windows in the simulation. The data ashow a resonance after a time delay of 0.5 ps, which canascribed to a recursion to the outer window after a full perin the bound region of the potential. This peak arises frthe fraction of the molecules that undergo head-on collisiNo further oscillations are evident, and the signal decexponentially pastt50.5 ps. The signals are simulated bincluding weighted contributions from three probe windowwhile using the same predissociation parameters as in580 nm data~see Fig. 9!. The results are not sensitive to thparameters of the inner window, which is fixed atR*52.75 and 2.9 Å, for the 490 and 515 nm data, respectivThe outer probe window parameters are adjusted. Thesumed locations of the probe windows are marked in FigThey are only approximately predicted by the vertically s

o. 20, 22 November 1997


econd

veebu

he

tsedwi

em

isre,e

essofsi-lf.e

denwith

uf-ndnureenicthe

f

theheglared

.

nd

n-r (er


vated one-dimensional difference potential. As in the cassolid state analysis, the data suggests that solvation is acpanied by a stretch of 0.1–0.2 Å in the ion-pair bolength.27

According to Fig. 5, at these probe wavelengths, wapackets on thea(1g) surface could also contribute to thsignal; however, a careful analysis shows that this contrition will be masked by theE←B resonance~see the Appen-dix!. The transient has little information content about tfinal electronic state.

The adequate reproduction of the observed transienFig. 9 establishes that the predissociation parameters usthe analysis of the 580 nm transient are also consistentthose at 515 and 490 nm.

A major difference between dynamics when the systis prepared in the deeply bound part of theB potential, at 580nm, versus those created in the anharmonic part near dciation is that the vibrational coherence decays prior to pdissociation. In fact, the classical vibrational coherencemeasure of which is the time dependent ensemble averagthe molecular bond lengthR(t)&, is lost after the first periodof motion in the simulations. Given the similarity in massof I atoms and CCl4, extensive energy loss occurs in the fircollision with the solvent, and the thermal distributionimpact parameters is sufficient to ensure that the disperin recombination times~or recursion times to the inner turning point! is larger than the subsequent vibrational haperiod. As a result R(t)& does not show any oscillationsThis is in contrast with the solid state, in which it has be

FIG. 9. Simulation of the 490 and 515 nm transients, using the three icated windows in Fig. 5.



ofm-

-

-

inin

th

so--aof

t

on

-

n

shown that structural order of the solvent ensures sudcage induced recombination, and therefore proceedspreservation of vibrational coherence.27 A sudden recombi-nation wave, arising from the fraction of molecules that sfer head-on collisions, is present in the liquid phase agives rise to the peak neart;0.5 ps. The contrast betweethis peak and the underlying tail is dictated by the structof the first solvation shell, which in turn is dictated by thsolute–solvent interaction potential in the ground electrostate. To reproduce the signal, it was necessary to useanisotropic I2(X) – CCl4 potential which sustains minima o1.5KBT along the linear geometry~seeVS in Table I!. Acomparison of the thermal solvent structure forced byanisotropic and isotropic potentials is shown in Fig. 10. Tanisotropic I2–CCl4 potential produces significant structurinof the first solvent shell, leading to maxima in the angudistribution along the molecular axis. To optimize avoidvolume, a;30% reduction of the distribution in the ‘‘T’’-geometry relative to that of the isotropic potential occurs

i-

FIG. 10. Structure of the CCl4 solvent for isotropic~top! and anisotropic~bottom! I2(X) – CCl4 potentials obtained by Monte Carlo sampling~106

configurations in each case!. The same contour levels are used in both paels. The anisotropic potential leads to a maximum along the internucleaz)axis of the molecule and a reduction of density in the ‘‘T’’ geometry ovthe isotropic distribution.

o. 20, 22 November 1997


tiaedi

en

ss

rinh

edu

onolingbltete

Irohahirn0t

of

th,

iththe

isde-so-oreionher-it isoreu-

twoin

rfer-odu-these

nts.rgy

onala

de

-nd. Itnce

tedpa-

are

gfulg,

ris-d

en-ly

a

dity,is

hee

51tia

timrmh

.


