- Email: [email protected]
On tunneling-dissociation at surfaces
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Surface Science North-Holland
287/288
(1993) 56-63
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On tunneling-dissociation
at surfaces
J. Harris Institut fiir Festkijrperforschung,
Forschungszentrum
Jiilich GmbH, D-51 70 Jiilich, Germany
and A.C. Luntz IBM Research, Almaden Research Center, San Jose, CA 95120, USA Received
3 August
1992; accepted
for publication
14 October
1992
The dissociation rates when molecules with strong internal bonds are incident at surfaces span a huge range. For some systems, typical rates are very small and depend significantly on conditions of incidence and on the surface temperature. In such cases, rates can be significantly influenced, and even dominated by quantum mechanical tunneling through activation barriers. We give a brief review of the main features to be expected when the rate of dissociation is tunneling dominated and discuss recent data for specific adsorption systems in light of these features.
1. Introduction A classification of molecule-solid dissociation systems is often made on the basis of “on-impact” (or direct) versus “precursor” dissociation. In the first case, the molecule dissociates during its initial collision with the surface and the outcome of this collision is either dissociation or back-scattering of the intact molecule. In the second case, the molecule traps in a quasi-stable state e.g. (of molecular chemisorption), which then decays on a time scale much longer than the initial collision time. This separation is of course not rigid or complete but serves to “typecast” the topologies of potential energy surfaces (PES) governing dissociation into categories with strikingly different dynamical behaviours. The “precursor” category is often further subdivided according to the nature or role of the precursor. In one class, the precursor (possibly subject to a physisorption interaction that depends only weakly on parallel coordinates) is an intact molecule that propagates along the surface 0039-6028/93/$06.00
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until either desorbing or encountering an “active site” (e.g. an impurity or a step), where dissociation occurs with high probability. In this case the PES is generally “open” and there is no marked energy barrier between reactants and products. If dissociation is a rare event, it is only so because the vast majority of incident molecules do not find their way to an active site. In another class, the precursor decays with the same probability in whichever unit cell of the surface it is adsorbed and does not require special sites. In this case dissociation is a rare event only if there is a substantial energy barrier along the reaction coordinate. Again, this separation between types of precursors is not rigid. A reaction occurring anywhere on the surface may be unactivated, but subject to massive steric hindering. “Bulk surface” and “active site” mechanisms may occur simultaneously, with one or the other rate limiting, depending on the conditions. We will consider in this paper only the simplest type of precursor, i.e. where there are no special active sites and the assumed low rate is caused by an energy barrier.
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.I. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
With this restriction upon the kind of precursor, the classification between “on-impact” and “precursor” implies a distinction regarding the location of the barrier primarily responsible for the low rate of dissociation. “On-impact” mechanisms assume that the important barrier is in the entrance channel so that the majority event for low-energy incoming molecules is backscattering (except at very low incidence energy and surface temperature, where substantial trapping into a physisorbed state may occur). Molecules that surmount, or penetrate the entrance channel barrier may encounter other, smaller barriers along the reaction coordinate, but ultimately will dissociate. The important distinctive feature is that the dissociation “decision” is taken in the entrance channel. “Precursor” mechanisms assume that the critical barrier is between the “precursor state” (presumed here to be a state of molecular chemisorption) and the dissociated state. Entry into the molecularly adsorbed state is then relatively easy and a low rate of dissociation is accounted for by the preference of this state for decay via other channels than dissociation (e.g. desorption). We assume here that the dynamics governing dissociation is adiabaticand so occurs on a single PES. This assumption is certainly justified for majority events and low energy incident molecules, but is not guaranteed for rare events, or when the incidence energy is very high. The purpose of this note is to outline and discuss the main characteristic features anticipated when tunneling dominates in the two cases of on-impact and precursor dissociation. We also compare this behaviour to some recent experimental studies, especially for alkane dissociation on metal surfaces, which, in the context of understanding C-H bond activation in catalysis, has been subject to detailed investigation.
2. Entrance-channel
tunneling
For on-impact dissociation, the incident molecule must either surmount or penetrate the entrance channel barrier, of height V*. If its total energy (including the vibrational energy
57
which can be released during the dissociation process) is less than I’*, then dissociation is only possible by tunneling. A large number of experimental and theoretical studies have shown that initial vibrational excitation in the bond that is broken is quite effective in promoting dissociation. However, it is usually preferable if equivalent energy is placed in the normal translational coordinate. That is, the dissociation probability for a molecule having vibrational energy E,~,,and translational energy lt is usually smaller than if the molecule is in its vibrational ground state and has translational energy et + eVib. This effect is well understood as a consequence of the kinds of PES that govern entrance channel activated dissociation. For the sake of simplicity, we here restrict the discussion to vibrationally cold molecules. One consequence of an entrance channel tunneling mechanism is that the dissociation probability, S, must depend approximately exponentially on the translational incidence energy, E, i.e. In S N et for lt K I/ *. The precise relation depends on barrier parameters, I/* and the width and shape of the barrier. Only if the barrier is perfectly parabolic does a strict exponential law hold. In general, a downward curvature of the log plot is expected since the barrier should be bell shaped, i.e. its width grows faster than parabolic as the energy is reduced. An approximate exponential dependence has been observed in many molecular beam experiments, e.g. for CH, incident at a W(110) [l], a Ni(ll1) [2] or a Pt(ll1) [3] surface. In the last case, a marked downward curvature was clearly evident in the data. All beam experiments were performed for a number of incident beam angles and it was established that the dominant dependence is on the normal translational energy, l t1 = lt COs*8,. These data are therefore strong evidence that the dissociation of CH, at metal surfaces and low beam energies is rate-limited by tunneling through an entrance channel activation barrier that depends primarily on the normal coordinate of the CH, from the surface plane. A second characteristic of a tunneling mechanism is a marked isotope effi?ct. This arises because the penetration of the molecule’s wave-
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J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
function in the barrier is influenced strongly by the relevant mass, MT, which will usually be of the order of the reduced mass of the vibrational coordinate of the bond that is broken. Since the dissociation of CH, results in chemisorption of an H atom and a CH, radical, the relevant mass is of the order of the proton mass. Deuterating will therefore have a pronounced effect on the tunneling and CD, should have a much lower rate of dissociation than CH,. (The isotope effect is also influenced by the change in zero point vibrational energy on deuteration.) A clear isotope effect was observed in the beam experiments mentioned above, but was about one order of magnitude smaller than would be expected on the basis of a simple tunneling model. The same rather modest isotope effect was found also in experiments conducted under quasi-thermal conditions and led Lo and Ehrlich in a series of papers to question the tunneling interpretation of CH, dissociation [4]. They argued that the observed isotope effect was simply too small to be compatible with a tunneling mechanism. Further doubt was cast on a simple tunneling interpretation by the finding of Luntz and Bethune that the CH, dissociation rate on Pt(ll1) depends approximately exponentially not only on the incident beam energy, et, but also on the inverse surface temperature, l/T, [31. These two dependencies seem in direct conflict, the one suggesting entrance channel tunneling, the other an activated process occurring when the molecule is in thermal contact with the surface. A dependence of entrance channel activated dissociation probabilities on T, could easily be understood if this refers to some change that takes place on the bare surface, such as the creation of vacancies or impurites that may display “active-site” characteristics. Since such processes are activated it would be easy on this basis to explain an Arrhenius dependence of S on l/T,. However, this would mean that the dissociation is ““active-site” dominated, and this is not compatible with the CH, data which shows a large roughly exponential translational activation up to large values of the dissociation probability at a fixed Ts. The resolution of this last conflict, which turned out also to resolve the question of the
