Electron-driven dynamics at the gas/solid interface: dissociation, desorption and reaction of adsorbed molecules

摘要

Faraday Discuss., 1993,96, 117-127 Electron-driven Dynamics at the Gas/Solid Interface: Dissociation, Desorption and Reaction of Adsorbed Molecules Richard J. Guest, Ian M. Goldby and Richard E. Palmer* Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, UK CB3 OHE Darren N. Bly, David M. Hartley and Philip J. Rous Department of Physics, University of Maryland Baltimore County, Baltimore, MD 21228-5398, USA This paper considers dynamical processes which can be initiated by low- energy (1-50 eV) electrons in adsorbed molecular layers. We have investi- gated the production of negative ions by electron-stimulated desorption from well ordered monolayer and multilayer films of 0, on graphite. Reson- ances are observed in the yield of both 0-and 0; ions, and are attributed to the process of dissociative electron attachment.In the monolayer regime, the 8 eV resonance which dominates the 0-yield at higher coverages is found to be suppressed, and dipolar dissociation dominates. This suppress- ion is attributed to the image potential, which attracts low-energy ions back to the surface. The angular distribution of 0-ions desorbed from the monolayer 6 and ( phases we found to be almost independent of the initial molecular orientation on the surface. Classical trajectory calculations indi- cate that the molecule becomes rotationally excited prior to dissociation, causing the initial orientational order to be lost. This marks a difference between the dissociation and desorption dynamics of physisorbed and chemi- sorbed molecules, where the angular distribution of desorbed fragments is generally taken to reflect the molecular orientation on the surface.1. Introduction Electron-capture mechanisms have been invoked to explain a number of dynamical phe- nomena occurring at the gas/solid interface. Low-energy electrons are important not only in direct processes such as electron-stimulated desorption2 (ESD) and similar elec- tron impact interactions, but also in a number of indirect effects, such as molecular beam scattering3 and dissociative ad~orption,~ where the electron originates in the sub- strate itself. It has been shown recently by several that low-energy electrons originating from the substrate play a crucial role in photon-stimulated desorption of an adsorbate from a substrate.The observation of all these electron-driven processes indi- cates the need for a good understanding of electron-molecule dynamics at surfaces. In this paper, we present the results of a study of the dissociation and subsequent dynamics of weakly bound (condensed or physisorbed) oxygen molecules on a highly oriented pyrolytic graphite8 (HOPG) surface. The use of the O,/graphite adsorbate system allows us to orient the molecules on the surface in two different geometries.' By varying the coverage we can select either the 6 phase (with the molecular axis approx- imately parallel to the surface) or the ( phase (with the molecular axis approximately perpendicular to the surface).This enables us to study the effects of molecular orienta- tion in electron stimulated desorption. Sanche," in his study of molecular films of 0, 117 Electron-driven Dynamics on polycrystalline Pt (where the orientation of the 0, molecular axes is not known), found that two molecular dissociation processes seen in the gas phase'' are preserved when the oxygen molecules are condensed onto a surface. These were dissociative attachment (DA) e-+ O,+O; -+O + 0-(1) and dipolar dissociation (DD) e-+O,-+OT-)O+ +O-(2) Sanche and co-workers12 have also demonstrated that negative ions produced by DA can react with co-adsorbed molecules, thereby illustrating the possibility of inducing chemical reactions on surfaces with low-energy electrons.In this paper we explore the reaction of 0-ions produced by DA and DD processes with neighbouring 0, mol-ecules in the O,/graphite system, and we investigate reaction cross-sections as a fuiiction of incident electron kinetic energy (Ekin). 