Spiers Memorial Lecture. Some remarks on surface reactions

摘要

FWU~UY 1993,96, 1-16D~SCUSS., Spiers Memorial Lecture Some Remarks on Surface Reactions J. Harris? Institut fur Festkorperforschung, Forschungszentrum Jiilich GmbH, 0-52425 Jiilich, Germany The driving force behind the advances that have occurred over the past decades in gas-surface dynamics has undoubtedly been improvements in equipment and experimental technique, but equally important has been the change of view this development has enforced; from a ‘thermal’ to an ‘atomistic’ picture of the phenomena. This has allowed, and even required, a fuller and more sharply defined interplay between experiment and theory. By analysing how this general development has occurred, and considering some of the advances in basic knowledge that it has made possible, features and procedures can be identified that suggest how further advances may be achieved in areas of relevance to types of surface reaction that remain poorly understood.1. Introduction Surface scientists have not had the good fortune to stumble on a phenomenon analo- gous to, say, high-temperature superconductivity, which has turned materials that pre- viously no-one had ever heard of into household words. Progress has occurred, but in steady, small steps each of which may seem insigificant, or invisible to those intimately connected with the field. It is then particularly important from time to time to pause and take stock, comparing, not with yesterday, but with the state-of-the-art a generation ago. If we do this, the most casual look sufices to establish the scale and substance of the advance.Today, STM ‘bugs’ crawl around on surfaces, mapping out the relief with sub-atomic resolution. Glancing incidence X-ray cameras pin-point atomic locations with kinematic accuracy in surface structures of bewildering complexity. The contrast with the sterling struggles of 1960s experimentalists to produce reliable field emission spectra, or theorists trying to make sense of LEED I-V curves, could scarcely be more startling. Certainly, in those days, the STM would have seemed an experimental and theoretical impossibility (and would be so regarded even today, if it had not been in- vented). A major driving force behind the sub-field of ‘gas-surface dynamics’ has been (and hopefully is) the desire to improve our understanding of chemical reactions on surfaces.In this regard, there seems to be developing (or has already developed) a fashion accord- ing to which surface science in general and by implication, gas-surface dynamics in particular, has ‘failed to deliver’ with respect to the ‘catalysis question’. To the extent that this opinion is held, it seems to me to be not only unfortunate, undermining as it does our sense of the value of what we do, but also quite inappropriate with regard to what actually has been achieved. Whether one has or has not ‘delivered on the catalysis t Present address: Biosym Technologies, Inc., 9685 Scranton Road, San Diego, CA 92121-3752, USA. Surface Reactions question’ depends entirely on what one thinks this is.If by ‘failure’ we refer to lack of impact on the industrial retort, then we may be factually correct, yet hopelessly nayve with regard to the timescales on which advances at the cutting edge shake down into everyday practice. These are determined by the teaching and learning chain, and not the fond wish of researchers to see their discoveries of today in place on the production line tomorrow. Clearly, the participants in these Discussions are cogniscent of the value of current and past activity in their field and it is not my intention to turn this introductory lecture into anything in the nature of a ‘pep-talk’. Nevertheless, at a time when all intellectual pursuits are being required to define their value more clearly to an increasingly sceptical body politic, it seems to me useful to take time out to reflect on some of the advances that have occurred, not with regard to technical capabilities which, as noted above, are quite obvious enough, but with respect to basic knowledge relating to the elementary processes that underly catalysis. 2.From the ‘Thermal’ to the ‘Atomistic’ A factor that has been quite important in opening up new avenues within the field has been the stage by stage adoption of an ‘atomistic’ mode of thinking: that is, a view of the dynamics in terms of individual collisions between particles and the substrate atoms that comprise the surface. Readers just now beginning their careers, or who have entered the field only recently, may raise their eye-brows here. ‘Was it not always SO?’ ‘How could it have been otherwise?’ In fact, it was otherwise, and in some circles still is, and even where it isn’t, some remnants of the old way of thinking remain and can lead to considerable confusion (even the word ‘gas’ in ‘gas-surface dynamics’ carries with it the flavour of Langmuir kinetics, BET isotherms etc.that formed the basic vocabulary of past generations of surface scientists). The explanation for this confusion, it seems to me, is that the ‘thermal’ -+ ‘atomistic’ transition did not occur by general agreement, uia cooperative reasoning and discussion as to the ‘right way to proceed’. It occurred as a by-product, an inevitable by-product, of an advance in equipment and experimental technique, with the shift of emphasis from thermal or quasi-thermal conditions to beam work, which has come to correspond (almost) to ‘scattering conditions’.So the confu- sion is due to the understandable difficulties that arise when data taken under (almost) scattering conditions are interpreted using a language that was developed during an era when almost all data were thermal in nature. Perhaps we can profitably illustrate one rather persistent kind of confusion uia the example of the ‘role of detailed balance’ in gas-surface dynamics. Detailed balance is an elementary property of a thermal ensemble but students of surface dynamics could conclude very readily on the basis of much literature that ‘detailed balance holds’ also with respect to processes that are manifestly far from thermal equilibrium.At the very least, one must certainly conclude from the state of the literature on this point that ‘whether detailed balance holds’ for this or that non-equilibrium process is an issue of considerable interest. Within a ‘quasi-thermal’ view of surface processes this may seem a quite reasonable contention. On adopting an atom- istic picture which acknowledges that the distributions measured in sticking or desorp- tion experiments result from averages over a large number of atomistic events corresponding to specific multi-particle trajectories, the matter appears in a different, and I would say, much clearer light. Consider a multiparticle trajectory corresponding to a particle-surface sticking event.The particle strikes the surface, causes a big dent in the lattice and sends a phonon pulse zapping into the bulk. This carries away the energy, the dent in the surface heals and the particle remains trapped as a result of its attractive interaction with the surface. (For definiteness, we may think of the interaction as of the physisorption type so J. Harris there are no complications with regard to surface chemistry). In the time-reversed event, the particle starts off on the surface, which, presciently and mysteriously, begins slowly to ‘de-heal’ itself, forming, for no reason that is at all apparent, a hollow into which the ad-particle gently nestles. Suddenly, a massive ’quake erupts at the surface, whaps the particle off into oblivion, but has no effect on the atoms of the surface other than to heal out the little hollow in which the ad-particle was resting leaving a perfect, apparently undisturbed lattice.This backward-time trajectory does, to be sure, correspond to a desorption event. However, whereas the sticking trajectory is obviously relevant with regard to typical conditions under which a sticking coefficient may be measured, the same is not true of the desorption trajectory. This is at the very least of highly dubious relevance for particle emission from a gently warmed surface, and scarcely any more plausible even if the desorption is done by ballistic phonon transport. The ballistic phonon will indeed strike the surface and lift the particle off, but the lattice will scarcely ‘de-heal’ in advance nor revert immediately after lift-off to equilibrium.Instead, the situation would be reversed. The lattice would remain at rest until the phonon pulse arrives and would reverberate long after the adparticle is gone. The mere fact that a time-reversed sticking trajectory represents a desorption event, then, is not sufficient to establish reciprocity laws between sticking and desorption prob- abilities because the set of trajectories that is averaged over in a non-equilibrium stick- ing measurement will not be the same as the set of trajectories that is averaged over in a desorption experiment. The two access regions of (multi-particle) phase-space may overlap, but will not overlap perfectly.In general, no statement about the consequences of imperfect overlap, e.g. in connection with reciprocity laws, can be made. Very poss- ibly, it may not matter much that different sub-sets of trajectories are involved, in which case the reciprocity laws which hold rigorously when the sub-sets are the same may still .in some sense ‘hold approximately ’. Thus, in non-equilibrium circumstances, detailed balance may very well ‘hold’ according to some criteria the investigator has decided (arbitrarily) are adequate in this regard, or it may not. Suppose the conclusion is arrived at on the basis of data taken for a specific non-equilibrium system, denoted ‘S’, that ‘detailed balance holds’ for that system. Does this mean that, although manifestly non- thermal processes are involved, ‘S’ is in fact a thermal system? Does it mean that detailed balance is obeyed by all non-equilibrium systems? Can we rely on it that ‘detailed balance holds’ also for any other system than the one that has been used in the specific study on which our conclusion was based? We can perhaps invoke Occam’s Razor and expect detailed balance to ‘hold’ for systems that we have good reason to believe are ‘similar’ to ‘S’,but we could not rely on it and no principle of science would be contradicted if it turned out that our expectation was false.Adoption of an ‘atomistic’ view shifts the focus away from questions that have meaning only with regard to ensemble behaviour and onto questions that relate to the microscopic behaviour that underlies phenomena.What processes are responsible for sticking, or desorption? What factors determine the actual values of sticking coefficients, or desorption rates, or chemisorption energies, or activation barriers? How can we describe surface processes theoretically in a way that is consistent with what we know of the microscopic composition of the system, and with the macroscopic observations made in the laboratory? The sceptic might say the former is simply not necessary because what really interests us is the collective behaviour of many billions of individual events occurring, say, inside a Bessemer converter. Who cares how a single molecule behaves when it hits a surface? If this view were to be held by anybody (and there may be some justification for suspecting that it is) then it is best dealt with via analogy with the proverbial knotted ball of wool.One may of course hope to disentangle this via fond hope of ‘an inspired guess’, but the consequences of hope being dashed or the guess turning out to be insufficiently inspired are likely to be quite unfortunate. Better the time-honoured principle of tackling a complex problem by splitting it into binary bits, Surface Reactions with each ‘bit’ a question that has a yes/no answer. This is a reliable procedure because progress is made whatever the outcome of a given trial. A binary question can only result when all variables of the system other than the one at issue are under control. This may seem in surface science (as it does, for example in biology) a hopelessly impos- sible ideal, but we should strive towards it nonetheless because (as in biology) advance is not contingent on going all the way.The more control we have, the closer we come to the ideal, the less we will find it necessary to have to rely on witchcraft. The requirement that experiments be conducted on an as near to yes/no basis as it is practical to get, places demands on the experimentalist, and also on the theorist whose responsibility it is to develop a predictive capacity. Common experience tells us that a ‘known’ experimental result induces a huge psychological bias and it is therefore not too surprising that sometimes theory ‘explains’ data that turn out to be erroneous (for one reason or another). This will happen from time to time for entirely honourable reasons, but it is no less ignominious to the theorist than turning out wrong data is to the experimentalist, whatever the reason, and very different indeed from the ‘erroneous but interesting prediction’, which, while it may lie somewhat below the ‘correct and interesting’ prediction in esteem, is rightly held to be much more glamorous than the ‘correct but ho-hum’ variety.The difference between theory predicting the result of an experiment that has not yet been performed, and reproducing a known experimental result cannot be too strongly emphasised. This may seem a very obvious point but I make no apology because there is a deplorable tendency within the trade to misuse the word ‘prediction’ as applying to both of the above, a merely linguistic slovenliness perhaps, but one that if not corrected most assuredly has the power to corrupt! Theo- retical prediction is an a priori business and requires the theorist to take his/her turn leading the climb, a vastly different experience from coming up on the rope.3. Sorption Interactions Any theoretical study of dynamical processes at surfaces must rely to a very consider- able extent on information about the relevant interactions between the particles. Many authors have pointed to this as a major stumbling block in making progress, though sometimes in a way that suggests it is ‘someone else’s business’. This may perhaps be carrying differentiation in science a bit far.No matter, the difficulty is to a considerable extent eliminated because there has been over the past decade a steady but very signifi- cant development, not only in techniques for calculating interactions, but also with regard to qualitative knowledge. Taken together, these are by now quite suficient to reduce the question of sorption interactions to a matter of how much time and energy we are prepared to pay for the knowledge, at least so far as most phenomena connected with surface reactions are concerned. We wish here to focus on basic knowledge and not on the calculational weaponry that is the theoretical counterpart to the development of supersonic nozzles, stagnation detectors and the like. However, since the field is heavily weighted on the experimental side, it may be useful just to note two factors that have been instrumental in connection with our knowledge of interactions.These are (i) the development of ‘density-functional methods’ for energy calculation (which have very recently and suddenly found wide- spread acceptance in quantum chemistry), and (ii) awe-inspiring advances in computa- tional power. Further details of what is now possible and what the not too distant future may bring in the field are given elsewhere in these Discussions.’ More relevant to the present contribution, and potentially of greater importance for the immediate future, are improvements in our understanding of the qualitative factors that determine the inter- actions that govern the behaviour of a given particle-surface system.Nothing startling has occurred in this regard, to be sure, and any reader who thinks this is little more than that surface scientists have, finally, understood a few principles of elementary chemistry J. Harris is hereby pardoned for holding the view (though one would be bound to think at least, if not to say, that this would reflect more an ignorance of, rather than a familiarity with, what can be found in the standard chemistry literature of yesteryear with regard to the interactions that govern the behaviour of molecules at solid surfaces). Traditionally, sorption interactions are classified as of the physisorption or chemi- sorption type and this is fine if we restrict ourselves to extremes of behaviour.Clearly, He is physisorbed and H is chemisorbed, but what about CO, NO, H20... ? Are these physisorbed or chemisorbed? The only sensible answer we can give to this question is to split it into binary bits, obtain two negatives and so conclude ‘neither’. For instance, the bond CO makes with most metals is relatively weak, scarcely any stronger than the bond Xe makes, but it is usually highly directional, with the molecule standing upright with the C-end down. Do we really want to put this molecule in the same class with the Ne atom? NO tends to bind more strongly than CO, but still very much more weakly than either N or 0 individually. Do we really think all four belong to the same class? H20 makes a weak bond that is compatible with physisorption.However, the bond is both highly ‘electrical ’ and directional and intermolecular interactions on the surface are so weird and different from dimer interactions in the gas phase one can hardly claim that the adsorbed molecule ‘retains its chemical identity’. Rather than force all of these cases unnaturally into categories where they do not really belong, it is much preferable to refer to intermediate adsorption and have done with it. This class then covers a pot pourri of cases whose common feature is that they do not correspond obviously to physisorption (weak binding and ‘chemically intact’ adsorbate and substrate) or to che- misorption (strong binding and ‘essential chemical change’). To these three categories, we can add a fourth to cover the interaction of ions with the surface.Here a central quantity of interest is the neutralisation of the ions as they approach the surface so this class is distinct from all the others in that it involves an inherent and vital element of non-adiabaticity. For the remainder, we remain within the adiabatic limit (which, while it will not always be everything,2 will usually be the dominant interaction we have to be concerned about). Significant progress has been made over the past decades in understanding the basic features of all four categories of interaction. Physisorption and chemisorption are inher- ently simple cases and the difference can readily be understood as a consequence of the electronic level structure of ad-particle and surface, as illustrated in Fig.1. The critical feature is the energetic position of the ad-particle’s HOMO and LUMO (highest occupied and lowest unoccupied molecular orbital) with respect to the metal’s Fermi level. For an open-shell atom or molecule, the HOMO and LUMO are degenerate (far right). A truly closed-shell atom or molecule has a deep-lying, fully occupied HOMO and a high-lying LUMO (shown far left as a positive energy resonance). When the ad-particle is far from the metal the latter behaves from the chemistry point of view in qualitatively the same fashion as a single atom having HOMO and LUMO degenerate at the Fermi level. The reason is that the electrons forming the metal’s conduction band are more effectively trapped within the bulk the deeper in the band they lie.Only the most energetic electrons penetrate very far into the selvedge and these are at or near the Fermi energy (and are also s or p electrons: the influence of d electrons will be con- sidered below). When these electrons encounter an ad-particle that attempts to penetrate the selvedge they react positively or negatively according to whether there is or is not space available on the ad-particle to accommodate them. If there is not, as is the case if the ad-particle has a deep-lying, filled HOMO and a high-lying LUMO, they are forced either to vacate the region occupied by the ad-particle, or to deform in such a way as to orthogonalise to the HOMO and to all other filled levels of the ad-particle.Both pro- cesses cost energy (band energy, if one will) so the total energy increases with ad-particle penetration, corresponding to a repulsive interaction and a force on the ad-particle tending to scatter it back into the gas. The ultimate origin of this force is the ‘lack of Surface Reactions LUMO -1 HOMO HOMO 2 Dc 0.1 eV Ds 0.1 eV D = several eVI l-physisorption intermediate chemis0rpt ion (w.H2) (e.g.CO) (e.g. H) Fig. 1 Diagram illustrating three types of adsorption. The metal’s local density of states projected onto an orbital localized in the selvedge is shown far left. The chemical behaviour depends on the relative positions of the incoming parricle’s HOMO and LUMO with respect to the Fermi level. From left to right, the orderings shown are typical for physisorption, intermediate adsorption and chemisorption with typical values of the well-depth D (see text for further details).Figure repro- duced with permission from ref. 42. space’ on the ad-particle that results from the Pauli principle restriction to two electrons per space orbital, which is why we refer to Pauli repulsion. (For transition-metal sur- faces and clusters there is available a mechanism that combats the Pauli repulsion, as discussed below.) If there is ‘space’ on the ad-particle, the metal electrons spilling out into the selvedge experience an attractive potential and electron sharing occurs (rarely, genuine electron transfer), resulting in the formation of a chemical bond and chemisorp- tion.3.1. Chemisorption and Physisorption The properties of the chemisorption bond are not drastically different from those of fam-iliar chemical bonds between open-shell atoms. The energetic balance is similar and the range of bond energies roughly the same as for di-atom bonds. The only essential differ- ence is the dimensionality: the energy