3518
J. Phys. Chem. 1994,98, 3518-3526
Photolysis of HCl in the Arz-HCl and Ar-HCl Clusters: The Cluster Size Effect A. Garcia-Vela' Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics The Hebrew University of Jerusalem, Jerusalem 91904, Israel, and Instituto de MatemLicas y Fisica Fundamental, C.S.I.C.,Serrano 123, 28006 Madrid, Spain
R. B. Gerber Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics The Hebrew University of Jerusalem, Jerusalem 91 904, Israel, and Department of Chemistry, University of California, Irvine, California 9271 7
U. Buck Max- Planck-Institut f i r Striimungsforschung, 0-37073Gbttingen, Germany Received: September 17, 1993'
The photodissociation dynamics of HC1 in the clusters A r r H C l and Ar-HC1 is studied in order to explore the cluster size effect. A quasiclassical trajectory approach is employed to simulate the photofragmentation dynamics. Interesting manifestations of the cage effect are found in the light and the heavy atom kinetic energy distributions, with important differences between the two clusters. The Ar and C1 distributions provide separate information on dynamical events which cannot be resolved in the hydrogen distribution. Only two different excitation wavelengths are used in the simulations. The cage effect is found to be strongly dependent on the wavelength employed to excite the HCl molecule. This is so to the extent that the trend of an increasing cage effect with the cluster size is reversed for the smaller wavelength. New types of resonance behavior are observed for the hydrogen motion in Arz-HCl compared with the Ar-HC1 cluster. An interesting difference between Ar-HCl and A r r H C l is that, in the latter case, Ar2 can form as product of the photodissociation, with a high yield for the two wavelengths. The dynamics of the process and the implications of the results are discussed.
I. Introduction The study of chemical reactions in van der Waals (vdW) and hydrogen-bonded molecular clusters has been pursued with increasing intensity in the past few years. This attention has been motivated by the specificadvantages offered by these systems in exploring important questions in chemical dynamics. One of the advantages is the possibility of controlling, at least to some extent, the initial relative orientations of the reagents.14 Indeed, the relative geometries of the atoms and molecules bound together in the cluster are restricted by the anisotropic vdW interactions between them. Studying a chemical process in a cluster environmentprovides, therefore, more possibilities of control than in bulk, gas, and liquid conditions, where all orientations and impact parameters are allowed for the reagents. However, the most interesting feature of these systems is probably the role they play as bridges connecting two limiting situations in which a chemical reaction may occur: gas-phase and condensed matter conditions. The condensed-phase situation is gradually approached by increasing the cluster size, which allows to explore the dependence on the size of the surrounding solvent upon properties of interest. These clusters can thus provide valuable information on the crossover limit between the behavior of a chemical process in the gas phase and the same process in a condensed matter (liquid or solid) environment. In addition, the smaller number of degrees of freedom of these systems as compared to those of condensed matter ones implies the advantage of a larger simplicity in their study. In order to explore the cluster size effect on a chemical process, the unambiguous selection of the size of the cluster to be studied is the first step. For a theoretical treatment this is trivially
* To whom correspondence should be addressed.
Abstract published in Aduance ACS Absrracrs, March 1 , 1994.
0022-3654/94/2098-3518$04.50/0
achieved. From the experimental point of view some techniques have been developed, based on the different kinematical behavior of the clusters in scattering experiments depending on their size. Such techniques were first applied to separate different sizes of Ar, clusters (up to a maximum of n = 6).9J0 The Ar, clusters are scattered from He atoms in a crossed molecular beam experiment,and the kinematicsof the collisionsand itsdependence upon the masses allow to separate individual cluster sizes. This size selection method was further applied to ethane clusters11.12 and more recently to methanolI3 and ethene-acetone heterogeneous ~1usters.l~In addition to the kinematical size selection technique, there exists a spectroscopicone. Thevibrational bands associated with the different cluster species are found to be shifted with respect to the corresponding absorption frequencies in the gas phase.I3 The shifts can reach several wavenumbers,and then, by appropriately tuning the excitation wavelength,one can excite a specific cluster size. Combination of both the kinematical and the spectroscopic techniques appears as a promising venue in order to select individual cluster species in the case of Ar,-HCl and other clusters and further study their photodissociation dynamics on a size-selected level. Among the solvent effects observed in chemical reactions in the solid or liquid phase, perhaps the most important and characteristic one is the so-calledcage effect.15 Optical excitation of an isolated diatomic molecule from its ground electronic state to a repulsive one leads to direct and extremelyrapid fragmentation of the diatomic bond. When the molecule, instead of isolated, is weakly bound to some solvent atoms or molecules, as in a solution or in a cluster, the dissociation process can be dramatically affected. The surroundingsolvent may confine the photoproducts within a cage, causing significant delays in their mutual separation or even preventing it. Such an effect, characteristic of condensed matter systems, has been also observed in small clusters like I r M 0 1994 American Chemical Society
Photolysis of HCl in Ar-HCI Clusters
(M being a rare gas atom or a diatomic molecule) both experimentally'6-20 and theoretically.21 Calculations have been reported22 which explored this effect in Xen-HI hydrogen-bonded clusters by increasing the cluster size from n = 1 to n = 12. The effect was also found in previous calculations on Ar-HC1.23.24 Recently, an experimental and theoretical study25 has confirmed the existence of a cage effect in the photodissociationdynamics of Ar-HBr. In the present work we study the photodissociation of HCl in both the Ar-HCl and Ar2-HCl clusters with two different excitation wavelengths. The focus is on differences between the cage effects for the two clusters. The manifestations of the cage effect are investigated through the kinetic energy distribution (KED) of the hydrogen photofragment, as in previous studies,23-25 but also through the corresponding KEDS associated with the heavier Ar and Cl atoms. As we shall see, these distributions are of considerable interest and can provide additional insights. The effect of the excitation wavelength is also explored. The paper is structured as follows. Section I1 presents briefly the potential energy surface used in the calculations and the quasiclassicalmethodology employed. In section I11 the results are showed and discussed. Some conclusions are given in section IV.
