photodissociation dynamics of hcl in solid ar: cage exit

Do

Photodissociation dynamics of HCl in solid Ar: Cage exit, nonadiabatictransitions, and recombination

Anna I. Krylova) and R. Benny GerberDepartment of Physical Chemistry and The Fritz Haber Research Center, The Hebrew University,Jerusalem 91904, Israel and Department of Chemistry, University of California, Irvine, California 92697

~Received 4 November 1996; accepted 22 January 1997!

The photodissociation of HCl in solid Ar is studied by non-adiabatic Molecular Dynamicssimulations, based on a surface-hopping treatment of transitions between different electronic states.The relevant 12 potential energy surfaces and the non-adiabatic interactions between them weregenerated by a Diatomics-in-Molecules~DIM ! approach, which incorporated also spin-orbitcoupling. The focus of the study is on the non-adiabatic transitions, and on their role both in thecage-exit of the H atom, and in the recombination process. It is found that non-adiabatic transitionsoccur very frequently. In some of the trajectories, all the 12 electronic states are visited during thetimescale studied. At least one non-adiabatic transition was found to occur even in the fastestcage-exit events. The other main results are:~1! The total yields for photofragment separation~bycage exit of the H atom! and for H1Cl recombination onto the ground state are roughly equal in theconditions used.~2! The cage exit events take place in the time-window between;70 fs and;550 fs after the excitation pulse, and are thus all at least somewhat delayed. The recombinationevents span a much broader time-window, from almost immediately after excitation, and up to;1100 fs and beyond.~3! The electronic energy relaxation events during the process dependsignificantly on symmetry and interactions of the states involved, and not only on the energy gapsbetween them.~4! Different electronic states reached in the course of the process exhibit differentpropensities with regard to the recombination versus cage exit outcome.~5! Spin-orbit interactions,and spin-forbidden transitions play an important role in the process, especially for recombinationevents. ©1997 American Institute of Physics.@S0021-9606~97!01916-8#

ngintwef

veponenio

asnndsearaspfteleitaof

nso-s in

de-

ionof,ceted

ngleis isor allto-ro-le onex-pa-ec-ndalro-nam-atic

e

I. INTRODUCTION

Cage effects and geminate recombination are amothe most important concepts in condensed-phase chemdynamics, and had been the topics of extensive experimeand theoretical studies throughout the years. In the pastdecades, there has been growing interest in exploring thphenomena in the context of photochemical processessmall guest molecules in a solid rare-gas environment.1–23

Experimentally, these systems have the advantage of seconvenient optical properties, especially the spectroscotransparency of the host rare gas solid in the relevant regiAmong the important experimental developments of recyears, there was the application of synchrotron excitattechniques by Schwentner and coworkers8–14 which made itpossible to access the dissociation bands of an increnumber of small molecules of interest. Another importanew direction was pioneered by Apkarian acoworkers20–22who applied time-domain femtosecond pulspectroscopy to study the cage effect for molecules in rgas solids. Theoretically, these systems are attractive becthe interaction potentials between the reactive molecularcies and the solid host atoms are relatively simple and oavailable. Another advantage of these systems is that atthe initial structure around the reagent, prior to photoexction, is typically well defined and can simplify the task

a!Present address: Department of Chemistry, University of California, Bkeley, California 94720.

6574 J. Chem. Phys. 106 (16), 22 April 1997 0021-9606/97/

wnloaded¬17¬May¬2001¬to¬128.125.104.142.¬Redistribution¬subject¬to

stcaltaloseor

ralics.tn

edt

e-usee-nast-

interpretation. Classical Molecular Dynamics simulatiowere first applied to microscopic modeling of molecular phtodissociation in solids, and to the corresponding reactionlarge rare-gas clusters, almost ten years ago,24,25 and havesince emerged as an extremely useful tool for gainingtailed insight into the dynamics of these processes.24–36Suchsimulations were able, for instance, to provide interpretatfor experiments on cage exit following photodissociationF2 ~Ref. 30! and of Cl2 ~Ref. 31! in rare gas solids. IndeedMolecular Dynamics simulations were able to reprodumany of the quantitative experimental features associawith the coherent cage vibrations of I2 in rare-gas solidsmeasured by ultrafast spectroscopy techniques.20–22 Whiletheoretical modeling of cage processes confined to a sipotential energy surface has been extensively pursued, thnot the case for non-adiabatic processes taking place fmolecule in a matrix. Realistically, however, most if not aof the systems studied in the context of molecular phochemistry in rare-gas solids involve some non-adiabatic pcesses, and these processes may play an important rothe timescale of the experiment of interest. A moleculecited to a dissociative state in a medium, beginning to serate into fragments, can with some probability undergo eltronic relaxation, possibly reaching its ground state arecombining on it. Only very few quantitative theoreticstudied were hitherto made of these extremely important pcesses. Semiclassical methods, rather than classical dyics, must obviously be used in describing such non-adiabr-

106(16)/6574/14/$10.00 © 1997 American Institute of Physics

¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/jcpo/jcpcr.jsp

o

so

ono-eio, ril

ecarreepb

ns

beandSe

oulee

toeste

te

cm

an

-nd1t d

-s

-

art

he

lets,nsns

as-nd-ves,

is-s-

e-

d

6575A. I. Krylov and R. B. Gerber: Photodissociation of HCl in solid Ar

Do

processes. Most related to the present work are the nadiabatic simulations of Gersonde and Gabriel37 of photoly-sis and recombination of diatomic molecules in rare-gasids, and the study of Batista and Coker38 on non-adiabaticprocesses in the caging of I2 in liquid Xe.

The purpose of the present article is to explore the nadiabatic dynamics following excitation of HCl to a dissciative state in solid Ar. We shall study the competition btween H-atom cage exit, leading to ‘‘permanent’’ separatof the photofragments and the process of recombinationsulting in electronic ground state HCl. Of central interest wbe the pathways of cascading through the large manifoldelectronic states involved, until the ground state is reachWe shall study by non-adiabatic simulations the physimechanisms whereby such processes occur, and the natuthe interactions that govern the transitions between diffeelectronic states. Important differences will be recognizbetween the present system as simulated here, and thecesses studied in Refs. 37 and 38. We chose HCl partlycause of the interesting properties of hydrogen as a~small!photofragment, and partly because photolysis of HCl, aother hydrogen halides in solids has already received conerable experimental attention.13,14,19,34

The structure of the paper is as follows: Sec. II descrithe system, the interaction potentials, and the non-adiabsimulation method. Sec. III outlines the main findings aprovides analysis. Concluding remarks are presented inIV.

II. SYSTEM AND METHODS

The simulations described in this study were carriedfor systems consisting of 255 Ar atoms and a HCl molecuinitially placed at a substitutional site of the argon latticPeriodic boundary conditions were imposed at the endsthe system. On the basis of previous simulations of phophysical and photochemical processes in solids, it ispected to be sufficient in size to describe the processeinterest without giving rise to noticeable unphysical ‘‘finisize’’ effects.