2. Experimental Methods The ESD experiments were performed in an ultra-high vacuum (UHV) chamber fitted with a pulse-counting mass spectrometer (Hiden Analytical) to detect the desorbed ions. The electron beam was produced by a custom-built computer-controlled low-energy electron gun; this was mounted on a turntable. In addition the system was equipped with an electron energy loss spectrometer (EELS) for structural characterisation of the 0, films.13 The HOPG sample was cleaved in air before mounting on a liquid-helium cold-finger with a base temperature of 20 K.The sample was regularly cleaned by heating to 900 K in UHV with surface cleanliness being monitored by EELS. Measurements of the angular distribution of desorbed ions were performed by rotat- ing the electron gun and sample in concert, with the mass spectrometer fixed in space. Owing to the limited angular range of the electron gun on the turntable (40"), scans were taken with the electron beam incident at three different angles to the surface to cover the whole angular range of interest. This produced three overlapping ion angular distribu- tions which were scaled in the overlap region (due to the angular dependence of the electron impact cross-section) to give the complete angular profile.3. Experimental Results and Discussion Fig. 1 shows the 0-yield as a function of incident electron energy for three different coverages of O,/graphite and two coverages of O,/Ar/graphite; these coverages corre- spond to the 6 and phases (i.e. 'lying down' and 'standing up' molecules, respectively) , three monolayers (ML) of 0, on the surface, and 1 ML of 0, adsorbed on 1 Langmuirt (L) and 5 L argon films on graphite. For the 3 ML case, the 0-yield has also been recorded with a 2 eV retarding potential applied to the mass spectrometer; this is shown as the open circles in Fig. l(c). For comparison, Fig. 2 shows the yield of O+ ions produced by electron impact on 3 ML O,/graphite as a function of incident electron energy. It can be seen that dipolar dissociation is the only dissociation mechanism operating here, as no signal is seen below ca.20 eV. Furthermore, it can be seen that the signal level for O+ is between one and two orders of magnitude less than for 0-.It is conceivable that this is some func- tion of the channeltron in the mass spectrometer, but there is no obvious physical reason why this should be the case. This implies that the 0' ion is more prone to re-neutralisation than the 0-ion; hence fewer escape the surface and are detected. -f 1 Langmuir (L) = Torr s. R. J. Guest et al. N 200025001 * C 0 Is, 5 -t400v) 1000L 0 500c,,-0 5 10 15 20 electron energy/eV 600000 400000 200000 0 5 10 15 20 electron e nerg y/eV Fig.1 Energy dependence of the 0-yield produced by electron impact on (a) 1 ML 6 phase, (b)1 ML phase, (c)3 ML of 0, on graphite, (d) 1 ML of 0, on 1 L of Ar on graphite and (e) 1 ML of 0, on 5 L of Ar on graphite. Also shown in (c) are the results obtained when a retarding potential (V,) of -2 eV is applied to the desorbed ions at the mass spectrometer (0).Electron angle of incidence = 60"and of emission = 30". 60 50 N 40 10 0 0 5 10 15 20 25 30 35 40 electron energy/eV Fig. 2 Energy dependence of the O+ yield produced by electron impact on 3 ML of 0, on graphite. Angles of incidence and emission as in Fig. 1. Electron-drivenDynamics It can be seen from Fig. l(c) that three DA resonances are observed in the electron energy range studied, at 8, 10 and 13.5 eV. These positions agree well with the reson- ances observed in 0, on polycrystalline Pt.I4 At higher incident-electron energies, dipolar dissociation is seen to occur.Although the resonances are very pronounced at 3 ML 0, coverage, they are seen much less strongly in the monolayer c phase, and are not detectable in the 6 phase. However, when an argon spacer layer is inserted between the oxygen layer and the graphite surface, the resonances appear again, with their inten- sity increasing with the spacer thickness. There are a number of possible explanations for this apparent quenching of the DA resonances in the monolayer regime on graphite. First, it could be due to a reduction in the resonance lifetime; such quenching has been proposed in resonance scattering experiments on other physisorption systems.15 However, resonance scattering studies from 0, on graphite16 have provided no evidence of such quenching. An alternative