II. Theoretical Approach Photodissociation of HCl both in Ar-HCl and in Ar2-HCl involves in our model excitation of the chemical bond from its ground electronic state lZ+to the I l l repulsive electronic state. Both the ground- and the excited-potential surfaces were constructed as a sum of pairwise interaction potentials. The ground-state surface was represented as an addition of the H-CI interaction, the Ar-Ar interaction,26and the H6(3) potential of Hutsonz' for each Ar-HCl vdW interaction. These potential surfaces predict a linear equilibrium c~nfiguration~~ in the case of Ar-HCl and a T-shaped geometry for ArrHC1, with the H atom pointing toward the center of mass of the Ar-Ar bond.28 Severalstudies have appeared recently in the literature discussing the topic of pairwise additivity and the influence of three-body forces in the ground state of Arn-HF ( n = l-4)28.29and ArTHCl (refs 30-32). In ref 31 a new potential was proposed for ArzHCl which incorporatesseveraltypes of three-bodycontributions. Although the new potential fits better the available experimental measurements, the differences with previous pairwise potential surfaces, like the one used in the present calculations (which is computationallyless costly) are not largein general. The potential proposed in ref 3 1 is probably the most accurate surface currently availablein order to study the dynamicsof A r r H C l in the ground state (e.g.,the vibrational predissociationdynamics). However, in the photodissociation process, thedynamicsoccurs in theexcited electronic state. In our problem, the ground-state surface determines only the initial state of the system. As shall be discussed below, we apply a scheme of separability of modes in order to characterize the initial state. The error caused by this approximation is probably at least of the same order as the small corrections introduced by the three-body terms of the new potential. A pairwise representationof the ground-state potential seems, therefore, accurate enough at the present level of the calculations. Much less is known about the effect of three-body interactions in the excited electronicstate of ArTHCl where photolysis occurs. In the absence of more information, we adopted a pairwise description also for the excited surface, which consisted of a sum of atom-atom potentials. However, supportfor a painviseadditive excited-state potential can be found in the agreement between theory and experiment in the related case of Ar-HBr, where a similar type of potential was used.25 The H-Cl interaction in the I l l state was obtained by fitting recent ab initio calculations33to an exponential,
The Journal of Physical Chemistry, Vo1. 98, No. 13, 1994 3519
F'$,(r) = A exp(-ar) with A = 590 245 cm-1 and a = 2.433 A-l. This fit is slightly different from that used in previous cal~ulations,2~.~~ due to the fact that the ab initio potential of ref 33 contains more points than that of Hirst and G u e d 4 employed in the earlier studies. Todescribe the Ar-H (ref 35) and the Ar-CI (ref 36) interactions, we used empirical potentials. The Ar-H potential used in this study is a more recent one than that employed in the calculations of refs 23 and 24. The same Ar-Ar interaction potential was used in the ground and in the excited state. As mentioned above, comparison between experiment and calculations on the photodissociation of Ar-HBr, where pairwise potential surfaces described both the ground and the excited state, showed a very good level of We believe this is a good indication that the assumption of pairwise additivity in the potentials is a reasonable one for the systems studied here. The characterization of the initial state of the system is an important part of the classical simulationof the photodissociation process. In order to sample the initial conditions for the classical trajectories, zero point energy vibrations are assumed for the different modes. All the modes are included in the simulations. By applying a scheme of separability of modes, the zero point energy and the associated wave function are calculated quantum mechanically for each mode. From these wave functions probability distributions are generated with which initial conditions uniformly distributed on a grid in phase space can be weighted. Once the set of initial conditions are determined, the system is optically promoted to the excited-state potential surface in the spirit of the Franck-Condon principle. Then, trajectories describing the fragmentation of the system are integrated from the initial conditions. Initial coordinate and momentum values are restricted to correspond to the (monochromatic) excitation energy employed. 111. Results and Discussion