A. Potential surfaces

The potential surfaces for the system were construcby a variant of the DIM~Diatomics in Molecules!39 method.The DIM approach was used by the present authors andworkers for the related topic of open shell, P-state atosuch as F(2P),40,41Cl(2P),42 and Ba(P) ~Ref. 43! in a rare-gas environment. The DIM method was used by BatistaCoker, in their study of I2 in liquid Xe,38 by Buchachenkoand Stepanov, in their study of I2Ar,

44 and previously byGersonde and Gabriel37 in simulations of photolysis of several diatomics in rare gas solids, but the latter authors didinclude spin-orbit interactions in their version of the metho

Consider first the HCl part of the system. There arestates, including degeneracies and the ground state, thasociate asymptotically to H(1S)1Cl(2P). Using an effectiveone-electron model for the Cl(2P) atom, and a ValenceBond approach, the 12 states can be written explicitly a

J. Chem. Phys., Vol. 106


n-

l-

-

-ne-lofd.le ofntdro-e-

did-

stic

c.

t,.of-x-of

d

o-s

d

ot.2is-

a

combination of thes-orbital of theH, andp-orbitals of theCl atom. The ground state1S0 is:

1S051

2@s~1!p0~2!1p0~1!s~2!#@a~1!b~2!

2b~1!a~2!#, ~1!

wherep0 is the p-orbital corresponding to the angular momentum projectionmL50. The3S1 states are:

3S151

A2@s~1!p0~2!2p0~1!s~2!#a~1!a~2!,

3S151

A2@s~1!p0~2!2p0~1!s~2!#b~1!b~2!, ~2!

3S051

A2@s~1!p0~2!2p0~1!s~2!#

3F 1A2

~a~1!b~2!1b~1!a~2!!G .For theP states, we write for convenience the spatial ponly:

1P~mL521!51

A2@sp211p21s#,

3P~mL521!51

A2@sp212p21s#,

~3!1P~mL51!5

1

A2@sp11p1s#,

3P~mL51!51

A2@sp12p1s#.

For nomenclature purposes it will be useful to order tVB basis functions. We will use the order:1P21,

1S0,1P11,

3P0,3S11,

3P12,3P21,

3S0,3P11,

3P22,3S21,

3P0. The first three states in this sequence are the singthe following three states are triplet states of spin functioa(1)a(2), thenext three states correspond to spin functio(1/A2) (ab1ba), and the last three states havebb spinfunctions. The above order is not necessarily that of increing energy. The potential energy curves of HCl correspoing to some of these states are shown in Fig. 1. These curtaken from the ab initio calculations of Bettendorffet al.,45

were used in obtaining the DIM potential surfaces, as dcussed below. The DIM electronic Hamiltonian of the sytem can be written in the form:

Hel~g,R!5HHClel ~g,RHCl!1VHAr~RH ,R1 ,... ,RN!

1VClAr~g,RCl ,R1 , . . . ,RN!

1VArAr~R1 , . . . ,RN!1VSO, ~4!

whereg denotes collectively the electronic degrees of fredom;R—the nuclear coordinates,R1 , . . . ,RN are the posi-tion vectors of the Ar atoms,RH ,RCl are the positions of theH and the Cl atoms, respectively, andRHCl5uRH2RClu.HHClel (g,RHCl) is the electronic Hamiltonian of the isolate

, No. 16, 22 April 1997


veqs

cae

e-ls

a

to

e

e

-en

a

rn-

bya

gle

dtor

ino

em,

ibe

udythe

c re-

tiveasforatsme-er-he

ys-on isthems.e

6576 A. I. Krylov and R. B. Gerber: Photodissociation of HCl in solid Ar

Do

HCl molecule. We assume that its eigenfunctions are gito good approximation by the Valence Bond model of E~1!–~3!. For the eigenvalues ofHHCl

el ,WnHCl(RHCl) which are

the potential curves of the molecule, we took the valuesculated by Bettendorffet al.,45 who used a very accuratab initio approach.

For VArAr in Eq. ~4!, representing the interactions btween the Ar atoms, we used a sum of pairwise potentia

VArAr~R1 , . . . ,RN!5(i. j

UArAr~Ri j !, ~5!

whereRi j5uRi2Rj u. For UArAr(R), the Ar-Ar pair interac-tion, we used the potential of Aziz and Slaman.46 ForVHAr , the interaction between the hydrogen and the Aroms, a sum of pair interactions was used:

VHAr~RH ,R1 , . . . ,RN!5(i51

N

UHAr~ uRH2Ri u!. ~6!

ForUHAr(RHAr) we used a Lennard–Jones function fittedthe H-Ar potential of Bickeset al.47 Consider next the termVClAr in Eq.~4!: Also this is taken to be a sum of pairwisCl-Ar interactions:

VClAr~g,RCl ,R1 , . . . ,RN!5(i51

N

UClAr~g,RiCl!, ~7!

whereRiCl5uRi2RClu. Models for such interactions werextensively pursued in the context ofP-state atom dynamicsin rare-gas hosts.40–43A very satisfactory empirical description is obtained by models that include not only the dep

FIG. 1. Potential energy curves of HCl~see text!.



n.

l-

,

t-

-

dence of the interaction on the Ar-Cl distance, but alsodependence on theorientationof thep-orbital of the Cl withrespect to the Cl-Ar axis. The anisotropy of theP-state atominteractions turns out to be of crucial importance in goveing the dynamics of the systems involved.40–43 Such an ac-curate Cl-Ar anisotropic interaction was determinedAquilanti and coworkers,48 and employed here, as well inprevious study on Cl atoms in solid Ar.42 It has the form

UClAr~g,RClAr!5UClAr~0! ~RClAr!1UClAr

~2! ~RClAr!P2~cosg!,~8!

whereg is an electronic coordinate, representing the anbetween the orientation of thep orbital of the Cl and theCl-Ar axis. The orientation angleg is thus, within the DIMmodel, the only electronic degree of freedom in Eq.~7!.UClAr( j ) (RClAr) are functions of the Cl-Ar distance only, an

are given in Ref. 48. Finally, the spin-orbit coupling operain Eq. ~4! is given by

VSO5D(i51

2

l i si , ~9!

where l i and si are the orbital angular momentum and spoperators of electroni , and the summation is over the twelectrons included in this model. ForD we took the spin-orbit splitting parameter of an isolated Cl(2P) atom ~0.109eV!, that should provide a good approximation.

The adiabatic potential energy surfaces of the systWn(R), are given by solution of the~electronic! Schrodingerequation:

Hel~g,R!fn~g,R!5Wn~R!fn~g,R!. ~10!

Thus, to obtain theWn(R), the HamiltonianHel(g,R) of Eq.~4! is diagonalized in the Valence-Bond basis, Eqs.~1!–~3!,at each configurationR of interest, whereR represents theposition of all the nuclei in the system. As we shall descrbelow, the determination of theWn(R) is actually done ‘‘onthe fly,’’ along computed trajectories for the dynamics.