isotope effect, involves a third characteristic of entrance channel tunneling mechanisms at surfaces, namely an essential dependence of the tunneling barrier on the coordinates of the lattice atoms. Although it might appear that on-impact entrance channel tunneling should be insensitive to Ts because the dissociation “decision” is made before thermal contact with the surface has been established, this is in fact not at all true. The surface temperature affects the motion of the substrate atoms and influences the outcome of the collision through the recoil of these atoms. The role this recoil can play in tunneling dissociation can easily be understood in a semi-classical picture. At elevated T, the surface atom or atoms nearest the incoming CH, will be moving with a velocity U, whose distribution corresponds to a mean energy per atom N k,T,. If at the moment of impact the surface atom is moving towards or away from the CH,, the relative velocities add or subtract and the effective collision energy is enhanced or suppressed accordingly. Very roughly, the tunnel probability at finite T, is obtained by convoluting the bare tunneling probability at 7; = 0 with the velocity distribution of the surface atoms. Since S grows e~onentially with the effective collision energy, it follows that the result of the convolution will be an exponential growth of S with Ts. In quantum-mechanical language, the effect can be understood in terms of a phonon-gain process. The incoming CH, picks up quanta of energy from the phonons and this assists the passage through the barrier. This mechanism gives a non-Arrhenius T, dependence, as is evident by the saturation of the tunneling probability at a finite limit at ys = 0. The actual dependence is roughly exponential growth from this constant value with T,, rather than the Arrhenius exponential fall-off with l/T$,. Over the limited temperature range covered in many experimental studies, however, the two dependencies are not easily distinguished. The importance of this effect depends sensitively on the ratio of molecular mass to surface atom mass. If this is very small, as for H, surface collisions, the velocities of the surface atoms are small compared with that of the incoming molecule and the surface behaves at all temperatures more or less
J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
as if it is rigid. For molecules with the mass of CH,, this is no longer the case. The effect is quite large and leads to qualitatively different dissociation behaviour at low and high T,. Beam data over a wider range of temperature and energy than available previously have confirmed that the q-dependence of S for CH,Pt(ll1) is indeed non-Arrhenius and entirely compatible with model calculations that included the recoil effect outlined above [S]. For surface temperatures of the order of 800 K commonly employed in beam and other experiments, the effect of recoil is so important that the overall rate of dissociation is completely dominated by thermally-assisted processes. The isotope effect is then that which one obtains for thermally-assisted processes and not for tunneling through a rigid barrier. The differences in the isotope effects at low and high temperature can easily be understood in terms of the simple picture given above. The effectiveness of recoil in promoting tunneling depends on the exponent with which the bare tunneling probability falls off with incidence energy. The steeper the fall off with energy, the greater the increase that will result from the thermal average over the effective collision velocity. Since S falls off more rapidly for CD, than for CH, (the exponent is roughly a m), the T, enhancement will be greater for CD, than for CH,. The overall isotope effect then becomes a strong function of T, and falls off rapidly as T, increases. Explicit calculations showed that the difference between the isotope effects expected at low and at high T, is easily one order of magnitude, thereby resolving the apparent discrepancy of observed ratios with tunneling models. A detailed study [6] showed that the entrance channel tunneling model accounts satisfactorily for all data taken for CH, dissociation on metals, whether under molecular beam, or quasi-thermal conditions, and apparently resolves long standing controversies about the nature of C-H bond activation in catalysis. Amongst the most important consequences of this mechanism is the very strong coupling it implies between the translational energy dependence and the surface temperature dependence of the dissociation probability, That is, the tem-
59
perature enhancement obtained for a molecule with translational incidence energy et depends strongly on lt. At low energies the T, dependence is dramatic, while at higher energies, where the incident velocity is large compared with thermal velocities, there is a relatively weak dependence on T,. As a result of this coupling, it is not possible to deduce sensible potential parameters such as barrier heights from Arrhenius-like plots over limited temperature ranges. In a quasi-thermal situation, with gas temperature Tg and surface temperature T,, different “apparent activation energies” are to be expected with respect to variation of T, at constant Tg and vice versa, and the precise values these have depend on the range of temperatures accessed in the experiment. The non-Arrhenius nature of the temperature dependence is only revealed in measurements, such as those of Winters [71, that span a sufficiently wide range of temperature. The evidence for an on-impact tunneling mechanism for dissociation of CH, on metals is thus comprehensive and rather convincing. This is an ideal case because the tunneling mass is small favouring barrier penetration, while the molecular mass is relatively large, implying substantial T, enhancement via recoil. In addition, the methane molecule is extremely stable and inert and gives rise to a high entrance channel barrier on metals owing to strong Pauli repulsion. The molecule behaves roughly like Ne until its overlap with surface orbitals is sufficiently large to allow chemical changes. H, is less inert than CH, and dissociates on many transition metals spontaneously. However, the PES that describe H, interacting with most simple and noble metals is characterized by strong Pauli repulsion and similar in form to that for CH, (see, for a review, ref. [S]). Hence, these systems are also expected to display entrance channel tunneling for low incidence energies. Clear experimental evidence for this has been published in recent years (see, e.g. refs. [9-1211, though the main focus of work has been more on the role of vibrational excitation than on detailed exploration of the tunneling behaviour in the deep sub-barrier region. These systems display little sensitivity of the dissociation probability to the surface temperature, in accor-
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J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
dance with the above remarks as to the weak coupling of H, to the lattice motion. In general, it is not an easy matter to deduce a value for the activation barrier height I/*. Fitting to theoretical results based on a low-dimensionality model PES is not reliable because the true PES is multi-dimensional. Even within a purely classical treatment, dissociation on a multi-dimensional PES does not display a sharp and abrupt on-set when the energy reaches I/ *. At this point dissociation is possible only if the molecule follows the reaction coordinate perfectly. Accordingly, S, will remain zero at I/* and will increase gradually as the energy increases and more trajectories find their way through the “holes” in the PES. This “steric effect” implies growth of S like some power of E-l/* rather than exponentially as for a tunneling dominated mechanism. However, the difference between the two dependencies may not be easy to distinguish in experiments. The importance of this point has been documented recently in several sets of explicit calculations (see for example refs. [13,14]). Basically, it means that the change from a tunneling to an “over the barrier” mechanism is gradual, is accompanied by no striking change in behaviour and can occur when the overall dissociation probability is still quite low. Tunneling mechanisms are clearly most relevant when one dissociation product is H. Nevertheless, this is only a question of relative rates and there is no reason in principle why heavier systems should not tunnel too. The dissociation of N, on Fe (111) [15] depends on translational incidence energy much as described above, suggesting an entrance channel tunneling mechanism. Explicit calculations for this case appeared to support this interpretation 1161 but failed to include recoil, which is a massive effect because of the large ratio of molecular to surface atom mass [17]. An isotope effect has been reported for the dissociation of 0, on Ag(ll1) and was suggested as evidence for some, unspecified tunneling mechanism [18]. Overall, the data base for these systems is still too sparse to allow clear conclusions. A complication in the case of N, and 0, is their tendency to chemisorb molecularly as well as in a dissociative state. Their PES are
therefore more complex than for CH,, or H, on simple and noble metals, where the molecules physisorb but do not chemisorb without dissociating.
