General discussion

摘要

Faraday Discuss., 1993,96,67-93 GENERAL DISCUSSION Dr. A. Hopkinson (IBM Research Center, Sun Jose, USA) opened the discussion: Regarding the comparison between an adsorption event, in which phonons propagate into the bulk from the impact site characterised by the adsorbate located in a ‘dent’ on the surface, and desorption; I do not agree that the reverse process of desorption, in which the solid lattice first deforms so that the adsorbate sits in a dent on the surface before one or more phonons converge at the adsorption site resulting in desorption, is in anyway unphysical or is in anyway not the exact time-reverse of the adsorption process. Dr. J. Harris (IFF der KFA Jiilich, Germany) replied: If I understand the thrust of your objection here it would seem the point you have missed perhaps is that, in the sticking event, which believers in detailed balance via microscopic reversibility regard as reciprocal to a desorption event, the initial dent in the lattice and the subsequent healing of the lattice can often, but not always, occur on quite different timescales.Prof. J. C. Polanyi (University of Toronto, Ontario, Canada) asked: In your calcu- lations on the effect of methane translational energy on the cross-section for the reaction CH; surface, did you also explore the effect of vibrational excitation in the CH4? I mention this since you have made the nice point that inclusion of surface recoil on impact has the effect of shifting the location of the crest of the energy barrier on the potential-energy surface (PES).You went on to say that in a case where this shift was to a Eater position along the reaction coordinate the inclusion of recoil led to a smaller probability for reaction. If, however, you rely on reagent vibration to provide a major fraction of the energy required for barrier crossing then this same shift in barrier crest due to surface recoil should enhance the reaction probability. Is it known whether this is the case? Dr. J. Harris responded: There is the usual vibrational enhancement you get in entrance-channel activated desorption that devolves from the kinds of energy diagrams that govern these processes. The enhancement has been demonstrated experimentally for CH4 dissociation on several metal substrates, and its magnitude is given roughly cor- rectly by the theory.The dependence of the effect on incident energy did not come out quite right so there are some details missing, but there is no reason to believe that we are missing anything of central importance. As a general comment in this context, I should say that the very nice clear-cut picture you have set out for gas-phase reactions, with early and late barriers accessed preferentially by translational and vibrational energy, does not quite translate through to the kinds of surface reactions we are discussing here. This is because of the broaden- ing of the levels at a metal surface. In the gas phase you can think in terms of decoupled coordinates in entrance and exit channels with a coupling region about the ‘seam’ that may have an extent that is less than 0.1 eV.On the surface however, this region will usually be of extent ca. 1.0 eV or more. This means that the behaviour of the system cannot be deduced from the PES near the seam but depends on couplings that occur as much as 1.0 eV away, basically spanning the entire energy diagram. In such a case the kind of seam you have and the exact placement of the saddle point on it does not give a unique guide as to how the system behaves because the coordinate couplings do not switch off fast on either side. A particularly cute illustration, easy to demonstrate on a suitable low-dimensionality diagram, is the manner in which a molecule with lots of vibrational energy but very little translational energy can nevertheless ‘climb’ a hill which appears to be predominantly 67 General Discussion ‘in’ the translational coordinate.As the system traverses the PES in the vibrational direction, sufficient vibrational -+ translational energy transfer occurs per pass to carry the system one stage further up the hill. You then get ‘positive feedback’, or what I have tried to dub ‘bootstrapping’, so that once the process has started it keeps on going until the seam is crossed. The hallmark of this kind of behaviour is a rather sharp threshold in incident translational energy below which an incident molecule is backscattered, having apparently interacted with the surface only very weakly, and above which the molecule dissociates.What you see in the gas phase is then at first sight quite puzzling. As the energy increases the molecules first scatter as from a mirror, then suddenly they disappear as though the mirror has become a perfect sink. Even in such cases, however, as seems to be generally observed in dissociation at metal surfaces, vibrational energy is less effective than translational energy in promoting dissociation; that is, if you have E of energy available then it is better to put all of this in translations than to divide it between translations and vibrations. Drs. D. J. Auerbach, C. T. Rettner and H. A. Michelsen (IBM Research Center, Sun Jose, USA) said : Your lecture addresses many interesting and controversial issues and will surely provoke much lively discussion.Let us begin by taking up one such issue, the question of the applicability of the principle of detailed balance. The paper stresses that there are severe limitations of the applicability of the principle of detailed balance to dynamics at the gas/solid interface. We agree that this principle should not be applied to all non-equilibrium systems. However, we believe that it can be usefully, and accurately, applied to relate a wide variety of adsorption and desorption data. In fact, the particular case discussed, that of the trapping and desorption of atoms is the very area where detailed balance has found its broadest application and longest list of There are two ways of reading your objections: 1. Detailed balance should not be applied to treat scattering experiments since it is not correct.2. Since, if detailed balance is not rigorously correct for gas-solid interactions under the conditions of molecular beam experiments, ‘tests’ of detailed balance are not partic- ularly interesting. If it works, it works; if it does not work it does not work. There are no interesting theoretical issues. We disagree with both of these statements. Indeed, it is well known that what is generally understood by the principle of detailed balance is noi rigorously applicable to dynamics at the gas/solid interface. There are quite fundamental objections. Wenaas’ for example, has pointed out that detailed balance requires both time-reversal invariance and invariance under reflection of spatial coordinates.The later symmetry is broken in particle-surface collisions. This is, however, a ‘straw man’, since this principle would, in any case, only be valid under equilibrium conditions. A closely related relationship, the principle of reciprocity, can be applied to derive the relationships relevant to gas-surface collisions, but this principle is again only valid at equilibrium. Even this principle, then, tells us little about what to expect for a non-equilibrium system. Instead, we must turn to considerations of time- reversal symmetry and the principle of microscopic reversibility, which are more gener- ally relevant to gas-surface studies under non-equilibrium conditions. The debate is not, then, about whether the principle of detailed balance applies to non-equilibrium surface science experiments. We agree that it does not.Rather, we are concerned with whether the recipe generally used to compare adsorption and desorption phenomena is valid. When ‘the principle of detailed balance’ is applied to gas-surface interactions, we are assuming that the energy distribution of a species leaving the surface with energy E in quantum state n is given by: f(n, E) dE = S(n, E)P(n, E) dE General Discussion where S(n, E) is the energy dependence of the adsorption probability of the species in state n, and P(n, E) is the relative population of this state with energy E. Eqn. (1) is identical to what would be predicted by the principle of detailed balance (were it valid for gas-surface interactions) and to what would be predicted using the principle of reciprocity for a system at equilibrium.The issue at hand, however, is to understand under what conditions eqn. (1) is valid for a non-equilibrium system. Grimley and Hoiloway4 have shown that trapping and desorption can be rigorously related to each other under non-equilibrium conditions; as a consequence of the time- reversal symmetry of the relevant wavefunctions. This prescription is also supported by detailed experiments concerning trapping4e~orption.