B. Surface-hopping molecular dynamics simulations

The non-adiabatic processes were simulated in this stby a semiclassical surface hopping algorithm, similar toversion proposed by Tully.49 Evidence from applications toprocesses related to the one studied here, e.g. electronilaxation ofP-state atoms in solids and in clusters,40–43 sup-ports the validity of the method at least on a semiquantitafooting. The accuracy of the method for large systems,studied here, is however still not known. A recent study~Ar!10Ba, ~Ar!20Ba, using a more accurate method that treboth electronic and nuclear degrees of freedom quantumchanically, shows that the method is valid for many propties, but also that it can be in significant error, e.g., for tpopulations of some of the electronic states.50 However, thequantum mechanical simulations are not yet feasible for stems as large as the one studied here, and our impressithat the Tully method is at least as satisfactory as any ofalternative, practical approximations for extended systeWe give here a brief outline of the algorithm, following th

, No. 16, 22 April 1997


eairgethfat

cf

l-.e,

iniatisn-

emve

acac

ra

om

iaf

ted

lis

yen

ts

:

rtsverare


Do

version used in Refs. 42 and 43. In this method, nuclmotions are treated by classical dynamics. Suppose thattially the system is on one of the adiabatic potential enesurfacesWn(R), whereR denotes the positions of all thnuclei. As long as non-adiabatic transitions do not occur,atoms are propagated by a classical trajectory on that surAt any point in time along the trajectory, one can computhe adiabatic potential surfacesWj (R) ~of which there are 12in the present case!, and the corresponding adiabatic eletronic statesf j (g,R) where g is the electronic degree ofreedom pertaining to the orientation of thep-orbital. This isdone ‘‘on the fly’’ by diagonalizing the electronic Hamitonian of Eqs.~4!–~9!, in the ‘‘Valence Bond’’ basis of Eqs~1!–~3!. The diagonalization yields uniquely the eigenvaluWj (R) at each configurationR of the nuclei. Note, howeverthat the electronic eigenfunctionsf j (g,R) arenot uniquelydetermined by the diagonalization. If theWj (R) are not ex-actly degenerate atR, thenf j (g,R) is ambiguous within anR-dependent phase factor exp(il(R)), wherel(R) is a real-valued function. In such cases, and if the Hamiltoniancludes only real-valued scalar potential functions, the adbatic states can be chosen to be real-valued, andalgorithm for calculating the non-adiabatic transitionswell-defined and valid.42,51,52 In cases where exact degeeracy occurs, the ambiguity in determining thef j (g,R) bydiagonalization poses a much more complicated probland a much more elaborate algorithm is necessary to ocome the difficulty. An example is a Cl(2P) atom in a rare-gas environment, where the two-fold Kramers degeneroccurs.42 In present case there is no permanent degenerhowever, due to spin-orbit coupling the adiabatic statescan-not be chosen real-valued. Here we apply gauge constsimilar to one described in Ref. 42: phases off i(g,R) werechosen to minimize deviation of the adiabatic states frreference ones:

l i~R!5arg minl iuuF i&2e2 il i ~R!uf i~g,R!&u, ~11!

whereF i[f i(g,R0) is the reference state being the adbatic state at a fixed configurationR0. Note that the phase o

.s

h



rni-y

ece.e

-

s

--he

,r-

yy,

in

-

F i is fixed. From Eq.~11! one obtains:l i5l i1 , where

^f i(g,R)uF i&5u^f i(g,R)uF i&ueil i1, which is equivalent to

the gauge:51

Im^F i uf i~g,R!&50, ^F i uf i~g,R!&.0. ~12!

Since the adiabatic electronic states are genera‘‘on the fly’’ along a trajectory R(t), we can writef j (g,R)[f j (g,t) for that trajectory. In the semiclassicasurface hopping method, the electronic degree of freedomdescribed by a wavefunctionc(g,t), that evolves in timeaccording to the Schro¨dinger equation:

i\]c~g,t !

]t5Hel~g,R~ t !!c~g,t !, ~13!

whereHel(g,R(t)) is the electronic Hamiltonian given bEqs.~4!–~9!, with the trajectory function substituted for thnuclear positionsR. We expand the electronic wavefunctioc(g,t) in the adiabatic basisf j (g,t):

c~g,t !5(j51

12

Cj~ t !f j~g,t !. ~14!

This leads to the following equations for the coefficienCj (t), as given by Tully:49

i\Ck~ t !52 i\(jCj~ t !^fkuf j&g1(

jCj~ t !Wj~R~ t !!.

~15!

Using the properties of the adiabatic eigenstates, we get

^fk~g,R!u“Rf j~g,R!&g

5^fk~g,R!u“RHel~g,R!uf j~g,R!&g

Wj~R!2Wk~R!. ~16!

Variation of normalization condition yields that the real paof diagonal matrix elements are equal to zero, howeimaginary parts can be non-zero. Expressions for themderived in:51

^fk~g,R!u“Rfk~g,R!&g52i

^Fkufk~g,R!&gImF(

lÞk

^Fkuf l~g,R!&g^f l~g,R!u“RHel~g,R!fk~g,R!&g

Wk~R!2Wl~R! G . ~17!

ithe-the.

faceticcted,

Using the classical motion of the nuclear coordinateR, the left hand side of Eqs.~16!, ~17! can be written

K fkU ]f j

]t L 5R~ t !^fk~g,R!u“Rf j~g,R!&g , ~18!

whereR is the velocity vector of the nuclei in the systemEqs.~16!–~18! provide a convenient way for the calculationof the time-dependent quantities^fkuf j&g which representthe non-adiabatic coupling. These also are computed ‘‘on tfly’’ with the propagation of the trajectoryR(t).

s

e

The classical propagation of the nuclei, together wEqs.~12!,~14!–~18! for the time-dependent electronic wavfunction and for the non-adiabatic couplings betweenf j (g,t), are the basis of the ‘‘surface hopping’’ algorithmSuppose that initially, att5t0, Cj (t0)51, Ck(t0)50 for kÞ j . The nuclei are then propagated on the adiabatic surWj (R). At each point along the trajectory the 12 adiabapotentials and the corresponding eigenstates are constru

and the non-adiabatic couplingsfkuf j&g are obtained.Eqs.~15! for the coefficientsCk(t), k51, . . . ,12 aresolved

, No. 16, 22 April 1997


-fds-

ipio’’-ivom

e

u

A

cy-

alnaarmith

eoiaonth

iokyne

annttiathjeo-

uto

i

hei

let

n-t iset.tontedion

ys-de-si-oused,sev-asesthefor

l of

iteon.nicty.is

17,

he

s alf a

fi-h asn.re-ingle,riesndasho-

tondral-

thefgapfirst


Do

numerically and their variation in time is followed. At sufficiently small time intervals, we test for the occurrence o‘‘surface hopping’’ event:uCku is compared with a generaterandom numberl, 0<l,1, and on the basis of this stochatic criterion it is decided whether a ‘‘hop’’ from surfacej tosurfacek has taken place or not. For stability of the resultswas necessary to test for the possible occurrence of hopeach 50 integration steps. This procedure, used by us alsRefs. 42,43 differs from the ‘‘minimum number of hopscriterion employed by Tully,49 but our tests for several systems suggest that in general the two algorithms should gsimilar results. Once a hopping event has occurred, at st5t1, we reset the values of the coefficients:Ck(t1)51,Cl(t1)50 for l Þ k. The procedure is then continued with thnuclei being propagated on the surfaceWk(R). The initialvalues for the propagation of the trajectory on the new sface are very similar to those discussed by Tully.49

