j . Phys. Chem. 1986, 90, 4483-4491
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FEATURE ARTICLE Dynamics of Dissociation and Energy Transfer in Molecular Collisions with Solid Surfaces 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 A. Amirav Chemistry Department, Tel-Aviv University, Ramat-Aviv 69978, Israel (Received: February 27, 1986) This article reviews recent progress in understanding the dynamics of molecular dissociation in impact on crystalline surfaces, a topic pursued by a combination of theoretical methods (trajectory calculations and impulsive collision models) with molecular beam scattering experiments. The studies reviewed deal with molecules such as I, and IC1 in collision with single-crystal surfaces of chemically inert insulators, e.g., MgO( loo), sapphire, and diamond. Dissociation in such systems is an elementary, single-collision process, advantageous for pursuing understanding on a first-principles basis. The main findings include the following: (1) Dissociation occurs by a centrifugal mechanism involving high rotational excitation upon impact. (2) Large energy transfer to the solid takes place in cases such as I,/MgO( 100) and I,/sapphire, the mechanism of which is shown by theoretical simulations to involve a shock-wave excitation of the solid upon the molecular impact. The effect of energy transfer to the solid on the dissociation probability depends strongly on the system, and the theoretical model provides an interpretation for this. (3) There are important qualitative differences between the results for a homonuclear collider and those for a related mass asymmetric molecule (e.g., I2 vs. ICl) regarding the energy dependence of the dissociation probability and the energy distribution of the products. It is argued that for the simplest systems studied a coherent picture seems to emerge for the various aspects of the dissociation process with good consistency between theoretical and experimental results. Major open problems and future directions in the field are discussed.
I. Introduction An exciting aspect of current research in the field of molecular interactions with surfaces is that powerful experimental tools, such as molecular beam scattering, and sophisticated theoretical simulation methods and models are beginning to unravel the microscopic nature of the phenomena involved. In this way, understanding from a first-principles basis is being gained of several gas/solid interaction processes which are of major chemical importance, e.g., rotational and vibrational energy transfer in molecular collisions with surfaces.’ The present article describes recent progress in understanding a fundamental, elementary chemical reaction at the gas-solid interface: the dissociation of small molecules upon impulsive collisions with chemically inert crystalline surfaces. Dissociation in such systems is caused by the repulsive wall of the molecule-surface interaction potential, which converts part of the translational energy of the colliding molecule into internal energy sufficient to overcome the binding forces between the fragments. Such collision-induced dissociation requires high impact energies, of the order of several electron volts at least. It is important to recognize the difference between this process and a dissociation that involves chemical binding interactions between the surface and the constituent atoms of the molecule. Catalytic dissociation at surfaces is of the latter type, and the dynamics of such processes has been actively pursued in recent years, both e ~ p e r i m e n t a l l yand ~ , ~ the~retically.~The (1) For a recent review see: Barker, J. A.; Auerbach, D. J. Surf.Sci. Rep. 1984, 4, 1. (2) See, for instance: (a) Balooch, M.; Cardillo, M. J.; Stickney, R. E. Surf. Sci. 1974, 46, 358. (b) Becker, C. E.; Cowin, J. P.; Wharton, L.; Auerbach, D. .I. J . Chem. Phys. 1977, 67,3394. (c) Bernasek, S . L. Adu. Chem. Phys. 1980, 41, 477. (d) Ceyer, S. T.; Somorjai, G. A. Annu. Rev. Phys. Chem. 1977, 28, 477. (e) Salmeron, M.;Gale, R. J.; Somorjai, G. A. J . Chem. Phys. 1977, 67,5324; 1979, 70, 2087. (f) Comsa, G.; David, R. Surf Sci. 1982. 117.71. ( Q ) Brown. L. S.: Bernasek. S . L. J. Chem. Phvs. 1982,82, 2110.‘(g) Robota,”H. J.; Viklhaber, W.; Lin, M. C.; Segner, J.; E h . G. Surf. Sci. 1985, 105, 101.
0022-3654/86/2090-4483$01.50/0
chemical binding interactions between the products and the surface, characteristic of “catalytic” dissociation, make this process inherently more complex than the impulsive, collision-induced dissociation that is the topic of the present article. The relative simplicity of dissociation in impulsive collisions with chemically inert surfaces, the fact that such processes can be studied and analyzed in terms of well-defined single-collision events, is an important attractive feature in pursuing this topic: Such processes offer one of the best prospects for understanding an elementary chemical reaction at the gas/solid interface from a first-principles basis. There are also other strong motivations for pursuing these processes. For instance, an important initiation mechanism for many radical chain reactions in a vessel involves cleavage of translationally hot molecules when the molecules strike the walls. Hardly anything is known on the dynamics of this basic initiation process. Dissociation of the type pursued here also occurs, at least as a primary process, when one carries out chemical reactions by bombarding solids with very energetic molecular ion beams, as pursued for instance by Rabalais et al. in their studies on N2+collisions and reactions with M o . ~ The present article mainly describes results obtained in collaboration between the respective theoretical and experimental groups of authors over the past few years; these results shed light on the dissociation dynamics in several simple systems, including molecules such as I2 in collision with single-crystal surfaces of MgO, diamond, and sapphire. The work and some of the con(3) For a recent review, see: Asscher, M.; Somorjai, G. In Aromic and Molecular Beam Methods; Scoles, G., Ed.; Oxford University: London, in press. , (4)See, for instance: (a) McCreery, J. M.; Wolken, G., Jr. J. Chem. Phys. 1976, 64, 2845. (b) Gelb, A.; Cardillo, M. J. Surf Sci. 1978, 75, 199. (c) Tully, J. C. Acc. Chem. Res. 1981, 14, 188. (d) Tantardini, G.F.; Simonetta, M. Chem Phys. Lett 87, 420. (e) Ron, S.; Shima, Y.; Baer, M. Chem. Phys. Lett. 1985, 116, 443. (f) Lee, C.-Y.; dePristo, A. E. preprint. (5) Baldwin, D.A,; Murray, P. I.; Rabalais, J. W. Chem. Phys. Lett. 1981, 77, 403.