~.~ In our paper, we have related recombinative desorption to activated dissociative chemisorption. Specifically, we have measured quantum-state-specific kinetic energy distributions of D, desorbing from Cu, which we have analysed uia eqn.(1) to obtain the corresponding quantum-state-specific adsorption probabilities. We have found that these inferred adsorption probabilities are fully consistent with detailed (non-equilibrium) adsorption measurements. So detailed balance holds for this system as well. We can certainly imagine circumstances under which eqn. (1) would not be expected to hold, whereupon detailed balance would not work. One key point is that the system under study must be fully reversible at the temperature of the experiments. Irreversible chemisorption e.g. of 0, on tungsten, could not be addressed using eqn. (1); nor could systems involving sputtering or damage to the surface. We also believe that the states of the surface species must follow a canonical distribution of energy characteristic of T,.If this distribution were perturbed, (yielding a distribution of states that differ significantly from equilibrium) then again detailed balance would not apply perfectly. We fully agree with Dr. Harris that such deviation would hardly be earth shaking. However, the issue of the precise circumstances and magnitude of deviations from detailed balance, seems to us to be a very fertile ground indeed for further investigation. In the example of the D, interactions with Cu discussed in our paper, eqn. (1) enables us to obtain details of the rotational state dependence of adsorption that we could not otherwise obtain. To allow the application of detailed balance to a wide variety of other systems, we need a better knowledge of the accuracy of this method under a wide variety of conditions. We believe that further theoretical studies and simulations can potentially shed much light on this important issue.1 E. P. Wenaas, J.Chem. Phys., 1971,54376. 2 E. W. Kuipers, M.G. Tenner, M. E. M. Spruit and A. W. Kleyn, Surf. Sci., 1988,205,241. 3 C.T.Rettner, E. K., Schweizer and C. B. Mullins, J. Chem. Phys., 1989,90, 3800. 4 T.B.Grimley and S. Holloway, Chem. Phys. Lett., 1989, 161, 163. Dr. J. Harris replied: I think my position on detailed balance is more clearly set out in my paper than it is in either of the two ‘ways of reading’ you do not agree with. To be concrete, my objection to the use of detailed balance in your own work refers to the notion that you can by these means ‘obtain’ quantities which ‘otherwise you could not obtain’. In my view, this involves a slight self-deception, at least it does if the word obtain is interpreted to mean measure.Since eqn. (1) is not a rigorous law in a non- equilibrium situation, we can refer only to whether deviations from it are large or small. If you establish that these deviations are small, in some restrictive, illustrative or aver- aged sense, with respect to a given system (which you have indeed done for the D,/Cu data), it is still a hypothesis that they remain small when applied to other situations. The results you obtain, on the basis of eqn. (1) holding in situations where you have not shown that it holds, may seem to you to have the force of ‘data’, but some aspects of them seem rather suspect from the theoretical point of view. I am not wishing the fol- lowing scenario on you, or predicting it, but it would not surprise me unduly if the last word with regard to some of your conclusions has yet to be spoken.If this does turn out General Discussion to be the case, then will we all get subjected to a fresh batch of papers reporting on the ‘surprising failure of detailed balance in H,/Cu scattering’? Yet another paper tiger slain ! In my opinion, the raw scattering data on the H,(D,)/Cu system that you present in your papers are quite outstanding and it is unnecessary and even retrograde to attempt to interpret them in terms of a vague quasi-thermal ‘theory’ that you yourself agree is not rigorous under the conditions that prevail in the experiment.Dr. S. Holloway (Uniuersity of Liverpool) communicated: You observe that on Ni(110) the sticking probability is unity, within experimental error, yet an elastic fraction is observed that suggests scattering from a weakly corrugated potential, typical of a physisorption interaction.’ You then pose the question of how a single adiabatic PES can account for these data. The possibility you suggest is that the dissociated fraction moves on the adiabatic ground-state PES while the elastic fraction remains on the non- adiabatic H,/Ni PES. You maintain that this seems quite likely because the reduction in the dissociation barrier (which facilitates the dissociation) is a consequence of s + d electron transfer at the surface and that this is a ‘slowish’ process.Exactly how slow, I wonder? How could one estimate the order of magnitude for remaining on such a non- adiabatic state after the adiabatic barrier has been crossed? An alternative explanation has been previously suggested and dynamical calculations have been performed, albeit for limited dimensionality, in order to quantify the effect., Suppose that the barrier to dissociation is constrained in some coordinate. Detailed calculations on simple metal surfaces have shown that molecules generally have lower barriers in the broadside orientation and also that certain parts of the unit cell have lower dissociation pathways than Restricting the argument to the former (and stronger) of these constraints, let us interpret the data by assuming that 95% represents the fraction of the solid angle (about 8 = 0’) which contains molecules that are in unfa- vourable orientations for dissociation.This implies that all molecules with polar angles in the ranges 0 -= B/degrees 18 and 72 B/degrees 180 could scatter elastically. The consequences of this would be that the scattered fraction would have a massive align- ment.6-8 If, on the other hand, this 5% were to scatter from the non-adiabatic H,/Ni repulsive wall as you suggest, then from measurements of the angular anisotropy on Cu,’ one might expect virtually no alignment in the scattered fraction. Therefore, the experiment that suggests itself is to measure the alignment moments of the scattered flux or perform a post-permeation experiment, measure the alignment and invoke detailed balance.1 H. J. Robota, W. Vielhaber, M. C. Lin, J. Segner and G. Ertl, Surf Sci., 1985, 155, 101. 2 G. R. Darling and S. Holloway, J. Chem. Phys., 1990,93,9145. 3 P. K. Johansson, Surf Sci., 1981, 104, 510. 4 P. J. Feibelman, Phys. Rev. Lett., 1991, 67,461. 5 D. M. Bird, L. J. Clarke, M. C. Payne and I. Stich, Chem. Phys. Lett., 1993,212,518. 6 S. Holloway and B. Jackson, Chem. Phys. Len., 1990,172,40. 7 X. Y. Chang and S. Holloway, Surf: Sci., 1991,251/252,935. 8 S. Holloway and X. Y. Chang, Faraday Discuss. Chem. SOC.,1991,91,425. 