C. The simulations

As the first step in the calculations, the system of 255atoms and a single HCl molecule~with periodic boundaryconditions at the ends! was equilibrated in the electroniground state at 17 K. This equilibration was carried out blong (;20 ps! trajectory run, following standard prescriptions of Molecular Dynamics simulations.53 At random timesafter equilibration, ‘‘snapshots’’ of the system~nuclear con-figurations, momenta! were recorded. The overall rotationand vibrational distributions on the ground state were alyzed: we found that HCl rotates almost freely in Ar latticetemperature used in our simulations. It results in uniforotational distribution, which is in a good agreement wquantum mechanical study of Schmidt and Jungwirth.54 Thevibrational coordinate distribution of the HCl internal modis very different from quantum one due to high frequencyHCl vibrations. However, the effect of this on photodissoction is small. This is especially the case for fixed excitatienergy and a narrow excitation window, which wash outdifference almost completely.

For each of these configurations, electronic excitatwas modeled in the spirit of the classical limit of the FrancCondon Principle: The system was promoted vertically bgiven excitation energy, retaining the positions and momeof all the nuclei upon excitation. The excitation energy wused was 7.22 eV, well within the observed absorption bof gas-phase HCl.13 With this energy, each excitation eveis found to land on one of the two lowest adiabatic potensurfaces of the system. In fact the population produced intwo states by all the excitation events is about equal. Protion of the two lowest adiabatic states onto the ‘‘bare’’ mlecular states shows that in effect only the3P0 states of theHCl was selected by the excitation wavelength used. Omotivation to study photodynamics following excitationtriplet P state was to study the process on thelowestexcitedstate of HCl. In this situation we expected that cage exit wbe relatively slow~due to low excess energy!. A commentshould be made on the possibility of exciting HCl to ttriplet P state experimentally: In one-photon experiments



a

tngin

ee

r-

r

a

-t

f-

e

n-ata

d

lec-

r

ll

t

is probably impossible to distinguish absorption to tripP state~allowed due to interaction with a matrix! from ab-sorption by the singletP state, because both these wide trasitions overlap, and because the transition dipole momenweaker, though not zero, for the excitation to the triplTherefore such an experiment is impossible in a one-phoframework. However, triplet states can be selectively exciin multi-photon experiments with suitable phase combinatof excitation photons.

After excitation into an excited adiabatic state, the stem was propagated according to the simulation methodscribed earlier, including occasionally non-adiabatic trantion events. Although in the Franck-Condon region only twadiabatic states can be accessed with the excited energyaway from the Franck-Condon region the gaps betweeneral of the potential surfaces become smaller, in some cintersect, and more adiabatic states can be reached incourse of the dynamics. Each trajectory was propagatedseveral picoseconds following the excitation event. A tota105 excitation trajectories was run.

We analyzed the statistical error introduced by the finsize of the statistical ensemble using a binomial distributiFor the observables which are averaged over all electrostates, 105 trajectories yield a relatively small uncertainF.i., statistical error for observed recombination yieldabout 4%. However, for state-dependent observables~asbranching ratios for distinct states! the statistical uncertaintyis much larger which is shown by large error bars in Figs.18.

III. RESULTS AND DISCUSSION

It will be convenient to organize the presentation of tresults around several of the main findings.

A. Time-dependence of cage exit and ofrecombination

We considered as a cage-exit event in the simulationsituation in which the H atom reached a distance of halattice constant or more from the~substitutional! site of theHCl center of mass prior to photoexcitation. While the denition is somewhat arbitrary, the results obtained are sucto be robust with regard to minor changes in the definitioWe note that in none of the trajectories did we have a ‘‘crossing’’ behavior: The H atom leaving the cage accordto the above definition, then returning later on. In principof course, such recrossings may take place. In the trajectowhere the H atoms exited the original cage, they were fouto ultimately reach an octahedral-interstitial site. This wfound to be the case also in earlier simulations on the ptolysis of HI in solid Xe,25 at least for relatively low photo-excitation energies. It is possible that at much higher phoenergies, less favorable sites such as the tetraheinterstitial site are also populated. We counted as arecombi-nationevent one in which the HCl molecule has reachedground electronic stateand in addition the kinetic energy othe H atom has decreased to a value well less than thebetween the ground adiabatic electronic state and the

, No. 16, 22 April 1997


,roleucsisrinicsc

nteitexp

ag

toa

ialtnrsr-r,inineew

agethe

exithe

iblemate-

xit’’d.n are-.rter.theenomtoofina-ci-onionhey,


Do

excited adiabatic state. The total energy of the system iscourse, conserved and in principle the system may cback after recombination has occurred to an excited etronic state, according to the above criterion. However, sa fluctuation requires highly coherent motion of all atomand, therefore, is of low probability. In the simulations thdid not happen. Figure 2 shows in histograms the numbecage exit events and Fig. 3 shows the number of recombtion events. Despite the limitations of the trajectory statistit is evident that recombination events occur over a mularger time range then cage exit events. The earliest recom-bination events occur about 15–20 fs after excitation, arecombination events keep occurring well beyond 1 ps laThe earliest cage exit events occur about 70 fs after exction, and are thus significantly delayed. The main cageevents occur, however, in the range of 0.15 ps to 0.25after the excitation, and beyond about 0.55 ps no more cexit events are found.

The distribution in time of cage-exit events is simpleinterpret. Almost free rotations of HCl molecule makesdirect exit hardly probable: In all the trajectories the initimpact of the H atom on the surrounding cage is such thahits a steeply repulsive potential wall due to the Ar atom arecoils. None of the trajectories sampled lead in the ficollision to the ‘‘window,’’ or transition state, where the barier for cage exit by the H atom is sufficiently low. Howevethis result may be influenced by minor changes in H-Arteraction potential: A slightly less repulsive potential cancrease the size of exit windows and yield some measurdirect events. It turns out that energy transfer in the first f

FIG. 2. Number of cage-exit events versus time.



ofssc-h

ofa-,h

dr.a-itse-

itdt

--of

collisions between the H atom and the surrounding cleads to some expansion of the cage and to widening ofcage exit ‘‘windows.’’ One of the following impacts of the Hatom lands on the favorable windows, and then cageoccurs. As found already in Ref. 25 in simulations of tphotolysis of HI in solid Xe, the H atom can ‘‘rattle’’ quite afew times between the cage walls, before reaching a posscage exit ‘‘window.’’ Figure 4 shows the path of the H atoin a trajectory that leads to relatively early cage exit,around 70 fs.~The figure shows the projection of the thredimensional path onto theX,Z plane of the crystal.! Also thepath of the Cl atom in that trajectory is shown. The cage ein this case was clearly delayed, following some ‘‘rattlingof the H atom in the cage, till the exit window was reacheFigure 5 shows the paths of the H and the Cl atoms itrajectory that leads to cage exit after 550 fs, which corsponds to one of the longest delays found in this system

Cage-exit event are peaked, however, at much shotimes, t'150 fs, and the time-distribution is quite narrowThe more collision the H atom undergoes in the cage,greater is its kinetic energy loss. After some rattling betwethe walls of the cage, when the kinetic energy of the H athas fallen below the barrier for cage exit, it is boundremain in the cage. Consider now the time-distributionrecombination events, shown in the Fig. 3. Some recombtion events occur already for times only 15–20 fs after extation. The mechanism for the very early recombinatievents is as follows: The H atom moves, upon excitatwith great impulse and strikes an Ar atom far away from tCl. At this point the H atom has no or little kinetic energ

FIG. 3. Number of of recombination events versus time.