In earlier ~ o r k . 5we ~ ~studied 9 ~ ~ the photofragmentation of HCl in Ar-HCl for a X = 193nm excitation wavelength. Manifestation of a cage effect was found in the final KED of the H photofragment. This distribution showed a tail in the region of low energies. Such a tail was associated with hydrogen atoms dissociating with a remarkably lower kinetic energy than that correspondingto photodissociation of an isolated HCl molecule. The hydrogen, initially trapped within the cage formed by the Ar and the C1 atoms, collides with them several times before dissociating. In the course of these collisions the light atom transfers part of its initial excess energy to the heavy ones, giving rise to the tail of the distribution. As mentioned before, this theoretical prediction was experimentally observed in the case of HBr photodissociation in Ar-HBr (ref 25). In this work the photolysis of HCl in the Ar-HCl and A r r H C l clusters is investigated for two different excitation wavelengths, namely, X = 193 nm and X = 157 nm, using new, more accurate potentials. A. Ar-HCI PhotodissociationDynamics. In the present study, the Ar,-HCl ( n = 1,2) photodissociation dynamics is analyzed not only through the hydrogen photofragment KED but also through those corresponding to the Ar and CI atoms. Such distributions in the case of Ar-HC1 are displayed in Figure 1 and Figure 2 for X = 193nm and X = 157 nm, respectively. Ensembles of 25 600 trajectories for X = 193 nm and 26 000 trajectories in the case of X = 157 nm were used to average the final results. The light atom KED associated with the two wavelengths (Figures l a and 2a) shows qualitatively the same trends as found previ0usly,23.2~Le., a tail in the region of low kinetic energies. The distributions peak at the recoil energy of the hydrogen corresponding to each excitationwavelength, as a consequence of direct photodissociation events of HCl within the cluster. The tails of the distributions are the signature of collisional, nondirect
3520
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994
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Figure 1. Kinetic energy distributions of (a) hydrogen, (b) argon, and
(c) chlorine fragments corresponding to photodissociation of Ar-HCI excitation wavelength.
with a X = 193 nm
photolysis events, in which the initially hot H atom cools by colliding with the heavy ones. Although no qualitative changes are found in the hydrogen KED when going from X = 193 nm to X = 157 nm, there is, however, a large quantitative difference. The low-energy tail of the X = 157 nm distribution is broader and more intense than that corresponding to X = 193 nm. This is explained in terms of the initial excess energy of the hydrogen atom, which is larger in the case of A = 157 nm. Consequently, although the maximum number of collisions between hydrogen and the heavy atoms is similar for both excitation wavelengths, the light particle transfers a larger amount of energy per collision for the smaller wavelength. On the other hand, the Occurrence
0.8
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energy (ev) Figure 2. Same as Figure 1 using a X = 157 nm wavelength.
of one, two, or more collisions between the light and the heavy atoms is more likely in the case of X = 157 nm. These two factors give rise to the more extensive tail observed in the distribution of Figure 2a. Additional interesting information is found in the Ar and C1 KEDS for the two wavelengths (Figures lb, 2b and IC, 2c, respectively). These distributions also display a tail, but now in the region of higher kinetic energies with respect to the main peak. This is consistent with the fact that the heavy atoms are gaining the energy transferred by the hydrogen in the collisions. As expected, the heavy atom distributions follow the same trend as the hydrogen one; Le., the corresponding tails are more pronounced when the shorter excitation wavelength is used. The argon KED is found to peak at a very low energy, corresponding
Photolysis of HCl in Ar-HCl Clusters to events in which the hydrogen dissociatesdirectly, only weakly interactingwith the Ar atom-this can beviewed as "soft collision" events. Direct photodissociation (noncollisional)events, which are the most probable ones, are the cause of the main peaks in each of the distributions of the three atoms. The tail of the argon KED reflects up to three collisions with the hydrogen. As discussed p r e ~ i o u s l y , ~however, ~ * 2 ~ among the collisional events the most likely one is the first collision between the H and the Ar atoms, which is reflected in Figure 2b in the large intensity of the tail up to =0.4 eV. The intensity of this KED (and also of the H and C1 ones) decreases gradually as the initial relative orientation of the cluster approaches collinearity. For a collinear geometry the maximum number of collisions, and therefore the maximum energy transfer, occurs between the light