9 L. Wilzen, F. Althoff, S. Anderson and M. Persson, Phys. Reu.B, 1991,43, 7003. Dr. J. Harris communicated in reply: There are really two issues here. Possibly, I erred by failing to make this sufficiently clear. The main point I wanted to stress relates to the question of the likely importance of non-adiabatic effects in surface processes. I suggested that if one is really serious about establishing this then there is a simple way of doing it, via the H,/Ni(llO) experiment (or an equivalent). I have not made an esti- mate of the ‘survival probability’ of the initial state in such a case (why is this dramat- ically more difficult than estimating an ion survival probability?) but it is certainly different from zero. Since the s + d transfer process is certainly a slowish process, while General Discussion an H2 round trip is rather fast, this might be thought of as, in some sense, an upper bound for ‘typical’ strengths of non-adiabatic fractions in surface processes.Now, whether or not the coherent fraction observed for Ni(ll0) is due to non-adiabaticity, it does appear to be in the per cent range, which is then ‘an upper bound for an upper bound’, if you will, So I guess I was trying to say, as an additional counterweight to Ronnie KoslofYs position, that, if the data we have available so far are correct, then the issue as to whether the non-adiabatic fraction is large or small may in fact already have been decided (if you believe all the bits and pieces in the argument, and with the restriction to processes with no sharp levels). The other issue is whether or not the coherent fractions that have been observed (for Ni and Pt only, as far as I know) are due to the non-adiabatic effect or to something else like bits of the adiabatic PES that bounce the H, rather than dissociate.I rather favour the non-adiabatic explanation for the case of Ni because it explains very neatly why the elastic fraction looks just as one would expect for a physisorption system. I would not expect ‘smooth surface’ behaviour in the other case (though this may be what low- dimensionality model calculations show). If a careful experimental study shows the strengths of the Bragg beams, as a function of surface temperature and incident energy, continuing to display ‘physisorption-like’ behaviour, then the interpretation would be strengthened.It should also be possible to distinguish between the adiabatic versus non-adiabatic explanation via the sensitivity to surface temperature, as well as via the isotope effect. So I do not think you need to go to the lengths you suggest. What is required in the first instance is measurement of the Bragg peak strengths as a function of T, and Ei, Oi just as in a standard He-diffraction experiment (though some way would have to be found to get rid of the H2 that dissociates). Prof. A. D. Buckingham (University of Cambridge) communicated : You emphasised the importance of polarization forces in the interaction of molecules with a metal surface. You indicated that these arise from a contribution to the electronic wavefunc- tion that can be represented by the transfer of an electron from the highest occupied orbital of the adsorbate to an unoccupied orbital of the metal or from the metal to the lowest unoccupied orbital of the adsorbate.In conventional intermolecular force theory such a contribution would be called a charge-transfer interaction. Polarization is due to distortion of the electronic structure of one molecule by the (non-uniform) electric field of the other; it can be described by a mixing of the occupied and unoccupied orbitals of one molecule due to the presence of the other. In the case of CO interacting with a metal, there will be a polarization of the metal by the electric field of the CO and this gives rise to an ‘image’ force of attraction.How important are such image forces? Is there experimental evidence for charge transfer between an adsorbate and the substrate? Dr. J. Harris communicated in reply: The term charge transfer is usually restricted to cases where the HOMO of one bonding fragment lies higher in energy than the LUMO of the other. Here, the opposite is the case and the partial occupation of the LUMO is governed by potential matrix elements that drive the ‘inelastic hop’. There is, of course, more than one matrix element involved and I can agree that it would be desirable to distinguish between e.g. intra-fragment and inter-fragment polarization. Sometimes the latter is referred to as ‘donation’ cf. the Blyholder picture of CO adsorp-tion with ‘donation’ of metal electrons CO 2n*-orbitals and ‘back-donation’ of CO lone-pair electrons to the metal.However, there does not seem to be any unanimity of nomenclature with regard to polarisation effects in general. As regards the second and third parts of your comment, there are charge displace- ments when molecules like CO are adsorbed on surfaces but these cannot ordinarily be General Discussion interpreted in terms of a charge transfer. The experimental monitor is the change in work function which depends linearly on the change in surface dipole that occurs on adsorption. It is possible to measure this, therefore, but not to convert it to a charge transfer because the extent of the region over which charge displacements occur is typi- cally as large as the bond distance. This kind of situation occurs also in molecules, a classic example being BF, whose dipole moment ‘points the wrong way’ and so, if inter-preted in terms of charge transfer, would imply that the boron atom is more electro- negative than fluorine ! Prof.R. A. Marcus (California Institute of Technology, USA) opened the discussion of Dr. Holloway’s paper: Ideas and results in papers here on the H, + Cu surface reac- tion have much in common as Halstead and Holloway have pointed out,’ with those introduced in the mid-sixties to treat the H + H, +H2 + H gas-phase reaction, with terms such as vibrational adiabaticity,’ local reaction path curvature, K(S) and (transverse) vibration frequency w(s),~ as seen in various papers in this Discussion.Some other ideas introduced for gas-phase reactions3 might also be extended to the H, + Cu reaction. For example, action-angle variables can be defined not only for vibrations, J, , but also for the 8 and the cp rotations, e.g. the actions J, and J,. Using the relevant canonical transformation one can then calculate these quantities from the coordinates and momenta along a classical trajectory. In this way adiabaticity and deviations from it could be explored. In particular, some rotational motions evolve into vibrations or into hindered rotations. A rather approximate formula connecting them has been suggested earlier,3 and its applicability to the present system could be studied. Rotationally non- adiabatic effects would be reflected in deviations from the formula. One trend noted in some of the present papers and seen earlier in classical trajectory studies of the H + H, reaction is the decrease, at low H, rotational angular momentum J, in the collision effectiveness with increase in J. This behaviour was interpreted earlier in terms of a statistical factor: closely spaced rotational energy states of H, evolve into more widely spaced bending vibrational states of the transition state H-H-H.This effect, well known in transition state theory, is described there in terms of ratios of partition functions and is a statistical way of describing steric hindrance effects (orientation requirements) : restricted orientation in the transition state corresponds to more widely spaced energy levels for that motion and to a smaller transition-state parti- tion function.A similar effect appears to occur in the H, + Cu reaction. A key question regarding further information on rotational effects concerns the rela- tive role of the J, (cartwheel) and J, (helicopter) motions in explaining the trends observed on the dependence of sticking and desorption coefficients on the rotational state. An experimental answer to this question would be obtained when one is able to measure the polarization of the rotating H, and D, molecules in the desorption experi- ments or the dependence of sticking on the polarization. 1 D. Halstead and S. Holloway, J. Chem. Phys., 1990,93, 2859. 2 R. A. Marcus, J. Chem. Phys., 1965,43, 1598. 