3. “Precursor”
tunneling
This introduces the second class of dissociation systems, the so called precursor dissociation where the rate limiting step occurs on the surface and involves the decay of a molecular intermediate into the dissociation products. This mechanism is of course not guaranteed by the mere existence of an intermediate molecular state. If this intermediate decays into the dissociated state faster than it is populated, then the system belongs to the “on-impact” class. Since the relative rates of population and decay of the intermediate are a function of incidence energy or surface temperature, it is possible, and even quite likely, that systems exist for which the dissociation rate is “on-impact” dominated under some experimental conditions and “precursor decay” dominated in others. We restrict ourselves here to outlining the behaviour to be expected if the decay of the precursor is rate limiting and tunneling dominated. As motivation for this discussion, we note the following experimental observation with regard to the system C,H,-Ir(llO), studied by Mullins and Weinberg [19]. At low energy and surface temperature, ethane adsorbs readily on Ir(ll0) as an intact molecule having a binding energy of about 0.3 eV. The molecular state is only quasi-stable, however, and decays via dissociation or desorption, with dissociation predominating at low T, and desorption predominating at higher T,. Mullins and Weinberg rationalized these data with a kinetic model on the assumption that the barrier to dissociation from the molecular state lies below the vacuum level so that the activation energy required for dissociation is less than that for desorption, i.e. in terms of a classical precursor model. However, at higher ethane incidence energy, a direct dissociation channel opens up, apparently via an onset at a normal translational energy of 0.4 eV. This experiment suggests that
J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
the dissociation barrier is of height about 0.4 eV with respect to vacuum and 0.7 eV with respect to the bottom of the molecular well. However, if this is the case, the probabilities of precursor decay via dissociation relative to desorption would in a classical model be essentially zero, in strong contradiction to the observation that dissociation of the molecular state predominates at low T,. On the other hand, a difficulty with the assumption that the dissociation barrier is very low as suggested by the precursor kinetic model is that it fails to explain why the direct dissociation channel appears to close at translational incidence energies below 0.4 eV. If the barrier between molecular and dissociated states is below the vacuum level, a gas-phase molecule can surmount it even if its kinetic incidence energy is zero. A similar situation arises with the system 0, on Pi(ll1) [20-221. Here essentially no on-impact dissociation occurs. Instead, a state of molecular chemisorption is populated (weakly activated with an entrance channel barrier of N 0.2 eV) which is stable on a time scale of hours for T, < 130 K, but dissociates in preference to desorption at higher T,. Again, a kinetic analysis can be made consistent with the data only on the assumption that the barrier to dissociation from the molecular state lies below the vacuum level. It is possible that these observations could be a feature of the extreme multi-dimensionality of the PES and the blocking of the direct channel due to a massive steric effect. However, it is not easy to see why the same steric effect should not be operative too for precursor dissociation by inhibiting decay of the molecular state via dissociation. An incoming molecule that traps in a state of molecular chemisorption samples many excited states before relaxing to low-lying states of the well and so should sample essentially the same region of phase space as a particle excited from a low-lying state via a thermal fluctuation. Hence, both precursor and direct processes should see roughly the same steric effects. Accordingly, if the barrier is low as suggested by the kinetic model, the direct channel should have a finite amplitude at low incidence energy, growing with energy in a manner that depends on details of the PES [23].