and the heavy atoms,24 but the probability of these events is very small in such a floppy cluster. For the same reason, the initial orientation between the H-Cl bond and the Ar atom also explains the large spreading of the final Ar kinetic energies corresponding to onecollision events in Figure 2b. In ref 24 we found that the number of collisions between the hydrogen and the heavy atoms correlates with well-defined ranges of the initial H-Cl bond orientation. The range correspondingto the first H/Ar collision is the largest one among thecollisional e~ents.2~ Within this range, going from larger to smaller initial angles (i.e., closer to the collinear configuration) results in a harder H/Ar collision,with more energy being transferred to the heavy particle and producing the spreading of final kineticenergies. Also interesting are the KEDSassociated with the chlorine atom (Figures IC and 2c). The distributions in this case are peaked at the recoil energy of the C1 atom corresponding to the wavelength used. The tails of these distribution have a lower intensity as comparedwith the Ar KEDs, since one or two collisions of H with C1 are less likely than the corresponding number of collisions with argon. As we see, the distributions of the three atoms reflect the collisions which occurred between the light and the heavy particles. The argon and chlorine KEDs present, however, an additional interesting feature. While in the hydrogen KED there are contributions from all the collisions, the collisions are partly separated in each heavy atom distribution, where only the collisions with either the Ar or the C1 atom contribute. The Ar and C1 distributions allow one to determine the amount of energy transferred to each heavy atom during the photodissociation process, then providing additional information to that of the hydrogen KED. B. ArrHCl Photodissociation Dynamics. In order to study the cluster size effect, the photolysis of the Ar2-HCl cluster was also simulated. The same two excitation wavelengths as before, X = 193 and 157 nm, were used, and ensembles of 48 000 and 61 084 trajectories were integrated in each case, respectively. FIgure 3a-c show the KEDs associated with the H, Ar, and C1 atoms (the two Ar atoms are indistinguishable) for X = 193 nm. Comparison between the hydrogen and chlorine distributions obtained for Arz-HCl photolysis with those corresponding to Ar-HC1 photodissociation using X = 193 nm shows a remarkable quantitative difference. The tails of the Ar2-HCl distributions are much more intense, meaning that more energy is transferred. Here we are comparing essentially the same excess energy of the hydrogen for both clusters. (The excitation wavelength is 193 nm for both Ar-HCl and Ar2-HC1.) The larger intensity of the distribution tails in the case of A r r H C l is the manifestation of a morepronounced cage effect with respect to the Ar-HC1 cluster. As expected, the light atom is more effectivelycaged as the number of surrounding solvent atoms increases. The difference between the Ar-HCl and the A r r H C l distributionsis even more dramatic in the case of the Ar KEDs. Figure 3b shows a clear secondary peak close to 0.2 eV, which correspondsto the first H/Ar collision. The Ar2-HCl distributions are thus different not only quantitatively from those of Ar-HC1 but also qualitatively (the case of the Ar distributions), allowing a clear distinction between the
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3521
energy (ev) 1.0
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energy (ev) Figure 3. Same as Figure 1 for photofragmentationof ArrHCl with a X = 193 nm wavelength.
two clusters. We also stress the fact that this qualitative change in the KEDs occurs for a very small solvent size: just two Ar atoms. The study of the A r r H C l photodissociation when using the X = 157 nm excitation wavdength also revealed very interesting effects. By extrapolating the results of Figures 1-3 discussed so far, one would expect the cage effect to be the most intense when the Ar2-HCl cluster is excited with the X = 157 nm wavelength. The calculated KEDs for the three atoms corresponding to this case are displayed in Figure 4 and show the opposite result. The tails of the three A r r H C l distributions are less intense than those corresponding to Ar-HCl for the same wavelength (see Figure 2). Again, the largest difference occurs in the case of the
3522 The Journal of Physical Chemistry, Vol. 98, No. 13, 1994
Garcia-Vela et al.
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Figure 5. Lifetime distributions corresponding to photodissociation of (a) Ar-HC1 and (b) ArrHCl with a h = 193 nm excitation wavelength (see text). 1.0,
I
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Figure 4. Same as Figure 3 using a X = 157 nm wavelength.