The choice of the ground state solute-solvent potenalso has a significant effect on energy dissipation in thecited state. This mechanical effect has recently beencussed in relation to the gas phase I2–Ar complex, in anattempt to resolve the one-atom cage effect controversy.28 InFig. 11, we show plots of the time dependence of thesemble averaged I2 energy,^E(t)&, for the 490 and 515 nmsimulations, and with isotropic and anisotropic I2–CCl4 po-tentials in the ground state. The curves are typical for dipation of Morse oscillators in condensed phase.29 Here, thedynamics is quite clear. Extensive energy loss occurs duthe first collision, which terminates with the molecule reacing a relatively harmonic part of its potential, in a relaxsolvent cage. Subsequent energy loss occurs at a mslower rate. The extent of energy loss in the first collisidepends on impact parameters and the timing of the csion. For a head-on collision, the earlier the collision durthe extension of the I–I bond, the larger is the availakinetic energy to transfer to the solvent. Thus, as illustrain Fig. 11, the anisotropic potential which gives a tighcollinear alignment, leads to more efficient energy loss.analyzing the energy dependence of predissociation pabilities, it is the internal energy during curve crossings tis required, rather than the energy of preparation. Thus wthe 490 nm excitation prepares the molecule with an inteenergy content of 5000 cm21, the predissociation rate of 68fs which can be extracted from an exponential fit to the daoccurs at the characteristic energy ofE;4000 cm21 ~seeFig. 11!. We will use this consideration in the analysisenergy dependence of predissociation probabilities.

E. The 640–600 nm transients

Excitation at 640 nm corresponds to preparation ofmolecule nearv50. It is clear from the transient in Fig. 3

FIG. 11. Vibrational energy decay for initial preparations at 490 andnm, above and below the dissociation limit of the molecule. The inienergy drop occurs upon collision with the solvent, in;100 fs, the subse-quent relaxation in the expanded cage is slow on the predissociationscale. The extent of initial energy loss depends on the extent of anhanicity at the preparation energy, and on the solvent structure: greater wusing the anisotropic potential which leads to earlier head-on collisions



lx-s-

-

i-

g-

ch

li-

edrnb-tleal

a,

e

that with this preparation, the molecule predissociates wnearly unit probability. Since no recursions can be seen,predissociation probability must be;100% per period.

Excitation at 600 nm prepares the molecule nearv510. In this case a first recursion of the wave packetclearly observed. This signal, which appears after a timelay of a vibrational period, is much broader than the renances observed at shorter wavelengths. If we were to ignnonadiabatic dynamics, we would be lead to the conclusthat the 600 nm preparation leads to a faster loss of coence than the 580 nm preparation, despite the fact thatcreated in the more harmonic part of the potential. The mlikely interpretation is that we are seeing trapping of poplation in the adiabats created at the intersection of thepotentials. A similar situation has recently been studiedtime resolved experiments on IBr in the gas phase.30 In con-trast with the gas phase, in condensed media, sharp inteences are not expected since the crossing is strongly mlated by the solvent. The classical simulations used inpresent work are ill suited for a realistic analysis of theeffects.

F. Energy dependence of predissociation

The expression of Eq.~9! is sufficiently flexible to en-able a phenomenological fit of the experimental transieWe carry out such an analysis mainly to establish the enedependence of predissociation rates. We treat the vibratirelaxation as a double exponential, an initial decay withtime constant of 100 fs, followed by a slow decay witht.10 ps. To fit the data faithfully, it is necessary to incluan exponential damping of the modulation, usingf (t)5exp(2t/T2) in Eq. ~9!. Operationally,T2 establishes damping of modulation, it incorporates effects of temporal aspatial resolution, and decay of vibrational coherenceshould not be interpreted as a true measure of coheredecay. The data can be well fit by this method, as illustraby examples in Fig. 12. Table II contains the extractedrameters. The extracted time constants of predissociationcomparable to vibrational periods~see Table II!, as such theyhave little meaning as rate processes. The more meaninnumber is the predissociation probability per crossinnamely,

P1251

2v~E!tLZ

~12!

in which the frequencies are calculated from the charactetic energies using the I2(B) Morse parameters. The extracteprobabilities are plotted as a function of characteristicergy, E, in Fig. 13. Since the probabilities monotonicalincrease asv50 is approached, the data is consistent withcrossing nearv50. However, the variation ofP12 with en-ergy is too small. In the standard LZ model, for a fixecoupling constant, a hyperbolic dependence on veloctherefore onAE is to be expected. Since the kinetic energyvaried in the experiment from;150 to 4000 cm21, at least afivefold variation in probabilities is to be expected yet tobserved variation inP12 ranges only from 0.65 to 0.4. Th