61
An alternative explanation for the observed behaviour takes as its starting point the absence of direct dissociation at low energy and efficient trapping in the molecular state. This behaviour will surely result if the molecular and dissociated states are separated by a high, thin barrier. At low incidence energy an incoming molecule will sample the molecular well, but be prevented by the barrier from dissociating. The molecule will lose energy and relax into the molecular state, which then decays on a much longer time scale, either by tunneling dissociation or by desorption as a result of a temperature fluctuation. Precursor decay is then governed not by a ratio of Boltzmann factors, but by the ratio of the tunneling rate, IYT,), to the desorption rate, II vexp( - W/k&), where T, is the surface temperature, W the depth of the molecular well and v a frequency factor. The dissociation probability is then given by S(T,) = r(T,)/[r(T,) + II(T An immediate consequence is that SCT,) approaches unity as T, --f 0 because ZYT,) saturates while II(T,) vanishes at zero temperature. This remains true even if the dissociated state lies higher in energy than the bottom of the molecular well (i.e. WmO,< WdiSS< 0) because temperature assisted tunneling from vibrationally excited molecular states is also possible. If 12denotes a state where the entire molecule vibrates against the substrate atoms, with excitation energy E,, we can write r(T,) = CJ-“P,~~,T,l, where /3,[k,T,] are the Boltzmann populations. Since E, < W, &[k,T,] and so T(T,) goes to zero slower than D(T,) even if r, = 0 for n less than some value where the excitation energy equals the difference in the well-depths. In such a case, the dissociated state can decay back into the molecular state, but this will not happen because the dissociation products are physically separated and the probability of an accidental encounter is astronomically small. These considerations are of course academic if the absolute rates are so low as to obviate observation of the decay of the precursor. What is important, however, is that the dissociation “decision” is determined by the ratio of small numbers and that, if a low temperature is maintained for long enough, dissociative tunneling must occur eventually. Thus, for sufficiently low T, the very
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J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
low rate at which tunneling occurs translates into a probability for dissociation of a single molecule on a clean surface that is limited only by the trapping probability into the molecular precursor. This can easily be of the order of unity and falls off as T, increases. In a thermal environment, of course, the dissociation probability falls because of blocking of the molecular sites. As the temperature is raised both the tunneling rate and the desorption rate increase. However, the latter will increase faster so the bias in favor of dissociation rather than desorption will lessen as T, increases and ultimately shift in favor of desorption as the majority event. A characteristic of precursor dissociation by tunneling is then that a preference for dissociation should give way to a preference for desorption as T, increases. A detailed analysis using a model PES relevant to C,H,-Ir(ll0) [24] gave a value of T, - 180 K for the crossover temperature, where the majority event switches from dissociation to desorption. This analysis was broadly consistent with the data of Mullins and Weinberg. An interpretation of these data in terms of precursor decay via tunneling is therefore possible, and would explain immediately why the direct channel appears to open suddenly at a relatively large value of the incidence energy since the model PES contains such a high barrier. A second characteristic of precursor decay via tunneling is a marked isotope effect. This would manifest itself most obviously in a lowered value of the crossover temperature, T,. In the model calculation referred to above, it was found that T, - 140 for C,D, as against N 180 K for C,H,. Currently, no experimental data are available to either confirm or deny such a prediction. The O,-Pt(ll1) system, which shows some features similar to C,H,-Ir(llO), displays negligible precursor decay on a time scale of an hour for T, < 130 K, which would be compatible with a tunneling mechanism in view of the large mass involved. A difficulty with a tunneling interpretation in this system is to reconcile the strong preference for dissociation versus desorption that occurs at higher T,. This could only be explained in terms of a relatively large crossover temperature and a strong T, enhancement of the tunnel-
ing rate. In view of the large mass and consequent strong coupling to lattice motion, a strong dependence is expected, though it remains unclear whether the effect can account satisfactorily for the data. We expect to report on this point in the future. While the above remarks are suggestive that a mechanism of precursor mediated dissociation by tunneling is likely in some cases, the evidence for this remains indirect and inconclusive. Further work, both experimental and theoretical is needed. Especially, a detailed experimental study of the decay of the molecular states under carefully controlled conditions would seem to be a prerequisite for progress. This requires populating the molecular state with the surface maintained at very low T, and warming gradually in small T, steps. If the dissociated state lies lower in energy than the molecular state, (Wdiss< I&,,), a hallmark of the tunneling mechanism is that the decay of this state must approach a constant as T, + 0. If the molecular state lies lower, (WmO,< Wdiss)then tunneling can only occur from excited states of the molecular well. The decay of the precursor will then be activated with an apparent activation energy that is roughly the difference in energy between the well-bottoms (assuming a dense level spectrum in the molecular well). To date, no study of a surface reaction has to our knowledge been carried out with sufficient sensitivity to either conclusively demonstrate this behaviour or to rule it out. As an example of the kind of study that is required, we cite the work of Alberding et al. [251, who considered the binding of CO molecules to hemoglobin chains (which may be thought of in some sense as “one-dimensional surfaces”). The relevant PES possesses three potential barriers, of which the innermost separates the ground state, with the CO closest to the Fe atom at the end of the chain, from an excited state characterized by a larger Fe-CO distance. The parallel with surface dissociation is not exact since the excited state corresponds essentially to an unbound CO, and the main chemical change occurs on the hemoglobin chain rather than the CO, which does not dissociate. A roughly equivalent surface situation might be transport between a physi-
J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
sorbed “precursor” state that is quasi-stable and a molecularly chemisorbed ground state of lower energy. Relaxation to the ground state was studied by populating the excited state with a laser pulse and monitoring its subsequent decay as a function of time using optical techniques and with precise temperature control. It was established that the rate of population approached a constant as the temperature was lowered and this was taken as evidence that the reaction occurs via a tunneling mechanism at low T( < 30 K) that goes into an “over the barrier” mechanism at higher T. By comparing data taken at the extreme ends of the temperature range reasonable barrier parameters for the reaction could be obtained. This classic study illustrates dramatically the point made above concerning precursor tunneling of heavy adsorbates. The associated rates are low, but nevertheless provide the dominant decay mechanism if rates for thermally activated processes are even lower. Since precursor tunneling is manifestly demonstrated for a CO molecule binding to hemoglobin, there is no reason to doubt that similar mechanisms play a role in reactions occurring on surfaces.
Acknowledgement We acknowledge gratefully support for this work via a NATO Collaborative Research Grant No. 0834.