Ar KED. The unexpected implication is that the cage effect in A r r H C l becomes smaller than in Ar-HCl when the cluster is excited with a h = 157 nm wavelength. This apparently surprising behavior can be explained in terms of the excited potential energy surface. Analysis of the excited-state potential seen by the hydrogen shows that the Ar-Ar bondconstitutes a potential barrier for the hydrogen passage. The excess energy corresponding to excitation with A = 157 nm is enough to allow the hydrogen to overcome such a barrier. Then the light atom is able to pass in between the two Ar atoms, feeling their repulsive interaction with less intensity than in Ar-HCl. The result is a less efficient energy transfer from H to the Ar atoms, which is refleted in the distributions of Figure 4. For a h = 193 nm wavelength, the initial excess energy of the light atom falls below the top of the
barrier. In this situation, the two Ar atoms in Arz-HCl act more effectively as a wall opposed to the hydrogen dissociation than only one Ar atom (as in Ar-HCl), producing a stronger cage effect. Therefore, exciting with A = 157 nm (or in general with any wavelength which provides enough energy to the hydrogen to overcome the barrier) can be viewed as opening a “hole” or “window” in the Ar-Ar barrier, through which the light atom can escape more easily. From these results we conclude that there exists a strong excitation wavelength effect which determines the magnitude of the cage effect in these clusters. The excitation energy effect is already present in the Ar-HCl cluster, as discussed above when comparing Figures 1 and 2. It is, however, in the ArTHCl cluster where the effect shows a more striking manifestation, being able to invert the trend of a more pronounced cage effect with increasing solvent size. We note that the existence of the Ar-Ar barrier for hydrogen dissociation is a size effect, aconsequenceofaddingonemore Ar atom to the Ar-HCIcluster. Such a barrier has a large effect on the photodissociation reaction, inducing a strong dependence on the excitation wavelength, which determines whether the hydrogen will overcome the barrier or not. The wavelength effect in Ar2-HCl should be experimentally detectable, since by tuning the excitation light to smaller wavelengths, a decrease in the tail intensity of the KEDs should be observed. C. Lifetime Distributions. It is also interesting to compare the lifetime distributions associated with the Ar-HCl and ArzHCl clusters for the two excitation wavelengths used. In Figure 5 we show the distributions corresponding to Ar-HCl (Figure 5a) and Ar2-HCl (Figure 5b) for A = 193 nm, and Figure 6 displays the same distributions for h = 157 nm. The lifetime distributions plotted in those figures represent the probability of the photodissociation process occurring in a certain time. All the distributions confirm the general trends found in the KEDs previously discussed. Each lifetime distribution presents a main
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3523
Photolysis of HCl in Ar-HC1 Clusters 1.0,
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Figure 6. Same as Figure 5 using X = 157 nm.
peak which (same as in the KEDS of Figures 1-4) corresponds to direct photodissociation events. We note the following: On one hand, the main peak of the A = 193 nm distributions appears at =49 fs, while in the case of X = 157 nm it does at -38 fs. This is not surprising since the H atom is initially hotter when the smaller wavelength is used, which causes the direct photodissociation events to be much faster in this case. On the other hand, what may appear somewhat surprising is that direct photodissociation takes in this case long times of about 40 or 50 fs. Actually, direct fragmentation of the H-Cl bond in these clusters takes around 10-15 fs. The reason why the main peaks of the distributions appear at longer times is due to an artifact of the calculation. One of the criteria to stop the integration of the classical trajectories is that the H-Cl distance reaches a maximum value (10 A in our case). Such a condition ensures that the H-Cl molecule is completely dissociated, and the H atom is out of the interaction region of the cluster at the end of the integration. To reach that maximum H-Cl distance takes some additional time with respect to the physically meaningful photodissociation time. This causes the lifetime distributions to be shifted to longer times (theshift being essentially the timeat which the main peakappears minus the 10-1 5 fs which typically takes direct photodissociation). Since the shifts are equivalentfor the same excitationwavelength, they do not affect the comparison of the lifetime distributions of Ar-HCl and Ar2-HCl shown in Figures 5 and 6. Focusing now on Figure 5 , the A r r H C l lifetime distribution presents another clear manifestation of a stronger cage effect in the larger cluster as compared with Ar-HCl. The tail of the Ar2-HCl distribution in the long time region is more intense and reaches longer times than the Ar-HCl one. This is a characteristic manifestation of the cage effect, Le., a greater delay of the photodissociation process as a consequence of the photofragment confinement by the solvent. As seen from Figure 5, the effect of adding one more Ar atom to the Ar-HCl cluster on the lifetime distribution is quite large. Despite the low intensity of the tail
of the Ar-HCl distribution correspondingto X = 193 nm, three small peaks can be discerned. Analysis of the trajectories shows that the first of these peaks, around 59 fs, correspondsto the first H/Ar collision. The difference in time between this peak and the main one is =10 fs, which is roughly the time it takes half a vibrational period of the hydrogen oscillating in the potential formed by the Ar-Cl ~age.~',3*The third peak, centered around 7 1 fs, is associatedwith two-collisionevents,Le., with thoseevents in which the H atom first collides with the argon and then with the C1 atom, finally leaving the cluster. This peak takes a slightly longer time (=12 fs) with respect to the first time difference of -10 fs. Such an effect was also found in hybrid quantum/ classicaP7and quantum/semiclassica13*calculations on the ArHCl photodissociation. It is due to the fact that, by the time the hydrogen reaches the C1 atom again, the A r . 