Vibrational excitation in NO/Ag scattering is discussed within the adiabatic approximation. Taking into account the observed change of NO stretch frequency on adsorption the observed magnitude and energy dependence of molecular vibrational excitation can be described with reasonable parameters. At low energies the observed temperature dependence can be explained semi-quantitatively by taking the coupling to phonons into account. It is pointed out that the observed temperature dependence poses problems in both the adiabatic as well as the nonadiabatic models. Further investigations are needed to obtain unambiguous results concerning the relative importance of adiabatic and nonadiabatic effects in NO/Ag scattering.

He atom surface scattering by dispersionless phonons is treated employing coupled channel (CC) calculations. At low energies, they predict a behavior opposite to perturbative Born or "exponentiated" Born approximation: strong resonant phonon stimulated elastic and inhibited inelastic scattering. The corresponding resonances have not been observed in earlier CC results since these have considered only the temperature dependence of the Debye-Waller factor at higher energy or omitted the attractive well. The resonances can be interpreted in terms of bound states in the attractive well with several excited vibrational quanta. They may be observable for, e.g., He scattering by a cold Xe/Cu surface.

The inelastic scattering of atoms by phonons of a semi-infinite solid involves infinitely many degrees of freedom and hence cannot be treated rigorously by any of the known numerical methods. An approximation which has been used successfully to explain experimental data is the exponentiated Born approximation (EBA). Here we compare this approximation for the scattering by an Einstein-model with two types of coherent state approximations (where the wave function is approximated by a Gaussian centered at the classical trajectory) and with the results of an exact coupled channel calculation. The EBA turns out to be close to the coherent state approximations, and all three agree rather well with the exact results except near thresholds and (in particular) resonances. The calculations are done for zero temperature T but excited initial states are considered from which nonzero T results can be obtained as Boltzmann averages.

Hydrogen molecules desorbing from silicon exhibit very low translational heating in spite of a high adsorption barrier. This ``barrier puzzle'' can be explained in terms of a strong phonon coupling leading to a strong energy transfer to phonons in desorption and, vice versa, to a strong phonon-assisted sticking. Recent kinetic and scanning tunneling microscopy data at higher coverages indicate the existence of a new barrierless reaction path which is supposed to dominate the high coverage reaction dynamics. However, recent data on translational and earlier results on vibrational heating at higher coverage indicate the presence of a high adsorption barrier well in accordance with low-coverage data on vibrationally and translationally assisted sticking. For the solution of this barrier puzzle we present kinetic and dynamic model calculations. We use nonequilibrium thermodynamics to formulate the coupled adsorption-desorption kinetics allowing for different weights for the 2H and 4H processes. We perform four-dimensional coupled channel calculations to treat the dependence of phonons, molecular vibrations and corrugation on these two reaction mechanisms. These calculations indicate that dramatic changes in the vibrational and translational dynamics due to the new barrierless reaction path may occur only near monolayer coverage.

An earlier Version of introducing optimized basis functions for reaction dynamics using coupled channel equations [W. Brenig, R. Brake, M.F. Hilf, Z. Phys. Chem. 197 (1966) 237] is generalized and simplified conceptually. Rather than beginning the procedure in the oscillator basis, we now start from a 'single channel' assumption to define a basis taking some of the dynamics of the variables perpendicular to the reaction path into account. Our earlier version using generalized oscillator states [W. Brenig, R. Brake, M.F. Hilf, Z. Phys. Chem. 197 (1966) 237] ('quantum trajectories') can easily be derived and generalized starting from the formalism presented here. The parameters of the quantum trajectories are now determined using Ehrenfest's theorem.To demonstrate the power of the method, we apply it to the corrugation problem in surface reactions. The use of optimized basis states again leads to a great reduction in basis size as compared to plane wave states. (C) 2000 Elsevier Science B.V. All rights reserved.

Several theoretical and experimental results on the dynamics of dissociative adsorption and recombinative desorption of hydrogen on silicon are reviewed.