curve as a function of ad-particle-surface separa- tion depends on the lateral position with respect to the surface mesh. Some aspects of this dependence are fairly obvious. For instance, an on-top approach will correspond to a steeper ‘back wall’ than a ‘hole’ or ‘bridge’ approach because the back wall is due (in the chemisorption case only) to descreening of the nuclear-nuclear repulsion. This switches on according to the rate of penetration of the electron density by the foreign nuclei.Other aspects are more subtle. For example, the energies of low-lying local minima (adsorption or incorporation sites) may be so close together as to lie within the reliability level of any theory. One point which has been rather slow to sink in (possibly J. Harris as a result of old-style ‘chess-board’ pictures of adsorption) is the importance of co- operative motion. Chemisorption bond energies are typically of the same order as the cohesive energies of solids and force constants holding chemisorbed species in their sites may be even larger than those operating between substrate atoms. Thus it will in general be incorrect to assume that chemisorption is a matter of the adparticle finding its optimal location, with the atoms of the substrate lattice remaining rigidly in place.This may seem to be the case with regard to high-symmetry adsorption sites, but the illusion is rapidly expelled when we consider, e.g. how the ad-particle moves between such sites. This point was dramatically and interestingly underscored when the actual route taken by A1 atoms undergoing ‘self-diffusion’ along an A1 surface was e~tablished.~ The physisorption interaction differs from its chemisorption counterpart in three important ways. First, it is much weaker, with binding energies typically 5-100 meV rather than in the eV range. Secondly, equilibrium distances from the surface plane are relatively large and comparable with the lattice spacing, so, thirdly, the potential is essentially one-dimensional, i.e.the lateral average dominates the behaviour. This com- prises a long-range Van der Waals attraction going over into a steep ‘back wall’ that arises because of Pauli repulsion due to penetration of the substrate electron distribu- tion by the ad-particle. The past decade has seen a fruitful interplay between e~periment~-~and theory7v8 and, bearing in mind that at the end of the 1970s there was not a single reliable measurement of a physisorption well depth on a metal surface, a substantial advance. The ideas developed by Lennard-Jones and collaborators half a century agog were demonstrated to be qualitatively correct and theory progressed further by using these ideas to construct a semiquantitative theory having a genuine predictive capacity in respect of actual values for well depths and level sequences and the manner in which these depend on properties of solid and ad-particle.However, the time when theory could be said to be ‘leading the climb’ was short indeed and there followed rapid and ignoble contact with the ground as each improvement in experimental soph- istication came on line and attention was focussed on properties occurring on a finer energy scale. As it turned out, theoretical predictions for quantities like the systematics of the lateral or rotational (for H,) corrugation, or the crystal-face dependence of the well depth’’ were found to be wrong even in trend.” To date there is little that can be said about this other than that (a) existing theory really cannot claim a ‘predictive capacity’ on this scale of energy, and (b) placing too much faith in ‘Occam’s Razor’ results in the invoking of ‘Murphy’s Law’! Experiment, then, is back at the head of the rope and may remain there for some time because none of the theoretical methods currently available looks capable of improvement to the required accuracy (hopefully yet another wrong prediction).3.2. Intermediate Adsorption A typical situation for intermediate adsorption is shown in the central column of Fig. 1. The frontier orbitals of the ad-particle, usually a stable molecule, straddle the Fermi level. The critical difference from the physisorption situation is that the LUMO is not safely out of harms way, but lurks rather close to the Fermi energy.This means the LUMO can become incorporated in the bonding via a polarisation effect, analogous to the role played by ‘atom-unoccupied’ orbitals in di-atom bonding (a striking example being the 2p orbital of Be, whose presence halves the bond-length of Be,). To see that a low-lying LUMO is likely to give an attractive contribution, one has only to consider that, if it were ‘even lower-lying’, the interaction would basically go over to something closer to the chemisorption type. The energy lowering involved can be thought of as due to an indirect or inelastic hop whereby a metal electron ‘occupies’ the ad-molecule’s LUMO. Recalling the origin of Pauli repulsion, and the fact that of necessity the LUMO is orthogonal to the molecule’s HOMO and all deeper lying orbitals, it is easy Surface Reactions to see why such a hop would relieve the repulsion and lower the energy.The energy source for the hop is a potential matrix element of the form (k I r 11) ,where I I) stands for the LUMO and I k) is a band state, so it is no surprise that the contribution to the energy takes the form where &k are the band energies, the energy of the LUMO and the sum over k refers to occupied band states. For the reason given above, metal levels near the Fermi level contribute most strongly SO &k zs E~ and, as noted, 6, c1,so the interaction is negative. A very obvious feature of an interaction of this type is the strong steric effect that devolves from the dependence of the matrix elements on the orientation of the molecule relative to the surface normal. In many cases, this is the strongest such dependence (because the molecular LUMO is often a strongly asymmetric orbital) and so determines the preferred orientation of the molecule when adsorbed on the surface, and the manner in which a low-energy molecule incident from the gas phase is steered towards the surface.The CO molecule tends to sit upright on metal surfaces with the C-end down because this is the orientation that maximises the value of the matrix element (kl (2n*),where 12.n*) is the molecule’s LUMO, and is strongly weighted on the C atom.I2 Similarly, the orientation of an isolated water molecule on a metal surface (0-down, HOH-plane tilted ca.55” from the normal) is determined by a competition between the angular dependences of matrix elements (k’ I PI 3a,) and (k‘ I V I Ib,), involving metal unoccupied levels I k’) and the two occupied lone-pair orbitals of H2O.I3 In this case, the molecule’s LUMO is very high-lying and the important polari- sation effect involves the metal’s ‘LUMO’, namely the band orbitals above the Fermi level. As will be recognised, these attractive polarisation interactions have the same form as they would were the molecule to interact with an isolated atom having HOMO I k) and LUMO equivalent to Iunequivalent to cocc I k’), and in fact this is a quite reasonable ‘zeroth order’ picture from which to approach the entire interaction.In fact, there exists an approximate energy scheme that is ideally suited to treating interactions between ‘complex’ partners (like a molecule and a surface, or two ad- molecules on a surface) which are in some sense ‘intact’.14 At its simplest level, which should be reliable on cot too fine an energy scale, all that is required is the evaluation of matrix elements and k-sums, as in eqn. (l), that involve band functions in the selvedge, and the molecular orbitals of the molecule. In this way, information about how the molecule will be steered as it approaches the surface, or another adsorbed molecule, can be obtained with minimum effort. A simple generalisation whereby the molecules involved are regarded as made up of units that remain intact throughout a chemical reaction allows direct application to the study of reaction pathways.The method has proved popular and successful in cluster, solid-state and surface problems (see, e.g. ref. 15-17). 