0 1986 American Chemical Society
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clusions are related to recent studies by several authors on the topics of rotationally and vibrationally inelastic scattering of molecules from surfaces. The implications of these studies to dissociation dynamics will be discussed. The emphasis in the article will be on the physical picture that emerges for the dissociation dynamics, on the theoretical considerations behind it, and on the comparison between theoretical and experimental results. A comprehensive account of the experiments will be published elsewhere. Some background as to the experimental work is given in section I. The dissociation mechanism and the role of the various molecular degrees of freedom in it are the topic of section 11. Energy transfer to the solid during the collision and its effect on the dissociation probabilities is discussed in section 111. The angular and velocity distributions of the products and their relation to the dynamics of the process are examined in section IV. The effects of high mass asymmetry, e.g., in the context of comparing IC1 with 12, are described in section V. The article concludes with a discusion of some important open questions in the field and with suggested directions for future research.
11. Experimental Approach Experiments on molecular dissociation induced by impulsive collisions with solid surfaces were pursued by molecular beam scattering technique^.^,^ Essential in these studies is the ability to accelerate the molecule to high translational eneregies, above the dissociation threshold, and to vary the kinetic energy in a broad range. This was accomplished by using a seeded supersonic beam of heavy molecules (e&, 12) in a light carrier gas of H e or H2 with a density of carrier particles much higher than that of heavy molecules. In this way the heavy molecules are accelerated to the light gas velocity, and for I,, for instance, kinetic energies in the range 1-10 eV are easily obtainede6 The kinetic energy is controlled by the nozzle pressure and temperature. The molecular beam is then skimmed and collimated before entering the ultrahigh-vacuum (UHV) chamber where it collides with the surface. The kinetic energy of the molecules was measured by using a time-of-flight (TOF) technique both before and after scattering from the surface. The incident molecular beam was mechanically chopped into pulses (15-20 p s ) , and its time of arrival at the quadrupole mass spectrometer (QMS) detector was then meas~red.~?~ The handling and the characterization of the surface target in the experiments was carried out as follows: The target, a single-crystal Mg0(100), sapphire (OOOI), or diamond (100) in the experiments pertinent to this re vie^,^^^ was mounted on a UHV manipulator. The crystal was cleaned and annealed at high temperatures (e.g., 900 O C for MgO). Surfac cleanliness and structural order was probed by specular and diffractive scattering of He. Such surface characterization was carried out before and after the I, scattering (to demonstrate that no damage was incurred to the crystal by the I, collisions, no overlayer was formed, etc.). Moreover, this test of surface structural order and cleanliness was pursued also during the I, bombardment, since the diffraction of the He carrier gas in its scattering from the surface was observed. Most dissociation studies were carried out at 300 "C, since at this (and higher) temperature the surface remains relative clean during the time of the experiment. The dissociation products were detected by a Q M S mounted at 45' to the incident beam. In the scattered beam TOF experiments or in intensity measurements aimed at high angular resolution, the Q M S was placed far from the surface (37 cm). In measurements aimed a t high solid angle integration of the scattered intensity, the Q M S was placed much nearer the surface (2.5 cm). Angular distributions were obtained by rotating the target surface, thus changing the beam incidence angle with respect to the latter, while keeping the detector fixed. It should be stressed that the experimental configuration implies serious constraints (6) Kolodney, E.; Amirav, A. Chem. Phys. 1983, 82, 269. (7) Kolodney, E.; Amirav, A.; Elber, R.; Gerber, R. A. Chem. Phys. Letr 1984, 111, 366.