The static, homogeneous, diagonal conductivityfor the normal quantum Hall effect at half filling of the lowest Landau level under certain conditions seems to approach the value e 2 /2 h . The deviations from this value in dynamical, inhomogeneous situations show anomalies with a nonanalytical behavior of σ ( ω , k ) in ω and k . Existing results concerning this behavior are briefly reviewed and improved, taking screening effects into account. The combination of low-frequency anomalies and screening effects turns out to have dramatic consequences suppressing the low-frequency conductivity very strongly. From our considerations we conclude that it should be possible to observe all these effects.

A version of a network model of quantum Hall systems is studied classically. We assume that randomness inherent in the problem enters the model via random heights of saddle points only. Wt use ideas from classical percolation theory to calculate numerically the fractal dimension d(f), the correlation length exponent nu, the diffusion coefficient D, the corresponding exponent k, and other parameters of interest. The width of the longitudinal conductivity peak scales with the classical localization length exponent nu.

Coupled channel equations involving oscillators are formulated in terms of optimized basis functions. Rather than expanding the wave functions in terms of oscillator states centered around the minimum of the potential we use generalized oscillator states centered around the maximum of the wave functions. The number of channels needed in such an expansion can be greatly reduced in particular in situations with large shifts (compared to the width) of the wave function maximum away from the potential minimum.The generalized oscillator states contain four parameters: A position, a momentum and a (complex) frequency which are determined self consistently along the reaction path. We consider these four parameters as the ingredients of a so-called quantum trajectory: The resulting self consistency equations are close to classical trajectory equations for the oscillator coordinates coupled to a quantum translational motion. The procedure can be made virtually exact by taking sufficiently many excited oscillator states (''channels'') into account.

Experimental and theoretical results on the dynamics of dissociative adsorption and recombinative desorption of hydrogen on silicon are presented. Using optical second-harmonic generation, extremely small sticking probabilities in the range 10(-9)-10(-5) could be measured for H-2 and D-2 on Si(111)7X7 and Si(100)2X1. Strong phonon-assisted sticking was observed for gases at 300 K and surface temperatures between 550 K and 1050 K. The absolute values as well as the temperature variation of the adsorption and desorption rates show surprisingly little isotope effect, and they differ only little between the two surfaces. These results indicate that tunneling, molecular vibrations, and the structural details of the surface play only a minor role for the adsorption dynamics. Instead, they appear to be governed by the localized H-Si bonding and Si-Si lattice vibrations. Theoretically, an effective five-dimensional model is presented taking lattice distortion, corrugation, and molecular vibrations into account within the framework of coupled-channel calculations. While the temperature dependence of the sticking is dominated by lattice distortion, the main effect of corrugation is a reduction of the preexponential factor by about one order of magnitude per lateral degree of freedom. Molecular vibrations have practically no effect on the adsorption/desorption dynamics itself, but lead to vibrational heating in desorption with a strong isotope effect. Ab initio calculations for the H-2 interaction With the dimers of Si(100)2X1 show properties of the potential surface in qualitative agreement with the model, but its dynamics differs quantitatively from the experimental results.

We show that vibrational spectra of molecules chemisorbed on metal surfaces can be affected by anharmonicity much more than usually estimated if various vibrational coordinates are coupled by non-diagonal terms. The strong coverage dependence of the linewidth of the adsorbate-metal vibrations of CO adsorbed on Pt(111) can be attributed to the multiphonon decay, enhanced by a strong coupling of the adsorbate motion to the in-plane displacement of the surrounding surface atoms.

We consider the screening properties of quasi-one-dimensional electronic states which may occur on low index surfaces (flat or stepped) of some fcc metals as localized chain states. Motivated by the analysis of experimental data on the H/Ni(110) system, we discuss the possible contributions to indirect interactions between two H adatoms which are mediated by such states. We first show in the linear model of screening that these interactions should exhibit long range oscillations which scale as d−1 for large distances d between the adatoms. We use experimental data for the indirect interactions in H/Ni(110) systems to obtain an order of magnitude estimate of parameters involved. It turns out that a relatively large phase shift ηa is required for such oscillations. We therefore also use a nonlinear model for the screening of adatoms, based on the Anderson Hamiltonian. This model yields an indirect interaction between two adatoms which is regular for all d and behaves asymptotically as ∼cos[2kF/d − 2ηa(εF)]d where kF is the Fermi wavevector at the metal surface. The physical significance of the parameters of the model derived thereof is discussed in the context of incomplete screening of H adatoms by quasi-one-dimensional electronic chain states existing on the substrate surface.