4. Dissociation Reactions In comparison with other properties, whose direct relevance for catalysis may not at first sight be apparent, dissociation is of obvious importance as the first stage in the chain from reactants to products. Much remains to be learned about dissociation, particularly in cases where the interaction in the entrance channel as the molecule approaches the surface is one of intermediate adsorption so that dissociation occurs after impact, pos- sibly through one or more intermediate states.Entrance-channel, or on-impact disso- ciation, where the initial interaction is of the physisorption type, is much better understood, largely as a result of a decade of work involving the H2 molecule. The J. Harris mechanism whereby H, can be made to dissociate on simple- and noble-metal surfaces emerged from theoretical studies in the early 1980s (see, e.g. ref. 18, 19), and resulted in a generic energy diagram that proved extremely fruitful in understanding both a priori and a posteriori data on H, dissociation and desorption.20-26 This energy diagram, which has also, with minor modifications, survived subsequent, more detailed theoretical can be understood in terms of the competition between two configurations that correspond to the molecule being in its singlet or triplet states.If the molecule approaches the surface in its 10; ground-state configuration the sequence of electronic levels is as in the left panel of Fig. 1 and so exhibits Pauli repulsion. The energy is low when the particle is far from the surface but the protons are close together (isolated H, + the bare surface) and grows as the molecule approaches the uppermost layer of ions and the electron clouds overlap. Accordingly, in this configuration, the intact mol- ecule is driven away from the surface. If the molecule is ‘prepared’ in its ‘triplet’ state with configuration 10: lo:, the energy of the isolated molecule-free surface geometry is increased by the amount of the singlet-triplet splitting (many eV), and is repulsive with respect to the H-H bond distance, D, so that left to itself the free molecule would dissociate. The interaction with respect to the molecule-surface distance, 2,is attractive, however, because the level sequence now has the form of the right panel in Fig.1 (except for the partially filled excited level, whose occupation and form we can for illustrative purposes imagine to be frozen), and so corresponds to chemisorption. In the second configuration, therefore, the molecule is driven towards a state of complete dissociation with two chemisorbed H atoms far apart but bound to the surface. A standard procedure for constructing a reasonable adiabatic energy for the disso- ciation process can be taken from gas-phase studies of ‘two-energy-surface’ reactions and amounts to hybridizing the two energies Emoland &iss in the 2D-space of 2 and D via where x is a mixing parameter.If x is small, which in gas-phase reactions is usually the case, ECZ, D] is essentially equal to the lower-lying of Edissor Emo,.The x values that are relevant to model reactions on a surface depend crucially on the nature of the surface and of the electronic states involved. If these are localised, which might be the case on insulator or semiconductor surfaces where there are large band gaps in the energy range where typical molecular orbitals lie, X-values may be of the same order as in the gas phase. On metal surfaces, however, the molecular orbitals lie within the metal’s band and the ordinarily discrete levels representing this or that molecular ‘state’ broaden into resonances.These are not as broad as the entire band, and a rough figure can be obtained by treating the molecular level as a quasi-bound state which can decay by tunnelling into the metal. The relevant value of x is then the width of the quasi- bound state, as given by a sum of overlap matrix elements of the form xkI (k I E) l2 (or, if one will, the convolution of the widths of the two levels involved in the ‘quasi-crossing’). Clearly, this will depend on where the molecule is relative to the surface, but if we are content with a ballpark figure, this would typically be in the range 1-2 eV. There is, then, an important difference between reactions that occur in the gas phase and on metal surfaces and, paradoxically, the latter are in some sense simpler because the extended nature of the metal’s electronic levels guarantees that all changes are gradual.This has two kinds of consequences. The first is that the broadening influences all structure in the energy on the surface. Thus, energy barriers will tend to be lower and broader [as exemplified by eqn. (2), for which the barrier height and width decrease and increase, respectively, with increasing x]. The second is that the ‘level-crossings’ on metal surfaces (such as occurs in the above example of H2 dissociation) refer to levels each of which has a substantial width. These widths are usually sufficiently large as to Surface Reactions imply rapid hopping of electrons on a timescale of the nuclear motion.Accordingly, as a general rule, reactions at metal surfaces are not of the ‘harpooning’ type, do not imply the sudden crossing of sharp levels, cannot properly be described in terms of simple Landau-Zener models, and (probably) are adiabatic to a greater degree than can be expected for a corresponding gas-phase reaction. On this basis, I suggest that it is not quite as naYve as might at first sight be supposed2 to regard dissociation at metal sur- faces, where this is a majority event with large probability, as occurring adiabatically (see also below). Whereas the two coordinates, 2 and D,on which the energy in eqn. (2) depends are clearly the most relevant for the dissocation process, a calculation which includes these coordinates and no others is of necessity restricted to describing qualitative behaviour.Although this is sometimes the subject of misunderstanding, it is quite obvious that a reduced geometry calculation does not include important steric effects and so cannot be interpreted in terms of absolute numbers. Even qualitative behaviour must be regarded as suspect if there is reason to believe that steric effects depend strongly on external parameters like the incident energy. An approach for dealing with multi-dimensional aspects of the energy is discussed in some detail elsewhere in these Discussions.’ This is clearly a difficult, challenging but rewarding task for theorists. In the case of H,, a complicating factor is the large rotational quantum, which inhibits the steering of the bond axis, and in fact a quantum treatment of all degrees of freedom is im~erative.