Photodissociation of HCl adsorbed on the surface of an Ar12 cluster: Nonadiabatic molecular dynamics...

JOURNAL OF CHEMICAL PHYSICS VOLUME 110, NUMBER 22 8 JUNE 1999

Photodissociation of HCl adsorbed on the surface of an Ar 12 cluster:Nonadiabatic molecular dynamics simulations

Masha Y. Niv, Anna I. Krylov,a) 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 92697-2025

Udo BuckMax-Planck-Institut fu¨r Stromungsforshung, Bunsenstraße 10, D-37073 Go¨ttingen, Germany

~Received 30 December 1998; accepted 17 March 1999!

The photodissociation of HCl adsorbed on the surface of an Ar12 cluster is studied by semiclassicalmolecular dynamics simulations, using a surface-hopping approach for the nonadiabatic transitions.The DIM method is used to construct the 12 potential energy surfaces that are involved, and thenonadiabatic couplings. The results are compared with previous studies on HCl embedded inside Arclusters and on the triatomic Ar–HCl cluster. The main findings are the following:~1! There is ayield of about 1% for recombination onto the ground electronic state of HCl, roughly the same asfor HCl embedded inside Ar12. ~2! Photodissociation lifetimes much longer than for Ar–HCl arefound. ~3! The kinetic energy distribution of the H atom shows large energy transfer to the cluster,greater than in the case of HCl in the embedded geometry in~Ar!12HCl. ~4! An interestingmechanism leads to the formation of some fraction of very ‘‘hot’’ Cl atoms.~5! About 10% of theCl is left trapped in (Ar)mCl clusters.~6! The branching ratioP1/2:P3/2 for the Cl atoms that leavethe cluster shows electronic cooling compared to the isolated HCl molecule case. The results throwlight on the role of local geometry in photodissociation/recombination processes, and in particularon the mechanisms pertinent in the case of surface-adsorbed species. The nature of the results,showing strong cage effects at the surface geometries is to a large extent a consequence of theencapsulation of the H atom, obtained for the structure of the~Ar!12HCl cluster. © 1999 AmericanInstitute of Physics.@S0021-9606~99!70222-9#

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I. INTRODUCTION

Photodissociation and recombination of moleculeschemically inert media is a fundamental topic in chemidynamics. Studies of such processes have been vigoropursued in recent years in solids, liquids, and clusters.specific attraction of clusters as media for exploring the pcesses is that the finite number of degrees of freedomsimplify the analysis, compared with condensed matterbulk, while at least some aspects of the processes in clu~e.g., the interaction potentials! should be closely related tthose in solids and liquids. There have been extensiveperimental and theoretical studies of photodissociationrecombination of diatomic and polyatomic moleculesclusters.1–12 The present paper is motivated mainly by tfollowing question: How does the photodissociatiorecombination dynamics of a molecule adsorbed at theface of a chemically inert cluster differ from the corresponing processes in the case that the molecule is embedinside the cluster? To explore this question, we carrysimulations on the photodissociation~and subsequent recombination, when it occurs! of HCl adsorbed at the surface oan (Ar)12 cluster. There are several reasons for choosingsystem:~1! Studies on the corresponding process for H

a!Current address: Department of Chemistry, University of Southern Cfornia, Los Angeles, California 90089.

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embedded inside an (Ar)12 cluster were carried out by threof the present authors.13 Calculations for other (Rg)nHX sys-tems, with X a halogen and Rg a rare gas, all for the ‘‘inside’’ position of the HX, were also reported in thliterature.8,14,15,44Also photolysis and recombination of HCin solid Ar were investigated in detail.16–18 ~2! Photodisso-ciation of HCl in the triatomic cluster Ar–HCl was studiemost extensively9–11,19–21in recent years, and the same prcess was investigated also for several other Rg–HX clusof similar structure.6,8 For Ar–HBr, both experimental andtheoretical results are available.6,42 These triatomic clustershave an element of structural similarity to the ‘‘surface ismer’’ of ~Ar!12HCl, since in both cases the hydrogen pointowards the ‘‘solvent.’’~3! Both the ‘‘embedded’’ and the‘‘surface adsorbed’’ isomers of~Ar!12HCl are predicted to be~locally! stable minima on the potential energy surface ofsystem.13 With the available state of the art potentials13 itappears that the ‘‘surface adsorbed’’ structure correspondthe global minimum of the potential energy.13,22 However,the barrier between the ‘‘embedded’’ and the ‘‘surface asorbed’’ isomers is very high, so in principle, with suitabexperimental approaches it may be possible to preparestudy both isomers.

