Photodissociation of HBr in and on Arn clusters: the role of the position of the molecule

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  • Photodissociation of HBr in and on Arn clusters: the role of the

    position of the molecule

    N. Hendrik Nahler,a Reinhard Baumfalk,a Udo Buck,*a Holger Vach,b Petr Slavcekc and

    Pavel Jungwirthc

    a Max-Planck-Institut fur Stromungsforschung, Bunsenstrasse 10, 37073, Gottingen, Germany.E-mail: ubuck@gwdg.de

    b Laboratoire de Physique des Interfaces et des Couches Minces CNRS-Ecole Polytechnique,91128, Palaiseau Cedex, France

    c J. Heyrovsky Institute of Physical Chemistry, Academy of Science of the Czech Republic andCenter for Complex Molecular Systems and Biomolecules, Dolejskova 3, 18223, Prague 8,Czech Republic

    Received 24th April 2003, Accepted 23rd June 2003First published as an Advance Article on the web 9th July 2003

    Photodissociation experiments are carried out for single HBr molecules which are embedded in the interioror absorbed on the surface of large Arn clusters. For the embedded case the size dependence is measured for theaverage sizes hni 51, 139, 230, 290 and 450. For the surface case and the average size hni 139 the sourcetemperature is varied from T 163 K to 263 K. The measured kinetic energy of the H atom fragments exhibitspeaks at zero and 1.3 eV which mark completely caged and unperturbed fragments, respectively. The results arecompared with Molecular Dynamics simulations which account for the quantum librational delocalizationof the HBr molecule. The location of the molecule in/on the cluster is obtained from a trajectory study of thepick-up process under realistic conditions. For the embedded case corresponding to a co-expansion experiment,three argon layers are sufficient to completely hinder the H atom, in perfect agreement with the calculations.For the pick-up experiment, the large change of the source temperature leads to very small changes ofcluster temperature dependent properties. Events starting from the second shell have a higher exitprobability than those coming from the surface.

    I. Introduction

    Photodissociation of molecules in condensed media is theobject of extensive experimental and theoretical efforts in che-mical reaction dynamics.1 Recently these activities have alsobeen extended to clusters of finite size ranging from singlesolvent atoms to hundreds of particles.2,3 The advantage ofworking with clusters is that the finite size simplifies the theo-retical treatment and a direct comparison with measurementsbecomes possible. On the experimental side, new observablesare accessible like the kinetic energy distributions of the dis-sociation products. They directly probe the probability of thecage exit and the cage effect depending on fast or slow velocityof the photo-fragments.The systems among the solvated molecules that attracted

    most interest by theoreticians are hydrogen halides interactingwith rare gas clusters. They have been treated using varioustheoretical approaches.416 They exhibit a rich behavior inthe electronically excited states leading asymptotically to theexcited and ground spinorbit states. Depending on the influ-ence of the couplings, the behavior changes significantly whengoing from HCl to HI.1719 The results of the calculationsdemonstrate that in small systems the influence of the raregas atoms on the dissociation process is quite weak.9,15,20

    The situation changes when the first and second shell of theicosahedral structures close at n 12 and n 54.4,6,8,11 Wenote that even for larger sizes a small amount of cage exit pro-cesses occurs. A new perspective was introduced when thehydrogen halide molecule was placed in the outer shell of therare gas cluster. For the n 12 case the cage exit probability

    was smaller than for the embedded case.10 This trend contin-ued for chromophores with two solvation layers and it becameclear that caging probability depends strongly on the specificsurface site and on the librational motion of the HXmolecule.13,14

    On the experimental side, experiments with well defined sizedistributions and an elaborate analysis of the product state orvelocity are still quite rare. The most detailed results are avail-able for molecular ions embedded in inert atomic or moleculargases.21,22 For neutral systems, the OClO and HNO3 moleculeshave been investigated in different cluster environments.23,24

    For hydrogen halides, either small systems2527 or neat clustershave been studied.28 The Gottingen group systematicallyinvestigated HBr and HI molecules and their complexes in dif-ferent rare gas clusters using the pick-up technique for placingthem on the surface and coexpansion to embed them into theinterior of the clusters.13,2931 This effort indeed led to the firstdirect comparison of measured and calculated kinetic energydistributions for HBrArn clusters.