3 R.A. Marcus, J. Chem. Phys., 1966,45,4500; 1967,46,959; 1968,49,2618. Dr. Holloway replied: It would indeed be possible to employ action-angle variables to good use in surface reactions. I intend to explore such avenues in the near future in a series of classical dissociation studies. I am, however, pessimistic when it comes to H, and D, dissociation: I believe that the quantum nature of the dynamics will prevail. Prof. Marcus communicated: This point on quantum effects is an interesting and important one : Certain quantum effects, namely nuclear tunnelling and quantum mechanical interference, are not captured by classical trajectories, though the former is General Discussion sometimes estimated approximately by extension to the complex plane, such as that in the so-called ‘Marcus-Coltrin’ path and in its descendants due to Truhlar, Garrett and co-workers.A different quantum effect is that in an adiabatic process, in which a change in vibrational energy, (n, + $)h(vi-vr), can be used to overcome (or, if adverse, increase) the energy barrier to reaction. In a vibrationally adiabatic process this energy difference is reproduced by a classical trajectory, namely by Ji(vi-vf), where J, is the action variable of the ith vibration, vi is the frequency of that vibration in the reactants, and v’ is its value in the transition state. [J, = (n,+ f)h]. Prof. Polanyi addressed Dr. Auerbach and Dr. Holloway: Dr. Holloway has present- ed some interesting new results on a quantum calculation of the effect of reagent rota- tion on reaction probability using a ‘late’ energy-barrier PES.He anticipates a convergence of these findings with the classical theory of the same phenomenon. On his PES there is a significant effect of reagent rotation on the probability that H, reacts with Cu( 11 1). The effect is twofold, and qualitatively mirrors that observed experimentally in gas- phase exchange reactions some years ago by means of infrared ‘chemiluminescence depletion’. Similar behaviour has also been found in crossed-beam experiments.394 The characteristic dependence of reaction probability and rotational quantum number, J, of the molecule whose bond is being severed is an initial decline followed by an increase. Ref. 2 suggests possible contributing factors.In the initial region of declining reaction probability the effect of increased J appears likely to be a decrease in the time that the molecule under attack spends in a favourable alignment for reaction with respect to the attacking gas atom or, in the present case, surface atom. This ceases to be important at high J when the molecule enters and leaves the preferred orientation many times in the course of a reactive encounter, becoming a ‘blur’ as seen by the attacking gas atom or surface atom. This would be expected to happen at lower values of J for longer approach times (lower collision energy). At high J, rotational energy will, for the first time, become significant in terms of the energy barrier to reaction. On a late-barrier (endoergic) PES the vibrational-rotational interaction will cause the bond under attack to stretch.This stretching (vibration) will be helpful in crossing a late barrier. This is not to say that this second effect, which causes reaction probability to increase with J, can only be conceived of as occurring on surfaces having a late barrier. If the relative timing of approach [e.g. BC(J) approaching a surface, S, to give disso- ciative adsorption] to rotation is correct, then the rotational motion should contribute to the compression of the B-S or C-S bond with resultant enhanced barrier crossing on an ‘early’ barrier surface. It is evident that the ratio of the approach time (B-S or C-S decreasing) to the rotational period (B-C executing a rotation in state J)is likely to play a crucial role in determining the contribution of rotation to reaction, in the gas or at the surface.These various points were discussed for a gas-phase reaction in ref. 2. 1 A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi and J. L. Schreiber, Faraday Discuss. Chem. SOC., 1973,55,252. 2 B. A. Blackwell, J. C. Polanyi and J. J. Sloan, Chem. Phys., 1978,30,299. 3 H. H. Dispert, M. W. Geis and P. R. Brooks, J. Chem. Phys., 1979,70,5317. 4 M. Hoffmeister, L. Potthast and H. J. Loesch, Book of Abstracts, XIZ, International Conference on the Physics of Electronic and Atomic Collisions, Gatlinburg, 1981. Drs. Rettner, Michelsen and Auerbach replied: We agree that there are strong simi- larities between our observations of the effect of reagent rotation on the reaction prob- ability of H, and D, at a Cu(ll1) surface and your earlier observations on gas-phase reactions. The analogies with gas-phase reactions are very instructive and have helped to Genera1 Discussion guide our approach to surface reaction dynamics. The explanations that we, and others, have offered to account for the role of rotation in dissociation dynamics are very close to your qualitative description of the role of rotational motion in A + BC reactions.One minor difference is worth noting, however. We do not believe that the incident molecule becomes a ‘blur’ until very high J. A D, molecule in J = 6 rotates only 40” during the time it would take to move forward 0.5 A at 0.6 eV, even in the absence of steric hindrances to rotation.The study of gas-phase reactions is generally more advanced than that of gas/surface reactions because of the added experimental difficulties of dealing with the surface case. The hydrogen/Cu system is the gas/surface system for which we have the most detailed knowledge. Let us take this opportunity to brag about the progress in surface chemical dynamics. Note that we have obtained not only the dependence of reactivity on reagent rotation, but also the dependence on reagent vibration and on reagent kinetic energy. This knowledge of the role of all three forms of energy is in fact the basis of the present study and allows us to ‘understand’ the thermal chemistry in microscopic terms.Drs. G. R. Darling and S. Holloway (Unitlersity of Liverpool) communicated in reply to Prof. Polanyi: We would like to thank Professor Polanyi for drawing our attention to useful references to a similar phenomenon in the gas phase. It is true that if the molecule rotates many times in an encounter with the surface it will appear to be a ‘blur’. For light diatomics, however, this would be equivalent to a very high J-state indeed. For instance, an H, molecule in the J = 10 state with 0.5 eV translational energy rotates only once in the time taken to travel 3 au, clearly not enough to become ‘a blur’. The rotational energy can be of assistance in overcoming an early barrier as out- lined, however, this effect occurs only for very particular initial conditions, which in all likelihood have very small measure in phase space.Prof. P. Tetenyi (Institute of Isotopes, Budapest, Hungary) addressed Dr. Auerbach : I would like to ask about the possible interpretation of the numerical values of the pre- exponential factor. It seems we are faced, presumably, with a compensation between the pre-exponentials and the activation energies: comparison of data from Fig. 4 and 9 of your paper indicates values of E of 0.44 and 0.607 eV while the respective In A values are -2.813 and 0.27. A compensation between the energy and entropy factors of the activation, a widely discussed, but not quite understood phenomenon, can take place. Would you please comment on this? Drs. Rettner, Michelsen and Auerbach responded : Compensation effects are said to occur when the pre-exponential factor and activation energy of a given reaction change in such a way as to have opposite effects on the reaction rate. Thus a reduction in the pre-exponential factor can partially offset, or compensate, the effect of decreasing activa- tion energy.In surface science, such effects are often seen in studies of reaction rates as a function of surface coverage, for example. In the context of our calculations for the D,/Cu( 11 1) system, one must first ask what it is that is to be changed, in order to look for compensation effects. The results that you mention do indeed show a compensation effect of sorts. The activation energy and pre-exponential factor obtained from the slope of the Arrhenius plot of Fig.4 are both smaller than those obtained from curve of Fig. 