~’ However, there is a trade-off in that the lightness of the ad-particle allows the inelastic coupling to the lattice to be negle~ted.~~ H2 is perhaps the only case where this can be said of a dissociation event.The generic energy diagram discussed above holds for most (possibly all) simple and noble metals, but does not hold when the substrate is a transition metal. The reason is simple, but far-reaching also because it explains an important element of the functional- ity of transition metals in catalysis. As we have seen, an intact H, molecule is repelled from a simple- or noble-metal surface because of Pauli repulsion due to overlap between the occupied molecular orbital of H, and metal orbital tails in the selvedge.The metal orbitals must either vacate the region occupied by the molecular orbital, or deform in such a way as to orthogonalise to it. In a transition metal, the s-p electrons that pen- etrate into the selvedge have a further possibility which is to ‘become’ d-electrons and ‘hide’ in the metal’s d-band. This costs very little energy, because (in somewhat simpli- fied language) the s-p electrons and d-electrons share a common Fermi level, and auto- matically reduces the overlap of occupied metal orbitals with the molecule’s HOMO because d wavefunctions are much more strongly localized about the ion cores than s and p wavefunctions. Accordingly, the Pauli repulsion as the molecule approaches the surface (i.e. in the entrance channel) is reduced.Numerically, the effect can be large enough to wipe out the entrance channel barrier to dissociation that is characteristic of all simple and noble metals, allowing spontaneous dissociation at the surface (see Fig. 2). The vital property of a transition metal in this regard, the partially filled d-band and a large density of d-states at the Fermi level, has its analogue for a cluster of transition atoms also. Here, a sequence of transitions can take place between different cluster levels that correspond to configurations that are successively more and more d-rich in the locality of the ad-molecule. The key to a low (or no) barrier, then, is the presence in the substrate of low-energy excitations that affect a local s-p to d transfer and so keep the tails of the substrate orbitals well away from the molecule’s HOMO until this has pen- etrated far enough into the surface to allow dissociative chemistry to occur.The above was argued with reference to H, dissociation which is not a prima facie case of a catalytic process (since catalysis is required to make H,, not to break it apart e.g. steam reforming). However, the arguments hold with no essential change for all molecules whose electronic structure is analogous to the left panel in Fig. 1. Typically,the HOMO will form the intramolecular bond that is to be broken, and transferring an J.Harris 11 / / / / / physisorption?/ 2 filled Fermi-level’ Fig. 2 Diagram illustrating (a) entrance-channel-activated dissociation : example, H, interacting with a noble metal. The upper panel shows schematically the behaviour of the energy as the metal-molecule system evolves along the ‘reaction coordinate’; the lower panel shows the elec- tronic density of states of the metal. (b)The effect on the energy of ‘d-holes’ at the the Fermi level of a transition metal (see text). For H, the energy lowering is sufficient to cause spontaneous dissociation for many transition metals, whilst for CH, a substantial barrier remains in all cases. Figure reproduced with permission from ref. 42. electron to the LUMO would effect the break. For this to happen in the gas phase a large amount of energy equal to the HOMO-LUMO splitting must be supplied.Near a surface, the ‘dissociated state ’ gains the adsorption energy of the reaction partners, while the ‘molecular state’ is destabilized due to the Pauli repulsion. Somewhere, a ‘crossing’ of these two situations will occur (in the sense above, implying a substantial ‘rounding’), at, if one will, a ‘transition state’ (implying a saddle-point geometry that corresponds to the highest point on the energetically most favourable path from reactants to products). The function of the catalyst as a means of making a dissociation reaction easier is thus clear since, if it exists at all, the energy of the transition state relative to vacuum must be smaller than the HOMO-LUMO splitting of the gas-phase molecule. The functionality of the catalyst will then depend on the accessibility of the transition state from the entrance channel (gas phase).The reason why transition metals, or transition clusters, are effective in breaking strong bonds of the type we are here considering is the strong suppression of the Pauli repulsion in the entrance channel which allows the transition state to be accessed easily. The catalyst will ‘work best’ the easier it is for a local s-p -+d transfer to occur (other things being equal). This can be enacted anywhere on a transition-metal surface, though there will usually be more and less favourable ‘sites’ within each unit cell. Also, since the local density of d-states (i.e.the s-p/d breakdown at and near the Fermi level) will depend on the local geometry, the s-p -+ d transfer may be easier (or harder), say, at steps, or edges, or on clusters presenting sites having a local geometry that is different from any that is exhibited on a surface. Such sites may then appear to be particularly ‘active’ (or inactive).32 In general, the argument why there are sites on surfaces or clusters that are more active than typical sites within a regular unit cell of a well characterised surface is rather simple: given the totality of local ‘chemical environments’ that are possible, it is quite unlikely that the one which best enables the dissociation of a molecule also minimises the energy of a flat crystal surface. An example which almost certainly fits the above picture is CH, dissociation, a process of immense industrial importance.The major constituent of natural gas, Surface Reactions methane is essentially inert and has an electronic structure similar to that of H,, but with an even larger HOMO-LUMO splitting. The extreme stability of CH, is of course the reason why it is present in such abundance in natural gas and organic waste. Accordingly, unlike H, ,CH, does not undergo spontaneous dissociation on transition metals. This is not because the s-p-+d transfer mechanism is not working, it works (probably) even better for CH, than for H, ,but because the Pauli repulsion on which it is superposed is particularly strong so the effect is not sufficient to reduce the barrier height to zero.Accordingly, CH, dissociation is activated on all metal surfaces, it is just much easier on transition metals than on simple or noble metals. Although it has not been unequivocally established (to the author’s knowledge), the above arguments with regard to ‘active sites’ apply to CH, dissociation as to other surface reactions so there probably exists a surface composition, or supported cluster, which ‘works’ better than anything currently in industrial use. This will not only be a matter of the ‘barrier height’ (i.e. the energetic location of the ‘transition state’). Other factors, for example the barrier geometry and its width along the reaction path, will play an important role. This is because CH4 dissociation displays interesting dynamics and certainly cannot be thought of at all in terms of ‘going over a one-dimensional barrier’.33 I consider this point briefly in Section 5.CH, dissociation is discussed in more detail in other contributions to these discussion^.