    14 For the embedded caseof HBrAr97 the agreement was quite convincing. In orderto verify also the theoretical predictions of the strong sizedependence of this behavior, we have carried out new measure-ments for the average sizes hni 57 and hni 130450. Thecomparison for the surface case indicated that some intensityat the cage exit was missing in the calculation. In addition,the cage exit probability for HIAr140 was smaller than thatfor HBr, and preliminary calculations were not in agreementwith the measurements. Therefore, we suggested that perhapsin the pick-up process the molecule penetrates a bit furtherinside thus leaving the outer shell. This idea was inspired by

    3394 Phys. Chem. Chem. Phys., 2003, 5, 33943401 DOI: 10.1039/b304511k

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  • the thorough study of Vach of the pick-up process,32 where asa rule-of-thumb it was found that the probability of goinginside increases with smaller size and larger attraction of themolecule. The latter is definitely the case when going fromHBr to HI. Therefore we decided to first simulate by Molecu-lar Dynamics the pick-up process and then carry out the calcu-lations for the dissociation process starting from the calculatedinitial conditions. Here, it came as a surprise that the probabil-ity for cage exit events starting from the second shell is largerthan for molecules in the surface. For HBrArn we added alsonew measurements for different source temperatures of the Arncluster beam. In this way, we hoped to test the theoreticalresult that the excitation of the librational motion completelychanges the cage exit probability. In this paper we concentrateon the HBrArn systems, while the results for HIArn will bepresented in a separate study.33

    II. Experiments

    In these experiments the HBr doped argon clusters are gener-ated in a molecular beam apparatus. The HBr molecules arephotodissociated with UV light deriving from a pulsed ns lasersystem. Within the same laser pulse the H atoms are ionizedvia a (2+1)REMPI (resonance enhanced multi-photon ioni-zation) scheme and are detected energy-sensitively in a WileyMcLaren time-of-flight mass spectrometer (WM-TOFMS)operating in the so called low-field mode. Details of this experi-mental setup have been described elsewhere.34,35 Here only ashort summary of the major components and the various tech-niques of cluster preparation is given, including the implemen-ted experimental improvements.13

    To prepare the HBr molecules in the surface region of theAr cluster, the cluster beam is first produced by a supersonicexpansion of neat Ar through a nozzle with conical shape witha diameter of 60 mm, an opening angle of 30 and a length of2 mm. The average cluster size of the Arn host clusters ishni 139. Increasing the nozzle temperature from 163 to263 K and adjusting the expansion pressure in the range from2 to 6 bar according to the relation provided by Hagena36

    should cause a slight rise of the internal energy of the Arn clus-ter at similar cluster size. Between the second and third cham-ber, which are both differentially pumped, the cluster beampasses through a scattering cell filled with HBr molecules ata partial pressure of 4 102 mbar. In the resulting pick-upprocess under these conditions, it is most probable that onlyone HBr molecule is adsorbed by the Arn cluster.

    13

    HBrArn clusters with the HBr molecule embedded in thecluster are produced by supersonic expansion of very dilutemixtures of 0.050.2% HBr in Ar through the above men-tioned nozzle. These conditions ensure that only one singleHBr molecule is embedded inside each cluster.13 The actualbeam data used in the present experiments are given in Table 1.Following mixed cluster preparation the cluster beam enters

    the chamber containing the two-stage Wiley-McLaren typeTOFMS.37 To suppress the H atom background from

    hydrocarbons, the WM-TOFMS is surrounded by a coppershield mounted on a high-pressure helium compressor whichresults in a vacuum pressure of 6 109 mbar. In order to dis-sociate the clusters, the polarized laser light is focused into theWM-TOFMS by a 400 mm lens. At their interaction point, thecluster beam, the dissociation laser, and the WM-TOFMS col-lection axis are oriented mutually perpendicular to each other.Thus, Doppler effects are eliminated in the photodissociationmeasurements. In all the present experiments the laser is line-arly polarized in the plane formed by the laser and the clusterbeam, at 90 to the collection axis. The H atoms from thedissociation process are ionized in the same laser pulse usingone-color (2+1)REMPI. The 243.06 nm light is generatedby mixing the fundamental of a Nd:YAG laser (Quanta RayGCR-5) with the frequency doubled output of a dye laser(LAS LDL 20505) operating at 630.15 nm and pumped bythe second harmonic of the Nd:YAG laser at 532 nm.The ions are extracted by a small electric field of 4 V into the