Calculations for photodissociation of HCl in Amatrices,17 and in the ‘‘embedded’’ isomer of (Ar)nHCl (n512, 54) ~Ref. 13! showed that nonadiabatic transitions b

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11048 J. Chem. Phys., Vol. 110, No. 22, 8 June 1999 Niv et al.

tween 12 different potential energy surfaces play a marole in the process, and they are in fact the key for evqualitative understanding of some of its important featurWe therefore carried out the calculations of the present stin the framework of nonadiabatic~semiclassical! moleculardynamics simulations.

The structure of the article is as follows: Section II dscribes very briefly the system, the interaction potentused for the system in the ground and in the excited etronic states, and the semiclassical ‘‘surface hopping’’ simlation method for dynamics. The description is brief sinthe interaction potentials and simulation method are the sas used for the ‘‘embedded’’ isomer~Ar!12HCl in a previousstudy.13 In Sec. III the main findings are discussed in relatito the properties found for other systems. Concludingmarks are brought in Sec. IV.

II. SYSTEM, INTERACTIONS, AND SIMULATIONMETHOD

A. Ground-state potentials

The interaction potentials used in the present study wthe same as employed for the ‘‘embedded’’ isomer~Ar!12HCl in Ref. 13. The potential function for the electronic ground state was written as a sum of Ar–HCl intertions and of Ar–Ar pair potentials. We used Hutson’s potetial for Ar–HCl,23 an Ar–Ar pair potential from Aziz andSlaman24 and the H–Cl vibrational potential from Bettendoet al.25 The minimum energy structure of Ar12~HCl! foundby simulated annealing is shown in Fig. 1.

Based on our studies so far, this seems to be the lowenergy isomer, lower in energy than the isomer with Hembedded inside the cluster.

As mentioned earlier, also the ‘‘embedded HCl’’ struture of ~Ar!12HCl is, however, locally quite stable. The energy barrier between the two isomers is very high, soformed, each of them should be stable in experimental cditions. Since cluster formation is often controlled by kinefactors, it should be possible to obtain experimentally bstructures, each by a different mechanism. Note that instructure of Fig. 1 the H atom is quite strongly ‘‘encaps

FIG. 1. Minimum energy structure of Ar12~HCl!.


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lated’’ between the Cl and the neighboring argon atoms. Tobviously will have a major effect on the photodissociatidynamics.

B. DIM potentials for the excited states

There are 12 electronic states, in terms of electronicgular momentum and spin, relevant to the photodissociaHCl→H(2S)1Cl(2P) in a medium of closed shell chemcally inert atoms. Krylov and Gerber17 used the diatomic-in-molecules~DIM ! method26,27 to construct the potential energy surfaces and the nonadiabatic couplingsphotodissociation of HCl in solid Ar, and this was followeby Niv et al.,13 for the ‘‘embedded’’ isomer of~Ar!12HCl.We use the same method here. We note that the DIM methas been used quite extensively in recent years for a vaof systems including the halogen–molecule/rare gas cplexes, and hydrogen–halide/rare gas complexes.16,28–31

Some support for the DIM potentials validity for the HCl/Asystems comes from agreement between the simulationKrylov and Gerber17 and experiments by Godderz, Schwenner, and Chergui32 on several properties of the photodissciation of HCl in solid Ar. However, not enough data aavailable yet for a full quantitative comparison and evalution of the DIM potentials. The DIM modeling of the systeuses valence bond formulation for the H–Cl interaction. Ptential energy curves of the HCl molecule taken from Btendorfet al.25 are used as input data for the constructionthe DIM surfaces. The interaction between the Cl atom aan Ar atom, modeled in terms of an effectivep orbital on theCl atom was taken from Aquilantiet al.33 The interactiondepends on the orientation of thep orbital with respect to theAr–Cl axis. For H–Ar interactions we used pair potentiafrom Ref. 34. Spin–orbit coupling, with a strength equalthat for isolated Cl(2P) atom was incorporated in the Hamitonian. The diagonalization of the electronic DIM Hamtonian was performed ‘‘on the fly,’’ at each point of thtrajectory of the atomic motions. The calculation of the adbatic potential energy surfaces, of the electronic eigenfutions and of the nonadiabatic couplings between anyelectronic states, all done ‘‘on the fly,’’ along the trajectoriof the nonadiabatic molecular dynamics simulations, flowed the procedure of Refs. 17, 13, where detailed desctions are given.