^^^^^ 5.Recoil Effects As remarked in Section 3.1, the cooperative nature of the chemisorption interaction has been rather slow to gain widespread recognition, a fact that one might in part attribute to the shackling influence of ‘chess-board models’ of adsorption. By the same score, the importance of the recoil of the surface as a result of impact by an incident molecule (of whatever interaction strength) has not always been recognised. This may be due to ‘first things first’, but may devolve also from the pictures that we see drawn (and draw ourselves) in the literature which suggest that ad-particles land on surfaces ‘on gossamer wing’.Language like ‘the initial collision excites phonons’ has a similar soporific effect. It is certainly not wrong but has a far too gentle ‘flavour’. With rare exceptions (restricted essentially to H2, He ad-particles), a particle-surface collision is a rather violent event which leaves a dent in the surface lattice whose extent can easily amount to a sizable fraction of a lattice spacing. The reason is that the lattice atoms in the impact zone are held in place by ‘springs’ linking them to other atoms of the substrate that are weak on a scale set by the impact. The springs will result ultimately in the healing out of the initial disturbance, but this may take time because of the small force constant and large mass.The strength of the springs can be estimated roughly by treating the ‘impact region’ of the lattice as a harmonic oscillator with mass equal to the surface atom mass, Msub,and spring constant corresponding to an oscillator quantum of the order of a typical phonon frequency. Since this is of order ca. 20 meV, which is only a few per cent of a typical impact energy, the surface behaves qualitatively throughout the initial impact like an array of independent masses. The outcome of the initial impact depends crucially on the ratio of adsorbate mass to substrate mass, p = (kfads/Msub)involved. If p 1 the ad-particle rebounds having transferred an energy to the lattice of order A = [4p/(1 + ,U)~]E~,~,where eimpis the impact energy.(We are deliberately vague about this and about quantities like Madsand Msubbecause they cannot be precisely defined: cimp comprises the initial gas-phase kinetic energy of the ad-particle plus some part of the interaction strength). An important feature of this result is the rapidity with which the ‘Baule factor’, [4p/(1 + p)’], approaches its maximum value of unity. For example, if p = 0.2, which is a typical value for many molecules and surfaces of interest, the Baule factor is almost 0.6. This is the reason why the ‘light ad-particle limit’, where the recoil J. Harris of the substrate is negligible because of the smallness of p, is restricted essentially to H2, D2and He.If p 1, the ad-particle does not rebound but barrels on into the lattice and keeps on going until sufficient lattice energy is stored up to bring its juggernaut motion to a halt. This is what happens when an Xe atom strikes most substrate lattices. Xe does not bounce, but crushes its way into the surface. An Ne atom, on the other hand, makes a dent and rebounds (unless the substrate is e.g. Li). If the ad-particle is an asymmetric molecule like CO, its interaction will be asymmetric and so its impact with the surface will make it spin. Again, neutral phrases like ‘trans -+ rot energy transfer’ do not do justice to the violence and the chaotic nature of the molecule’s motion. This sounds, and is very simple, but I offer no apology for this and can in fact point to at least one contribution to the present Discussions which does not do justice to the chaotic and violent nature of the interaction that governs collisions between virtually all asymmetric molecules and virtually all surfaces (he knows who!).In spite of the appar- ent simplicity of the phenomena, and of a quite substantial body of experimental and theoretical work, the detailed sticking and scattering behaviour of asymmetric molecules making mechanical collisions with surfaces remains a remarkably challenging problem. In large part this is because it is not at all easy to split it into ‘binary bits’. Every feature is important, and everything affects everything else (so it has been at least, in all the calculations I have ever done for such systems).For many years a discussion was conducted in the literature as to the nature of the excitations that are responsible for energy loss when particles hit surfaces. Are these “electronic’ or ‘phononic’? Again, this problem, now solved, appears more straightfor- ward than it did when we did not know the answer. The electron-hole pairs of a metal are excited to a substantial degree by ad-particles only when the electronic structure of the molecule-surface system displays a reasonably narrow resonance that either crosses the Fermi level during the round trip, or sits at the Fermi level when the ad-particle is near its equilibrium location in the well.36 The motion of the molecule on and near the surface will raise and lower the resonance and so will correspond to the sloshing about of electrons back and forth between substrate and adsorbate which ‘heats up’ the elec- tronic system at the expense of the nuclear motion.The narrower the resonance, the slower the ‘hopping rate’ and so the more violent the change that occurs per hop. In extreme cases, this is a matter of ‘harpooning’, and the ‘electron-hole’ pairs that result from the ‘harpooning’ process may be observable in the form of ‘exoelectrons’. If there is no such resonance (and in fact for many purposes, even when there is), it is usually reasonably safe to assume that during a particle-surface collision the electron distribu- tion responds instantly to the motion of the nuclei, whose motion is dominated by a single potential-energy surface.The only mechanism for energy loss is then via the lattice. With rather rare exceptions, then, the energy loss when particles hit surfaces occurs predominantly through the recoil of the lattice, which shoots a sound-wave pulse off into the bulk. Since lattice recoil is so important in particle-surface impact phenomena, it is not surprising that it plays a role also in dissociation proce~ses.