    WM-TOFMS. This operation in the above mentioned low-field mode causes a splitting of the peaks originating from ionswhich are directly ejected toward the detector and those withan initial velocity in the opposite direction; then latter ionsare decelerated in the extraction field and then their velocitiesare reversed. In this way we are able to detect slow fragments,even those with initially zero kinetic energy, which give rise toa signal between the peaks of fast ions. Examples of TOF spec-tra can be seen in Fig. 1. To derive the key value, the kineticenergy of the H atoms, from the TOF spectra we carry out acomplete simulation of the particle trajectories taking intoaccount the photodissociation process with its angular distri-bution, the velocity of the cluster beam, the finite interactionvolume, the detector dimensions, the different electric deflec-tion fields, and the electronic response function of the detector(MCP).13,29 The different contributions which can be derivedfrom the measured kinetic energy of the H atom, Ekin(H),are best discussed in terms of the energy balance of the photo-dissociation

    hn EintHBr D0 EintBr EkinBr EkinH Eclu1

    where the laser excitation energy hn and the dissociationenergy D0 of HBr (3.745 eV)

    38 are known, and Ekin(H) is mea-sured. The kinetic energy of the Br fragment is known from

    Fig. 1 Measured time-of-flight distributions for HBrAr139 at differ-ent source temperatures. For the explanation of the peaks see text.

    Table 1 Beam data

    HBr embedded in Arn

    Diameter of conical

    nozzle/mm60 60 60 60

    Expansion

    pressure/bar

    3.8 3.8 5.0 4.6

    Nozzle temperature/K 283 229 213 172

    Fraction of

    HBr in Ar (%)

    0.1 0.1 0.2 0.05

    Average cluster size hni 51 139 230 450

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  • conservation of momentum. The excitation of the upper spinorbit state (Br*) of the Br product channel is allowed for by theterm Eint(Br) and is measured as energy loss of the H atom.The influence of the cluster is expressed by the continuousenergy loss Eclu of the H atoms caused by collisions and cap-turing processes with the Ar cage. This leads to delayed exitor perfect caging, depending on the position of the HBr mole-cule in the cluster environment and the initial direction of theH atom recoil. The HBr molecules are mainly prepared in theirground rotational and vibrational state in the co-expansion aswell as in the pick-up process (Eint(HBr) 0).The structure of an H atom TOF spectrum can be explained

    with the help of Fig. 1. The fastest H atoms detected are thosethat originate from the photodissociation of HBr with Br in itsground spinorbit state as partner fragment, and that leave thecluster unperturbed (1a). The next peak (1b) can be assigned tothe same process, but with (Br*) as the partner fragment. SomeH atoms undergo several collisions and display delayed exit(2). The amount of H atoms with zero kinetic energy (3) isclearly not negligible, and is the result of a large number ofcollisions with the Ar cluster cage.

    III. Experimental results

    A. Surface case

    The calculations showed only a very weak size dependence sothat new measurements in this direction are not necessary.There was, however, a dramatic change predicted by the pre-excitation of the librational mode. In such a case nearly allH atoms are able to leave the cage unperturbed, while in thelibrational ground state most of them stay in the cage. We triedto simulate the excitation by increasing the cluster tempera-ture, which should, in turn, be evoked by heating the clustersource. The results of the time-of-flight spectra for HBrAr139 at six different source temperatures are displayed inFig. 1. In order to keep the same cluster size, the source pres-sure was varied accordingly. At a first glance, there is no dif-ference in the spectra, although the source temperature wasvaried by 100 K from 163 to 263 K. A closer look at the resultsexhibits for the ratio Rtof of perfect caged (the peak in themiddle) to cage exit events (the two outermost peaks) a slightincrease from Rtof 8 to 10 as is shown in Fig. 2. We note thatthis ratio reduces to about Rked 1.7 when transformed tokinetic energy distributions (see Section VI). Nevertheless thetheoretical predictions with excited librations reveal the pre-dominance of cage exit events with Rked 0.4 to 0.02. Appar-ently we are not able to excite the libration by increasingthe source temperature by 100 K. The large changes in thesource temperature lead to very small changes only in thecluster temperature.