Gerber and Amirav 50 0 40 0 C
L N 300
+I 1z
J
200
-0
10 0 0 00 v i b r a t i o n energy ( e . v 1 Figure 1. Histogram of final vibrational energy distributions in collision of I2 with a rigid surface of 2.0 eV.8
r o l o j i o n energy ( e . v . 1
Figure 2. Histogram of the final rotational energy distribution in collisions of I2 with a rigid surface at 2.0 eV.8
on the information obtained: e.g., when scanning is done over the angle between the surface and the incident beam, the component of the incident velocity normal to the surface is different for each angle; hence, the angular distributions measured involve essentially some averaging over different initial velocity vectors. We shall see in subsequent sections that some of the most interesting theoretically predicted effects concerning the angular and velocity distributions of the fragments cannot be tested experimentally due to such limitations of the experimental arrangement. 111. Dissociation Mechanism 1 . Centrifugal Mechanism. As a convenient reference point
in discussing the dissociation dynamics, it is useful to consider a model in which a rigid, nonvibrating solid is assumed. It will be seen later that several (though not all) of the physical features of the dissociation are correctly given by such a model, and we shall outline the conditions and extent of its validity in some detail. In any case, the simplicity of the rigid-surface model renders it a helpful starting framework. A useful hint on the nature of the dissociation dynamics in this case is obtained by considering first vib-rotational excitation in molecular impact on surfaces at energies that are high compared with the vibrational energy spacings but below the dissociation threshold. Figures 1 and 2 show respectively the vibrational and the rotational energy distributions produced by collision of I2 with a model representing a flat static surface.8 The collision energy (2.0 eV) is below the dynamical threshold for dissociation in this system. The energy distributions shown were obtained by classical trajectory calculations, assuming a repulsive exponential interaction potential between each atom of the molecule and the surface8 and taking the incident I2 to be in its vibrational and rotational ground state. A set of 540 trajectories were calculated, representing a sampling over initial orientation angles and vibrational phases.8 Figures 1 and 2 show that the rotational mode is far more effective than the vibrational one in receiving collision energy. (8) Gerber, R. B.; Elber, R. Chem. Phys. Lett. 1983, 102, 466.
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4485
Feature Article The mean rotational excitation energy is by 2 orders of magnitude larger than the vibrational one. Moreover, the rotational distribution shows a propensity for large energy transfers (>so% of the collision energy), while for vibration only low excitations are possible. A simple interpretation of this behavior is given, for instance, in terms of a sudden approximation for both the vibrational and rotational degrees of freedom.8 The transition amplitudes are then given by8.9
where xuand Y Jare the final vibrational and rotational states, xo and Yoare the initial states, and v(t9,p) is an elastic scattering phase shift computed for each molecular orientation angle t9 and each internuclear separation p. xo(p) is strongly localized around the equilibrium position, hence transitions to high final v are very unlikely since for no p region will xv overlap with xo. The p dependence of 7 is weak and cannot alter the above consideration. Yo(@, on the other hand, gives equal weight to all incident 0. An orientation of 0 exists that gives a substantial nonvanishing contribution to the 0 integral for each J value. Thus there are also orientations that produce large rotational transitions which correspond to a “maximal torque” condition. More precisely, one has here an example of the rotational rainbow effect,’*I3 results in maximal transition probabilities for large AJ transitions. The rotational rainbow effect in surface scattering was observed experimentally by Auerbach et al.1° and was studied theoretically in depth by Schinke,I’ Polanyi and Wolf,I2 and Barker et al.I3 The findings of the present case are merely a manifestation of this effect at high collision energies, when vibrational rigidity of the molecule cannot be assumed. It turns out that the above behavior persists also above the dissociation threshold: Dissociation was found to take place if the rotational torque upon impact on the surface provides a centrifugal repulsion sufficient to overcome the interatomic binding.I4 Qualitatively, trajectory calculations certainly bring this out. A crude quantitative model for the dissociation probabilities, based on the centrifugal mechanism, was also p r ~ p o s e d . ’ ~ It is based on the assumption that dissociation occurs if, and only if, the angular momentum received by the molecule upon impact corresponds to a centrifugal energy sufficient for overcoming the attraction between the atoms. Quantitatively, the dissociation condition is W P C )
+ 52/(2/lPc9 > 0
(2)
where Wis the interaction potential between the atoms; pc is the intermolecular distance a t the instance of collision, taken as the equilibrium separation; p is the reduced mass; and J is the angular momentum administered to the molecule upon impact. The probability of the molecule receiving a given value of J can be estimated from a rigid-rotor calculation treating the rotational excitation in the sudden appro~imation.~ The dissociation probability is then readily obtained from eq 2. Results comparing this simplistic model with “exact” classical trajectories for I2 collisions with a static surface are shown in Figure 3.14 The model is seen to provide at least semiquantitative agreement with the “true” dissociation probabilities. Calculations for other colliders, e.g., Li2, also support the centrifugal mechanism.I4 Note that the crude centrifugal model always overestimates the true dissociation probabilities. One reason for this is that the method ignores “double collision” events in which the molecule, following an initial (9) Gerber, R. B.; Yinnon, A. T.; Shimoni, Y.;Kouri, D. J. J . Chem. Phys. 1980, 73, 4397. (IO) Kleyn, A. W.; Luntz, A. C.; Auerbach, D. J. Phys. Reu. Lett. 1981, 47, 1169. (11) Schinke, R. J . Chem. Phys. 1982, 76, 2352. (12) Polanyi, J. C.; Wolf, R.J. Ber. Bunsen-Ges. Phys. Chem. 1982,86, 356. (13) Barker, J. A,; Kleyn, A. W.; Auerbach, D. J. Chem. Phys. Lett. 1983, 97, 9. (14) Gerber, R. B.; Yinnon, A. T.; Shimoni, Y.; Kouri, D. J. J . Chem. Phys. 1980, 73, 4397.