5l

eo-en

o. 20, 22 November 1997


eexthyv

,,

ynd3

f

tom

heearan-

ure-tered.is-

hich

tos in

in-

ionstheer,

-o

in

ross-


data simply cannot be fit under the assumption of a fixcoupling constant. Anticipating the discussion in the nsection, it is possible to fit the data under the assumptionthe effective coupling is determined by driven solvent dnamics, and that the dynamical coupling scales with thebrational amplitude of I2, i.e., asE1/2. Thus we assume amodified LZ model, in which the dynamical coupling^V12&

d, is a linear function of vibrational amplitude where

^V12&d5^V12&

e~11aAE! ~13!

in which ^V12&e is the effective coupling constant given b

the structure of the solvent at equilibrium with the groustate I2. The data fits this model, as illustrated in Fig. 1with ^V12&

e5175 cm21, a50.0082 cm21/2 ~based onuD(]V/]r )u513 200 cm21 Å21!. The required increase o

FIG. 12. Examples of fits to the data using Eq.~9!, from which the energydependent predissociation probabilities are extracted.

TABLE II. Parameters extracted from analytical fit to transients@Eq. ~9! ofthe text#.

l~nm!a ^E&(cm21)b 1/cv(fs)c tLZ~fs!d PLZe T2(fs)f

490 4000 620 680 0.44 500515 3300 460 580 0.39 500535 2800 400 510 0.39 500548 2600 381 480 0.39 400557 2350 362 400 0.45 400580 1640 320 330 0.48 -600 1166 299 310 0.48 220620 700 281 280 0.50 170640 150 265 210 0.63 100

aExcitation wavelength.bCharacteristic energy after energy loss in first collision, and assumTe(B)515 400 cm21.

cVibrational half-period at characteristic energy.dPredissociation time constant obtained from the fit to Eq.~9! of the text.eExperimental predissociation probability per crossing.fDamping constant of observed modulation.



dtat-i-

,

the effective coupling constant~see inset to Fig. 13! is;50%, between preparations of the molecule at the botand near the top of the potential.

V. DISCUSSION

Analysis of theB state transients is possible under tassumption of a single predissociation channel, located nv50. This does not preclude the presence of weaker chnels, due to other crossings. In fact, in solid state measments where the vibrational dynamics proceeds with tighcoherence, several weaker crossings are clearly observ31

In the liquid phase, the likely candidates for the main predsociation channel can be narrowed toB9(1u), 2g anda(1g)surfaces~see Fig. 1!. Of these, theB9 surface may be elimi-nated based on the analysis of the 580 nm transient, westablished the crossing to be atR.3.05 Å. TheB9 crossinghad previously been invoked as being active in this systemrationalize the observed nonmonotonic decay of intensitieresonant Raman progressions of I2 in CCl4.

32 A recent theo-retical analysis allows the reinterpretation of that data asterference in scattering from the twoRR active surfaces,B9and B, without invoking coupling between them.33 The ex-tant data and analysis does not allow a direct distinctbetweena(1g) and 2g channels of predissociation. The firof these is commonly preferred, since it would involve tchange of only one unit of angular momentum. HowevDIM analysis shows that the 2g surface can also be active.10

In either case, the crossing involves a solvent inducedu→gandDVÞ0 transition. Accordingly, the off-diagonal potential surface that induces the predissociation must fulfill tw

g

FIG. 13. The energy dependence of predissociation probabilities per cing does not fit the standard Landau–Zener expectation~dashed line!. Thedata can be fit using a dynamical coupling which is a linear function ofE1/2

~vibrational amplitude!, and is shown in the inset~normalized to the cou-pling constant at equilibrium!.

o. 20, 22 November 1997


eene

ns

reob

revee

se

tod

aiokin

itsttelit,tioin

-th

ureinvorni

e

th

tatec-

lid

p-in

-secu-

r aon

dt,nicary

he

,face

odd

verg,s.ityionry.