4 1 distance is somewhatlarger than initially as a result of both the first collision with argon and the recoil energy gained by the chlorine. It takes the hydrogen then a longer time to cross this distance. The second small peak, around 67 fs, is an addition of contributions coming from long-lived one-collision events and short-lived two-collision events. The intensity associated with higher collisional events is very small in this distribution. Regarding the Arz-HCl distribution of Figure 5, we can distinguish two clear peaks in addition to the main one. The dynamics of A r r H C l is, however, much richer than that of Ar-HCl, and the collisional events are less distinctly separated in this case. So, the peak covering the region between 60 and 80 fs comes mainly from contributions of onecollision and two-collision events and a few short-lived threecollision events. The smaller peak correspondsto long-lived twocollision events and three-collision events, and higher collisional events contribute to the rest of the tail. While in the case of Ar-HCl each collisional event can be easily assigned, Le., the first collision of hydrogen is with Ar, the second with C1, the third with Ar again, and so on, this is less clear for Ar2-HC1. Except for the first collision of hydrogen, which must be with Ar, in Ar2-HCl the second collision of the H atom can be either with the other Ar atom or with the C1 atom. This implies that there are events in which the third collision can be either with the C1 or with one Ar atom. Therefore, there are two different possibilities for two-collision events and for three-collision events, and each possibilitytakes a somewhat different time. For a higher number of collisions the number of possibilities also increases, but thesecollisionalevents are much less likely. Due to the higher number of collisional possibilities, with different (but not too different) times associated, the mixing of the collisional events in the peaks of the lifetime distribution is larger than in Ar-HCl. Figure 6 shows the same comparison as Figure 5, but for X = 157 nm. The larger intensity of the Ar-HCl distribution tail for longer times than that of the main peak confirms the inversion of the cage effect for these cluster sizes when that wavelength is used. There are two peaks in the Ar-HC1 tail; the first one associates mainly with one-collision events, whereas the second peak contributes two-collision events and long-lived one-collision events. Although some mixing is present in the peaks of the Ar-HCl lifetime distributions (both for X = 193 nm and for A = 157 nm), it is still possible to assign, at least some of the peaks, to separate collisional events. This is not the case for the flat Ar2-HC1 distribution tail of Figure 6b, due to both the mixing above discussed and the low intensity of the tail which does not show really distinguishable peaks. An interesting feature is observed, however, in this tail. Despite its low intensity, the Ar2HCl tail reaches longer times than the Ar-HCl one. It means that although with small probability, there are photodissociation events in which, even for X = 157 nm, the Ar2-HCl cluster is still able to cage the H photofragment more effectively than Ar-HCl. These are resonance events which shall be discussed next. D. Resonance Vibrations of the Hydrogen. It was found in previous studies on Ar-HCl photodissociation that the hydrogen
Garcia-Vela et al.
3524 The Journal of Physical Chemistry, Vol. 98, No. 13, I994 2.0
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Figure 7. Resonance trajectory corresponding to ArrHCl photodissociation with a X = 193 nm excitation wavelength (see text).
Figure 8. Resonance trajectory corresponding to ArrHCl photolysis with a X = 193 nm excitation wavelength (see text).
atom has resonances (i.e., temporary trapping events) in the excited-state p ~ t e n t i a l . ~ ~ J ~Such " resonances occur along the internuclear Ar*-Cl axis of the cluster. The light atom moving in those resonances oscillates severaltimes between the two heavy particles. The same type of hydrogen resonances occur in the excited state of Arz-HCl, when the H-Cl bond adopts a collinear or near-collinear configuration with one of the Ar atoms. What essentially happens in these cases is that the Ar-HCl situation is reproduced in the A r r H C l cluster by the H-Cl molecule and one Ar atom, with the other Ar atom basically playing a "spectator" role. One could perhaps think of the A r r H C l cluster as an addition or combinationof two coupled Ar-HCl monomers. Thus, it would not appear very surprising that in some dynamical events only one of the Ar-HCl monomers plays the main role. In such cases, the ArrHCl dynamics is not very different from that of the Ar-HCl cluster. However, in the above picture the fact that in A r r H C l there are actually two Ar-HCl monomers enriches the dynamics, giving rise to new resonance behavior in which the two monomers play an equally active role. This is better illustrated in the H atom trajectory showed in Figure 7, for a X = 193 nm wavelength. In the figure, the circles with the Ar and the C1 labels denote only approximately the relative positions of the heavy particles at t = 0. These labels are drawn for the sake of clarity, but the real, exact positions of the heavy atoms are out of the scale of the figure and change with time along the trajectory. The figure displays oscillation of the hydrogen along the A w C l axis of the two monomers, which in this case are nearly equivalent from a dynamical viewpoint. This new resonance motion can be viewed roughly as the combination of the hydrogen resonance oscillations which would occur in two separate Ar-HCl clusters, when they are coupled with the same relative orientationsas the two monomers inArrHC1. Of course, this type of resonance cannot appear in the smaller Ar-HCl cluster, since the presence of two Ar atoms is required. As discussed elsewhere,374 the hydrogen resonance motion in the Ar-HCl cluster is essentially associatedwith the Ar-Cl axis of the cluster. It is worth noting that in the resonance of Figure 7 there is periodicityof the H motion along the twoAr...Cl axes (associated with the H-Cl stretching mode) and also along the H-Cl bending coordinate. Such periodicityof different motions implies therefore different frequencies associated with those motions. That is, in A r r H C l there appear more complicated resonances which involve periodic motion in a higher number of cluster modes than in the case of Ar-HCl. In the same spirit is the resonance trajectory plotted in Figure 8, also for X = 193 nm. In this trajectory the hydrogen motion takes place in a different way, since most of its collisions are with the Ar atoms (only one H/Cl collision occurs).