, No. 16, 22 April 1997


onfa

te

ap-ra-into-forsi-isergynsr, inCl—alltheherena-en-nicloster-lec-n—ps.n andtoryreiongetheur.the

arto

er

fast


Do

but has high potential energy. Some of the configuratiwhere the Cl atom and the H atom are mutually quite~although within the cage! are favorable for transition intothe ground electronic state, since the excited adiabatic po

FIG. 4. The paths of the H and the Cl atoms in a trajectory leading to ecage exit~after 0.07 ps!. X andZ are two axes defining a crystal plane, onwhich the path is projected.

FIG. 5. The paths of the H and of the Cl atom in a trajectory leading to vdelayed cage exit~after 0.55 ps!.



sr

n-

tial surface crosses with the ground state surface, orproaches the latter very closely, for some such configutions. The fact that the H atom has little velocity at this pois favorable for the transition, since it implies that the hydrgen remains at the vicinity of that configuration at leastsome brief time interval, over which the nonadiabatic trantion can occur. After the electronic transition, the H atomaccelerated over the ground-state adiabatic potential ensurface, gaining kinetic energy that it later loses by collisioto the Cl and the Ar atoms. The system remains, howevethe ground state. Figure 6 shows the path of the H andatoms in a trajectory that leads to very early recombinationbasically a single excursion of the H atom to the cage whas sufficed for the occurrence of the process. Unlikeabove direct nonadiabatic crossing to the ground state, tare many events in which the system carries out many nodiabatic transitions, cascading down the manifold of pottial energy surfaces, until ultimately it reaches the electroground state. In fact, in all cases where the hydrogen hasalready the kinetic energy amount necessary for it to ovcome the cage-exit barrier, relaxation onto the ground etronic state and recombination onto it are bound to happeyet the process may take some time, well beyond 1Figure 7 shows the paths of the H and of the Cl atoms itrajectory in which the point of recombination on the groustate is reached 1.4 ps after the excitation. In this trajecthe H atom collided 20 times with the cage walls beforecombination. It turns out that already 0.5 ps after excitatthe H atom was already cold to the point of excluding caexit. However, the nonadiabatic electronic transitions allway to the ground state took a much longer time to occThe results of the simulations and the view afforded on

ly

y

FIG. 6. The paths of the H and of the Cl atoms in a trajectory leading torecombination~after 0.02 ps!.

, No. 16, 22 April 1997


tbeeuon

both

xiigla

isa

abw

.

ro-rtly

Theex-

lds

re--al-ticforInHn-ig.

atki-la-ki-ofandClion

erme


Do

dynamics in time of the cage exit and recombination evendepend of course on the interaction potential. It is possithat the ‘‘real’’ H-Ar potential, for instance, is less repulsivthan the one we used. It is conceivable that in this case thwill be much less delay of cage-exit, perhaps some measof direct cage exit will take place. We estimate, however,the basis of the trajectories we examined that norealisticH-Ar potential is likely to change the fact ofat least animportant component of delayed cage exit events. Welieve this conclusion is likely to remain robust, regardlessthe uncertainty, important as it is, as to the accuracy ofpotentials.

B. Yields for cage exit and for recombination

The yield for cage exit at timet after the excitation pulseis given by: Yex(t)5*o

t pex(t8)dt8, where pex(t8) is theprobability per unit time for cage exit.Yrec(t), the yield forrecombination, is similarly defined. The yields for cage eand for recombination as a function of time are shown in F8. The yields for the two processes are roughly of simimagnitude for t*1 ps, with Yex somewhat larger thanYrec. The asymptotic long-time ratio between the yields54:46(64.5%!. It is interesting to compare this result withrecent experiment: Schwentner and coworkers14 observed30%–40% dissociation efficiency with uncertainty of 30%the excitation of 7.2 eV. Therefore, the calculated and oserved photodissociation yield are in good agreement. Hoever, the comparison must be treated with caution, sincethe simulation the initial excited state was the triplet only

FIG. 7. The paths of the H and of the Cl atoms in a trajectory ending in vdelayed recombination~after 1.4 ps!.



s,le

rere

e-fe

t.r

t--in

Because of the delayed nature of cage exit in this pcess, while some recombination events take place shoafter the excitation,Yrec(t) is larger thanYex(t) for veryshort times, the crossover point being around 0.125 ps.results should depend on the excitation energy, and onepects that for higher excitation energies the ratio ofYex toYrec will be larger. Accurate measurements of the two yieshould be of great interest.

C. Cage exit and cooling mechanism for the H atom

The excitation energy used in the simulations corsponds to an excess energy of 2.5 eV~in gas phase photodissociation!. Due to the mass ratio between H and Cl,most the entire excitation energy is converted into kineenergy of the hydrogen. The energy suffices, in principle,yielding a hot distribution for the H atoms after cage exit.fact, the simulations show that the kinetic energy of theatoms right after cage exit is not very high. The kinetic eergy distribution immediately after cage exit is shown in F9. The hottest H atoms have kinetic energies of;0.5 eVonly at cage exit, and the maximum of the distribution isabout half this energy value only. Figure 10 shows thenetic energy of the H atom in a trajectory leading to retively fast cage exit. In the upper part of the figure, thenetic energy along the trajectory is compared with resultsa model assuming hard-sphere collisions between the Hisolated Ar or Cl atoms. The lower figure shows the H-distance versus time, and this provides also the collistimes ~the maxima ofRH2Cl correspond to H-Ar collisions,

yFIG. 8. The yields for cage exit and for recombination as a function of tiafter the excitation pulse.

, No. 16, 22 April 1997


interepwid,eolth

ththlet

-th

ith

heianratns

on-ee in

antveryes,ingsenbe-isec-onsns

l theur-lec-re-heagee

hthergy

xit cu-

mme


Do

the minima correspond to H-Cl encounters!. The number andtimes of collisions from the bottom of Fig. 10 were usedthe simple ‘‘hard-sphere collisions’’ calculation. We nothat by Fig. 10, the cooling of the H by the Ar lattice is moefficient than that by isolated hard sphere collisions, escially for longer times. It seems that as the H atom slodown, it can interact with collective modes of the soltransferring energy more effectively. Also, at least for slowhydrogen, longer ranges of the H-Ar interaction play a rnot included, of course, in the hard sphere model, makingcooling more efficient.