C. Semiclassical ‘‘surface hopping’’ simulations ofthe dynamics

The algorithm used for the dynamics is discussedRefs. 13 and 17. It is a variant of the ‘‘surface hoppingmethod for nonadiabatic processes, developed by Tully35 andby others. In this approach, nuclear motions are treatedclassical and described by classical trajectories. The etronic state is described by a time-dependent wave functhat incorporates the effect of nonadiabatic coupling. Telectronic state is evaluated along each trajectory. At einstant in time, the nuclei are taken to move on one ofadiabatic potential energy surfaces. Changes in the compelectronic wave function are used as the criterion forprobability of ‘‘hopping’’ to another adiabatic potential en


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11049J. Chem. Phys., Vol. 110, No. 22, 8 June 1999 Niv et al.

ergy surface. When the criterion for a ‘‘hopping’’ eventsatisfied at some point, the nuclei are taken to experiencinstantaneous switch to the other potential surface, and tpropagation is pursued classically on the latter until theterion for the next ‘‘hopping’’ event is met. The criteria fo‘‘hopping’’ events, and the initial conditions for propagatioof the nuclei~after hopping has occurred! on the new poten-tial surface, are discussed in Refs. 17 and 13. These criand conditions can be different in different variants of t‘‘surface hopping’’ method, though for HCl in solid Asome testing suggests that the results of the variant useTully35 and that employed by Krylov and Gerber17 seemto give similar results. Also, suitable adaptations of t‘‘surface hopping’’ method are necessary for treating cof exact degeneracy of electronic states~such as Kramersdegeneracy!,36 and for cases where spin–orbit interations are present in the Hamiltonian~the system studied herewith spin–orbit coupling included, is of that type!.36,37

We note that several other groups have used the ‘‘surhopping’’ method in recent applications to photodissciation/recombination processes in solids, liquids,clusters,12,31,37,38and that comparisons with experiment sugest the method is successful also for these systems.

D. The initial state

We took the cluster to be in its vibrational ground stabefore electronic excitation. A normal-mode calculation wcarried out for the structure shown in Fig. 1. An all-moseparable wave function was obtained in the harmonicproximation. Using the Wigner function a distribution of psitions and momenta from the above wave function wcomputed as initial values for the classical simulation.13 Thenormal mode harmonic treatment is probably mostly in erfor the libration motion of the HCl. Though this is likely tbe a significant error, e.g., for vibrational spectroscopy inelectronic ground state, some exploration of the possibleof libration anharmonicity on the photodissociation dynaics has indicated that our results should not be stronglyfected.

Using the computed Wigner positions-momenta distribtion, initial conditions were sampled from this set. Excitatiwas modeled in the spirit of the classical Franck–Condvertical promotion onto the excited potential energy surfawith a given excitation energy. We chose excitation eneof 6.4260.07 eV, which corresponds~approximately! to 193nm laser. The HCl molecule was excited into the1P1 state.120 excited-state ‘‘surface-hopping’’ trajectories wepropagated for the~Ar!12HCl system, providing reasonablstatistics for our purposes here.

III. RESULTS AND DISCUSSION

In the presentation of the results, we focus on sevemain findings.