~’ At the simplest possible level, this amounts effectively to the dynamical renormalisation of an activation barrier, V* +(1 + p)V*, and arises because the gas-phase kinetic energy of the incoming par- ticle is ‘in the laboratory frame’ rather than in the relative coordinate with respect to the impact zone.This effect is particularly important for tunnelling reactions, where the recoil effect can lead to a massive suppression of the tunnelling probability (the impact carries the ‘barrier’ away from the particle trying to tunnel through it). If the surface is at elevated temperature, the thermal motion of the surface atoms in the impact zone may at the time of impact be moving towards or away from the ad-particle. If the latter, then the tunnelling probability will be further suppressed. If the former, the tunnelling probability will be enhanced by an amount that increases exponentially with the surface 14 Surface Reactions temperature. This then corresponds to phonon-assisted tunnelling, which is known to be important in connection with bulk diffusion of H and has recently been shown to explain satisfactorily the surface temperature dependence of CH, dissociation at metal surfaces.9 6. The Future In Section 2, we noted the importance of the ‘thermal’ +‘atomistic’ transition, with the latter associated with experiments conducted under (almost) scattering conditions. It may (or may not) have been wondered here what exactly is meant by ‘almost’. This is, that a true scattering experiment must be ‘state-to-state’ with respect to the entire scat- tering system comprising probe and target. In surface science, the term ‘state-to-state’ is commonly used as referring to the state of the probe alone, with the initial state of the target (and therefore the final state also) undefined because of the finite surface tem- perature, T,.For some purposes, the consequences of finite T, are either not severe, or are readily estimated, in which case experiments at liquid-nitrogen temperature, or even room temperature may be adequate. For other properties, much lower temperatures are necessary. This a matter of the energy scale on which the phenomena under investiga- tion occur. Although ingenious techniques38 allow properties like the trapping behav- iour of weakly interacting particles to be studied even when ad-particles are desorbed on a microscopic timescale, such techniques are not available for phenomena occurring on the surface. Accordingly, our knowledge of entrance-channel behaviour, with regard to associative trapping and dissociative sticking, is much more firmly based than is exit channel, or intermediate channel behaviour on the surface.I suggest that very significant progress with regard to the behaviour of complex molecules that are trapped and undergo reactions via intermediates on the surface will result on development of practi- cal and reliable techniques for maintaining surfaces at temperatures that span the entire range down to about a few Kelvin and can be controlled to an accuracy of ca. 1 K. Theory can contribute towards this development most effectively not by supporting low-temperature studies explicitly (although this is certainly useful too) but by attempt- ing to get ‘ahead of the game’. The weaponry is coming on line and there is no reason for reticence! The number of reaction systems of interest is potentially infinite, and the number for which the nature or properties of the intermediate states are poorly known is also essentially infinite.As such, it should be possible to find a case that is of some interest, and is at the same time theoretically tractable. Clearly, a serious treatment of multi-dimensional aspects of the energy surface is imperative and we are here not refer- ring to calculations that can be knocked off in an afternoon. However, the rewards would be great and a single prediction of the properties of a hitherto unsuspected reac- tion intermediate on the basis of serious theory could be just the impetus that is needed, the jerk on the rope, to move the field along a notch.The point will be raised in these Discussions that we have in the past paid far too little attention to the possibility that many important processes at surfaces may occur non-adiabatically.* I have referred to this several times already and do not wish to belabour the point that, insofar as we are speaking of metal surfaces, non-adiabatic effects should be expected to be considerably less important than in gas-phase reactions. Nevertheless, I fully agree that it is an interesting question and a matter that is in need of clarification. In this connection, I would like to expand on a suggestion made some time ago that may be the key to establishing a firm, experimental measure of the likely importance of non-adiabaticity in dissociative collisions on transition metals.19i39 For systems like e.g.H,-Ni(l the dissociation probability is unity within experimental error. Nevertheless, an elastic fraction is observed that suggests a weakly corrugated interaction for intact H, of the type that is characteristic of physisorption. How shall these two facts be reconciled? The very large dissociation probability would J. Harris 15 seem to demand that the PES is ‘open’ with respect to the H-H bond direction irre- spective of incidence conditions. That is, forces act on the protons that are sufficiently strong and fast-acting to drive them apart no matter what bond orientation and impact parameter the molecule were to choose, but if this is so, how can we account on the basis of a single PES for an elastic fraction at all? And if it is not so, and there is a small region of phase space where these forces do not operate:’ then how can it be that the resulting elastic scattering is characteristic of a residual interaction that is only weakly corrugated with respect to the surface lattice (and so seems to imply that the ‘fraction’ of the surface from which the reflected fraction emanates is ‘flat ’)? This observation is intriguing and, of itself, deserving of attention.Even if it can be explained within the framework of a general treatment of the scattering that employs only a single PES, then the explanation is likely to be interesting (e.g. a consequence of unquenched rotation during the round trip?), but an alternative explanation is even more intriguing.This is that these observations (assuming they are right) suggest major- ity adiabatic (dissociation) and minority non-adiabatic (diffraction) events. This seems quite likely in view of the manner in which dissociation occurs, as discussed above. The s +d transfer at the Ni(ll0) surface wipes out the entrance channel barrier, but is in some sense a ‘slowish’ process (because d-levels at the Fermi surface have a large effec- tive mass). Accordingly, there must be some amplitude for the d-holes at the surface to remain unfilled in the time it takes for the H, to make its traverse. This amplitude determines the weight of the fraction of H2 that experiences, not the adiabatic inter- action that leads to dissociation, but a physisorption interaction, and scatters as though the Ni surface displays the same kind of entrance channel barrier as a Cu surface would.This possibility, therefore, not only explains the observation of an elastic fraction, but also gives the reason why this fraction appears to experience a physisorption interaction. The reason is that the elastic fraction does experience a physisorption interaction! If it were to turn out that this ‘majority adiabatic/minority non-adiabatic’ explanation is correct then the relative importance of non-adiabaticity for any substrate can be deter- mined as the ratio of the relative strengths of the two fractions (measured, of course, at low 7J. The result would, I believe, confirm the above contention that non-adiabatic processes are of minor importance in dissociation at metal surfaces, but even if this does turn out to be the case, it would be a major step forward to have established it as a matter of experimental certainty rather than theoretical conjecture.In conclusion, the reader will certainly be expecting in these introductory remarks, to the extent that they purport to relate to adyances in and the future of the field, some mention of laser chemistry at surfaces. 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