9(f). However, we would not consider this behaviour a true compensation effect. Rather, it is a manifestation of the fact that the plots are curved. The effect that you refer to can be understood by studying Fig. 9 in detail. The different lines have very different curva- tures. For molecules in a single v-J state, when E, + W,we obtain a straight line with slope equal to E, and intercept equal to In (A).When E, and W are comparable, the plots are curved. Over a limited range of temperatures, these curved plots would give General Discussion smaller activation energies and pre-exponential factors. The intercept (at 1/T = 0) would, however, be the same.Prof. K. Kunimori (University of Tsukuba, Ibaraki, Japan) said: Some people believe that hydrogen chemisorption on metals is a structure-sensitive process; i.e. the sticking probability depends strongly on the surface structure of metal crystals. It seems to me that, in your calculation, you consider such effects only by using the width parameter [W in eqn. (7a)l. What about the active sites on the metal surface? (1) What do you think about the effect of stepped sites? Even if you use the flat Cu( 11 1) surface, some defects, including steps, may be present on the surface. (2) What about the more open Cu surfaces or the stepped surfaces? (3) In your study using the flat Cu( 11 1) surface, your conclusion is that the translational energy is important, while vibrational and rotational energies are relatively unimportant.However, if you think about the effect of active sites in more detail (as a chemist), you would expect that the rotational and/or vibrational motions of the molecule are also important for the disso- ciative adsorption on some active sites. In conclusion, I do not think it would be sufficient to elucidate the mechanism and dynamics of the dissociative chemisorption in detail using only the parameter W in your calculation. Drs. Rettner, Michelsen and Auerbach replied: We do not believe that defects on our Cu(ll1) sample play an important role in our measurements. The reason is simple. We observe sticking probabilities below lop6.As you correctly point out, the surface must have a substantial number of step sites and other defects. If the sticking probability were strongly enhanced at these sites, we would not observe such small sticking probabilities.The following observations support this view. As part of a closely related study of H, dissociation on the Cu(ll1) surface, we accidentally measured the sticking on a surface that had been sputtered at 100 K, but not annealed. For Ei = 0.3 eV, the sticking prob- ability was found to be ca. 0.002, which is indistinguishable from the measurement on the annealed surface. The surface damaged in the former case was evident from the fact that the shape of the TPD spectrum for H, desorption looked quite different from that for the annealed surface. More generally, we must certainly agree that the reaction probability may depend on the site or impact point.Further, the reaction may have different behaviour on different faces of Cu. We have so far only made measurements on Cu(l11). Our measurements are simply an average over the impact sites within the unit cell. This average will affect the width of the adsorption function, W,as you suggest. This, however, is not the only effect of averaging over sites. Different sites probably have different effective barriers, which would be represented via the E, parameter of the adsorption functions. If some sites have much higher barriers, the saturation value of the sticking probability will be reduced. This effect would be represented via the A parameter in the adsorption func- tion.Thus all of the parameters in the adsorption function are likely to be influenced by the effect of different sites on the surface. Your speculations that the role of vibration or rotation might be increased at certain active sites are interesting. Perhaps experiments on other, more open faces of Cu will reveal such effects. Prof. 6. D. Billing (University of Copenhagen, Denmark) said: The point I wish to raise is that the sticking probability is strongly site dependent. We find in our D,/Cu calculations variations in the dissociative sticking probability of ca. 15 orders of magni- tude as a function of where the molecule hits the surface within the unit cell. Thus, in principle, we have an infinite number of activation barriers.Is there any hope that from General Discussion experimental data one can obtain information on the site dependence of the activation barrier ? Drs. Rettner, Michelsen and Auerbach replied: The results of our experiments are simply the sum over the contributions from different sites or impact points on the surface. We have no way of controlling the impact site experimentally. Thus the simple answer to your question is no, there is no direct experimental way of obtaining the site dependence. We may hope to gain some insight into this question from comparison with theoretical studies, such as your own, and by studies on different surface orientations. Dr. K. W. Kolasinski (Fritz-Haber-Institut, Berlin, Germany) said: I would like to return to the discussion of detailed balance.As we have seen in the work of Auerbach et al., the H,/Cu system is an example where this principle works beautifully, even under non-equilibrium conditions. The adsorption and desorption results are perfectly consis- tent and detailed balance can be used to synthesize the desorption results from the adsorption data and vice versa. However, I would like to present some recent results which apparently contradict detailed balance or, more accurately stated, contradict the common perception of detailed balance. As Prof. Harris stated, adsorption and desorption correspond to two regions of con- figuration space which need not necessarily have perfect overlap. At equilibrium this overlap is perfect.Indeed, it must be, as the principle of detailed balance is one of the foundations of chemistry and it must hold at equilibrium. But what if the initial condi- tions of the desorption experiment are not related to the initial conditions of the adsorp- tion experiment by a simple equilibrium in the molecular coordinates? In this case we cannot predict the properties of the desorption distribution based on the results of adsorption experiments. This is not a contradiction of detailed balance. It is, however, a case in which it is invalid to apply detailed balance as is commonly done. For the H,/Si system, we have results which appear to contradict detailed balance. Specifically, my co-workers and I at Stanford have measuredlP3 the internal state dis- tributions of H, , HD, and D, thermally desorbed from Si(lO0) and Si(ll1).In Berlin we have measured4 the translational energy of D, desorbed from Si( 100) and Si( 11 1). This enables us to sum the internal and translational energies of desorbed D, in order to determine the height of the saddle-point in the desorption transition state. This value should be closely related to the activation energy for adsorption if detailed balance holds. We obtain a value of 40 & 60 meV. This value stands in contradiction to the activation barrier height obtained by the heated nozzle experiments of Ho et aL5 and various calculation^^^^ which estimate a value of 1-2 eV. The low value that we measure is also extremely difficult to reconcile with the estimated sticking coefficient of -c That is, it is difficult to reconcile these diverse data if only the molecular degrees of freedom are considered.For the H,/Cu system, all of the gross characteristics can be explained simply be considering the molec- ular degrees of freedom. We believe that a consistent interpretation of the adsorption-desorption results can be proposed for the H,/Si system without invoking a contradiction of detailed balance, if the surface degrees of freedom are assumed to play an essential role in the dynamics. Because of the highly localized, covalent bonding in the HJSi system, the surface degrees of freedom play a much more active role in the adsorption-desorption