-

, it

Be


criteria: It must haveu symmetry and must act along thperpendicular to the molecular axis. Note, these requiremare contingent upon the preservation of the molecular invsion symmetry andV as a good quantum number, conditiowhich are well established by the spectroscopy of I2 in theseweakly interacting solvents. The two identified criteria akey to rationalizing the difference between observed prabilities of predissociation in liquid CCl4 versus solid Kr, aswe expand below.

The result that predissociation in liquid CCl4 is fasterthan in solid Kr is unexpected if many-body probabilities aassumed to result from the scalar sum of probabilities operturbers. To see this, consider a coupling matrix elemwhich is only a function of separation between I2 andquencher. For a polarizable quencher, which does not itundergo electronic transitions, the expectation is thatV}aQ /R6.34 The effective coupling in the two phases, priordisturbance of the solvent by the I2 dynamics, can be relateas

^V& l

^V&s'

a l^( iR26d@R2Ri #& l

as^( iR26d@R2Ri #&s

~14!

in which the summation inside the angle brackets is overpositions of the solvent for an instantaneous configuratand the angular brackets imply ensemble averaging by tathe average over realized configurations; (l ) represents liquidCCl4 and (s) represents solid Kr. The strongR dependenceimplies that the coupling is determined by the local densof the solvent, mainly by the radial distribution of the firsolvent shell, which in turn depends on the assumed inmolecular potentials. Despite the fact that the polarizabiof CCl4, a510.5 Å3, is significantly larger than that of Kra52.48 Å3, the local density of the solvent dictates the raof Eq. ~14! to be 0.23; i.e., the predissociation probabilitythe liquid phase would be expected to be a factor of;20smaller ~probability }^V&2!. Contrast this with the experimental observation that the predissociation probability inliquid phase is a factor of 10 larger.

Similar conclusions are reached if the off-diagonal sface is taken to haveg symmetry, as in the real positivfunction assumed in the treatment by Ben-Nun and Lev~BL!.11 While they assume the predissociation to proceedB(0u)→a(1g), they use the expression given by Yardley fthe leading term in the perturbative analysis of electroquenching by a polarizable collision partner34,35

VB2a523

2

I BI Q

~ I B1I Q!

aB2aaQ

RI 22Q6 ~15a!

with the further decomposition

aB2a5a i cos2~q!1a' sin2~q! ~15b!

in which the polarizability of the quencher,aQ , is coupled tothe polarizability associated with the real transition betweelectronic statesB anda of I2, and I Q and I B represent theionization potentials of the solvent and I2(B), respectively.35

Using the value they recommend for the anisotropy oftransition polarizability (a i /a'51.8). After explicitly



tsr-

-

rnt

lf

lln,g

y

r-y

e

-

eia

c

n

e

evaluating the ensemble averages over liquid and solid sdistributions, but now taking the angular anisotropy into acount

^V& l

^V&s'

a i^( iaB2a~q!R26d@R2Ri #& l

as^( iaB2a~q!R26d@R2Ri #&s~16!

we obtain that the predissociation probability in the sostate should be a factor of;7 larger than in the liquid. Thusas in the case of strictly additive probabilities, the discreancy with experiment is nearly 2 orders of magnitude andthe wrong direction. Indeed, the ratio predicted in Eq.~16! issmaller than that of Eq.~14!. This is a result of the assumption thata i.a' and that the solute–solvent potential we uleads to a local solvent distribution peaked along the molelar axis in the liquid phase~see Fig. 10!. Note, however, thiseffect is somewhat artificial, since as we argued above, foDV51 transition the parallel component of the transitidipole, and hencea i must vanish.

The electrostatic model offered by Roncero, Halberstaand Beswick~RHB!, in their treatment of the predissociatioof the I2–Ar complex, has the proper form for the electroncoupling.12 In second-order perturbation, which is necessto obtain a coupling through the solvent polarizability,34,35

the leading electrostatic term for the requisiteu→g transi-tion in I2 is the dipole–quadrupole operator; terms of tkind36

^Qm&125(i

^B~0u1!uQu i u&^ i uumua~1g!&

~E2Ei !. ~17!

RHB show that this leads to anR27 distance dependenceand derive the angular dependence of the coupling surunder this electrostatic expansion12

VB2a~RHB!5A sin~u!@4 cos2~u!21#

R7 . ~18!