explanation of the apparent quenching of the DA resonances arises if we consider the effect of the image potential on the dynamics of the desorbing ion at the surface.For an ion to be detected, it must have sufficient velocity normal to the surface so that it can overcome the image potential and reach the mass spectrometer. Photoemission' and electron scattering13 studies have shown that the image potential in monolayer O,/graphite (6 or 5 phase) is ca. 1.5 eV; in the multilayer regime, on the other hand, the polarisation potential drops to ca.0.6 eV. If the 0-ions are emitted with an Ekinof the order of 1.5 eV, many more will be seen emerging from the multilayer on graphite than the monolayer. From Fig. l(c), we know that ions produced from the 8 eV DA resonance have less than 2 eV kinetic energy since applying a 2 V retarding potential to the mass spectrometer causes the resonance to disappear. Thus a far smaller proportion of the ions emitted from the monolayer will have suficient Ekinto escape the surface, compared with the multilayer regime. (The intensity differences between the 6 and c phases are a result of the different orientation of the molecular axis on the surface and will be discussed later.) Inserting the argon spacer layer has the effect of increasing the distance of the oxygen molecules from the surface, thereby reducing the image potential, and allowing more ions to escape the surface and be detected.We now turn to measurements of the angular distribution of emitted 0-ions. Fig. 3 shows the distribution of 0-ions emitted from the c phase of O,/graphite via DA and DD processes and from the 6 phase via DD. The angular distributions have been fitted with Gaussian distributions and the best-fit half-width half maxima (HWHM) are as follows: 5 phase DA, 21"; c phase DD, 28" and 6 phase DD, 35". Electron-stimulated desorption ion angular distribution (ESDIAD) measurements represent an established method of determining molecular orientation on a surface,18 and it is usually assumed that the molecule dissociates such that the fragments fly off along the direction of the bond axis.The results shown in Fig. 3 clearly show that this assumption is not valid for the O,/graphite physisorption system as for both 'lying down' and 'standing up' mol- ecules, the ion angular distribution peaks along the surface normal direction. To explain these angular distributions, it is necessary to consider the dynamics of the desorbing oxygen fragments. In principle, the measured angular distribution will depend on a number of factors: (i) the initial molecular orientation on the surface, (ii) the dynamics of the dissociation process and (iii) image potential effects as the 0-ion recedes from the surface. The effect of the image potential on the trajectory of the desorbing ion has been considered in some detail by Clinton" and Miscovic et aL2' The component of ion velocity normal to the surface is reduced, whereas the velocity parallel to the surface is unaffected.This has the effect of increasing the polar angle of desorption of the 0-ion away from the surface normal. The magnitude of the broadening depends on the ion Ekin,its initial direction and the strength of the image potential. If the normal component of velocity of the ion is suficiently small, the ion will be recaptured by the image potential and presumably re-neutralised. Image potential effects can account for R. J. Guest et al. t 0 10 20 30 40 50 60 70 80 90 emission angle, @/degrees Fig. 3 Experimental angular distributions of 0-ions produced by electron impact on 0, physi-sorbed on graphite.(a) 1 ML c phase, 8 eV electrons, (b) 1 ML c phase, 20 eV electrons and (c)1 ML 6 phase, 20 eV electrons. The results were obtained using three different electron incidence angles with respect to the surface normal (see text): 65" (a),35" (+) and 5" (m). In each case, the (-data have been fitted with a Gaussian distribution peaked along the surface normal best-fit HWHM of 21 & lo(5 phase, 8 eV), 28 & 3 ([ phase, 20 eV) and 35 f3" (6 phase, 20 eV). ) with the width of the 5-phase angular distribution as they increase the polar angle of desorp-tion, but they cannot explain the &phase distribution peaking along the surface normal