1.00
1
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4
P
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9 00
translation energy ( e . v . 1
Figure 3. Dissociation probability vs. energy for I, scattering from a rigid surface:I4 (-) centrifugal model; (A) classical trajectory simulation.
impact on the surface which excites it to a high J, may rotate after this collision rapidly enough to strike the surface again with its second end. This second collision, not included in the crude model, may deactivate the high J. Trajectory calculations suggest that a corrected centrifugal model, which allows for this effect, should be of excellent accuracy. 2. Direct Dissociation us. Formation of Metastable States. The indications for the importance of the centrifugal mechanism of dissociation bring up an interesting possibility, namely that a significant fraction of rotationally excited metastable states could be produced by the collisions in certain conditions. After the collision with the surface, the relative motion of the two atoms is governed by the effective potential Wdp) = W(p) + 52/(2/lp2), where J is the angular momentum acquired by the molecule in the encounter. For very high J, WJ(p)is purely repulsive, which corresponds to a directly dissociating state. Consider, however, lower J states for which WJ(p)has a local maximum at a distance pm, say. Trajectories resulting in final states having vibrational energies in the range (3) and for which the atoms emerge after the collision at mutual distances p < pm correspond to bound states (of infinite lifetime) in the framework of the classical calculations, although they have an internal energy above the dissociation threshold. Quantum mechanically, such states have of course a finite lifetime since they decay by tunneling through the centrifugal barrier. A classical approximation for the “true” quantum mechanical probability for collision-induced dissociation is thus given by
P & s ~ t a t ) (=E Pdl,‘4(E) )
+ fim”(E)
(4)
where Pdjss(d) is the probability for direct dissociation obtained from the classical trajectory calculations and P(ms)is the (classical) probability for producing a metastable molecular state in a collision a t kinetic energy E will the surface. Whether in an experiment a metastable state will be recorded as a bound molecule or as dissociation fragments depends on whether the (tunneling) lifetime of that state is longer or shorter than its time of flight to the detector. The probability for producing such rotational metastable states was calculated classically for I2 in collision with a flat model ~ u r f a c e . ’ ~The calculations assumed Morse interactions with a well depth of 1.0 eV between each I atom and the solid. The incoming I2 molecule was taken in normal incidence to the surface. A probability of about Hms)i= 6% was found for metastable-state production in that system in collisions at E = 5.5 eV. The dissociation energy of I, is 1.54 eV). Very recently, the probability of metastable-state formation was calculated for IC1 in impact on a flat static surface m0de1.I~ In this case purely repulsive, exponential interaction between each atom and the surface was used. Only collisions at normal incidence to the surface were considered. Hms)(E)was found to increase steeply as the energy (15) Elber, R.; Gerber, R. B. J . Phys. Chem. 1984,88, 1571.
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The Journal of Physical Chemistry, Vol. 90, No. 19, 1986
is increased above the threshold value for dissociation (-2.2 eV), reaching a value of P(ms)= 10% at E = 2.5 eV. P(ms)then decreases as E increases, falling to about 1.0% at E = 5.0 eV. The relatively large production of metastable states slightly above the threshold of dissociation and the fall-off of P(ms)as the energy is increased beyond that range are easily interpreted in terms of the centrifugal model: Collision energies at or slightly above threshold do not suffice for producing extremely high final rotational states. The significantly populated states following impact have J values corresponding to a W,(p) with a local maximum, and a significant fraction of the final states satisfy condition 3, representing a state metastably bound by the centrifugal barrier. As the collision energy is much increased, the most populated J states produced by the impact are much higher and correspond to purely repulsive W,(p), which has no metastable states. The main conclusion regarding P(ms)f r o m the classical trajectory simulations of ref 15 and 16 is that metastable-state formation is probable enough in favorable conditions (near threshold) to permit their experimental detection. An experiment with this aim in mind should be worth trying, as it could directly confirm the centrifugal mechanism. 3 . Experimental Evidence and the Question of Other Mechanisms. Direct experimental verification of the dissociation mechanism is not avilable as yet. The best available test is a comparison between the experimentally measured dissociation es and those calculated from a theoretical model (which by available knowledge on the systems involved appears reasonably realistic). We postpone the detailed comparison and relevant figures to section IV, where also calculations that include surface vibrations are discussed and tested. However, we stress already at this point that the dissociation probabilitiesfor I,/MgO( 100) calculated by classical trajectories as a function of collision energy (up to incidence energies of 10 eV) are in excellent agreement with the corresponding experimental data.? These trajectory calculations, when analyzed, show that dissociation occurs by the centrifugal mechanism. The agreement between experiment and the theoretical calculations in this case is particularly weighty, since a good argument can be made in this case that a reasonably realistic model was used.7 (Information is available on the MgO surface structure, on the potential function that governs the MgO crystal vibrations, and on a crude level, also on the I,/MgO interaction potential;? see section IV.) Important also is the fact that in impulsive collisions, the steep repulsive part of the molecule/surface potential controls the dynamics, and within this framework the results are not sensitive to fine details of the interaction. Experimental dissociation probabilities were compared with theoretical results also in the case of 12/sapphire(0001) and 12/diamond(100). In both cases the agreement is very good (see section IV), although not as striking as in the case of 12/MgO(100). The confidence in the parameters used in the theoretical calculations, e.g., the molecule/surface interaction potential, is less good than in the case of I,/MgO. Also the trajectories calculated for I,/sapphire and 12/diamond show that dissociation in these systems occurs by the centrifugal mechanism. We conclude that substantial, if not direct, experimental evidence is available f o r the centrifugal mechanism of dissociation f o r collisions of I2 with chemically inert, oibrationally stiff insulator surfaces such as MgO, sapphire, and diamond. Some alternative mechanisms are directly excluded by available experimental data. Any mechanism involving sticking to the surface can be ruled out by the experimental angular intensity distribution. Figure 4 shows the measured QMS detector signal for I2 collisions with a sapphire surface as a function of the angle between the incident beam and the surface normal. (The detector is kept fixed at 45", as discussed in section 11). Figure 4A shows results at an incidence energy of 2.4 eV for which dissociation is not evident. The I' and 12' curves are similar in shape with a ratio of 2. (The I' signal is entirely due to electron-induced dissociation in the Q M S ionizer.) In Figure 4B, at a collision energy E = 9.8 eV. dissociation is evident. as the ratio of atomic
-
(16) Bacic. Z.; Gerber, R B. J Phys. Chem., in press.