    B. Embedded case

    For the embedded case, a strong size dependence was predictedwith no cage exits for HBrAr146 that corresponds to threecomplete solvation layers. Because this is a very importantresult that can be directly used to test both theoretical andexperimental concepts, we have measured the size dependence.The experimental kinetic energy distributions are presented inFig. 3 for the average sizes hni 51, 139, 230 and 450.Together with the already published result for hni 97 (ref.13) the whole interesting size range is now covered. We defi-nitely observe the predicted trend in the measurements. Thepeak around 1.3 eV which indicates those H atoms which leavethe cluster without being disturbed gets smaller and smallerand, finally, disappears completely at hni 450. This signatureof a complete caging, occurs, however, at larger average sizesthan predicted theoretically for single sized clusters.

    IV. Simulation of the pick-up process

    A. Calculational methods

    To study the pick-up process, we used molecular dynamicssimulations, i.e., we integrated the Newtons equations ofmotion for all interacting particles, which yielded theirphase space trajectories. Analyzing those trajectories, we thendeduced the microscopic properties of the system, such asenergetics, structure, and dynamics. In the present work, werepresent the interactions between the Ar atoms and theHBr and the HI dopant by pairwise 612 Lennard-Jones

    Fig. 2 Measured ratio Rtof of caged to cage exit events as functionof the source temperature from the data of Fig. 1.

    Fig. 3 Measured (points) and calculated (bars) kinetic energy distri-butions of embedded HBrArn clusters for different sizes. The averagecluster size of the measurements is indicated. The calculations arecarried out for n 54 and n 146.

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  • potentials,39 that are truncated at a cutoff distance rcut of2.5s (see ref. 40):

    urij 4eijsijrij

    12 sij

    rij

    6" #2

    Here, rij is the distance between particles i and j, and eij andsij are the standard Lennard-Jones parameters for the inter-atomic potential well depth and distance, respectively.For rare gas systems (Ne, Ar, Kr and Xe), such a potential

    should be suitable since all the interparticle interactions have aspherical symmetry. For the HBr and HI molecules, however,the two-parameter Lennard-Jones (LJ) potential of eqn. (2)can only be an approximation due to their inherent anisotropy.To account qualitatively for the possible influence of the mole-cular anisotropy on the pick-up dynamics, the actual HBrArpotential surface was averaged over all orientations and thenfitted to a LJ potential. The results are shown in Fig. 4 andin Table 2. A similar procedure was carried out for HIAr.The potentials for both systems are reasonably well repro-duced, which justifies this approximation. This is in accordwith results obtained by Perera and Amar previously. Theyshowed that while precise spectral widths and shifts in theIR spectra are sensitive to the anisotropic part of the potential,the simple two-parameter spherical potentials are completelysufficient to determine the final cluster structure.41

    The equations of motion were integrated using the Gearfifth-order predictor-corrector algorithm40,42,43 with a timestep Dt of 10 fs, which provided good conservation of energythroughout the whole simulation: the relative energy conserva-tion error is typically smaller than 109 in our present work.Repeating several of our calculations with a time step of1 fs, we found all results on energetics, structure, and dynamicsunchanged within the statistical uncertainties, which demon-strates the reliability of the computed quantities. We also recal-culated several selected trajectories without any cutoff radius,but did not find any significant deviation from the results withrcut 2.5s. Several trajectories were propagated for up to 1 msto achieve quasi-experimental conditions. The obtained results,however, agree perfectly with those for typical trajectorydurations of 50 ns.To accelerate the calculations, we employed a vectorizable

    neighbor list according to the algorithm suggested by Gupta.44

    This scheme leads to outstanding vectorization and very highcomputational intensities on a NEC SX-5 super computer.Every ten time steps, our MD program regroups all particlesinto clusters and counts the number of particles in each ofthose assigned clusters. In this manner, we are able to followall thermodynamical properties of the largest cluster even incase of partial fragmentation or evaporation directly duringthe simulation runs. To decide whether or not a given atombelongs to a cluster, we employed the following simple scheme:

    a particle j belongs to the same cluster as a particle i if thedistance rij between those two particles is smaller than a typi-cal, critical distance Rcl . Following the literature, we choosea critical distance of 1.9s.40,45 To make the actual sorting moreefficient, we used the algorithm proposed by Stoddard.46