dynamics than in the case of H,/Cu. When H atoms are chemisorbed on a Si surface, the surface relaxes and the vibra- tional properties of the surface also change substantially.In a desorption experiment, this allows the system to explore regions of configuration space which are effectively closed channels for adsorption on the clean surface. Some of the channels available in the desorption experiment correspond to low activation barrier events in the molecular General Discussion coordinates. In desorption, the adsorbates can effectively wait until they find favourable conditions for recombination and it is these low-barrier pathways that we observe. In adsorption, it is highly improbable that the low-barrier configurations present them- selves to an incident molecule because they are not within the range of normal thermal excitations of the clean surface.Furthermore, during the impulsive collision between an incident hydrogen molecule and the surface, the molecule can neither force the surface into the proper configuration (due to the mass mismatch) nor can it wait around for the surface to readjust and attain a favourable configuration. Therefore, only the high- barrier pathways are probed in the adsorption experiments. In summary, since the initial conditions of adsorption and desorption experiments are so different, in particular, because the surface configuration is so different in the two experiments, it is not valid to apply the principle of detailed balance to the observation of activated adsorption and to conclude that the desorbed molecules must have a highly energetic, non-equilibrium distribution.That is, detailed balance cannot be used carte blanche to relate adsorption and desorption distributions if the degrees of freedom of the surface play an integral role in the adsorption/desorption dynamics. There may be a substantial activation barrier for this system. However, if such exists, it is in the coordi- nates of the surface atoms and, therefore, it is impossible to probe its energetic nature directly on the basis of desorption product distributions. 1 K. W. Kolasinski, S. F. Shane, and R. N. Zare, J. Chem. Phys., 1992,96,3995. 2 S. F. Shane, K. W. Kolasinski, and R. N. Zare, J. Chem. Phys., 1992,97, 1520. 3 S. F. Shane, K. W. Kolasinski, and R. N. Zare, J.Chem. Phys., 1992,97, 3704. 4 K. W. Kolasinski, W. Nessler, A. de Meijere and E. Hasselbrink, Phys. Rev. Lett., submitted. 5 W. Ho, personal communication. 6 C. J. Wu, I. V. Ionova, and E. A. Carter, Surf. Sci., 1993, 295, 64. 7 2. Jing and J. L. Whitten, J. Chem. Phys., 1993, 98, 7466. Drs. Rettner, Michelsen and Auerbach replied: You have raised a number of inter- esting points. First, let us consider your new results for the HJSi system. We do not accept that you have shown that detailed balance does not work for this system. In order to compare adsorption and desorption experiments, the two processes must be related quite precisely. The velocity distribution in desorption at a given angle can be obtained from detailed balance if the curve for the adsorption probability, as a function of kinetic energy, is known for that angle.What appears to be known for this system is that the adsorption probability is small for all energies up to ca. 1 eV. What curve should be used to predict the velocity distribution for desorption? One that is rigorously zero until 1 eV? We need to know the numbers. Since the form of the velocity distribu- tion in desorption predicted from detailed balance is insentitive to absolute adsorption probabilities, it is only the shape of the adsorption curve that matters. For example, regardless of how small the adsorption probability is, if the probability is roughly constant at all kinetic energies up to 1 eV, we would expect a roughly Boltzmann distribution for desorption. In order to comment further, one needs the actual form of the adsorption curves.In addition to using the actual form of the adsorption curve, one should use the curve appropriate to the actual desorption conditions, including surface temperature. You state that: ‘In adsorption, it is highly improbable that the low-barrier configu- rations present themselves to an incident molecule because they are not within the range of normal thermal excitations’. Since the range of normal thermal excitations depends critically on the actual surface temperature, we need to know absolutely the dependence of the adsorption probability on kinetic energy for the surface temperature employed. Curves for lower surface temperatures (even guessed ones) should only be used very cautiously.These arguments notwithstanding, we agree that detailed balance cannot be used to relate adsorption and desorption in a totally general manner (see our comments on Dr. General Discussion Harris’s paper). In particular, detailed balance should not be applied to systems that would not exist under equilibrium conditions. But we are not aware of any reason why the H,/Si system should not follow this principle. In our opinion, careful application of the principle of detailed balance will be shown to hold for this system. The comparison must await measurements of the adsorption probability us. kinetic and internal energy under the conditions used in your desorption measurements. Prof. M. Rocca (University of Genova, Italy) commented: I should like to mention in this discussion on detailed balance that the surface can be strongly modified by adsorp- tion.In particular, I suggest that much can be learned from the 0, interaction with Ag, Pd and Pt where dissociation is observed only above a critical temperature, K,of the order of 150 K. It has been demonstrated experimentally that increasing translational energy does not help in overcoming the barrier of dissociation [in Genova for O,/Ag(llO) and in San Jose by A. Luntz for O,/Pt(lll)]. We have evidence for OJAg(l10) that the effect is connected to the onset of a local roughening of the surface which is closely related to the dissociation process and which is inhibited for tem- peratures less than T,.In the theoretical description of the chemisorption process one should therefore consider the possibility of a temperature-dependent PES. Dr. Holloway responded: I think that it is possible to conceive of trajectories in scattering that will never give rise to dissociation no matter how high the initial kinetic energy is raised. The timescale for a trapped particle to dissociate via a thermal mecha- nism is so long (approximately lo1, times as long as a scattering event) that in this time it will explore a sufficiently large region of phase-space to find the requisite ‘hole’ through which to pass and dissociate. Dr. J. Harris communicated in response to Prof. Rocca: You are quite right to say that large scale changes akin to surface phase transitions can have a strong influence on the kinds of trajectories that contribute to, in particular, desorption phenomena.Any cooperative motion of the surface will influence the desorption of adsorbed particles in a way that would not be mirrored in the concomitant sticking process. This is especially clear cut in the case where the cooperative motion is in some sense ‘adatom induced’. Here you have quite obviously a situation where the desorption and sticking processes access quite different regions of phase space. Prof. S. Stolte (Vrije University, Amsterdam, The Netherlands) addressed Dr. Auer- bach: Your paper, in which you extract from experimental data on quantum-state-spe- cific dynamics the thermal rate of adsorption for the D2/Cu( 11 1) system for T = 300 to 1000 K triggers also for me the dzbated view-point of detailed balance and micro- reversibility. Are we really ready to wave the flag for the H, ,D2/Cu( 11 1) system, i.e.are there currently experimental data available confirming on thermal systems your results as shown in Fig. 4 and 5? Drs. Rettner, Michelsen, and Auerbach replied: It is not possible to make a detailed comparison with thermal data on the rates of dissociative adsorption for two reasons: 1. The results discussed here are on D, interactions with