direction; to understand this, it is necessary to consider the dynamics of the molecular dissociation process itself. Electron-driven Dynamics 4.Theoretical Methods In order to understand the experimental ion angular dis ributions, we have implemented a semi-classical trajectory calculation to explore further \he dissociation dynamics of the O,/graphite system. The electronic excitation produced by electron impact is modelled as a vertical, Franck-Condon transition, placing the molecule on an excited-state molecule-surface potential-energy surface (PES) and on a repulsive branch of the 0; intra-molecular PES. As the system propagates over this multi-dimensional PES the electronically excited molecule may de-excite or desorb and/or fragment. The classical Hamiltonian of the molecule-surface system is derived from the clas- sical three-body problem.Hasselbrink2' employed a similar model to study state dis- tributions in photon-stimulated desorption of chemisorbed diatomic molecules in which the surface is represented by a point mass.? The system of coordinates appropriate to the (diatomic) molecule-surface system is : r, the internuclear separation of the adsorb- ate; z, the normal surface-adsorbate centre-of-mass separation; and 6, the orientation of the molecular axis with respect to the surface normal. The conjugate momenta are P,, P, and J, respectively. The Hamiltonian of the system is,22 where p is the reduced mass of the molecule, m is the reduced mass of the molecule- substrate system, V,, is the intramolecular potential and Vms is the molecule-surface potential.For O;, the intramolecular PES for dipolar dissociation was fitted to calcu-lation~.~~*~~We took the A2H, state to be the predissociating state of O;, crossing adiabatically to the 'Zi state which is asymptotic to the ion pair. The intramolecular PES for dissociative attachment via the A 'nuI compound state was fitted to the calcu- lations of Michels and Harri~.~~,'~ The ground-state O,/graphite interaction potential was modelled as the sum of a (repulsive) overlap term and an (attractive) dispersion term, 3V;;urf-mol = A exp(-Kz) -Cz-(4) The free parameters were fitted to the surface-molecule interaction potential derived from a sum of Lennard-Jones 0-C pair potentials.These pair potentials were obtained from Bethanabotla and Steele,27 and reproduce the temperature-dependent orientation- a1 order of the O,/graphite system. Using this approach the well-depth for the fitted 0, on graphite physisorption potential was found to be 80 meV, comparable with the value of 90-100 meV cited by Vidali et a1.28 The form of the model excited-state O,/graphite potential depends upon the disso- ciation channel. For the 0; state leading to dipolar dissociation, the molecule-surface interaction potential of the predissociating state was taken to be of dipole-image dipole form. After curve-crossing onto the ion-pair state, this term was replaced by the inter- action potential of the pair of ions and their individual images in the substrate.For dissociative attachment, the dominant interaction is that of the molecular ion with its image. Upon molecular fragmentation the additional electron was localised on one or other at om. The ground-state configuration of the system prior to excitation of the molecule was described by a joint probability distribution of the coordinates in a six-dimensional phase space. The ground-state molecule-surface and intramolecular vibrational wave- ? This assumption places the molecule-surface system in a rotating frame, resulting in spurious centrifugal forces. Consequently, in deriving the Hamiltonian we represent the surface as a semi-infinite object to ensure that the molecular dynamics is calculated in an inertial frame.R. J. Guest et al. functions were determined from the ground-state PESs described above. The distribu- tion of molecular orientations of the ground state for both the [ and 6 phases was obtained from the molecular dynamics simulations of Bethanabotla and Steele.28 The conjugate momenta were obtained by Fourier transformation. The de-excitation of 0: and electron detachment from 0; were modelled by a product of relaxation probabilities, P(z, r) = C exp(-az)exp(-br) (5) 'The parameters C, a