As desired, the angular dependence of the function iswith respect to inversion~see Fig. 14!. It is this signed, an-gularly anisotropic function that needs to be summed othe solvent distribution to obtain the effective couplin^V12&, prior to squaring, to obtain transition probabilitieWhile a strictly electrostatic model, and therefore its validmay be debated, the form will lead to extensive cancellatwhen summed over a solvent distribution of high symmet

The off-diagonal DIM surface of Batista and Coker~BC!has the same symmetry properties.9~a! The angular dependence of their surface fits the form

VB2a~BC!5A sin~u!cos8~u!

R6 ~19!

and is shown in Fig. 14. In contrast with the RHB surfaceis sharply peaked at 15° and vanishes at 90°, it has anR26

dependence, and a magnitude 2 orders larger atR55 Å ~seecomparison in Fig. 14!. Given the very different origins ofthe functions, it is not too surprising that the BC and RHforms differ in their detail, yet, both functions have thproper symmetry.

o. 20, 22 November 1997


leuagte

e

ioivoisdblfeinbiv

g-n

ioC

idin

ted

-

theaticomtioneof

las-in

ol-

ts

hatte,sehedy-gerhe

m,ex-

re inmi--

s, itC

mes

HB


As before, the magnitude of the effective matrix ement, u^V12&u, is obtained by summing over instantaneosolvent configurations and then taking the ensemble averWe evaluate Eqs.~18! and ~19!, under the assumption thathe A coefficient is proportional to the polarizability of thsolvent molecule.~Based on the value reported for Ar,12 inthe RHB model we useA533105 and 1.33106 for Kr andCCl4, respectively. In the BC form, based on the value givfor Xe,9 we useA523107 and 8.43107 for Kr and CCl4,respectively.!

The effect of solvent structure on solute predissociatprobability can be gleaned from calculations of the effectmatrix elements using static thermal distributions of the svent. The results of these static calculations, using bothtropic and anisotropic I2(X) –solvent potentials, are collectein Table III. Beside the difference in magnitudes, the tashows that the RHB and BC models make somewhat difent predictions. Both models predict a reduction in couplwhen using the isotropic potentials, an effect that cantraced to the reduction in local density. Despite the extenscancellation due to local symmetry, due to theR27 depen-dence, the RHB model predicts somewhat larger couplinsolid Kr than in liquid CCl4 for both the isotropic and anisotropic potentials. The BC model, for the anisotropic potetial, predicts the liquid phase coupling magnitude to befactor of 1.6 larger than the solid state, to be compared wthe experimental value of 2.7. Within the statistical errorsthe calculation, when using isotropic potentials, the B

FIG. 14. Cuts of the off-diagonal surfaces coupling theB and thea poten-tials evaluated at 5 Å. The BC curve is the DIM surface of Ref. 9, and Ris the electrostatic surface of Ref. 12.



-se.

n

nel-o-

er-gee

in

-athf

model predicts nearly equal couplings for solid Kr and liquCCl4. The absolute magnitudes of the BC predictions aresurprisingly good agreement with experiment. The predicsolid state value ofu^V12&

eu552 cm21 should be comparedwith the experimental value of 65 cm21, and the liquid phasevalue of 82 cm21 is only a factor of 2 smaller than the experimental determination of 175 cm21.

Since the couplings are determined by asymmetry insolvent structure, probabilities calculated based on stthermal distributions are expected to be quite different frthose determined dynamically. In the latter case, the moof the driven I2 oscillator will lead to cage distortions, thextent of which should depend on the initial preparationthe molecule. We carry out such calculations using the csical trajectories for 490, 515, and 580 nm preparationsliquid CCl4 ~60 trajectories each!. Now, the effective cou-pling is computed as an average over all crossings

u^V12&du5

1

N (j

N

(i

V12~r ,q;t j* !d@r2r i # ~20!

in which r i represent the instantaneous positions of the svent atoms at the crossing timet* ~at R* 53.16 Å!, and thesummation is over allN crossings of the swarm. The resulare summarized in Table III.