D. Electronic transitions in cage exit and inrecombination

We consider now the trajectory corresponding tofastest cage exit event. The upper part of Fig. 11 showsH-Cl distance versus time for that trajectory. The middpanel shows the adiabatic potential energy surfaces alongtrajectory, and the bottom figure gives the electronic statethe system as a function of time.~The numbers of the electronic states of the system, from 1–12, correspond toordering of the states as described in Sec. II.! For this par-ticular trajectory cage exit occurs after two collisions wthe cage walls~and two collisions with the Cl atom!. As seenfrom Fig. 11~c!, the electronic state changes already in tfirst collision, and cage exit does not occur from the initstate. In fact, there are over 15 nonadiabatic transitions alothat trajectory, mostly during the two collisions with the Aatoms, although during each collision several nonadiabtransitions take place. Actually, several nonadiabatic tra

FIG. 9. Kinetic energy distribution of H atoms immediately after cage e



e-s

ree

ee

heof

e

lg

ici-

tions take place during the cage-exit stage itself. We cclude thatnonadiabatic transitions may occur even in thfastest cage exit events, and indeed they play a major rolthe detailed dynamics of the cage exit event. As Fig. 11~b!shows, the nonadiabatic transitions occur when the relevadiabatic potential energy surfaces cross, or approachclosely~we show only some of the potential energy surfacfor clarity!. In many cases these crossings or near crossarise when the Cl atom is relatively far from the hydrog~this reflects on the degeneracies and the small splittingstween Cl(2P) atom states in a matrix, when no H atompresent!. Figure 12 shows the most delayed cage-exit trajtory. In this case the H atom leaves the cage after 9 collisiwith the cage walls. The number of nonadiabatic transitiothroughout this event is very large, as seen in Fig. 12~c!. Infact, throughout the process, the system goes through al12 electronic states of the manifold. Very interestingly, ding the trajectory the system reaches twice the ground etronic state, but the kinetic energy of the H atom hasmained sufficiently high, leading to back transitions to texcited adiabatic potential surfaces, and ultimately to cexit. Thus,return to the electronic ground state during thprocess is not a sufficient condition for recombination. Also,as we saw,nonadiabatic transitions are important for botfast and slow cage exit events, but in fast cage-exit eventssystem only reaches a few of the excited potential ene

. FIG. 10. Upper part: Kinetic energy of the H atom versus time in a partilar trajectory resulting in fast cage exit~solid line!. The black dots give thekinetic energy from a ‘‘hard-sphere’’ collision model between the H atoand Ar or Cl. Bottom part: The H-Cl distance versus time in the satrajectory.

, No. 16, 22 April 1997


gng

bime

a3afaurtanyei

thth

telen

–ms

ralriestomre-arininu-

ofx-ingm

theela-

c-s,ec-are

n-heherude

ex ob-

t


Do

surfaces, while in a very delayed cage exit it may go throuall the electronic states of the manifold involved, includithe ground state.

We consider now electronic transitions during recomnation events. Figure 13 corresponds to the fastest reconation event seen in the simulation, in which the hydrogundergoes only a single collision with the cage walls.As thisfigure shows, this may suffice for recombination, but is actu-ally not typical and most trajectories resulting in recombintion involve at least two collisions with the walls. As Fig. 1shows, the recombination occurs due to direct nonadiabtransitions, when the H atom hits the cage wall and isfrom the Cl atom. Another brief nonadiabatic event occduring the collision: The system returns to the excited sfor a very brief time interval, then goes back to the groustate. Finally, Figure 14 shows results for the most delarecombination event we calculated. The recombinationthis trajectory occurs 1.4 ps after recombination. Duringprocess, the H atom undergoes about 20 collisions withcage walls. Actually, aftert'0.5 ps, the H atom is in thiscase already too cold for cage exit. However, the syscarries out a long and slow excursion in the space of etronic states. It spends most of the time in the electrostates which have the index numbersn>5 ~see Sec. II forthe number labeling!, although it also reaches the states 1for a very brief time duration, hopping almost at once frostate to state. The system reaches the electronic ground

FIG. 11. Electronic transitions in a trajectory leading to the fastest cage~a! The H-Cl distance versus time in the trajectory.~b! Adiabatic potentialenergy surfaces along the trajectory.~c! The electronic state of the systemversus time. The states are numbered from 0–11,n50 is the ground stateandn51,2 are the states of initial excitation. Highern corresponds to thehigher energy.



h

-bi-n

-

ticrsteddnee

mc-ic

4

tate

only once, when recombination occurs. As Fig. 14~b! shows,during the trajectory the H atom is in regions where seve~excited! electronic surfaces are very close, and thus carout very frequent hops from state to state. Indeed, the H aoscillates nearly all the time between the Cl atom andgions very far from it, in ‘‘remote’’ corners of the cage, nethe wall. This trajectory is an example of a long excursiona large subspace of the electronic states, with almost contous hops from state to state.

E. Electronic state populations versus time

Figure 15 shows the populations as a function of timethe two lowest excited adiabatic states, those initially ecited. It is evident that the decay is extremely fast, havessentially the timescale of the first collision of the H atowith the cage walls~about 10 fs!. As we noted previously,nonadiabatic transitions, from the excited states toground state or to other excited states, take place with rtively high probability when the Cl atom is far from the Hatom, which is the origin for the relation between the eletronic population lifetimes and the occurrence of collisionin particular the first one. As this, and the results of substion 4 above show, nonadiabatic transitions in this systemextremely fast.

For purposes of interpretation it is convenient to cosider the populations of the ‘‘bare’’ electronic states of tHCl molecule, that is the states without the effect of tenvironment. We stress that this can only be done as a c

it.FIG. 12. Electronic transitions in a trajectory leading to the slowestserved cage exit.~a! The H-Cl distance versus time.~b! Adiabatic potentialenergy surfaces along the trajectory.~c! The electronic state of the system aeach time. For numbering of states, see Fig. 11, and Sec. II.

, No. 16, 22 April 1997


kjepvTCltsc-rofelplesnpestiotioe,oe

nus

om

ch

m-

ch

rsus


Do

approximation, and not in all cases. The approach we tooto project the adiabatic state at each point along the tratory, on the ‘‘bare’’ state of HCl. Only when a single overladominates strongly, can we expect the interpretation‘‘bare’’ states to have simple observable consequences.reason for pursuing interpretations in terms of ‘‘bare’’ Hstates is that their symmetries provide very helpful insighFigure 16 shows the variation in time of the ‘‘bare’’ eletronic states of HCl throughout the photodissociation pcess. These populations were constructed on the basis ooverlap with the adiabatic states, as noted above. Thesetronic states must be considered to be very strongly couby the dynamics, since the rate of nonadiabatic transitionthe system is very high. Nevertheless, although electrostate populations can change very rapidly in time, the polations do not seem statistically distributed over the timcale shown. Partly this perhaps is due to the recombinaand cage exit processes, that are still ongoing—the formaof 1S0 provides a ‘‘sink’’ for the other states. In any casneither the time behavior, nor the ratios of the populationsdifferent states suggest that a statistical distribution has breached.Note for instance that the3P0 and

3P2 states, thathave very similar energies, have very different populatioover the time-interval shown. This is of interest for the issof (electronic) state selectivity in condensed phase proces.