~1! Electronic transitions and recombination:Most trajecto-ries describe very fast photodissociation, on a time scof 100 fs or less. In many of these cases, the energhydrogen produced upon photolysis just strikes onetwo of the argon atoms of the cluster, then recoils a


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leaves the cluster. However, in all of the computed tjectories at least one nonadiabatic transition betweenferent electronic states took place in the course ofdynamics. Indeed, the average number of nonadiabtransitions per trajectory is between 5 and 6. Figureshows the electronic state of the system vs time alonparticular trajectory. The electronic states were enumated from 1 to 12, with increasing number correspondto increasing electronic energy. For simplicity of intepretation, we also assigned the potential energy surfaby projecting the wave functions onto the states ofisolated HCl molecule. Obviously such an assignmenalways approximate and can be meaningless at sconfigurations, for which the symmetry breaking effecof the environment on the states if HCl is extremesevere. As Fig. 2 shows, the system makes a ‘‘hoppintransition some 40 fs after photoexcitation, from the intially excited state, that has mostly a1P1 character, toanother excited state, also of~mostly! 1P1 character.Then, at about 45 fs after excitation, the system maketransition to the ground electronic state. No recombintion, however, takes place; the kinetic energy of theatom is way above the attractive well of the1S0 curve ofHCl, and the H atom is at this stage already on its wout of the ‘‘cage’’ seen in Fig. 1. Other nonadiabattransitions take place at later times; these occur for cfigurations where the H atom is relatively far from thremaining (Ar)mCl(2P) cluster, and the relevant potential energy surfaces are degenerate for these asympH¯Cl distances. Indeed, these transitions have nonificant physical consequences for the process. The lest part of Fig. 2 shows the adiabatic potential energof the system computed along the trajectories. Thustransition between1P1 and1S0 at about 45 fs occurredindeed at a point of near crossing between the relevpotential surfaces. The nonadiabatic transition at ab110 fs took place essentially in the asymptotic regionthe potential surfaces, for large H~Ar!mCl distances.Another aspect of the dynamics is shown in the midpart of Fig. 2. It shows the H Cl distance vs time.

FIG. 2. ~a! The electronic state of Ar12~HCl! vs time along a particulartrajectory. ~b! The H Cl distance along the trajectory.~c! The adiabaticpotential energy surfaces of the system along the trajectory.


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Clearly, there was a cage effect in the course of parthe trajectory, since two oscillations of the HCl dis-tance are visible, before the departure of the H atfrom the cluster~which begins aftert'60 fs!. The 1P1

→1S0 nonadiabatic transition took place, however, ding the second oscillation of the HCl distance, whenthe H atom was still inside the cage. In summary, in ttrajectory, a nonadiabatic transition to the ground sttook place, but without recombination since the H atohas not imparted sufficient energy to the Ar atoms.cage effect is present in this trajectory as reflected inoscillations of the H Cl distance. There is a fraction otrajectories showing qualitative behavior of this typWe conclude therefore that nonadiabatic transitionswell as cage effects play a significant role in the proceIndeed, we found that recombination of HCl onto tground state takes place in two of the trajectories coputed.Despite the poor statistics, we think this resultphysically significant. In studies of photodissociationHCl in ArHCl no recombination event was found imany thousands of trajectories. The crude recombinayield we estimate here, of the order of 1%, roughly tsame as computed previously for the case of the ‘‘ebedded’’ HCl in ~Ar!12HCl.13 Interestingly, about 10%of the trajectories sample the ground state in the ‘‘sface’’ geometry, and 2% dissociate from this state,only 1% of the trajectories that sample the ground stin the ‘‘embedded’’ geometry. In general, the numbernonadiabatic transitions is higher for the present ‘‘sface’’ geometry; the average number of nonadiabatransitions is 5.560.5 per trajectory for the ‘‘surface’’geometry, 3.660.4 transitions per trajectory on averagfor the ‘‘embedded’’ geometry. The same tendencyfound for cage effects, as we shall see later. We conclthat the ‘‘encapsulated’’ geometry of surfaces-adsorbHCl gives rise to significant nonadiabatic and cagingfects, perhaps more so than ‘‘embedded’’ structures.

~2! Kinetic energy distribution of H atoms:The kinetic en-ergy distribution of the hydrogen atoms from photolysof Ar12~HCl! is shown in Fig. 3. The results for th

FIG. 3. Kinetic energy distribution of H atoms from photolysisAr12~HCl!. Results for ‘‘embedded HCl’’ and for ‘‘surface HCl’’ clusteisomers are compared.