and b were adjusted to give a mean relaxation time of 5 fs. Computational implementation involved numerical integration of Hamilton's equa- tions, starting from a random set of initial coordinates derived from the ground-state distributions. The time interval for each integration step was 0.1 fs.Between each step of the integrator, relaxation of the excited state was allowed with the appropriate probabil- ity. The trajectory of each excited molecule was followed for 12 ps. After this time inter- val the average ion surface separation was greater than 296 A and the average ion-ion distance was beyond 773 A.This process of coordinate selection, integration, test and trajectory calculation was repeated in order to assemble a representative sample of desorbed atomic ions. Typically, the trajectories of 105-107 molecules were followed, resulting in a final yield of several thousand ion fragments. 5. Theoretical Resufts First we consider dipolar dissociation, occurring for incident electron energies above a threshold of ca.17 eV. The calculated ion angular distributions of desorbed 0-ions from both the 5 and 6 phases are shown in Fig. 4. The calculated ion fluence was convolved with the angular resolution function of the mass spectrometer which has a half-width of ca. 7.5". The calculated ratio of 0-yields, 5 : 6, was ca. 50 : 1, in reason- able agreement with the experimental ratio of ca. 100: 1. Both distributions peak normal to the surface. The calculated ion angular distribution from the 5phase is signifi- cantly narrower than that of the 6 phase. When fitted to Gaussians, the HWHM of the calculated ion angular distributions are 32" & 3" and 24" & 4" for the 6 and 5 phases, respectively. These calculated widths are in good agreement with the experimental dis- tributions, which have HWHM of 35" k 3" for the 6 phase and 28" k 3" for the c phase.In the c phase, the ground-state 0, molecules are, on average, oriented normal to the surface. Thus, the observed and calculated distributions of 0-ions from the 5phase appear to be in accord with the conventional ESDIAD mechanism, in which the momentum transfer to the dissociation fragments occurs predominantly along the bond axis.,' This interpretation assumes that, on the timescale of dissociation, the orientation of the bond axis remains fixed with respect to the surface. This interpretation fails when applied to the ion angular distributions obtained from the 6 phase because, prior to dissociation, the 0, molecules are oriented, on average, parallel to the surface.Both the calculated and experimental angular distributions of ions have greatest fluence in the direction normal to the surface. The similarity between the [ and 6 phase angular dis- tributions suggests that the initial orientational order of the 0, molecules is lost during the dissociation process. The trajectory of a typical desorbing molecule is shown in Fig. 5. Upon excitation the predominant motion is the rapid expansion of the intramolecular bond. The kinetic energy associated with this motion (given by the difference between the potential energy of the molecule in its initial excited-state configuration and the dissociation limit of the excited-state intramolecular potential well) is of the order of 4 eV; almost two orders of magnitude larger than the molecule-surface binding energy of 80 meV.Consequently, the expansion of the intramolecular bond forces the end of the molecule nearer the surface against the hard repulsive wall of the molecule-surface potential. This collision Electron-driven Dynamics 0 10 20 30 40 50 60 70 60 90 emission angle to normalidegrees emission angle to normalidegrees Fig. 4 Calculated angular distributions of 0-ions from 0, physisorbed on graphite. (a) 1 ML 6 phase DD, (b) 1 ML [ phase DD, (c) 1 ML 5 phase DA, with the electron localised on the atom closest to the surface, (d) 1 ML ( phase DA, with the electron localised on the atom farthest from the surface and.