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[2] M.B. Lee, Q.Y. Yang and S.T. Ceyer, J. Chem. Phys. 87
(1987) 2724. [3] A.C. Luntz and D.S. Bethune, J. Chem. Phys. 90 (1989) 1274. [4] Tai-Chin Lo and G. Ehrlich, Surf. Sci. 205 (1988) L813. [5] J. Harris, J. Simon, A.C. Luntz, C.B. Mullins, and C.T. Rettner, Phys. Rev. Lett. 67 (1991) 652. [6] AC. Luntz and J. Harris, Surf. Sci. 258 (1991) 397. [7] H.F. Winters, J. Chem. Phys. 64 (1976) 3495. [8] J. Harris, Appl. Phys. A 47 (1988) 63. [9] A Winkler, G. Anger and K.D. Rendulic, Surf. Sci. 220 (1989) 1. [lo] B.E. Hayden and C.L.A. Lamont, Phys. Rev. Lett. 63 (1989) 1823. [ll] H.F. Berger and K.D. Rendulic, Surf Sci. 253 (1991) 325. [12] CT. Rettner, D.J. Auerbach and H.A. Michelsen, Phys. Rev. Lett. 68 (1992) 1164. [13] U. Nielsen, D. Halstead, S. Holloway and J.K. Norskov, J. Chem. Phys. 93 (1990) 2879. [14] A.J. Cruz and B. Jackson, J. Chem. Phys. 94 (1991) 5715. [15] C.T. Rettner and H. Stein, Phys. Rev. Lett. 59 (1987) 2768. [16] G. Haase, M. Asscher, O.M. Becker and R. Kosloff, Surf. Sci. 206 (1988) L880. [17] M. Hand and J. Harris, J. Chem. Phys. 92 (1990) 7610. [18] P.H.F. Reijen, A. Raukema, U. van Slooten and A.W. Kleyn, J. Chem. Phys. 94 (1991) 2368. [19] C.B. Mullins and W.H. Weinberg, J. Chem. Phys. 92 (1990) 4508. [20] AC. Luntz, M.D. Williams and D.S. Bethune, J. Chem. Phys. 89 (1988) 4381. [21] A.C. Luntz, J. Grimblot and D.E. Fowler, Phys. Rev. B 39 (1989) 12903. [22] C.T. Rettner and C.B. Mullins, J. Chem. Phys. 94 (1991) 1626. [23] S. Holloway and J.W. Gadzuk, J. Chem. Phys. 77 (1985) 5203. [24] A.C. Luntz and J. Harris, J. Chem. Phys. 96 (1992) 7054. [25] N. Alberding, S.S. Chan, L. Eisenstein, H. Frauenfelder, D. Good, T.M. Nordund, M.F. Pert&, A.H. Reynolds and L.B. Sorensen, Biochemistry 17 (1978) 43.
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Surface Science North-Holland
287/288
(1993) 56-63
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On tunneling-dissociation
at surfaces
J. Harris Institut fiir Festkijrperforschung,
Forschungszentrum
Jiilich GmbH, D-51 70 Jiilich, Germany
and A.C. Luntz IBM Research, Almaden Research Center, San Jose, CA 95120, USA Received
3 August
1992; accepted
for publication
14 October
1992
The dissociation rates when molecules with strong internal bonds are incident at surfaces span a huge range. For some systems, typical rates are very small and depend significantly on conditions of incidence and on the surface temperature. In such cases, rates can be significantly influenced, and even dominated by quantum mechanical tunneling through activation barriers. We give a brief review of the main features to be expected when the rate of dissociation is tunneling dominated and discuss recent data for specific adsorption systems in light of these features.
1. Introduction A classification of molecule-solid dissociation systems is often made on the basis of “on-impact” (or direct) versus “precursor” dissociation. In the first case, the molecule dissociates during its initial collision with the surface and the outcome of this collision is either dissociation or back-scattering of the intact molecule. In the second case, the molecule traps in a quasi-stable state e.g. (of molecular chemisorption), which then decays on a time scale much longer than the initial collision time. This separation is of course not rigid or complete but serves to “typecast” the topologies of potential energy surfaces (PES) governing dissociation into categories with strikingly different dynamical behaviours. The “precursor” category is often further subdivided according to the nature or role of the precursor. In one class, the precursor (possibly subject to a physisorption interaction that depends only weakly on parallel coordinates) is an intact molecule that propagates along the surface 0039-6028/93/$06.00
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until either desorbing or encountering an “active site” (e.g. an impurity or a step), where dissociation occurs with high probability. In this case the PES is generally “open” and there is no marked energy barrier between reactants and products. If dissociation is a rare event, it is only so because the vast majority of incident molecules do not find their way to an active site. In another class, the precursor decays with the same probability in whichever unit cell of the surface it is adsorbed and does not require special sites. In this case dissociation is a rare event only if there is a substantial energy barrier along the reaction coordinate. Again, this separation between types of precursors is not rigid. A reaction occurring anywhere on the surface may be unactivated, but subject to massive steric hindering. “Bulk surface” and “active site” mechanisms may occur simultaneously, with one or the other rate limiting, depending on the conditions. We will consider in this paper only the simplest type of precursor, i.e. where there are no special active sites and the assumed low rate is caused by an energy barrier.
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.I. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
With this restriction upon the kind of precursor, the classification between “on-impact” and “precursor” implies a distinction regarding the location of the barrier primarily responsible for the low rate of dissociation. “On-impact” mechanisms assume that the important barrier is in the entrance channel so that the majority event for low-energy incoming molecules is backscattering (except at very low incidence energy and surface temperature, where substantial trapping into a physisorbed state may occur). Molecules that surmount, or penetrate the entrance channel barrier may encounter other, smaller barriers along the reaction coordinate, but ultimately will dissociate. The important distinctive feature is that the dissociation “decision” is taken in the entrance channel. “Precursor” mechanisms assume that the critical barrier is between the “precursor state” (presumed here to be a state of molecular chemisorption) and the dissociated state. Entry into the molecularly adsorbed state is then relatively easy and a low rate of dissociation is accounted for by the preference of this state for decay via other channels than dissociation (e.g. desorption). We assume here that the dynamics governing dissociation is adiabaticand so occurs on a single PES. This assumption is certainly justified for majority events and low energy incident molecules, but is not guaranteed for rare events, or when the incidence energy is very high. The purpose of this note is to outline and discuss the main characteristic features anticipated when tunneling dominates in the two cases of on-impact and precursor dissociation. We also compare this behaviour to some recent experimental studies, especially for alkane dissociation on metal surfaces, which, in the context of understanding C-H bond activation in catalysis, has been subject to detailed investigation.