    The Orsay group47 estimated using electron diffraction mea-surements that the final temperature of large argon clustersproduced by supersonic beam expansion is (32 2) K.Furthermore, they proved that the resulting clusters are solid.For Ar clusters smaller than about 750 atoms they assigned anicosahedral geometry while for larger cluster they found a fccstructure. In accord with these experimental observations, westarted out all trajectories with solid, icosahedral structuresof our Ar130 clusters and we assigned an initial rotationaland vibrational temperature of 32 K to all our clusters. Beforeinteracting with the buffer gas, all clusters were equilibratedfor about 100 ns to allow complete equilibration. To mimicthe experimental situation, we sampled the initial velocity ofthe HBr molecules from a MaxwellBoltzmann distributionat 300 K. The argon clusters were assumed to enter the pick-up cell with a velocity of 490 ms1 as in the experiments.The density in the pick-up cell was chosen to be low enoughfor each host cluster to pick up precisely one HI molecule.To analyze the dynamical behavior of the dopant upon pick-

    up, we calculated its distance Rcom from the center of mass ofthe cluster as function of time. Similarly, we also calculated theradial, species resolved cluster densities r(Rcom) defined as thenumber of particles of a given species within a spherical shell ata radius Rcom and with a thickness Dr of 0.025s (Rcom is mea-sured from the cluster center of mass). The r(Rcom) values pre-sented in this work have been calculated at the end of thesimulation runs and have been averaged over 100 or 200 trajec-tories. While Rcom as function of time shows the instantaneousdopant position in the host cluster, the density r(Rcom) givesthe most probable final position of the HBr molecules in theargon cluster after the cluster cooled evaporitavely back toits initial temperature of about 32 K.

    B. Results

    In our MD simulations, we varied the initial cluster beam velo-city according to the experimental velocity spread between 470and 510 m s1, but we did not observe any significant changesin the results. While the icosahedral configuration shouldclearly be the most likely one for an argon cluster of about130 atoms,47 we also determined the penetration depth forfcc-like and amorphous structures. Also, we run trajectoriesfor initial cluster sizes between 102 and 140 atoms. For allcases where the initial cluster structure was well thermalizedaround the minimum energy structure, the results alwaysturned out to be very similar to each other. Even for the smal-lest investigated cluster size, considering a potential well depthof 266 K and a head-on collision between the arriving clus-ter and the dopant molecule at 300 K, the incident, solid argoncluster never underwent a complete phase transition to theliquid state.Due to the collision-induced heating, the initial Ar130 clus-

    ters lose on average two argon atoms (in the case of eij 174 K). After cooling down back close to the initial

    Fig. 4 The interaction potential of HBrAr and HIAr averagedover all orientations, and the corresponding fit to it based on theLJ-potential form (solid lines).

    Table 2 Positions of the molecule in the cluster for different potential

    parameters. The parameters for the ArAr interactions are sij 3.405A and eij 119.8 K

    sij/A eij/K 3rd 2nd Surf. Molecule

    (1) 3.55 174.0 0.50 0.50 HBr

    (2) 3.71 193.0 0.77 0.23 HI

    (3) 3.57 212.0 0.91 0.09

    (4) 3.57 266.0 0.25 0.75

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  • temperature, all clusters resume again icosahedral or icosa-hedral-like structures. This is shown in Fig. 5, which displayssnapshots from for the first 50 ns of the simulation. In Fig.6, we present several typical trajectories from the 200 simula-tion runs performed for Ar130 . The HBr trajectories can bedivided to those staying close to the surface and those thatstart to penetrate inside the argon cluster. In all cases thedopants find their final radial position (with some fluctua-tions) after about 45 ns. None of the trajectories led to a finalHBr position in the very center of the cluster nor close to thefirst shell. The final trajectories end up in two positions, at 3sand 2.5s, close to the surface and two positions, at 2.2s and1.8s, close to the second shell.We display our results more quantitatively in Fig. 7 where