However, although differently, we again see periodicity of motion in the same modes of the cluster as in the above resonance. The initial orientation of the H-Cl bond is what basically determines the occurrence of either the trajectory of Figure 7 or that of Figure 8. (For the latter one the initial H-Cl orientation is closer to the T-shaped configuration.) The trajectories of Figures 7 and 8 show a picture of real trapping of the light atom inside the cluster, with similar characteristics to that found in photodissociation processes in matrices of rare gas atoms. The duration in time of the trapping is of course strongly dependent on the solvent size and in our case is still small compared to the matrix environment. The important point is, however, that a smaller cluster like A r r H C l is already able to originate a trapping picture which begins to approach the condensed matter situation. In the above we discussed new resonances which involve collisions between the hydrogen and all the heavy particles (the two Ar and the C1 atoms). There is an additional new type of resonancein which the light atomonly collides with the Aratoms. These resonances appear when the hydrogen has enough energy to overcome the Ar-Ar barrier (when the X = 157 nm wavelength is used). In this case the hydrogen atom dissociates from the cluster by escaping in between the two Ar atoms. The dissociation is not direct, however, and the light particle collides a few times with the two Ar atoms, vibrating along the Ar-Ar axis. Figure 9 shows a typical example of this type of resonance, where two complete vibrations of the hydrogen can be observed. The frequenciesassociated with these hydrogen resonancesalong the Ar-Ar axis are, in principle, different from those of the other resonance types, which would make possible todistinguishbetween them. It should also be noted that dependingon the initial excess energy of the hydrogen (determinedby the excitationwavelength), different resonances will be populated. This provides an experimental means of selecting different resonances of this type by tuning the excitation wavelength (provided that the wavelength allows the H atom to overcome the Ar-Ar barrier). We finally stress the fact that resonance trajectories like that of Figure 9 take typically a time between 58 and 70 fs. By looking at the lifetime distribution of Figure 6, we see that these events occur with a probability which, although small, is not negligible at all. E. Ar2ProducQ. From the chemical point of view, one of the most interesting features of the A r r H C l photodissociation dynamics is the possibility of formation of Ar2 molecules as products of the cluster fragmentation. By analyzing the trajectories integrated for ArrHCl, we find a 14.2% of the photolysis events leading to Arz products for X = 193 nm, while this fraction increases to 21.1% in the case of A = 157 nm. The mechanism of formation of Arz molecules is related to essentially direct
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3525
Photolysis of HCl in Ar-HCl Clusters 0.s 1
-0.1
I
-
-...I -0.3 -3.0
-2.0
-1.0
0.0
x
(if 2.0
3.0
4.0
Figure 9. Resonance trajectory corresponding to ArrHCl photodissociation with a X = 157 nm wavelength (see text). photodissociation events in which the hydrogen dissociates interacting very weakly with the Ar atoms. The light atom therefore cannot transfer to the Ar-Ar bond enough energy to break it. The C1 atom separates from the cluster due to the recoil energy gained from the H-Cl bond fragmentation, and finally a Arz product remains. Such a mechanism is favored for configurations of the Arz-HCl cluster in which the initial relative orientation of the H-Cl and Ar-Ar bonds is very far from the T-shaped geometry. The reason of the smaller fraction of Arz products for A = 193 nm is expected from the fact that the hydrogen is more strongly confined due to the presence of the Ar-Ar potential barrier. In this case, the events in which the hydrogen has to collide with the Ar atoms, breaking the Ar-Ar barrier (and therefore the Ar-Ar bond) in order to dissociate, are more likely, as seen from Figures 4 and 6b. This causes the Ar2 production to decrease. The experimental implications of this finding are important. The amounts of Arz products predicted by the calculations are rather large and should be experimentally detectable. Experimental investigationof this finding should prove interesting.