Cu(ll1) while the thermal data is for H,. We have made measurements for H, but have not yet completed the kind of analysis reported here. 2. There is a lack of modern high-quality thermal adsorption measurements on well characterized single crystal surfaces. Prof.Marcus asked Dr. Kolasinski: In your description of a lack, or possible lack, of microscopic reversibility in the Si + H, system, was the desorbed H, typically formed in a vibrationally excited state? If so, in the reverse process, was the sticking of the incom- General Discussion 79 jng H, also studied as a function of vibrational state of the H,? If not, it would appear that the experiments do not yet test microscopic reversibility. Dr. Kolasinski replied: In our experiments at Stanford, we did indeed find an enhanced population of v = 1, ca. 20 times greater than the thermal expectation at the surface temperature. This amounts to ca. 8% of the total population being desorbed in v = 1 for D, and 1% for H,.The adsorption of H, on Si(100) has been investigated by Ho's group at Cornell. They used molecular beams produced with the aid of a heated nozzle. Such a source produces a beam which is translationally as well as vibrationally hot. The amount of vibrational excitation which they could achieve was comparable in magnitude to that which we observed in desorption. They observed no sticking which could be attributed to the interaction of molecular hydrogen with the surface. An experiment in which a vibrationally excited state has been prepared spectroscopically and scattered from the surface, such as that for the H,/Cu system performed by Hodgson et al.', has yet to be carried out for the H2/Si system. 1 A. Hodgson, J.Moryl, P.Traversaro and H. Zhao, J. Phys.: Condens. Matter, 1991,3,5217. Dr. Holloway asked Dr. Auerbach: How can I begin to reconcile the fact that I believe that (J, m,) states will have dissociation functions S (Ei, J, m,) that depend critically upon m, and yet the shape of the experimentally determined S(E,, J) appears to be independent of J? Drs. Rettner, Michelsen and Auerbach replied: You raise a very interesting and important question. We do not fully understand why our observed adsorption functions seem to have the same width, W, and saturation value, A, independent of J. One might speculate that this behaviour is related to a strong anisotropy which mixes different M states, but this is only a loose speculation. Further work is needed to resolve this ques- tion.Prof. D. A. King (University of Cambridge) addressed Dr. Auerbach and Dr. Hol- loway: My comment relates to the problem of detailed balance in relation to adsorption and desorption processes. I wish to give three very different examples, each illustrating the care with which the principle must be applied. 1. Some years ago, we' reported angle-resolved thermal desorption data for N, from W{110}, which was shown to exhibit a lobular distribution which was attributed to a barrier for the dissociative adsorption process of 17.4 kJ mol -Subsequently, Auerbach and coworkers2 studied the adsorption process using a supersonic beam source, and reported a variable adsorption barrier, averaging 41 kJ mol- ', apparently contradicting our work.However, in the desorption process molecules adsorbed on the surface select the lowest available activation barrier, whereas in the adsorption process both the molecular orientation and the point of impact at the surface are random, and many unfavourable collisions are sampled. Indeed, the data of Auerbach and co-workers2 clearly show a threshold for the adsorption process at ca. 17 kJ mol-l, in very good agreement with the desorption data.3 2. Recently we have attempted to adsorb N2 dissociatively on Pt{ 1001 [(hex-R) and (1 x l)] using a supersonic beam source, and we had no success at all, even up to beam energies of 3 eV obtained using a hot nozzle and helium ~eeding.~ However, when Pt is heated in ammonia, decomposition to gaseous N, is observed, implying that there should be a dissociative adsorption path.Detailed balance is, however, maintained. Thus, Foner and Hudson' measured the vibrational state distribution of N, formed during NH, decomposition over Pt at 1000°C, and report that N, is desorbed with v 3 5, leading to a zero sticking probability regardless of translational energy for vibra- tionally cold N, . General Discussion 3. Adsorbate-induced surface restructuring raises the question of the proper sticking probability to be used in applying detailed balance to a desorption process, where the surface restructures during or after desorption. This can be a very large effect. For example, the Pt(100) clean surface is stable with a hex-R 0.7" reconstruction; the 0, sticking probability on this surface at thermal beam energies is ca.3 x 10-l4; but on the metastable (1 x 1) surface it is ca. 0.2.6 Since the (1 x 1)-+ hex-R 0.7" transition is rather slow, in this case desorption would (temporarily) leave a (1 x 1) surface, and the proper value for s is therefore likely to be 0.2, and not 3 x I believe that this example is relevant to the problem raised by Dr. Kolasinski. There are no situations where detailed balance is flouted, but the details may some- times be obscure. 1 R. C. Cosser, S. R. Bare, S. M. Francis and D. A. King, Vacuum, 1981,31,503. 2 J. Lee, R. J. Madix, J. E. Schlaegel and D. J. Auerbach, Surf Sci., 1984,143,626. 3 R. Raval, M. A. Harrison and D. A. King, in The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, ed.D. A. King and D. P. Woodruff, Elsevier, Amsterdam, 1990, vol. 3A, p. 39. 4 X.-C. Guo, J. Bradley and D. A. King, unpublished results. 5 S. N. Foner and R. L. Hudson, J. Chem. Phys., 1984,80,518. 6 X.-C. Guo, J. M. Bradley, A. Hopkinson and D. A. King, Surf Sci., 1993,292, L786. Drs. Rettner, Michelsen and Auerbach replied: Your examples are all very good illus- trations of the care that must be used in the application of detailed balance in relating adsorption and desorption processes. Indeed, unless care is taken, apparent violations of detailed balance arise. Your first example illustrates this point rather well. In addition to your comments, we note that the N,/W(1 10) desorption data are relevant to the covered surface.These results cannot be related to adsorption measurements on the bare surface. In fact, the adsorption results were found to be almost independent of incidence angle. Applying the principle of detailed balance, we would conclude that the desorbing mol- ecules should follow a cosine distribution, in clear contradiction to the measured desorp- tion angular distributions. We suspect that the lobular distributions result from strong lateral interactions present on the covered surface. Another case that illustrates the care that is needed in applying the principle of detailed balance is that of adsorption and desorption measurements for the H,/Cu system. Adsorption is found to scale quite accurately with the energy associated with motion normal to the surface.This scaling means that the energy required to activate the adsorption process varies strongly with the angle of incidence. Yet, Comsa and David have reported1 that the mean energy of molecules desorbed after recombination is almost independent of the angle of desorption. This behaviour is an apparent contra- diction of detailed balance. A careful examination, however, shows that these desorption results are fully consistent with normal energy scaling for the adsorption and detailed balance., The apparent discrepancy arises essentially because the adsorption does not increase as a step function of the energy of incidence. 1 G. Comsa and R. David, Surf Sci., 1982,117,77. 2 H. A. Michelsen and D.J. Auerbach, J. Chem. Phys., 1991,94,7502. Prof. King communicated in response to Drs. Rettner, Michelsen and Auerbach: I was very interested in your comment on the N2/W{ 1101 system. Certainly, if the adsorp- tion path were the reverse of the desorption path, a sticking probability for dissociative N, adsorption which is invariant with incident angle is only consistent with cosine law desorption. However, I cannot agree with the suggestion that our observation of a lobular (ca. COS~.