(e) 1 ML [ phase DA, with the electron randomly localised on either 0 atom.In each case the data have been fitted with a Gaussian distribution about the surface normal (+--) with best-fit HWHM of 18 & 2" (5 phase DA), 24 f4" ([ phase DD) and 32 f3" (6 phase DD). results in energy transfer into rotational and translational modes; as the molecule is thrown away from the surface its orientation is randomised. This molecule-surface collision, and the subsequent rotational excitation, is the dynamical origin of the similarity between the angular distributions of the 6 and [phases. This mechanism explains the similarity of the ion distributions from both phases but does not explain the existence of the peak normal to the surface. En route to the mass- spectrometer the desorbing ions must escape the image potential well.As indicated above, the height of this barrier, for both the 6 and [ phases, is ca. 1.5 eV.r3i17 The mean Ekinof the desorbing 0-ions was found to be ca. 2 eV. The similarity of the ion Ekin and the barrier height implies that the image potential acts as a filter, selecting for desorption only those ions with the largest components of velocity normal to the surface. Ions desorbing at larger angles relative to the surface normal arc back into the surface. We now consider dissociative attachment. Since DA produces an ion and a neutral atom, an additional degree of freedom enters the problem: the location of the trapped electron upon dissociation of the molecule. Fig. 4(c) and (d) show the calculated 0-ion R.J. Guest et al. 10 0-2-0-6-4-2 0 2 4 60-8-8-6-4-2 0 2 4 6 8 distance in the plane of the surface/A Fig. 5 Trajectory evolution of a desorbing molecule. The time between frames is 1 fs; (a)0.0 fs-(h)7.0 fs. angular distributions when the electron is localised, on the 0 atom, respectively, closer to and farther from the surface. Fig. 4(e) shows the resulting distribution if the electron is randomly localised on either 0 atom. Again, the model distribution, like the experimen- tal distribution, Fig. 3, is peaked on normal. The HWHM of the calculated and experi- mental distributions are 18" f2" and 21" & lo,respectively. 6. Reactions on Surfaces In addition to studying the dissociation dynamics of 0, ,we have explored the chemical reactions which can occur between the 0-ions produced by DA and neighbouring oxygen molecules. We found that in addition to 0-ions, it was possible to detect with the mass spectrometer 0; ions emitted from the surface.0, is formed by the collision of an 0-ion produced by DA (or DD) with another 0, molecule 0-+o,+o, (6) Fig. 6 shows the yield of 0; ions from a 4 ML film of OJgraphite as a function of incident electron energy; the figure shows a broad peak at ca. 13.5 eV with a shoulder at ca. 8 eV. Comparing the 0; spectrum (Fig. 6) with the 0-yield (Fig. l), we see that the 8 eV feature is almost completely suppressed in the 0; yield, such that the spectrum is domi- nated by the 13.5 eV DA resonance. This effect appears to be another manifestation of the polarisation potential effects; for 0; to escape the surface and be detected, it must have sufficient velocity normal to the surface to escape the surface polarisation potential EEectron-driven Dynamics 15 ll,llll,llrll,l,lll,llll ---e --em -N lo --5--c-.-m m-0" 5-e 0\fie*--? -eme 3 --(estimated to be 0.6 eV at this coverage17).It is possible to estimate the kinetic energy of the desorbing 0; species by considering a simple binary collision model for this reac- tion. In this model, the 0-ion coalesces with a stationary 0, molecule, and there is no significant exchange of momentum with neighbouring molecules. The reaction is exo- thermic, liberating 1.75 eV of energy3' (assuming reactants and products are in their ground states), but conservation of momentum requires that the kinetic energy of the 0, species is one third of the initial 0-kinetic energy.Sambe and Ramaker3' have assigned dissociation limits to the 0; DA resonances and this allows the kinetic energy of the fragments from an isolated 0, molecule to be determined. Thus for the 13.5 eV resonance the maximum 0-&in is ca. 3.75 eV, whereas for the 8 eV resonance, it is ca. 2.25 eV. This gives values of 1.25 and 0.75 eV for the 0; ion Ekin,respectively. It is readily apparent that the 0; ion &in at 8 eV incident-electron energy is close to the value of the polarisation potential whereas at 13.5 eV electron energy it is signifi- cantly greater.Thus, only a few 0-trajectories from the 8 eV resonance lead to desorp- tion (those close to the surface normal direction), while many more trajectories may lead to desorption at 13.5 eV, explaining the dominance of the higher energy DA resonance in the 0; yield spectrum. Conclusions We have studied the desorption of negative ions (0-and 0;) produced by low-energy electron impact on physisorbed films of oriented 0, molecules on graphite. The relative contributions to the 0-yield from DA and DD are dependent on the thickness of the adsorbate layer. This result is explicable in terms of the relative magnitudes of the ion Ekinand the image/polarisation potential, which also appears to determine the yield of 0; ions as a function of incident-electron energy.We have also measured the angular distribution of emitted 0-ions; these are found to be independent of the initial molecu- lar orientation on the surface, suggesting a loss of orientational order on the timescale of dissociation. Classical trajectory calculations show that this is due to rotational excita- tion of the molecule during the dissociation process and we anticipate that this could be a quite general feature of the dissociation dynamics in physisorption systems. We are grateful to the UK SERC and the Royal Society for financial support of this work. R.J.G. wishes to thank ICI for a CASE studentship. P.J.R. acknowledges support from the Donors of the Petroleum Research Fund, administered by the American R. J.Guest et al. 127 Chemical Society, and P.J.R. and D.N.B. acknowledge support from the UMBC Desig- nated Research Initiative Fund. We thank Dr. A. W. Moore of Union Carbide for providing the HOPG crystals. References 1 R. E. Palmer, Prog. Surf. Sci., 1992,41, 51. 2 R. D. Ramsier and J. T. Yates, Surf: Sci. Rep., 1991, 12, 243. 3 A. Danon and A. Amirav, Phys. Rev. Lett., 1988,61,2961. 4 C. T. Rettner and C. B. Mullins, J. Chem. Phys., 1991,94, 1626. 5 St-J. Dixon-Warren, E. T. Jensen and J. C. Polanyi, Phys. Rev. Lett., 1991,67,2395. 6 R. A. Bennett, R. G. Sharpe, R. J. Guest, J. C. Barnard, R. E. Palmer and M. A. MacDonald, Chem. Phys. Lett., 1992, 198, 241. 7 G. Dujardin, L. Hellner, L. Phillipe, R. Azria and M. J. Besnard-Ramage, Phys.Rev. Lett., 1991, 67, 1844. 8 M. S. Dresselhaus and G. Dresselhaus, Adv. Phys., 1981, 30, 139. 9 R. J. Guest, A. Nilsson, 0.Bjorneholm, B. Hernnas, A. Sandell, R. E. Palmer and N. Mirtensson, Surf: Sci., 1992, 2691270,432. 10 L. Sanche, Phys. Rev. Lett., 1984,53, 1638; J. Phys. B, 1990,23, 1597. 11 D. Rapp and D. D. Briglia, J. Chem. Phys., 1965,43, 1480. 12 L. Sanche and L. Parenteau, J. Chem. Phys., 1990,93,7476. 13 E. T. Jensen, R. E. Palmer and P. J. Row, Phys. Rev. Lett., 1990, 64, 1301; Chem. Phys. Lett., 1990, 16, 204; Surf: Sci., 1990,237, 153. 14 R. Azria, L. Parenteau and L. Sanche, Phys. Rev. Lett., 1987,59, 638. 15 K. Jacobi, M. Bertolo and W. Hansen, J. Electron Spectrosc. Relat. Phenom., 1990,54/55, 529. 16 R. E. Palmer and P.J. Rous, Rev. Mod. Phys., 1992,64,383. 17 A. Nilsson, R. E. Palmer, H. Tillborg, B. Hernnas, R. J. Guest and N. Mirtensson, Phys. Rev. Lett., 1992,69,2426. 18 T. E. Madey and J. T. Yates Jr., Surf: Sci., 1977,63,203. 19 W. L. Clinton, Surf: Sci., 1981,112, L791. 20 Z. Miscovic, J. Vukanic and T. E. Madey, Surf: Sci., 1984, 141, 285. 21 E. Hasselbrink, Chem. Phys. Lett., 1990, 170, 329. 22 E. Whittaker, Analytical Dynamics, Dover, New York, 4th edn., 1944. 23 F. R. Gilmore, J. Quant. Spectrosc. Radiat. Transfer, 1965,5, 369. 24 P. M. Dehmer and W. A. Chupka, J. Chem. Phys., 1975,62,4525. 25 H. H. Michels and F. E. Harris, in Seventh International Conference on the Physics of Electronic and Atomic Collisions: Abstracts of Papers, North-Holland, Amsterdam, 1971, vol. 11, p. 1170. 26 G. J. Schulz, Rev. Mod. Phys., 1973,45, 3. 27 V. Bathanabotla and W. Steele, Can. J. Chem., 1988,66,866. 28 G. Vidali, G. Ihm, H-Y. Kim and M. W. Cole, Surf. Sci. Rep., 1991,12, 133. 29 See, for example: T. E. Madey, S. A. Joyce and A. L. Johnson, in Interactions of Atoms and Molecules with Surfaces, ed. V. Bortolani, N. H. March and M. P. Tosi, Plenum, New York, 1st edn., 1990. 30 Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 72nd edn., 1991. 31 H. Sambe and D. E. Ramaker, Surf: Sci., 1992,2691270,444. Paper 3/03074A; Received 27th May, 1993