E
= 2.4 eV
IOo 20' 30' 40' BE A M - SU R FACE ANG LE Figure 4. 1, scattering from sapphire: the molecular and atomic iodine measured signal at the QMS detector vs. the surface-beam axis angle. (A) Signals at collisions energy 2.4 eV. (B) Signals at collision energy 9.8 eV.
to molecular iodine is increased by more than a factor of 2 compared with that in Figure 4A. The angular resolution in this figure is low (*So). However, it is clearly seen that the scattering of both the I fragments and the nondissociated molecules is high directional, centered near the specular angle. A mechanism involving trapping of the molecule or of the dissociation fragments should result in a much broader, cos B type distribution. An interesting mechanism of molecular dissociation and of energy-transfer processes in collision with surfaces has recently been proposed by Gadzuk and H ~ l l o w a y , ' ~who - ' ~ describe it as "surface harpooning". It is assumed in this mechanism that as the molecule approaches the surface an electron from the solid is transferred to it, to produce a temporary negative ion. It is further supposed that as the ion leaves the surface the electron hops back, but the vibrational state of the neutral molecule may be excited, possibly in the dissociative continuum, because of electron-to-vibrational energy transfer associated with hops of the electron. In the mechanism of Gadzuk and Holloway, the dissociation dynamics is determined by the occurrence of crossings between the relevant electronic energy curves, by the LandauZener probabilities for transitions at the crossings, and by Franck-Condon type overlaps between vibrational states pertaining to different electronic c u ~ v e s . ' ~ -For ' ~ collisions of, e.g., halogen molecules with metals, the model is certainly intuitively most reasonable. Gadzuk and Holloway suggest that surface harpooning could be pertinent to dissociation also at insulator surfaces such as Mg0.19 No quantitative estimate was, however, given by the authors on the magnitude of the curve-crossing probabilities in any such concrete system, and in fact no evidence is available that suitable curve crossings occur and are dynamically accessible in pertinent realistic cases. Therefore, surface harpooning must tentatively be viewed as an interesting but as yet unsubstantiated conjecture. Further work on this mechanism, aimed at providing quantitative estimates for the dissociation probabilities it yields, is clearly desirable. IV. Excitation of Solid Vibrations and the Effects on Dissociation The question of the role of surface vibrations in the collision process is one of profound interest. If, for instance, a model using a static nonvibrating description of the surface could give rea( 1 7 ) Gadzuk, J W , Holloway, S Chem Phys Lett 1985, 114, 314 (18) Holloway, S , Gadzuk, J W Surf S n 1985, 152, 838 (19) Gadzuk, J W , Holloway, S J Chem Phys , i n press
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4487
Feature Article
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THEORETICAL EXPERIMENTAL
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Figure 6. Kinetic energy loss of nondissociated I2 molecules scattered KINETIC ENERGY ( e V )
from ~ g 0 ( 1 0 0 ) . ~
...
Figure 5. Dissociation probability vs. collision energy for 12/MgO(100): Calculationsfor a rigid-surface model and for a vibrating solid are compared with experiment. The experimental surface temperature was 275 OC.
...