~0) desorption distribution is due to lateral interactions between adatoms. Firstly, we found a cos 8 distribution for N, recombinative desorption from W/{ 3101, independent of coverage,' despite the clear existence of lateral interactions in the adlayer; the essential difference between (110) and (310) surfaces is that N, disso- General Discussion ciative adsorption is activated on the former but not on the latter.There are many other examples of quasi-cos 8 desorption distributions for systems where the adsorption process is non-activated, even where strong lateral interactions exist, and also of lobular distributions for activated systems. Secondly, since recombinative desorption necessarily involves adatoms moving into neighbouring sites during the process of desorption, it is difficult to see how lateral interactions with the rest of the adlayer would be anything more than a second-order effect on the desorption distribution. Of course, I am not suggesting that detailed balance is violated in this case.Rather, I think that your observation, coupled with ours, remains unexplained. The temperatures at which the two experiments, adsorption and desorption, were conducted are very dif- ferent, and this may be the underlying reason. For instance, a well ordered p(2 x 2) structure, attributed to underlayer adsorption, is only formed after annealing:2 the adatoms may be adsorbed into a less stable overlayer state at lower substrate tem- peratures, whereas desorption occurs from the more stable underlayer state. But clearly, more experiments are needed to resolve this. 1 R. C. Cosser, S. R. Bare, S. M. Francis and D. A. King, Vacuum, 1981,31, 503. 2 C. Somerton and D. A. King, Surf. Sci., 1979,89,391. Dr. E. Hasselbrink (Fritz-Haber-Institut, Berlin, Germany) communicated to Prof.King: Do you mean that, loosely speaking, detailed balance is a nice principle, and that if it does not produce the right results, one only has to think harder to lift the apparent contradiction? This would indicate that the principle is not useful to predict desorption characteristics from adsorption data or vice versa, but rather only allows a check, by comparison of both sets of data, whether all changes of the system occurring upon desorption or adsorption have been considered appropriately. Prof. King communicated in reply: No, that is not what I mean at all. Detailed balance is an excellent tool, but it must be used with care and understanding; and it can be very useful in making predictions.Let me illustrate this by expanding on my N,/Pt{100) example to make a clear prediction. We know from the work of Stoner and Hudson that the associative desorption of N, from Pt produces vibrationally excited N, (v 2 5) only. From detailed balance we therefore predict a finite sticking probability only for gaseous vibrationally excited N, . We have found experimentally in accordance with this, that s = 0 for ground state N, . Now we can confidently predict significant sticking for 2, 2 5. Of course, this is a consequence of time reversal of trajectories. The N,/Pt{lOO} results can be interpreted using the simple PES sketched in Fig. 1, with a so-called late barrier. Because of the height and position of the barrier, any trajectory taken by a desorbing molecule will involve significant molecular vibrational excitations (e.g.trajec-tory A, shown as a full line). An unsuccessful adsorption trajectory, B, is shown as a dashed line. By time reversal we readily see that only trajectories like A can lead to dissociation. Prof. Marcus communicated : In respect of the discussion on microscopic reversi- bility, I would like to add a few remarks which supplement those already present' in the literature. Suppose we consider for the sticking experiment an incident beam of molecules with known velocity, known angle of incidence to the surface, and in a known internal state (rotational-vibrational-electronic) or in a known distribution of internal states. We con- sider a desorption experiment for a solid sparsely populated with the absorbate, and consider the case of an (assumed) equilibrium distribution of the adsorbate on the various surface sites, a surface with a known temperature.This local equilibrium General Discussion dN-N Fig. 1 Schematic potential-energy surface representing dissociative adsorption of a molecule such as N, restriction will exclude certain systems from the present comment. State-to-state reversi- bility (microscopic reversibility) is a consequence, of course, of the laws of dynamics, be they quantum or classical. When these state-to-state quantities are averaged over an equilibrium ensemble, one obtains a microscopic reversibility for an equilibrium system (more precisely, detailed balance, since were are now dealing with an ensemble).It is only for constrained ensembles that possible departures from detailed balance may occur. However, detailed balance should follow for the ensemble assumed above, upon averaging the state- to-state quantities over that ensemble. 1 T. B. Grimley and S. Holloway, Chem. Phys. Lett., 1989, 161, 163, and references therein. Dr. J. Harris communicated in reply: Your argument is subject to the formal objec- tion that the ‘assumed thermal distribution’, insofar as this refers to adsorbates of finite binding energy, must correspond to zero coverage. Certainly, this may be a purely formal objection of the ‘nit-picking’ variety, However, the point is not that such things as ‘quasi-equilibrium’ or approximate reciprocal relationships, as they follow from assumed conditions of detailed balance, do not occur.The statement is only that they may or may not occur, In order for the concept of detailed balance in non-equilibrium ensembles to be useful it would be necessary to establish which systems, or classes of systems, can be relied upon to exhibit ‘quasi-equilibrium’ distributions (or within which bounds of accuracy it would be legitimate to assume such distributions). Prof. A. Gonzalez Ureiia (Universidad Complutense de Madrid, Spain) said: This is a question for Dr. Auerbach related to Dr. Holloway’s comment about the fact that no resonances are shown in your data on the energy dependence of the dissociation prob- ability. I would like to know the translational energy resolution that you have in your experiments.As you know in both crossed-beam and beam-surface scattering experi- ments resonances have only been noticed when collision energy resolutions of a few meV or even lower were achieved. Drs. Rettner, Michelsen and Auerbach replied: We do not believe the lack of SUE-cient energy resolution is the explanation for the fact that we do not observe the reson- ance which appear so prominently in the calculations of Dr. Holloway and co-workers. The calculated resonances are indeed much broader than the width of the adsorption functions we report. The calculations are for restricted dimensionality. Thus one possible General Discussion explanation for the difference between our observations and the calculations is that averaging over the full dimensionality of the problem reduces the resonance effects.This explanation, however, has some problems. One might expect such averaging to yield adsorption functions much broader than those we observe. Further work is required to understand the differences between our observations and the calculations. Dr. Holloway added: Probably the width of the resonances and thresholds are sufi-cient to be observable at low surface temperatures using existing technology. Prof. H. Zacharias (University of Essen, Germany) communicated : The inhibition of hydrogen sticking at low J with increasing rotational motion that you report in your paper, may reflect a more general behaviour. Earlier we have observed experimentally a strong rotational cooling in the desorption of H, and D, from Pd(100)' in the tem- perature range 325-740 K.At a surface temperature of ca. 725 K, for example, a rota- tional temperature of ca. 340 K was observed for D,. This ref