FIG. 13. Electronic transitions in a trajectory leading to the fastest recbination.~a! The H-Cl distance versus time.~b! Adiabatic potential energysurfaces along the trajectory.~c! The electronic state of the system at eatime ~for the state numbering, see Fig. 11, and Sec. II!.



isc-

iahe

.

-theec-dinicu--nn

fen

sees

-FIG. 14. Electronic transitions in a trajectory leading to the slowest recobination event.~a! The H-Cl distance versus time.~b! Adiabatic potentialsurfaces along the trajectory.~c! The electronic state of the system at eatime ~for state numbering, see Fig. 11, and Sec. II!.

FIG. 15. The populations of the two lowest excited adiabatic states vetime. The states shown are the ones initially excited.

, No. 16, 22 April 1997


avecexithsateth

bi

ted

oanatth

heth

usthter

ichac-the

t

or

andandThei-

t

c-ng

ter-to-u-

usf theheac

exit


Do

F. Propensity of different electronic states with regardto cage exit versus recombination

Finally, we address the following issue: How doesgiven electronic state, reached by the system in a given edictate the future evolution? Are they states of pronounpreference with regard to recombination versus cage eAnd what are the interactions or mechanisms that bring‘‘preference’’ about? One may expect, perhaps, since thia system of low symmetry and very frequent nonadiabtransitions, that significant ‘‘preferences’’ are unlikely to bfound. Interestingly, this is not the case. Figure 17 showsquantityDPrec2ex[(Prec2Pex)/P for the different adiabaticstates.DPrec2ex is a measure of the preference for recomnation as opposed to cage exit for the state.P is the average~over line! population of the state,Pex is the probability of atrajectory which has reached that state to continue ultimato cage exit,Prec is the corresponding probability to proceeto recombination. We note that the average populationsmost adiabatic states are about the same, which is due tlarge frequency of nonadiabatic transitions in the system,to the modest energy spacings between the excited stFigure 17 shows only very partial correlations betweenDPrec2ex and theorder of the adiabatic states.Since the or-der is approximately in accord with increasing energy of tstates it is clear that energy cannot be the only or even

FIG. 16. The populations of the ‘‘bare’’ electronic states of HCl verstime. The populations were constructed on the basis of the project oadiabatic states onto the bare states~see text!. The relative energies of thesstates in anisolatedmolecule are given by Fig. 11, however in a matrix tenergies of these states change due to the coupling induced by an interwith Ar atoms.



ntdt?isisic

e

-

ly

ofthedes.e

e

main factor in determining the propensity for exit versrecombination. Note that only for the first, second and fourexcited states the propensity for recombination is greathan for cage exit (DPrec2ex.0), while for the third excitedstate this is not true. It is this non-monotonic behavior whindicates most strongly that in addition to energy, other ftors must be important in determining the propensities ofstates. Figure 18 showsDPrec2ex ~defined as above! for thedifferent ‘‘bare’’ states of the HCl molecule. The single1P1 and the tripletS states (3S0 and

3S1) show no prefer-ence either for recombination or for cage exit, while f3P states there is a very strong dependence ofDPrec2ex ~the‘‘preference’’ measure! on the projectionmj of the orbitalangular momentum. The largerumj u is, the stronger is thepreference for cage exit over recombination. To understthis, consider the spin-orbit coupling between the states,the coupling between the states due to the Ar atoms.ground1S0 state is coupled by the interaction with the envronment only to the1P1 state. The spin-orbit interactioncouples the ground state to3P0. The latter is thus the mospreferable state for recombination. The3P2 state is notcoupled by spin-orbit interaction to any other state. Eletronic transitions from this state can only occur by coupliwith 3P0,

3S1, due to the environment. The state3P1 iscoupled by spin-orbit interactions to the1P1 state, which inturn is coupled to the ground state by the electrostatic inaction with the Ar. This scheme of coupling, consideredgether with Fig. 18, leads to the following important concl

e

tion

FIG. 17. DPrec2ex for the different adiabatic states.DPrec2ex

5 (Prec2Pex)/P measures the preference for recombination over cagefrom the state. For states which favor recombinationDPrec2ex.0, whilestates favoring cage exit haveDPrec2ex,0.

, No. 16, 22 April 1997


ntid

icneaenvtre

ime

shthnveharmthece

smsor

theme,d,dy-e as-be-ndablences in

rdM.m-

l

ive

r, J.

, J.

hys.

m.

vetio


Do

sion: The spin-orbit interactions are the most importafactor for recombination, while the interaction with the solplays a less major role.

IV. CONCLUDING REMARKS

In this paper we used non-adiabatic Molecular Dynamsimulations to explore cage exit, electronic transitions arecombination following photolysis of HCl in solid Ar. Onof the fundamental features that emerge is the frequency,importance, of non-adiabatic transitions between differelectronic states. Such transitions were found to occur ein the fastest cage-exit events, and essentially they conmuch of the cage exit and recombination dynamics in timVery rapid changes of the electronic state populations in toccur, especially immediately after photodissociation. Dspite the frequent nonadiabatic transitions in this system12 electronic states, the populations of the states are nottistically distributed over the timescale of the process. Tvery interesting dynamics of the electronic states, andbehavior in time of both cage-exit and recombination evestrongly underline the need for femtosecond time-resolspectroscopic experiments to study such processes. Sucperiments should open very exciting directions for comping with theory and confirming, or rejecting, the mechanisproposed. Of special importance would be studies ofelectronic state dynamics—the variation in time of the eltronic populations that clearly require ultrafast time-resolv

FIG. 18. DPrec2ex for the different ‘‘bare’’ states of HCl.DPrec2ex5 (Prec2Pex)/P measures the preference for recombination ocage exit from the state. For states which favor recombinaDPrec2ex.0, while states favoring cage exit haveDPrec2ex,0.



sd

ndtenol.e-ofta-eetsdex--se-d

techniques. The simulations suggest particular mechanifor cage exit~reflected, e.g., in the time-delay predicted fthese events!, and for electronic transitions~many of thetransitions occur when the H atom moves far away fromCl, configurations for which the adiabatic potentials becodegenerate or closely spaced!. These predictions dependhowever, on the validity both of the DIM potentials useand on the surface-hopping method for the non-adiabaticnamics. For condensed matter processes, neither of thessumptions can be taken for granted. Direct comparisontween non-adiabatic Molecular Dynamics simulations acorresponding experiments for the same systems may beto throw light on these important questions, and advaconsiderably our knowledge on non-adiabatic processecondensed phases.