The comparison of the 490 nm preparation shows tthe RHB model predicts a larger coupling in the solid stawhile now the BC model clearly predicts the liquid phacoupling to be larger by a factor of 2.7 almost identical to tratio observed experimentally. Both models predict thenamical effect observed experimentally, both show a larcoupling for preparation near the dissociation limit of tmolecule~at 490 and 515 nm!, in comparison to preparationdeep in the bound part of the potential~at 580 nm!. The CBmodel shows a;30% increase between 580 and 490 nwhich compares quite well with the energy dependencetracted from the experiment~inset to Fig. 13!. As far as theabsolute magnitudes are concerned, the BC predictions anearly quantitative agreement with experiment, the dynacal couplings being;50% of what is observed experimentally. Given the good agreement observed in our analysiis not clear to us why in the original simulations of Bextremely rapid predissociation was observed in solid Ar.9~b!

We should perhaps re-emphasize that our analysis assu

TABLE III. Predictions of effective electronic coupling (cm21).

Static,u^V12&eu

Anisotropic Isotropic

Kr(s) CCl4( l ) Kr(s) CCl4( l )RHB 8.5 5.9 5.9 5.2BC 59 83 47 43

Dynamic,u^V12&du

490 nm 515 nm 580 nm

Kr(s) CCl4( l ) CCl4( l ) CCl4( l )RHB 11 6.8 7.6 5.7BC 39 108 109 82

o. 20, 22 November 1997


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classical Landau–Zener, with a crossing fixed along thecoordinate, and a fixed gradient of the difference potentiathe crossing point.

Independent of the detailed forms of the off-diagonsurface, the analysis clearly establishes the difference indissociation probabilities between solid and liquid phasebe predominantly one of structure: Extensive cancellationprobability occurs in the highly symmetric solvent cagethe solid. Also, the simulations establish that indeed soinduced solvent fluctuations enhance the predissociaprobabilities when large amplitude vibrations are set imotion. This effect was summarized in the experimental dusing the modified LZ model, in terms of an electronic copling that varies linearly with vibrational amplitude. In thcase of the RHB model, we should note that, althoughmagnitude of the dipole–quadrupole interaction is too smto explain the observed predissociation rates, the mechais sound and should contribute to the overall rates. Moreoin the case of I2–Rg van der Waals complexes where texcited state is prepared in the ‘‘T’’-shaped geometry ofground state, since the BC surface vanishes, the RHBpling will dominate. This would explain the success of tRHB treatment of predissociation in the vdW complexes12

VI. CONCLUSIONS

Through ultrafast pump-probe measurements and thretical analysis we have described the predissociationI2(B) in liquid CCl4. The data is sensitive to a single crosing nearv50, and consistent with a nonadiabaticu→g tran-sition. This intramolecular electron transfer can be thoughoccur via symmetry breaking of the solvent structure, andsuch is sensitive to equilibrium distributions and dynamicsthe first solvation shell. The seemingly surprising differenbetween liquid phase and solid state data can be explainethe difference in structural order in the two media anddipolar coupling that drives the nonadiabatic dynamicsthis case. That asymmetric cage vibrations induce such ndiabatic transitions in highly symmetric isolation sites in ragas matrices, has previously been noted in simulations.37 Thedynamical effect of symmetry breaking due to stirring of tliquid by the vibrationally excited molecule, leads to predsociation probabilities of;1 per period which are nearlindependent of internal energy content in the molecule. Teffect could be summarized in the experimental data bysuming an electronic coupling between surfaces that deplinearly on vibrational amplitude. The results are in neaquantitative agreement with theory, when consideringDIM off-diagonal surface,VB2a , recently provided byBatista and Coker.9

In addition to predissociation, the analysis provides iportant details of dynamics in the liquid phase. Vibrationrelaxation and coherence are sensitive to solvent strucThe CCl4 data are consistent with a first solvation shellwhich the distributions peak along the molecular axis. Tin turn signifies an anisotropic I2(X) – CCl4 potential. Theuse of such a potential in simulations is able to reproducepump–probe transients, allowing a more detailed dissec



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of the underlying dynamics with some confidence. In tanharmonic part of the potential, near the dissociation limupon the first collision with the solvent cage, the molecuundergoes a large energy transfer and complete scrambof classical vibrational phases. The subsequent dynamicscurs in a relaxed cage, in the more harmonic region ofinternal potential. The resulting biexponential energy decis characterized by a;100 fs drop followed by a slow decaon a time scalet.10 ps. The latter decay process can notwell determined from the experiments, since predissociaoccurs on a much shorter time scale. However, it is clearwhen prepared deep in theB state potential, predissociatioproceeds with complete retention of vibrational coherenThis picture was already evident in the studies by Scheet al., and our results are in general agreement with thobservations and conclusions.5

Given the detailed understanding of electronic predisciation in this molecule, and the sensitivity of the processsolvent structure and dynamics, it can be used to charactehosts in various media, such as supercritical fluids aglasses. Given our assessment of the DIM surfaces, it sethat through an iteration with experiments, a rather a coplete description of the nonadiabatic dynamics of the fmanifold of electronic states can be expected.