    we averaged over all trajectories. As already qualitativelyobserved in Fig. 6, the HBr dopants land dominantly and withroughly equal probabilities in two sites. Clearly, these sites cor-respond to the surface and the second shell of the final icosa-hedron. The final temperature of all clusters was between 31and 34 K. As can be seen in Fig. 5 and in the analysis of theresults, the HBr molecules always tend to occupy argon substi-tution positions in the final binary icosahedrons.In the course of the work we carried out a series of simula-

    tions for different size parameters of the potentials. The results

    for the relative population of substitutional positions in thedifferent shells of the Arn clusters are given in Table 2. Theparameter set (2), which corresponds to the angular averagedHIAr potential, results in a somewhat deeper penetration intothe second shell. This is to be expected since the well depth isdeeper than for the HBr system (1). This effect is not compen-sated by the larger s which is for both system larger than thatof the ArAr interaction. If we increase the value of the welldepth further, as is demonstrated with the parameter sets (3)and (4), the molecules penetrate deeper and deeper in thecluster. For e 266 K, no molecule is left in the surface shelland 25% are found in the third shell.

    V. Calculations of the photodissociation

    A. Applied methods

    The methodology of photodissociation simulations is exten-sively described in our previous study.14 Here, we provide onlya brief summary. We expect strong quantum effects for mole-cular clusters under cryogenic conditions. In our case, thequantum effects are represented primarily by the initial zero

    Fig. 6 Typical trajectories representing the instantaneous distanceRcom(HBr) of the HBr molecule from the center-of-mass of the cluster.Two positions end up close to the second shell (2s) and two close to thesurface (2.53.0s).

    Fig. 7 Radially resolved species densities for Ar atoms and HBrguest molecules in Ar130 host clusters as a result of a pickup processunder quasi-experimental conditions. The dotted lines give the densityof the Ar atoms and the black lines that of the HBr dopants.

    Fig. 5 The calculated structure of the initially icosahedral argon hostcluster Ar130 after the collision with the dopant HBr molecule fordifferent times of the MD simulation. Note the reconstruction of theicosahedral shape.

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  • point delocalization. On the other hand, upon photoexcitationseveral electronvolts of excess energy are pumped into thesystem, thus, the importance of quantum effects decreases.We have, therefore, applied to the photodissociation dynamicsa description based on the Wigner trajectories approach, inwhich the initial quantum character is respected while thedynamics is governed by a classical laws of motion.The initial wavefunction has been obtained in two steps.

    First, we have found a minimal cluster geometry and second,for this geometry, we have calculated the ground state wave-function. The minimization procedure was of a local character.Thus we have first chosen the cluster isomer and then we havelocally optimized the cluster geometry. Note that the delocali-zation of the HX molecule was respected during the process ofminimization. For the calculation of the total wavefunction,we have assumed the separability of librational, cage, andHBr vibrational modes.The initial wavefunction has been mapped on a classical

    phase space distribution via a Wigner transformation. Sincein the experiment monochromatic laser light is used, theWigner function was filtered in such a way that the differencebetween the excited and the ground state was hn. Thedynamics after excitation by a 243 nm laser pulse takes placeprimarily on two electronic potential surfaces, which corre-spond to the 1P1 and

    3P0 states of HBr. With the ground stateasymptote correlates partially also the 3P1 state which we didnot take into account. For the HI molecule, we have testedthat the KEDs obtained from the 1P1 and the