2. Entrance-channel
tunneling
For on-impact dissociation, the incident molecule must either surmount or penetrate the entrance channel barrier, of height V*. If its total energy (including the vibrational energy
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which can be released during the dissociation process) is less than I’*, then dissociation is only possible by tunneling. A large number of experimental and theoretical studies have shown that initial vibrational excitation in the bond that is broken is quite effective in promoting dissociation. However, it is usually preferable if equivalent energy is placed in the normal translational coordinate. That is, the dissociation probability for a molecule having vibrational energy E,~,,and translational energy lt is usually smaller than if the molecule is in its vibrational ground state and has translational energy et + eVib. This effect is well understood as a consequence of the kinds of PES that govern entrance channel activated dissociation. For the sake of simplicity, we here restrict the discussion to vibrationally cold molecules. One consequence of an entrance channel tunneling mechanism is that the dissociation probability, S, must depend approximately exponentially on the translational incidence energy, E, i.e. In S N et for lt K I/ *. The precise relation depends on barrier parameters, I/* and the width and shape of the barrier. Only if the barrier is perfectly parabolic does a strict exponential law hold. In general, a downward curvature of the log plot is expected since the barrier should be bell shaped, i.e. its width grows faster than parabolic as the energy is reduced. An approximate exponential dependence has been observed in many molecular beam experiments, e.g. for CH, incident at a W(110) [l], a Ni(ll1) [2] or a Pt(ll1) [3] surface. In the last case, a marked downward curvature was clearly evident in the data. All beam experiments were performed for a number of incident beam angles and it was established that the dominant dependence is on the normal translational energy, l t1 = lt COs*8,. These data are therefore strong evidence that the dissociation of CH, at metal surfaces and low beam energies is rate-limited by tunneling through an entrance channel activation barrier that depends primarily on the normal coordinate of the CH, from the surface plane. A second characteristic of a tunneling mechanism is a marked isotope effi?ct. This arises because the penetration of the molecule’s wave-
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J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
function in the barrier is influenced strongly by the relevant mass, MT, which will usually be of the order of the reduced mass of the vibrational coordinate of the bond that is broken. Since the dissociation of CH, results in chemisorption of an H atom and a CH, radical, the relevant mass is of the order of the proton mass. Deuterating will therefore have a pronounced effect on the tunneling and CD, should have a much lower rate of dissociation than CH,. (The isotope effect is also influenced by the change in zero point vibrational energy on deuteration.) A clear isotope effect was observed in the beam experiments mentioned above, but was about one order of magnitude smaller than would be expected on the basis of a simple tunneling model. The same rather modest isotope effect was found also in experiments conducted under quasi-thermal conditions and led Lo and Ehrlich in a series of papers to question the tunneling interpretation of CH, dissociation [4]. They argued that the observed isotope effect was simply too small to be compatible with a tunneling mechanism. Further doubt was cast on a simple tunneling interpretation by the finding of Luntz and Bethune that the CH, dissociation rate on Pt(ll1) depends approximately exponentially not only on the incident beam energy, et, but also on the inverse surface temperature, l/T, [31. These two dependencies seem in direct conflict, the one suggesting entrance channel tunneling, the other an activated process occurring when the molecule is in thermal contact with the surface. A dependence of entrance channel activated dissociation probabilities on T, could easily be understood if this refers to some change that takes place on the bare surface, such as the creation of vacancies or impurites that may display “active-site” characteristics. Since such processes are activated it would be easy on this basis to explain an Arrhenius dependence of S on l/T,. However, this would mean that the dissociation is ““active-site” dominated, and this is not compatible with the CH, data which shows a large roughly exponential translational activation up to large values of the dissociation probability at a fixed Ts. The resolution of this last conflict, which turned out also to resolve the question of the
isotope effect, involves a third characteristic of entrance channel tunneling mechanisms at surfaces, namely an essential dependence of the tunneling barrier on the coordinates of the lattice atoms. Although it might appear that on-impact entrance channel tunneling should be insensitive to Ts because the dissociation “decision” is made before thermal contact with the surface has been established, this is in fact not at all true. The surface temperature affects the motion of the substrate atoms and influences the outcome of the collision through the recoil of these atoms. The role this recoil can play in tunneling dissociation can easily be understood in a semi-classical picture. At elevated T, the surface atom or atoms nearest the incoming CH, will be moving with a velocity U, whose distribution corresponds to a mean energy per atom N k,T,. If at the moment of impact the surface atom is moving towards or away from the CH,, the relative velocities add or subtract and the effective collision energy is enhanced or suppressed accordingly. Very roughly, the tunnel probability at finite T, is obtained by convoluting the bare tunneling probability at 7; = 0 with the velocity distribution of the surface atoms. Since S grows e~onentially with the effective collision energy, it follows that the result of the convolution will be an exponential growth of S with Ts. In quantum-mechanical language, the effect can be understood in terms of a phonon-gain process. The incoming CH, picks up quanta of energy from the phonons and this assists the passage through the barrier. This mechanism gives a non-Arrhenius T, dependence, as is evident by the saturation of the tunneling probability at a finite limit at ys = 0. The actual dependence is roughly exponential growth from this constant value with T,, rather than the Arrhenius exponential fall-off with l/T$,. Over the limited temperature range covered in many experimental studies, however, the two dependencies are not easily distinguished. The importance of this effect depends sensitively on the ratio of molecular mass to surface atom mass. If this is very small, as for H, surface collisions, the velocities of the surface atoms are small compared with that of the incoming molecule and the surface behaves at all temperatures more or less
J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
as if it is rigid. For molecules with the mass of CH,, this is no longer the case. The effect is quite large and leads to qualitatively different dissociation behaviour at low and high T,. Beam data over a wider range of temperature and energy than available previously have confirmed that the q-dependence of S for CH,Pt(ll1) is indeed non-Arrhenius and entirely compatible with model calculations that included the recoil effect outlined above [S]. For surface temperatures of the order of 800 K commonly employed in beam and other experiments, the effect of recoil is so important that the overall rate of dissociation is completely dominated by thermally-assisted processes. The isotope effect is then that which one obtains for thermally-assisted processes and not for tunneling through a rigid barrier. The differences in the isotope effects at low and high temperature can easily be understood in terms of the simple picture given above. The effectiveness of recoil in promoting tunneling depends on the exponent with which the bare tunneling probability falls off with incidence energy. The steeper the fall off with energy, the greater the increase that will result from the thermal average over the effective collision velocity. Since S falls off more rapidly for CD, than for CH, (the exponent is roughly a m), the T, enhancement will be greater for CD, than for CH,. The overall isotope effect then becomes a strong function of T, and falls off rapidly as T, increases. Explicit calculations showed that the difference between the isotope effects expected at low and at high T, is easily one order of magnitude, thereby resolving the apparent discrepancy of observed ratios with tunneling models. A detailed study [6] showed that the entrance channel tunneling model accounts satisfactorily for all data taken for CH, dissociation on metals, whether under molecular beam, or quasi-thermal conditions, and apparently resolves long standing controversies about the nature of C-H bond activation in catalysis. Amongst the most important consequences of this mechanism is the very strong coupling it implies between the translational energy dependence and the surface temperature dependence of the dissociation probability, That is, the tem-