0
sonable results, the task of theoretical calculations of dissociation dynamics would be enormously simplified. We thus proceed now to examine the validity of the rigid, nonvibrating surface model. Figure 5 shows the dissociation probabilities for the 12/MgO(100) system as measured in molecular beam scattering experiments7 in comparison with results calculated from the static-surface model (and also with results obtained from a simulation that includes solid vibrations, which will be discussed later). The results show that the rigid-surfacemodel is in remarkable , agreement with experimental dissociation probabilities,essentially over the entire range of collisions energies e ~ p l o r e d .On ~ the other hand, time-of-flight experiments were also carried out to determine the kinetic energy loss of I2 molecules that did not undergo diss ~ c i a t i o n .Very ~ large kientic energy losses were found, of the order of 50% of the incidence energy, implying extensive energy transfer to the solid. This seems in apparent contradiction to the success of the nonvibrating surface model in predicting the dissociation probabilities for the same system. Interesting also was the fact that calculations allowing only for motions of the surface atoms (or restricted to include vibrations of a f a u solid layers only) grossly underestimated the measured energy transfer.’ To resolve the apparent contradiction, extensive simulations were carried out which included the motions of many solid atoms. Calculations were done for a successively increasing number of solid atom layers until convergence was obtained with regard to their effect on the collision dynamics. Such convergence occurred when about 100 or more vibrating layers were included in the calc~lations.~ The details of the model will not be discussed here.7 We note only that (1) a potential function for the vibrations of the MgO solid was constructed from the pairwise ion-ion interactions (Mg2+/ This model provides also the anMg2+; Mg2+/02-; 02-/02-). harmonic part of the potential, which proved a major importance. (2) The 1 2 / M g 0 (crystal) interaction was also obtained from a model assuming painvise forces between each I atom and the ions of the solid. The potential was refined to give the best fit to the time-of-flight experiments, although the sensitivity of the results to potential parameters is not great in this case. (3) The classical trajectory calculations were carried out by assuming that the solid atoms are initially all in their classical positions; Le., the initial state of the solid was taken as the classical T = 0 K state. This greatly reduces the computational effort associated with sampling over initial state configurations. These calculations reproduced to good approximation both the dissociation probabilities (see Figure 5 above) and the measured energy transfer to the solid, shown in Figure 6. The finding from the simulation and the interpretation that emerges are as follows: Excitation of solid vibrations in this case takes the form of a shock wave. As seen in Figure 7, the energy distribution of this shock wave shows a structure of two components. The excitation that propagates first
68.6
I
X
%
I
h
v
(
o0o 0 00
20 0
. . .. 60 0
40 0
80 0
100
N Figure 7. Energy distribution in the Mg 0 solid at the instant when I2 leaves the interaction range. N is the layer number: N = 0 the outer
most surface layer. is very localized, its energy spread only over a few (- 7) atom layers. This shock component is highly anharmonic and maintains its form during propagation, and tentative evidence suggests that it can be described as a soliton. (This shock wave corresponds to a coherent cascade of “hard” collisions between crystal atoms.) The second component of the shock wave is spread over many more atom layers and is harmonic in nature. It is a “conventional” multiphonon excitation pulse. Note that no localized phonon picture can account for the energy transfer. Thus, I2 energy transfer to a localized light stiff oscillator, such as MgO, in the gas phase is inefficient due to chattering effects. First energy from the heavy collider is indeed transferred to the light atom of the oscillator, but this atom will recoil from the second end of the oscillator and return much of the excess energy to the heavy collider before the latter gets aways. We expect soliton-like excitations such as found here to be relevant to a broad range of high-energy collision processes where the collider is much heavier than the solid atoms. Indeed, a similar behavior was seen in classical trajectory simulations of Hg atoms in collisions with Mg0(100),20 and also in this case the theoretically computed energy transfer was in good accord with the experimental results.*O Although energy transfer to the solid is large, its effect on the dissociation is very small. It turns out that for the 12/Mg0 system the molecule begins to rotate upon impact slightly before it significantly “presses in” the surface atom, which begins the excitation of the solid. Thus the rotational torque is administered somewhat before the nonrigid behavior of the solid begins, and it is this torque that determines whether dissociation will occur. The relative time scales of rotational and solid-mode excitations are, though, system dependent. For 12/sapphire, where (20) Kolodney, E.;Amirav, A,; Elber,R.; Gerber, R. B. Chem. Phys. Lett. 1984, 113, 303.
4488
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986
Gerber and Amirav
* *
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0
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v )
Figure 8. Dissocation probability vs. collision energy for 12/sapphire (+) vibrating solid model; (0)experiment; (*) rigid-surface model.