    3P1 states arepractically identical.33 This is caused by the fact that thehydrogen kinetic energy distribution is dominated by theavailable excess energy and not by the particular shape ofthe repulsive potential. It has been shown18 that for the excita-tion wavelength 243 nm the non-adiabatic transitions do notplay a role in the photodissociation dynamics. Since the HBrmolecule is promoted close to the crossing point of the 1P1 and3P0 states, it is thus unlikely that the molecule would return toit during the dissociation process. Thus, we assume that theBr*/Br branching ratio in rare gas clusters does not differ sig-nificantly from the gas phase value. This has been confirmed inrecent experiments for neat (HBr)n clusters, which give a valueof 0.2 for this branching ratio29 compared to 0.18 obtained forthe monomer molecule. Wigner trajectories were propagatedon both excited surfaces and measurable quantities wereweighted by this ratio. 700 Wigner trajectories provided con-verged results. The total simulation time was 1.5 ps with atimestep of 0.0241 fs.

    B. Results

    The kinetic energy distribution of the H atoms after the photo-dissociation of HBr in a substitutional position in the surfacedepends only weakly on the cluster size. It is characterizedby a large fraction of caged H atoms and a small fraction offree cage exit events.14 The reason for stronger caging is theconstraint librational motion of H atom, which is alwayspointing in the direction of the cluster. In contrast, when theHBr molecule is situated in the second shell, the H atom, asin the embedded case, almost freely rotates. This means thatthe cage exit probability through one shell is at least equal tothe caging probability where, in the opposite direction, severalshells have to be passed through. The calculations for HBrAr55 , as displayed in the upper part of Fig. 8, show exactly thisbehavior. If this model is correct, then the cluster with next lar-ger shell, HBrAr146 , should exhibit the same amount of cageexit, but a slightly higher caging probability. This is indeed thecase as is seen in the lower part of Fig. 8. We conclude, some-what against intuition, that the cage exit probability of H, theatom from the photodissociated HBr molecules, is higher whenHBr is the second shell compared to the surface position. Noteat this point that for the case of HBrArn surface clusters the

    photodissociation simulation result can be affected by theseparation of the HX vibration and the hydrogen librationalmotion in the initial wavefunction. The problem arises fromthe fact that the 243 nm excitation which correlates with thered tail of the HBr absorption spectrum, where the interactionof hydrogen with argon atoms, starts to play a significant roledue to the increase in the HBr separation. While the calculatedtrend with the increasing cluster size is reliable, the quantita-tive ratio between the slow and fast components can be slightlydifferent.

    VI. Comparison with experimental results anddiscussion

    A. The embedded case

    The calculations for HBrAr54 from ref. 14 show a very goodagreement with the measurement presented in Fig. 3 for theaverage argon cluster size hni 51. In the case of two closedicosahedral shells, the number of caged H atoms is about thesame as those which directly exit. This main feature of thecalculation is also well reproduced in the experiment.If about half a shell is added in the calculation for n 97,

    the number of cage exiting H atoms drops appreciably. Again,the results of the measurement and the calculations are verysimilar as was shown in refs. 3 and 14. Finally, no H atom withappreciable kinetic energy leaves the cluster for n 146 in thecalculation. Such result is observed in the experiment only forhni 450. Where does this discrepancy come from? In thiscase of the complete elimination of cage exit H atoms, the factstarts to count that we have to deal with a size distribution.The argon cluster size distribution is known to be a lognormal one48 with the lower limits of the width at half maxi-mum of nlow 93, 117 and 182 for the average sizes hni 230,290 and 450. Now it is quite obvious that in the first two casesthere are still sizes in the distribution that allow the H atoms toescape. Only for the average size hni 450 even the smallestclusters in the distribution have n above 146 and no highenergy H atom can leave anymore the cluster cage. Thus, alsoin this case the experiment is in complete agreement with thecalculation.The results clearly indicate that three icosahedral solvation

    layers are sufficient to suppress cage exit of high energy Hatoms, while for two layers the numbers of caged and cage

    Fig. 8 Calculated kinetic energy distributions of HBrArn with HBrin the second shell for two sizes.

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  • exiting hydrogens are about the same. The good agreementbetween theory and experiment also indicates that both theexperimental concept and the approximations applied in thecalculations are reasonable. This means that the coexpansionleads indeed to completely embedded HBr geometries in thecluster. Also all the ingredients of the calculation the quantummechanical preparation of the initial librational motion, theinclusion of the two excited potentials only, and the use ofthe new repulsive HAr potential are accurate enough todescribe this process in a realistic way.