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perature enhancement obtained for a molecule with translational incidence energy et depends strongly on lt. At low energies the T, dependence is dramatic, while at higher energies, where the incident velocity is large compared with thermal velocities, there is a relatively weak dependence on T,. As a result of this coupling, it is not possible to deduce sensible potential parameters such as barrier heights from Arrhenius-like plots over limited temperature ranges. In a quasi-thermal situation, with gas temperature Tg and surface temperature T,, different “apparent activation energies” are to be expected with respect to variation of T, at constant Tg and vice versa, and the precise values these have depend on the range of temperatures accessed in the experiment. The non-Arrhenius nature of the temperature dependence is only revealed in measurements, such as those of Winters [71, that span a sufficiently wide range of temperature. The evidence for an on-impact tunneling mechanism for dissociation of CH, on metals is thus comprehensive and rather convincing. This is an ideal case because the tunneling mass is small favouring barrier penetration, while the molecular mass is relatively large, implying substantial T, enhancement via recoil. In addition, the methane molecule is extremely stable and inert and gives rise to a high entrance channel barrier on metals owing to strong Pauli repulsion. The molecule behaves roughly like Ne until its overlap with surface orbitals is sufficiently large to allow chemical changes. H, is less inert than CH, and dissociates on many transition metals spontaneously. However, the PES that describe H, interacting with most simple and noble metals is characterized by strong Pauli repulsion and similar in form to that for CH, (see, for a review, ref. [S]). Hence, these systems are also expected to display entrance channel tunneling for low incidence energies. Clear experimental evidence for this has been published in recent years (see, e.g. refs. [9-1211, though the main focus of work has been more on the role of vibrational excitation than on detailed exploration of the tunneling behaviour in the deep sub-barrier region. These systems display little sensitivity of the dissociation probability to the surface temperature, in accor-
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J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
dance with the above remarks as to the weak coupling of H, to the lattice motion. In general, it is not an easy matter to deduce a value for the activation barrier height I/*. Fitting to theoretical results based on a low-dimensionality model PES is not reliable because the true PES is multi-dimensional. Even within a purely classical treatment, dissociation on a multi-dimensional PES does not display a sharp and abrupt on-set when the energy reaches I/ *. At this point dissociation is possible only if the molecule follows the reaction coordinate perfectly. Accordingly, S, will remain zero at I/* and will increase gradually as the energy increases and more trajectories find their way through the “holes” in the PES. This “steric effect” implies growth of S like some power of E-l/* rather than exponentially as for a tunneling dominated mechanism. However, the difference between the two dependencies may not be easy to distinguish in experiments. The importance of this point has been documented recently in several sets of explicit calculations (see for example refs. [13,14]). Basically, it means that the change from a tunneling to an “over the barrier” mechanism is gradual, is accompanied by no striking change in behaviour and can occur when the overall dissociation probability is still quite low. Tunneling mechanisms are clearly most relevant when one dissociation product is H. Nevertheless, this is only a question of relative rates and there is no reason in principle why heavier systems should not tunnel too. The dissociation of N, on Fe (111) [15] depends on translational incidence energy much as described above, suggesting an entrance channel tunneling mechanism. Explicit calculations for this case appeared to support this interpretation 1161 but failed to include recoil, which is a massive effect because of the large ratio of molecular to surface atom mass [17]. An isotope effect has been reported for the dissociation of 0, on Ag(ll1) and was suggested as evidence for some, unspecified tunneling mechanism [18]. Overall, the data base for these systems is still too sparse to allow clear conclusions. A complication in the case of N, and 0, is their tendency to chemisorb molecularly as well as in a dissociative state. Their PES are
therefore more complex than for CH,, or H, on simple and noble metals, where the molecules physisorb but do not chemisorb without dissociating.
3. “Precursor”
tunneling
This introduces the second class of dissociation systems, the so called precursor dissociation where the rate limiting step occurs on the surface and involves the decay of a molecular intermediate into the dissociation products. This mechanism is of course not guaranteed by the mere existence of an intermediate molecular state. If this intermediate decays into the dissociated state faster than it is populated, then the system belongs to the “on-impact” class. Since the relative rates of population and decay of the intermediate are a function of incidence energy or surface temperature, it is possible, and even quite likely, that systems exist for which the dissociation rate is “on-impact” dominated under some experimental conditions and “precursor decay” dominated in others. We restrict ourselves here to outlining the behaviour to be expected if the decay of the precursor is rate limiting and tunneling dominated. As motivation for this discussion, we note the following experimental observation with regard to the system C,H,-Ir(llO), studied by Mullins and Weinberg [19]. At low energy and surface temperature, ethane adsorbs readily on Ir(ll0) as an intact molecule having a binding energy of about 0.3 eV. The molecular state is only quasi-stable, however, and decays via dissociation or desorption, with dissociation predominating at low T, and desorption predominating at higher T,. Mullins and Weinberg rationalized these data with a kinetic model on the assumption that the barrier to dissociation from the molecular state lies below the vacuum level so that the activation energy required for dissociation is less than that for desorption, i.e. in terms of a classical precursor model. However, at higher ethane incidence energy, a direct dissociation channel opens up, apparently via an onset at a normal translational energy of 0.4 eV. This experiment suggests that
J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
the dissociation barrier is of height about 0.4 eV with respect to vacuum and 0.7 eV with respect to the bottom of the molecular well. However, if this is the case, the probabilities of precursor decay via dissociation relative to desorption would in a classical model be essentially zero, in strong contradiction to the observation that dissociation of the molecular state predominates at low T,. On the other hand, a difficulty with the assumption that the dissociation barrier is very low as suggested by the precursor kinetic model is that it fails to explain why the direct dissociation channel appears to close at translational incidence energies below 0.4 eV. If the barrier between molecular and dissociated states is below the vacuum level, a gas-phase molecule can surmount it even if its kinetic incidence energy is zero. A similar situation arises with the system 0, on Pi(ll1) [20-221. Here essentially no on-impact dissociation occurs. Instead, a state of molecular chemisorption is populated (weakly activated with an entrance channel barrier of N 0.2 eV) which is stable on a time scale of hours for T, < 130 K, but dissociates in preference to desorption at higher T,. Again, a kinetic analysis can be made consistent with the data only on the assumption that the barrier to dissociation from the molecular state lies below the vacuum level. It is possible that these observations could be a feature of the extreme multi-dimensionality of the PES and the blocking of the direct channel due to a massive steric effect. However, it is not easy to see why the same steric effect should not be operative too for precursor dissociation by inhibiting decay of the molecular state via dissociation. An incoming molecule that traps in a state of molecular chemisorption samples many excited states before relaxing to low-lying states of the well and so should sample essentially the same region of phase space as a particle excited from a low-lying state via a thermal fluctuation. Hence, both precursor and direct processes should see roughly the same steric effects. Accordingly, if the barrier is low as suggested by the kinetic model, the direct channel should have a finite amplitude at low incidence energy, growing with energy in a manner that depends on details of the PES [23].