the mass units of the solid are more comparable to I,, solid excitation does not lag behind the rotational torque, and the rigid-surface model does not give reasonable dissociation probabilities in this case. Indeed, this is clearly seen in Figure 8, which compares the experimental dissociation probabilities for 12/sapphire measured by Kolodney and Amirav” with a classical trajectory calculation using a rigid-surface model and with a simulation that includes the vibrations of many solid atoms.22 The vibrating solid model gives much better results than the rigid-surface model, although the agreement with experiment is not as good as in the case of 12/Mg0. This can be attributed to the fact that interaction potentials, surface structure, and the potential for solid vibrations were probably more poorly modeled in the case of T2/sapphire, since little data is available on this system. Dissociation probabilities and energy transfer to the solid were also studied for I2 collisions with diamond(100). The calculated (and measured22b)dissociation probabilities show a behavior very similar to the case of 12/Mg0but saturate at a higher value (PdlSs = 0.65). On the other hand, T O F measurements on the nondissociated I2 molecules indicate a relatively inefficient energy transfer to the diamond (e.g., at a collision energy of 5 eV, the average kinetic energy loss is less than 0.5 eV). Preliminary trajectory simulations suggest an interesting interpretation for this behavior. Upon impact of I, upon the diamond crystal, one or several surface atoms are excited, and a cascade of collisions with other carbon atoms in the solid begins. However, in diamond the restoring forces acting on each atom are so strong that the excitation pulse just initiated is “pulled back” by these restoring forces before propagation across more than a few atoms and is returned to the I2 molecule by a surface atom colliding with it. (The high inertia of I2 is crucial for this to happen.) Essentially this is a modified version of the chattering mechanism in the gas phase which prevents large energy transfer between a heavy collider and a stiff oscillator of light mass. The very high vibrational stiffness of the diamond crystal and the very low C/12 mass ratio are especially favorable for this behavior, and we expect that systems exhibiting such “chattering effects” in collisions with solid to be rare. Finally, we wish to draw attention to another experimental finding pertinent to the role of surface vibrations in the dissociation process for which no convincing theoretical interpretation is as yet available: In the case of 12/Mg0, increasing surface temperature was found to greatly enhance the dissociation probabilities, as seen in Figure 9. ?he low temperature side, Ts30% compared with the static surface case. (It is only the peak of the faster atoms that moves in the direction of lower velocities due to energy transfer to the surface.) (c) The peak of the fragment energy distribution corresponding to the faster atom has a Poissonian shape. The width of the distribution and peak position are simply related to surface properties. (d) For normal incidence on a highly corrugated surface, the fragment angular distribution can be fitted rather well with cos" B,n >> 1. Such distributions are known, e.g., from thermal desorption studies The present results show that a similar of chemisorbed behavior can arise also in impulsive dissociation.
VI. Mass Asymmetric Molecules Heteronuclear colliders of considerable mass asymmetry give rise to additional interesting effects in the dissociation dynamics. We briefly describe here two such features, obtained within the framework of the rigid-surface model.16 Figure 12 shows the dependence of the dissociation probability on the collision energy for several molecules, as computed by classical trajectory calculations. The difference between the shapes for I2 and for IC1 has the following origin. The IC1 molecule may strike the surface with the I side or with the C1 side first. The two orientations are very different with regard to the possible occurrence of dissociation. Dissociation when the heavy atom hits first requires much higher energy, since a surface collision of this kind mainly tends to reflect the direction of the center-of-mass momentum located very near to the heavy atom, and only a small fraction of the collision energy goes to the relative I-Cl motion. Dissociation associated with the lighter atom striking first has thus a lower dynamical threshold, and its contribution to the fragmentation probability actually reaches saturation before the translational energy becomes large enough for the second type of orientation to contribute. This is thus the origin of the "intermediate plateau" behavior in the energy dependence of the dissociation probability of strongly mass asymmetric molecules such as ICl. Note that the effect is more pronounced in the curve for the total dissociation probability Pdiss(tot)(E) than in the curve showing the direct collision dissociation probability Pdis,'d)(E) (both quantities were defined in the context of eq 4), although it appears in both cases. A similar mechanism is behind an interesting behavior in the energy distribution of the dissociation products of ICI, shown in Figure 13. As can be seen from Figure 13, at relatively low collision energies (4.5 eV) the C1 fragment emerges as the more energetic one, while at high incidence energies (1 1.O eV) the I product carries more energy.16 When interpreting this, one should first recall that in section V it was pointed out that the first atom to strike the surface emerges with the higher energy since it is the second atom which collides with it and transfers energy to it, when the first atom is still at the proximity of the wall. At 4.5-eV collision energy, the only collisions that result in dissociation by our earlier discussion in this section are the "Cl-first" ones. Hence
Fragment energy (eV)
Figure 13. Energy distribution of the fragments in IC1 dissociation on a rigid surface at E = 4.5 eV (top) and E = 11.0 eV (bottom).16
Fragment energy (eV)
Figure 14. Energy distribution of the fragments in IC1 dissociation on a rigid surface at E = 11.0 eV:I6 (a) results for "I-first" collisions; (b) results for "C1-first" collisions.
this atom emerges as the more energetic one. At high incidence energies, as pointed out above, both the "C1-first" and the "I-first" mechanisms contribute to dissociation. However, the "I-first" collisions produce much more sharply peaked energy distributions than the "Cl-first" ones. This emerges clearly in Figure 14,where the distributions produced by the two types of collisions are shown separately. The net result is that at high energies the "I-first" dissociative collisions dominate the fragment energy distributions, and I emerges as the more energetic atom. The above examples show that dynamical effects due to mass asymmetry can be reflected even in the qualitative behavior of observable properties of dissociation processes. Experimental studies of dissociation of mass asymmetric colliders have recently begun (e.g., on IBr/MgO) and will be pursued extensively in future studies.