    B. The surface case

    For the measurements that are carried out in the pick-uparrangement, we show in Fig. 9 the kinetic energy distributionof photodissociated molecules for one of the time-of-flightdistributions which are obtained for the average cluster sizehni 139. This measurement is first compared with a calcula-tion, where the HBr molecule is at a substitutional position inthe surface of the Arn cluster. While the low kinetic energy partis in good agreement with the measurement, the intensity atkinetic energies that correspond to direct cage exit around1.3 eV is too small in the calculation. This result is similar tothe findings for hni 97.3,13 If we, however, add the resultsobtained for HBr in the second shell with 0.5 probability,the agreement between experiment and simulation improvesappreciably. The fraction used in this comparison, 0.5 for eachcomponent, corresponds exactly to the calculated distributionof sites in the simulation of the pick-up process (see SectionIV). We should, however, keep in mind that the cage exitfraction may be underestimated in the photodissociationsimulation for the surface case.The idea to increase cage exit by exciting the libration modes

    in the range from 50 to 80 cm1 by simply heating the clustersource could not be realized in the experiment. The theoreti-cally predicted dramatic increase of cage exit events was notobserved, actually, a slight decrease of direct cage exits wasmeasured when the source temperature was increased by 100K. This temperature would be sufficient to excite the lowestlibrational mode provided that the temperature rise of thesource is completely transferred to the cluster. This is, how-ever, quite improbable, since the argon cluster regulates itstemperature by cooling through evaporation as was alsodemonstrated in the simulation of the pick-up process inSection IV. As a result only a slight increase of the cluster

    temperature is indirectly observed by the measurable effect inthe ratio Rtof of caged to cage exit events. The actual clustertemperature is estimated to vary between 30 and 36 K.Let us shortly discuss the influence of the higher temperature

    on the cage exit events for HBr molecules placed in the surfaceor in the second shell. Generally, at higher temperatures, thedistances between the Ar atoms slightly increase. This meansthat for molecules in the second shell the cage exit probabilityincreases, while for those kept in the surface it decreases, sinceit is easier for the H atoms to penetrate deeper inside the clus-ter. According to these considerations, the experimental result,i.e., the decrease of cage exit events, is better reproduced byassuming surface HBr molecules. This is in contradiction withthe result displayed in Fig. 9. In fact, in the investigation of theHIArn

    33 and HClArn49 systems, there is a clear evidence that

    only surface states are observed. We have already emphasizedthat the worse agreement between simulations and experimentfor the surface photodissociation of the HBr molecule in thesurface of large argon clusters may be caused by the samplingof the initial wavefunction where the coupling between theHBr vibrational and librational motion is neglected. Note thatthis is neither a problem for the photodissociation of HI with a243 nm laser pulse (i.e., close to the HI absorption maximum),nor for HBrNen systems (since the interaction between neonand hydrogen is not as strong as that between argon andhydrogen). In addition, we also note that the ArAr inter-action used in the pick-up simulations is the standardLennard-Jones one.50 If one uses the parameters of from theAzizSlaman ArAr potential,51 then the molecules mostlystay on the surface.33 Therefore, the prediction of the locationof HBr in the second shell should be considered as preliminary,although it leads to a better reproduction of the experimentthan calculations assuming a surface isomer. Here also anexperiment at the dissociation wavelength of 193 nm shouldclarify the situation, since at this wavelength in the maximumof the FranckCondon overlap the applied theoreticaldescription should work.

    Acknowledgements

    This work was supported by the Deutsche Forschungsge-meinschaft in SFB 357. H. V. gratefully acknowledges Prof.Gerhard Torchet and Marie Francoise de Feraudy for theircontinuous interest in our work and for many fruitful discus-sions. Most of the calculations in Palaiseau were carried outat the French National Computer Center IDRIS. We like toacknowledge the computer time that was allotted for the pre-sent study and thank the entire consulting team for their con-stant help and patience. Support of the Czech Ministry ofEducation to the Center for Complex Molecular Systemsand Biomolecules (Grant No. LN00A032) is gratefullyacknowledged.

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