ACKNOWLEDGMENTS

We gratefully acknowledge the support by AFOSR, uder a University Research Initiative Grant No. F496200251, which made this work possible. We thank N. Halbstadt for stimulating discussions and for providing us wthe derivation of the electrostatic model. We thank V. Batiand D. Coker for providing us the DIM points for the ofdiagonalB–a surface. We acknowledge feedback givenM. Ben-Nun and R. Levine upon reading a preprint of thpaper.

APPENDIX

Given that the crossing betweenB(0u1) and a(1g) sur-

faces has been identified as the most likely channel of pdissociation, and the fact that in the experimental rangewavelengths, in particular at 490 and 515 nm a probe renance between I* I* (1u) anda(1g) is expected, we considethe likely contribution of this probe window to the observesignal. To simulate signals arising from the final statepredissociation, we use trajectories propagated on theB po-tential to generate initial conditions for continuation on ta(1g) surface. This is accomplished by storing the instanneous positions and momenta of all particles for every tithe trajectories reach the intersection between the two potials, and subsequently continuing trajectories on thea(1g)surface for an additional 250 fs. Thus a given trajectorytheB surface may spawn-off as many new trajectories asnumber of times it passes the crossing point. Thesea(1g)state trajectories are then given their appropriate LZ weigand used for reconstructing the observable signal as beWhere contributions to the signal occur from both inside aoutside theB surface, we recognize that transition dipo

o. 20, 22 November 1997


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moments need not be the same, and adjust the relativetributions to reproduce the experimental signal.

In Fig. 15 we show the best reproduction of the signwhen we constrain the simulation to two windows, onethe B surface to reproduce thet50 peak, and one on tha(1g) surface. A dissection of these contributions is agiven in the figure. Since the predissociation probabilities;60% per period, the net flux through each window is coparable, yet to obtain comparable intensities to the signais necessary to assume a factor of 20 larger transition difor the resonance on thea(1g) surface. This reduction insignal intensity is the result of the dramatically different vlocities of the packets as they pass through the respecprobe windows, due to the instantaneous kinetic energythe packet during observation. There is no reason to exthe I* I* (1u)←a(1g) transition to be stronger than the asorption from theB state. In fact, the opposite is true. At thlarge internuclear distances at issue, the I* I*←I2 transitioncan be regarded as a two-electron transition, and shoulsignificantly weaker than theE←B charge transfer transition. Indeed, in the course of the spectroscopic studiesI* I* fluorescence spectra, we have searched and failed toany emissions due to I* I*→I2 transitions,16 although a very

FIG. 15. Simulation of the 515 nm transient with one window locatedeach of theB anda(1g) surfaces. The composition of the simulated signis given in the lower panel:~dashed line!—contribution fromB state;~solidline!—contribution froma(1g) state. In the composite signal thea(1g) statecontribution is multiplied by 20.



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weak emission ascribed to this transition is observed in renance Raman spectra in the solid state.38 Thus, both due tothe very weak transition strength, if at all detectable, and adue to the acceleration of trajectories on this surface, inpresent experiments, the contribution of a probe signal frthe a(1g) surface is completely negligible.

1T. J. Chuang, G. W. Hoffman, and K. B. Eisenthal, Chem. Phys. Lett.25,201 ~1974!.

2A. L. Harris, J. K. Brown, and C. B. Harris, Ann. Rev. Phys. Chem.39,341 ~1988!.

3T. J. Kang, J. Yu, and M. Berg, J. Chem. Phys.94, 2413~1993!.4D. E. Smith C. B. Harris, J. Chem. Phys.87, 2709~1987!.5N. F. Scherer, D. M. Jonas, and G. R. Fleming, J. Chem. Phys.99, 153~1993!.