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present ‘‘surface adsorbed HCl’’~that was excited by6.42 eV! geometry are compared with those for the ‘‘embedded HCl’’ isomer~that was excited by 7 eV!.13

The comparison is quite striking. The energy distributiin the ‘‘embedded HCl’’ case is dominated by hotatoms; trajectories with H atoms having kinetic energabove 2.0 eV constitute 5565% of the ensemble. In the‘‘surface’’ geometry, trajectories with H atoms havinkinetic energies above 1.42 eV constitute only 1462%of the ensemble. In both cases, the number of nonabatic transitions in the ‘‘hot’’ trajectories is lower bfactor of 2 than in the ‘‘cold’’ trajectories.Interestingly, in the small ArHCl cluster, essentially onhot hydrogens are produced, with a relatively smamount of energy transfer to the Ar atom.6,9 Clearly the‘‘encapsulated’’ geometry implied by the structureFig. 1 is very conducive to energy transfer, as theatom impacts on the Ar12 subsystem~and subsequentlyrecoils, striking also the Cl atom!. From the ‘‘embeddedHCl’’ isomer, most H atoms emerge through ‘‘holes’’ ithe surrounding argon shell, imparting only modeamounts of energy. This prediction merits experimenattention.

~3! Comparison with preliminary results on photolysisArn(HBr) cluster: Experiments corresponding to oucalculations for Ar12~HCl! were not reported yet. However, very recently Baumfalk and Buck39 carried out ex-periments on the photolysis of HBr in Arn(HBr) clusters.Some preliminary results are at hand, and we shbriefly comment on the relation to the present calcutions. The experiments of Baumfalk and Buck involvpassing a beam of (Ar)n clusters through a cell whichcontains HBr molecules at low pressures~pick up ar-rangement!. The conditions are such that capture ofmore than a single HBr molecule at the surface ofcluster is expected. This arrangement suggests formaof the ‘‘surface adsorbed’’ Arn(HBr) geometry~calcula-tions by the present authors indicate this is also energcally more stable than the ‘‘embedded’’ one!. The ‘‘cap-tured’’ HBr molecule is then photolysed using a laserwavelength 243 nm, and the kinetic energy distributiof the H atoms is measured by a~211! REMPI tech-nique at the same wavelength in a time-of-flight maspectrometer. The very preliminary results give a disbution peaked at zero velocities.39 In contrast with re-sults previously obtained for neat (HBr)n clusters7 and inagreement with the present calculations for the ‘‘surfaadsorbed’’ isomer of Ar12~HCl!, Baumfalk and Buck didnot observe a component of fast H atoms.39 The resultsof this experiment, including dependence of the behavupon cluster size will be published soon, when modetails are available. The experimental arrangemenof course, very suitable also for studies of ‘‘surface asorbed HCl’’ in Arn(HCl), and such experiments will beattempted in the near future.

~4! Lifetime distribution of the photodissociated clusteFigure 4 shows the probabilityP(t) of finding the hy-drogen inside the cluster at timet after photoexcitation.The mean lifetime of the excited cluster is of the order


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140 fs, and there is an appreciable probability of torder of 20% for finding the hydrogen in the clustert'200 fs. In the case of ArHCl, for instance, the lifetimes are much shorter. The issue of whether resonaexist in the photolysis of Ar–HCl was discussed extesively in the literature.9–11,19–21 However, any reso-nances predicted in that case are far shorter in lifetthan found here. The present system thus represenqualitative jump from ArHCl to Ar12~HCl! in thestrength of the cage effect, when measured in termsthe lifetimes induced.

~5! Kinetic energy distribution of the Cl atom:Figure 5shows the kinetic energy distribution of Cl atoms dissciated from Ar12~HCl! after excitation. The surprisingfeature is the long tail of very hot Cl atoms producePossibly measurable numbers of Cl atoms with energof the order of 0.8–1.0 eV are produced, though aspected, the distribution peaks at much colder Cl atoThe following mechanism seems at work in producithe very hot Cl atoms: in the initial impact on the Ar12

part of the system, in some of the trajectories the hydgen compresses very strongly the soft cluster. Whencompressed cluster expands, it pushes the H atom, w

FIG. 4. ProbabilityP(t) of finding the H atom in the cluster at timet afterphotoexcitation.