IV. Conclusions Photodissociation of HC1 in both the Ar-HCl and Arz-HCl clusters has been simulated using a quasiclassical trajectory approach in order to explorethe cluster size effect. Two different excitations wavelengths, namely A = 193 nm and A = 157 nm, are used in the calculations. The hydrogen is found to collide up to severaltimes with the heavy atoms beforedissociating. During the collisions the light atom transfers part of its initial excess energy to the argon and chlorine. The dynamics is analyzed through the H photofragment kinetic energy distribution, as in previous work, but also through the KEDS corresponding to the heavier Ar and C1 atoms. While the hydrogen KED reflects all the collisions of this atom with the heavy ones, the contributions to the Ar and C1 distribution are caused by collisions with these atoms only. The information contained in the hydrogen KED is thus separated in the heavy particle distributions. A more pronounced cage effect is found in the photolysis of Arz-HCl as compared with the Ar-HCl cluster for the A = 193nm wavelength. This is a result of the stronger confinement of the light atom when the cluster size is increased. This behavior of the cage effect with the cluster size is, however, inverted when the X = 157 nm excitation wavelength is used. In this case the cage effect for hydrogen dissociation is weaker in Arz-HC1 than in Ar-HCl. The reason lies on the excited Dotential surface. which oresents a potential barrier (the Ar-Ar'bond) in front of the ligk atom. For a A = 193 nm excitation the hydrogen has not enough energy to overcome the barrier and sees a larger and more consistent
wall ahead of it than in the Ar-HC1 cluster, which causes its stronger confinement. The excess energy provided by the X = 157 nm wavelength does allow the light particle to overcome the barrier, opening a window in the Ar-Ar wall. The H atom can now escape through that window more freely than in the case of Ar-HCI, where the wall of the H atom (in this case only one atom) is still present. Therefore, the magnitude of the cage effect in these clusters becomes strongly dependent on the excitation wavelength or, in other words, on the specific region of the excited potential surface which is populated by the laser excitation. This excitation wavelength effect on the photodissociation dynamics is present in both the Ar-HCl and the Arz-HCl clusters, but only in the second case is the effect able to reverse the magnitude of the cage effect. We note, however, that is not obvious that the inversion of the cage effect tendency to increase with the cluster size will remain for clusters with larger sizes (using either a A = 157 nm or other wavelengths). This will depend on the specific features of the potential surfaces associated with the different clusters. Different types of resonance behavior are found for the hydrogen motion in the A r r H C l cluster, also as a consequence of a more complicated potentia1 surface than in Ar-HCl. In addition to resonances of the same type as those previously observed in calculations on Ar-HCl, new resonances are detected which involve periodic motion of several cluster modes. Among them, perhaps especially interesting is the resonance motion of the H atom temporarily trapped between the two Ar atoms before escaping. The different types of resonances are expected to have different frequencies associated, which would make possible to distinguish between them. One of the most interesting findings of the present work is the formation of A2 products, as a result of direct dissociationof the hydrogen. Initial geometriesof thecluster far from the T-shaped equilibrium configuration favor the escaping of the light atom without colliding with the Ar atoms. Not enough energy to break the Ar-Ar bond is transferred, and Arz moleculesarise as products of the cluster photodissociation. The high fractions of Ar2 products predicted for the two excitation wavelengths makes reasonable to expect that its experimental detection should not be very difficult. Finally, we note that although important differences were found in this work between photolysis of HCl in Ar-HCI and in Ar2HCl, the differencesare not as extreme as those found in a previous study between Xe-HI and Xe,-HI with n 1 5 (ref 22). In the latter case the difference was most dramatic because for n 1 5 essentially all the photodissociation behavior was determined by resonances, and the latter were also much longer lived. This suggests that there is ais0 much to be gained from a careful and systematic study of photolysis in larger clusters, with significant changes essentially for each added atom. We propose to pursue this further for higher Ar,,-HCl clusters. Acknowledgment. We thank Prof. C. Wittig for helpful comments. We also thank Prof. M. H. Alexander for providing his ab initio HCl potential for theexcited state prior to publication. It is a pleasure to dedicate this article to Joshua Jortner, from whose pioneering work on clusters we learned so much. The Fritz Haber Research Center is supported by the Minerva Gesellschaft fur die Forschung, mbH, Munich, Germany. This research was supported by CICYT, Spain, Grant PB87-0272, and by the Comunidad Aut6noma de Madrid, Grant 064192. This work was also supported by a Grant from the Ministry for Science and Arts, Land of Neidersachsen, Federal Republic of Germany (to R.B.G. and U.B.). Part of this workwas done when the authors were members or visitors of the Institute of Advanced Studies of the Hebrew University.
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