6R. Zadoyan, M. Sterling, and V. A. Apkarian, J. Chem. Soc. FaradTrans.92, 1821~1996!.

7C. Lienau, J. C. Williamson, and A. H. Zewail, Chem. Phys. Lett.213,289 ~1993!; C. Lienau and A. H. Zewail,ibid. 222, 224 ~1994!.

8Q. Liu, C. Wan, and A. H. Zewail, J. Chem. Phys.105, 5294~1996!.9~a! V. S. Batista and D. F. Coker, J. Chem. Phys.105, 4033~1996!; ~b! V.S. Batista and D. F. Coker, J. Chem. Phys.106, 7102~1997!.

10A. A. Buchachenko and N. F. Stepanov, J. Chem. Phys.104, 9913~1996!.11M. Ben-Nun, R. D. Levine, and G. R. Fleming, J. Chem. Phys.105, 3035

~1996!.12O. Roncero, N. Halberstadt, and J. A. Beswick, J. Chem. Phys.104, 7554

~1996!.13C. Teichteil and M. Pelissier, Chem. Phys.180, 1 ~1994!.14R. M. Bowman, M. Dantus, and A. H. Zewail, Chem. Phys. Lett.161, 297

~1989!.15R. S. Mulliken, J. Chem. Phys.55, 288 ~1971!.16A. Benderskii, R. Zadoyan, and V. A. Apkarian, J. Chem. Phys.107, 8437

~1997!, preceding paper.17J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird,Molecular Theory of

Gases and Liquids~Wiley, New York, 1954!.18C. H. Becker, P. Casavecchia, Y. T. Lee, R. E. Olson, and W. A. Les

J. Chem. Phys.70, 5477~1979!.19B. E. Grigorenko, A. V. Nemukhin, and V. A. Apkarian, Chem. Phy

219, 161 ~1997!.20M. Ovchinnikov and V. A. Apkarian, J. Chem. Phys.105, 10312~1996!.21F. Yu. Naumkin and P. J. Knowles, J. Chem. Phys.103, 3392~1995!.22M. Sterling, R. Zadoyan, and V. A. Apkarian, J. Chem. Phys.104, 6497

~1996!.23L. D. Landau and E. M. Lifshitz,Quantum Mechanics~Pergamon Press

Oxford, 1977!; C. Zener, Proc. R. Soc. London, Ser. A137, 696 ~1932!.24L. Onsager, J. Am. Chem. Soc.58, 1486~1936!; R. Fulton, J. Chem. Phys

61, 4141~1974!.25J. C. D. Brand and A. R. Hoy, Appl. Spectrosc. Rev.23, 285 ~1987!.26J. Tellinghuisen, J. Chem. Phys.76, 4736~1982!.27Z. Li, R. Zadoyan, V. A. Apkarian, and C. C. Martens, J. Phys. Chem.99,

7453 ~1995!, and references therein.28J. Y. Fang and C. C. Martens, J. Chem. Phys.105, 9072~1996!.29J. S. Bader, B. J. Berne, E. Pollak, and P. Hanggi, J. Chem. Phys.104,

1111 ~1996!.30M. J. J. Vrakking, D. M. Villeneuve, and W. A. Stolow, J. Chem. Phy

105, 5647~1996!.31R. Zadoyanet al. ~unpublished!.32J. Xu, N. Schwentner, and M. Chergui, J. Chem. Phys.101, 7381~1994!;

J. Xu, N. Schwentner, S. Hennig, and M. Chergui, J. Chim. Phys.92, 541~1995!; Xu, N. Schwentner, S. Hennig, and M. Chergui, J. Raman Sptrosc.28, 433 ~1997!.

33M. Ovchinnikov and V. A. Apkarian, J. Chem. Phys.106, 5775~1997!.34C. A. Thayer and J. T. Yardley, J. Chem. Phys.57, 3992~1972!.35A. D. Buckingham, inIntermolecular Forces, edited by J. O. Hirschfelder

~Interscience, New York, 1967!.36N. Halbertadt~private communication!.37K. Kizer, Ph.D. thesis, UCI, 1997.38A. I. Krylov, Ph.D. thesis, Hebrew University of Jerusalem, 1996.

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predissociation dynamics of i2 b in liquid ccl4 observed...

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