FIG. 5. Kinetic energy distribution of the Cl atom from photolysisAr12~HCl!—‘‘embedded’’ and ‘‘surface-adsorbed’’ isomers are compare


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in turn pushes the Cl atom. The hard core of the H atinteraction with the Cl is thus the potential which tranfers almost directly the impulse of an Ar atom in iexpansion. This gives rise to large energy transfer, mso than in a single isolated ‘‘collision’’ of an H atom ana Cl.

~6! Effect of clustering on the Cl(P1/2)/Cl(P3/2) branchingratio: The model used in this work cannot addressissue of the branching ratio in photodissociation of islated HCl. In order to quantitatively calculate the brancing ratio in pure HCl a very accurate description of ttransition moments and of the adiabatic potentials anonadiabatic couplings~especially at long ranges! isneeded. This topic has been treated by rigorous calctions treating both electronic structure and nuclearnamics at a quantum level.40 Unfortunately, such ap-proaches are presently restricted to small, few atsystems. The potentials used in the present study areaccurate enough for this purpose. We can, however,the present model to approximately calculate the effof the solvation in argon cluster on theP1/2/P3/2 branch-ing ratio. Nonadiabatic dynamics following photoexcittion to the highest electronic state of the system corlating with the Cl(P3/2) limit yielded 20%62% of the Clatoms on the Cl(P1/2) state, while excitation to the lowest state correlating with the Cl(P1/2) limit yielded35%62% of the Cl atoms on the Cl(P1/2) state. Usingthe experimental branching ratio for photoexcitationthe wavelength 193.3 nm, 0.6960.02, for the free HClmolecule,43 which is in good agreement with the theoreical value,40 we can provide a rough estimate for thbranching ratio in the case of Ar12~HCl!. We evaluatethis branching ratio to be approximately 0.4. Our predtion is, therefore, that the interaction with the Ar12 cagecauses electronic cooling of the Cl atoms emerging frthe cluster, resulting in branching ratio measurably lowthan the branching ratio of the isolated molecule.

~7! The anisotropy factor for the photodissociationAr12(HCl): The anisotropy factor is one of the moimportant quantities used to characterize photodissotion processes.41 It can be conveniently computed as folows. Let e be the electric field vector of the polarizelight, andm be the transition moment vector associatwith the excitation. Then, each photodissociation trajtory is weighted by a factorW5ue–mu2.The direction ofm in the laboratory frame is sampled fothe initial state~it is determined by the orientation of thH–Cl axis in the initial conditions!. g is defined as theangle between the final velocity vector of the H atoand the direction ofe. The finalg-angle distribution willbe of the following form:I~g!}11bP2~cos~g!!,whereP2 is second-order Legendre polynomial. The aisotropy parameterb(21<b<2) can readily be ex-tracted from the calculated angular distribution. The agular distributions for the ‘‘surface adsorbed HClisomer of Ar12~HCl! and for the ‘‘embedded HCl’’ iso-


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mer are both shown in Fig. 6, and compared withdistribution for the free HCl. The case of free isolatHCl represents, of course, the extreme case of an antropic distribution withb521. The value ofb for the‘‘adsorbed HCl’’ isomer of Ar12~HCl! is 0.1360.05,close to the isotropic limit~b50! and to the calculatedvalue for the ArHCl system~b50.11!.9 The error esti-mate is not small, but the result is significantly differefrom zero. The reason for the positive sign is the folloing: In the ‘‘surface adsorbed’’ case the H atom alwaundergoes collisions with one or more of the argonoms, which greatly change the direction of the initvelocity. The consequence is that the distribution ismost isotropic, but there is a slight preference for Homs to recoil at directions almost perpendicular tooriginal HCl axis~these directions are close to parallelthe electric vector of the polarized light!. The situationtherefore somewhat resembles the dissociation of amolecule with parallel excitation~where b is 12! andresults in positive sign inb.In the ‘‘embedded HCl,’’ the hydrogen can break outsome cases with only soft collisions with the argonoms of the solvation envelope, and the distribution otained from the ‘‘embedded HCl’’ isomer is somewhcloser to the free HCl limit, withb520.5060.05.