ACKNOWLEDGMENTS

We thank Dr. Leonid Baranov, Masha Niv, Dr. BurkhaSchmidt and Professors N. Schwentner, V. A. Apkarian,Chergui and V. Bondybey for helpful discussions and coments. This research was supported by a grant~to RBG!from the Israel Science Foundation~operated by the IsraeAcademy of Sciences!. The part of this work done at UCIrvine was supported by the University Research Initiaton Advanced Cryogenic Propellants, funded by AFOSR.

1V.E. Bondybey and L.E. Brus, J. Chem. Phys.62, 620 ~1975!.2L.E. Brus and V.E. Bondybey, J. Chem. Phys.65, 71 ~1976!.3V.E. Bondybey and C. Fletcher, J. Chem. Phys.64, 3615~1976!.4P. Beeken, M. Mandic, and G.W. Flynn, J. Chem. Phys.76, 5995~1982!.5P. Beeken, E.A. Hanson, and G.W. Flynn, J. Chem. Phys.78, 5892~1983!.

6M.E. Fajardo and V.A. Apkarian, J. Chem. Phys.85, 5660~1986!.7M.E. Fajardo and V.A. Apkarian, Chem. Phys. Lett.134, 1 ~1987!.8R. Shriever, M. Chergui, H. Kunz, V. Stepanenko, and N. SchwentneChem. Phys.91, 4128~1989!.

9R. Shriever, M. Chergui, O. Unal, N. Schwentner, and V. StepanenkoChem. Phys.93, 3245~1990!.

10J. McCaffrey, H. Kunz, and N. Schwentner, J. Chem. Phys.96, 2825~1992!.

11H. Kunz, J. McCaffrey, R. Shreiver, and N. Schwentner, J. Chem. P94, 1039~1991!.

12J. McCaffrey, H. Kunz, and N. Schwentner, J. Chem. Phys.96, 155~1992!.

13K.H. Godderz, N. Schwentner, and M. Chergui, Chem. Phys.209, 91~1996!.

14K.H. Godderz, N. Schwentner, and M. Chergui, J. Chem. Phys.105, 451~1996!.

15H. Kunttu and V.A. Apkarian, Chem. Phys. Lett.171, 423 ~1990!.16A.I. Katz and V.A. Apkarian, J. Phys. Chem.94, 6671~1990!.17E.T. Ryan and E. Weitz, J. Chem. Phys.99, 1004~1993!.18E.T. Ryan and E. Weitz, J. Chem. Phys.99, 8628~1993!.19D. Labrake, E.T. Ryan, and E. Weitz, J. Chem. Phys.102, 4112~1995!.20R. Zadoyan, Z. Li, P. Ashjian, C.C. Matrtens, and V.A. Apkarian, ChePhys. Lett.218, 504 ~1993!.

21R. Zadoyan, Z. Li, C.C. Matrtens, and V.A. Apkarian, J. Chem. Phys.101,6648 ~1994!.

22Z. Li, R. Zadoyan, V.A. Apkarian, and C.C. Matrtens, J. Phys. Chem.99,7453 ~1995!.

23R. Fraenkel and Y. Haas, Chem. Phys. Lett.214, 234 ~1993!.24R. Alimi, R.B. Gerber, and A. Brokman,Stochasticity and IntramolecularRedistribution of Energy~Reidel, Dordrecht, 1987!, p. 233.

25R. Alimi, R.B. Gerber, and V.A. Apkarian, J. Chem. Phys.89, 174~1988!.26R.B. Gerber, R. Alimi, and V.A. Apkarian, Chem. Phys. Lett.158, 257

~1989!.

rn

, No. 16, 22 April 1997


er,

-

m

d

uss.

s.


Do

27R. Alimi, A. Brokman, and R.B. Gerber, J. Chem. Phys.91, 1611~1989!.28R. Alimi, R.B. Gerber, and V.A. Apkarian, J. Chem. Phys.92, 3551

~1990!.29R. Alimi, V.A. Apkarian, and R.B. Gerber, J. Chem. Phys.98, 331~1993!.30R. Alimi, R.B. Gerber, and V.A. Apkarian, Phys. Rev. Lett.66, 1295

~1991!.31R. Alimi, R.B. Gerber, J.G. McCaffrey, H. Kunz, and N. SchwentnPhys. Rev. Lett.69, 856 ~1992!.

32R.B. Gerber and A.I. Krylov, inReaction Dynamics in Clusters and Condensed Phases, edited by J. Jortner~Annual Reviews Inc., Palo Alto, CA,1994!, pp. 509–520.

33A.I. Krylov and R.B. Gerber, J. Chem. Phys.100, 4242~1994!.34R.B. Gerber, A.B. McCoy, and A. Garcia-Vela, Annu. Rev. Phys. Che45, 275 ~1994!.

35H. Schroder and H. Gabriel, J. Chem. Phys.104, 587 ~1996!.36A. Brokman and C.C. Martens, J. Chem. Phys.102, 1905~1995!.37I.H. Gersonde and H. Gabriel, J. Chem. Phys.98, 2094~1993!.38V.S. Batista and D.F. Coker, J. Chem. Phys.105, 4033~1996!.39F.O. Ellison, J. Am. Chem. Soc.85, 3540~1963!.40A.I. Krylov and R.B. Gerber, Chem. Phys. Lett.2312, 395 ~1994!.41A.I. Krylov, R.B. Gerber, and V.A. Apkarian, J. Phys. Chem.189, 261

~1994!.



.

42A.I. Krylov, R.B. Gerber, and R.D. Coalson, J. Chem. Phys.105, 4626~1996!.

43A.I. Krylov, R.B. Gerber, M.A. Gaveau, J.M. Mestdagh, B. Schilling, anJ.P. Visticot, J. Chem. Phys.104, 3651~1996!.

44A.A. Buchachenko and N.F. Stepanov, J. Chem. Phys.104, 9913~1996!.45M. Bettendorff, S.D. Peyerimhoff, and R.J. Buenker, Chem. Phys.66, 261

~1982!.46R.A. Aziz and M.J. Slaman, Mol. Phys.58, 679 ~1986!.47R.W. Bickes, B. Lantszch, J.P. Toennies, and K. Walaschenski, DiscFaraday Soc.55, 167 ~1973!.

48V. Aquilanti, D. Cappelletti, V. Lorent, E. Luzzatti, and F. Pirani, J. PhyChem.97, 2063~1993!.

49J.C. Tully, J. Chem. Phys.93, 1061~1990!.50P. Jungwirth and R.B. Gerber, J. Chem. Phys.104, 3651~1996!.51A.I. Krylov and L.Ya. Baranov~unpublished!.52C.A. Mead, Rev. Mod. Phys.64, 51 ~1992!.53M.P. Allen and D.J. Tildesley,Computer Simulations of Liquids~Claren-don, Oxford, 1987!.

54B. Schmidt and P. Jungwirth, Chem. Phys. Lett.259, 62 ~1996!.

, No. 16, 22 April 1997


photodissociation dynamics of hcl in solid ar: cage exit

Documents