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An alternative explanation for the observed behaviour takes as its starting point the absence of direct dissociation at low energy and efficient trapping in the molecular state. This behaviour will surely result if the molecular and dissociated states are separated by a high, thin barrier. At low incidence energy an incoming molecule will sample the molecular well, but be prevented by the barrier from dissociating. The molecule will lose energy and relax into the molecular state, which then decays on a much longer time scale, either by tunneling dissociation or by desorption as a result of a temperature fluctuation. Precursor decay is then governed not by a ratio of Boltzmann factors, but by the ratio of the tunneling rate, IYT,), to the desorption rate, II vexp( - W/k&), where T, is the surface temperature, W the depth of the molecular well and v a frequency factor. The dissociation probability is then given by S(T,) = r(T,)/[r(T,) + II(T An immediate consequence is that SCT,) approaches unity as T, --f 0 because ZYT,) saturates while II(T,) vanishes at zero temperature. This remains true even if the dissociated state lies higher in energy than the bottom of the molecular well (i.e. WmO,< WdiSS< 0) because temperature assisted tunneling from vibrationally excited molecular states is also possible. If 12denotes a state where the entire molecule vibrates against the substrate atoms, with excitation energy E,, we can write r(T,) = CJ-“P,~~,T,l, where /3,[k,T,] are the Boltzmann populations. Since E, < W, &[k,T,] and so T(T,) goes to zero slower than D(T,) even if r, = 0 for n less than some value where the excitation energy equals the difference in the well-depths. In such a case, the dissociated state can decay back into the molecular state, but this will not happen because the dissociation products are physically separated and the probability of an accidental encounter is astronomically small. These considerations are of course academic if the absolute rates are so low as to obviate observation of the decay of the precursor. What is important, however, is that the dissociation “decision” is determined by the ratio of small numbers and that, if a low temperature is maintained for long enough, dissociative tunneling must occur eventually. Thus, for sufficiently low T, the very
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J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
low rate at which tunneling occurs translates into a probability for dissociation of a single molecule on a clean surface that is limited only by the trapping probability into the molecular precursor. This can easily be of the order of unity and falls off as T, increases. In a thermal environment, of course, the dissociation probability falls because of blocking of the molecular sites. As the temperature is raised both the tunneling rate and the desorption rate increase. However, the latter will increase faster so the bias in favor of dissociation rather than desorption will lessen as T, increases and ultimately shift in favor of desorption as the majority event. A characteristic of precursor dissociation by tunneling is then that a preference for dissociation should give way to a preference for desorption as T, increases. A detailed analysis using a model PES relevant to C,H,-Ir(ll0) [24] gave a value of T, - 180 K for the crossover temperature, where the majority event switches from dissociation to desorption. This analysis was broadly consistent with the data of Mullins and Weinberg. An interpretation of these data in terms of precursor decay via tunneling is therefore possible, and would explain immediately why the direct channel appears to open suddenly at a relatively large value of the incidence energy since the model PES contains such a high barrier. A second characteristic of precursor decay via tunneling is a marked isotope effect. This would manifest itself most obviously in a lowered value of the crossover temperature, T,. In the model calculation referred to above, it was found that T, - 140 for C,D, as against N 180 K for C,H,. Currently, no experimental data are available to either confirm or deny such a prediction. The O,-Pt(ll1) system, which shows some features similar to C,H,-Ir(llO), displays negligible precursor decay on a time scale of an hour for T, < 130 K, which would be compatible with a tunneling mechanism in view of the large mass involved. A difficulty with a tunneling interpretation in this system is to reconcile the strong preference for dissociation versus desorption that occurs at higher T,. This could only be explained in terms of a relatively large crossover temperature and a strong T, enhancement of the tunnel-
ing rate. In view of the large mass and consequent strong coupling to lattice motion, a strong dependence is expected, though it remains unclear whether the effect can account satisfactorily for the data. We expect to report on this point in the future. While the above remarks are suggestive that a mechanism of precursor mediated dissociation by tunneling is likely in some cases, the evidence for this remains indirect and inconclusive. Further work, both experimental and theoretical is needed. Especially, a detailed experimental study of the decay of the molecular states under carefully controlled conditions would seem to be a prerequisite for progress. This requires populating the molecular state with the surface maintained at very low T, and warming gradually in small T, steps. If the dissociated state lies lower in energy than the molecular state, (Wdiss< I&,,), a hallmark of the tunneling mechanism is that the decay of this state must approach a constant as T, + 0. If the molecular state lies lower, (WmO,< Wdiss)then tunneling can only occur from excited states of the molecular well. The decay of the precursor will then be activated with an apparent activation energy that is roughly the difference in energy between the well-bottoms (assuming a dense level spectrum in the molecular well). To date, no study of a surface reaction has to our knowledge been carried out with sufficient sensitivity to either conclusively demonstrate this behaviour or to rule it out. As an example of the kind of study that is required, we cite the work of Alberding et al. [251, who considered the binding of CO molecules to hemoglobin chains (which may be thought of in some sense as “one-dimensional surfaces”). The relevant PES possesses three potential barriers, of which the innermost separates the ground state, with the CO closest to the Fe atom at the end of the chain, from an excited state characterized by a larger Fe-CO distance. The parallel with surface dissociation is not exact since the excited state corresponds essentially to an unbound CO, and the main chemical change occurs on the hemoglobin chain rather than the CO, which does not dissociate. A roughly equivalent surface situation might be transport between a physi-
J. Harris, A.C. Luntz / On tunneling-dissociation at surfaces
sorbed “precursor” state that is quasi-stable and a molecularly chemisorbed ground state of lower energy. Relaxation to the ground state was studied by populating the excited state with a laser pulse and monitoring its subsequent decay as a function of time using optical techniques and with precise temperature control. It was established that the rate of population approached a constant as the temperature was lowered and this was taken as evidence that the reaction occurs via a tunneling mechanism at low T( < 30 K) that goes into an “over the barrier” mechanism at higher T. By comparing data taken at the extreme ends of the temperature range reasonable barrier parameters for the reaction could be obtained. This classic study illustrates dramatically the point made above concerning precursor tunneling of heavy adsorbates. The associated rates are low, but nevertheless provide the dominant decay mechanism if rates for thermally activated processes are even lower. Since precursor tunneling is manifestly demonstrated for a CO molecule binding to hemoglobin, there is no reason to doubt that similar mechanisms play a role in reactions occurring on surfaces.
Acknowledgement We acknowledge gratefully support for this work via a NATO Collaborative Research Grant No. 0834.
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