~8! Fragmentation of the cluster in the photodissociatiprocess:There is extensive ‘‘evaporation’’ of heavy aoms from the cluster, due to the energy imparted byinitially hot hydrogen in collisions with argon atoms anwith Cl. Getting the accurate, final size distributionsdifficult, since the evaporation follows energy redistribtion between the atoms of the cluster which takes plon a much slower time scale than the primary photolyFrom the molecular dynamics simulations, we find thabout 90% of the Cl atoms leave the cluster as freeoms, and about 10% are trapped also after a long tim(Ar) mCl clusters. As for the ‘‘evaporation’’ of Ar atomsfrom the cluster, consider Fig. 7. It shows the sizdistribution of the cluster~only pure Ar clusters are considered! at several time points after photoexcitation. Itevident that appreciable loss of Ar atoms from the cl

FIG. 6. Angular distribution of H atoms from photodissociationAr12~HCl!. The distribution is with respect to the direction of the polarizlight electric field.


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ter occurs already within 1 ps of the excitation. The moprobable number of Ar atoms in the cluster at this stais 10, and the evaporated Ar atoms leave the clustesingle atoms. However, evaporation on much slowtime scales continues. After 10 ps, a very broad clussize distribution is obtained, with an average sizeabout 6 Ar atoms. The shift towards smaller cluster sizgoes on, and after 50 ps the abundancy of a cluster gdown monotonously with its size. It should be of greinterest to attempt time-domain experiments of t‘‘evaporation’’ process.

IV. CONCLUDING REMARKS

In this study we investigated by simulations photodissciation, electronic transitions and recombination in a realismodel of HCl adsorbed at the surface of a rare-gas clusThe results and comparison with previous studies ofsame process in other clusters throw light on the role of logeometry in the basic photochemical processes studied.conclusion is that the surface-adsorbed geometry in thisalistic model leads to very important caging effects, and ato appreciable nonadiabatic transitions in the process, thtwo aspects being related at least to an extent.

The qualitatively important occurrence of some recobination onto the ground state following photolysis; the dmatic effect of the clustering in this case on the velocdistribution of the hydrogen atoms; the substantial effectthe clustering on the Cl(P1/2):Cl(P3/2) ratio; the almost iso-tropic angular distribution obtained in this system—all theoffer potentially useful future experimental handles on tdynamics in this case, and provide possible tests forsimulation results. It is gratifying that very preliminary experimental results for Arn(HBr) seem to be in accord withthe prediction regarding the velocity distribution of theatoms. However, a more detailed and definite experimetest is still underway, and should be very important for thtopic. An important point that must be kept in mind is thfollowing. The initial state geometry of the~Ar!12HCl clusterin our calculations implies encapsulation of the H atomthe neighboring Ar and Cl atoms. This undoubtedly is a k

FIG. 7. Cluster-size distribution of pure argon clusters after photodissotion of Ar12~HCl!.


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factor for the relatively strong cage effects found for thcase of ‘‘surface adsorbed’’ system. We do not expect sstrong effects for surface structures for which the H isencapsulated. Interpretation of experimental data muscarried out with attention to the nature of surface geometr

We stress that the results should be relevant also to ptochemistry at surfaces. Studies of related surface syste.g., photolysis of molecules adsorbed on rare-gas fishould be very desirable in the light of the results obtainhere.

ACKNOWLEDGMENTS

We thank Dr. B. Schmidt and Dr. P. Jungwirth for helful discussions. The work at the Hebrew University was sported in part by a grant from the Israel Science Founda~to R.B.G.!, and by the DFG, Federal Republic of Germain the framework of Sonderforschungsbereich 450~toR.B.G.!. The research in Go¨ttingen was supported by thDeutsche Forschungsgemeinschaft in SFB 357~to U.B.!.The research at the University of California, Irvine and G¨t-tingen was supported in part by a NATO grant~to U.B. andR.B.G.!.

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Photodissociation of HCl adsorbed on the surface of an Ar12 cluster: Nonadiabatic molecular dynamics...

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