VII. Conclusions and Future Directions The examples discussed in this article are encouraging in demonstrating that studies which combine molecular beam scattering experiments with simulations and other theoretical methods can unravel the details of elementary reaction processes in molecular collisions with surfaces. The collision-induced dissociation processes that were the topic of this study are surely among the simplest in the area of surface reactions and the easiest to interpret on a first-prinicple basis. Of the findings, we stress mainly two concepts which appear to be of broad applicability and interest: the centrifugal or rotational mechanism for dissociation of diatomics in surface collisions and the shock-wave-like excitations of a solid of light atoms when struck by a heavy molecule, excitations that at least in some cases have a soliton form. In this new topic, it is clear that the results already obtained
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J. Phys. Chem. 1986,90, 4491-4498 merely scratch the surface of the rich phenomena awaiting investigation in the near future. We mention here, quite subjectively, a few of the problems that merit immediate exploration. (1) Other surfaces, other mechanisms: For types of surfaces very different from those considered here, very .different mechanisms of dissociation may become relevant. As mentioned in the review, Gadzuk and H ~ l l o w a y ’ ~ proposed -’~ an electron jump mechanism which should apply to dissociation on metal surfaces and also perhaps to other substrates. Experimental demonstration of this should be very valuable. It seems very likely that still other new mechanisms of dissociation may exist, and a search for these mechanisms by theory and experiment should be of major interest. (2) Polyatomic dissociation: Some of the most interesting questions for such systems are the branching ratios for different fragmentation processes, the internal energy distributions of the products, and the relevance of statistical models. No studies were reported on this topic. (3) Vibrational excitation of molecules: While direct vibrational excitation was found unimportant for diatomic colliders, the situation may be very different for polyatomics, in particular those for which major rotational mode participation seems unlikely. Few reliable studies are available on vibrational energy transfer in surface collisions.
(4) Excitation of solid modes in the dissociation process: In addition to the shock-wave excitations described in this study and the familiar phonon excitations, other types of excitations may exist. For metals and semiconductors the electrons may also play a major role. ( 5 ) Relation of collision-induced dissociation to “catalytic” dissociation: Although in the respective limiting cases the two processes are different, as argued at the outset of this review, intermediate behavior may well exist in suitable systems. Exploration of this point should be worthwhile. It appears reasonable to expect, in view of the available experimental and theoretical technology, that rapid progress can be made on the many open problems in this field.
Acknowledgment. We are deeply indebted to our collaborators Drs. R. Elber and Z Bacic (Theory) and Dr. E. Kolodney (Experiment) whose role in much of the work described in this review was large. Work described here was supported by the US.-Israel Binational Science Foundation (by Grants No. 3209 and 3210 to the authors) and by the Foundation for Basic Research of the Israel Academy of Sciences. The Fritz Haber Research Center at The Hebrew University is supported by the Minerva Gesellschaft fur die Forschung, mbH, Munchen, BRD.
SPECTROSCOPY AND STRUCTURE Multiple Scattered Wave Study of the Relativistic and Nonrelativistic Electronic Structure and Bonding for cls-Dlammined/chloroplatinum(I I ) Fernando Zuloaga* Pontifcia Universidad Cat6lica de Chile, Facultad de Quimica, Casilla 61 77, Santiago, Chile
and Ramiro Arratia-PCred School of Engineering, University of Santa Clara, Santa Clara, California 95053 (Receiued: September 30, 1985)
A detailed analysis of the valence molecular orbitals of cis- [Pt(NH3)$12] is presented. Ground-state results for the relativistic
D i m scattered wave (DSW) calculationsand its nonrelativistic limit (DNR (c = m)) together with the nonrelativistic SchrGdinger multiple scattered wave (MSW) results show the importance of relativistic effects in this molecule. The analysis yield interesting features; e.g., relativistic effects increase the relative splitting between levels containing significant 5d metal character. The Pauli decomposition for the orbitals showing large contributions from metal atoms suggests that spin contaminations are significant. Furthermore, the established MOs reveal that L 5d(Pt) donation is low in comparison to L 6p(Pt) donation so that metal p orbitals play a fundamental role in the bonding scheme for this molecule. Contour maps for the relativistic HOMO level show the existence of a Cl-C1 bonding region and suggest that an almost neutral ligand C12 molecule exists in the complex, its free molecular electronegativity value is drastically reduced, and the Pt atom is responsible for this result.
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I. Introduction Over the past decade, the chemistry of the simple inorganic molecule cis- [Pt(NH3)2C12],cis-DDP, has undergone explosive growth, much of it due to the fortuitous discovery of its anticancer activity.’ Its planar structure has been known for over a century, and its synthesis, physical properties, and reactions are continuously revised.2 Despite these extensive efforts to understand its chemistry, little work has been done concerning its electronic ‘Current address: Department of Chemistry, Simon Fraser University, Burnaby, B.C., Canada, V5A 1S6.
0022-3654/86/2090-4491$01 S O / O
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structure and bonding properties. The review of Gray3 in 1965 followed a SCF-X, study4 that was without success in both interpreting the spectral data and answering the question whether ordinary nonrelativistic quantum mechanical methods are appropriate for this molecule containing heavy atoms whose spin(1)Romberg, B.; van Camp, L.; Trosko, J. E.; Mansour, V. H. Nature (London) 1969, 222, 385. (2) Lippard, S. J. Science 1982, 218, 1075. (3) Gray, H.B. In Transition Metal Chemistry, Vol. 1, Carlin, R.L., Ed.; Arnold: London, 1965. (4) Barber, M.; Clark, J. D.; Hinchliffe, A. J . Mol. Struct. 1979,57, 169.
0 1986 American Chemical Society