In two earlier papers a numerically stable solution of the stationary Schrödinger equation for coupled channels was presented. The Schrödinger function and its first derivative were expressed in terms of two matrices: A so-calledlocal reflection matrix (LORE) and aninverse local transmission matrix (INTRA). These matrices obey very simple boundary conditions: They approach asymptotically zero (one) on one side of the reaction path and the reflection (transmission) matrix on the other side. Hence by propagating both matrices along the reaction path one can determine directly the observable scattering matrix elements without ever having to calculate wave functions. On the other hand it is often useful to know the wave functions, for instance in order to interpret scattering data in terms of ‘flow patterns’ etc. Although the relation between theINTRA-LORE and the wave function is simple, a straight forward calculation is not possible. It would involve an inversion of theINTRA which is numerically ill behaved. In this paper we describe a numerically stable method of computing the wave function and illustrate by two examples of surface reactions.

Recent observations of a direct reaction between adsorbates and hydrogen atoms incident from the gas phase are interpreted in terms of an Eley-Rideal reaction. A detailed comparison of the experimental data for the HD/Cu(111) system with quantum mechanical model calculations corroborates such an interpretation. The peculiar isotope effect observed can be understood from the different dynamical implications of appropriately rescaled potential energy surfaces. The width of the measured time-of-flight spectrum is explained from the overlapping contributions of the populated vibrational levels. The angular distributions are rationalized by contributions both from 'indirect' events, where the incident atoms make several bounces in the surface well prior to reaction, and 'direct' reactive events.

We have studied the screening properties of quasi-one-dimensional electronic states which may arise in the troughs of reconstructed (110) surfaces of some fcc metals (Ni and Cu) as chain states localized in the direction perpendicular to the troughs. Motivated by the analysis of the experimental data on the HNi(110) system, we discuss the indirect interaction between two H adatoms which is mediated by such states. Using first a linear model of screening of impurity potentials we show that such interaction should exhibit long range oscillations which scale as d−1 for large distances d between the adatoms. By fitting this result to the experimental data available for the HNi(110) system we found that a relatively large shift ηa was required to describe these oscillations. This has lead us to use a nonlinear model for the screening of adatoms, based on the Anderson Hamiltonian of impurity screening. This approach yields an indirect interaction between two adatoms which is regular for all d and behaves asymptotically as ~ cos[2kFd − 2ηa(ϵF)d where kF is the Fermi wavevector at the metal surface. The physical significance of the parameters of the model derived thereof can be interpreted in the context of incomplete screening of H adatoms by quasi-one-dimensional electronic chain states existing on the substrate surface.

The velocity correlation function of electrons in two dimensions and strong perpendicular magnetic fields is determined by numerical simulation in semiclassical approximation. The correlation for particles on extended trajectories turns out do decay ∝t−6/7 for large times. The correlation averaged over all trajectories decays approximately ∝t−2 (again for large times). The maximum conductivity between Hall plateaus comes out close toe2/2h.

Recent experimental results on the desorption of D2 from Si show practically no translational heating indicating a low barrier for adsorption. This seems to be at variance with the extremely low sticking coefficient found in adsorption experiments indicating a very high barrier. In order to understand this apparent discrepancy we consider a simple model of local lattice relaxation allowing for different barriers in adsorption and desorption processes. After taking the dynamics of this relaxation into account it turns out that detailed balance “in principle” is valid. “In practice”, however, it can not be applied for very large energy releases from lattice distortions. Our model predicts very strong phonon assisted sticking.

Velocity correlation functions in the time domain offer a new approach to the dissipative conductivity in the quantum Hall effect at half-filled Landau bands. We describe two methods of calculating these functions directly by wave packet propagation techniques. We address the question whether quantum effects modify the high field diffusion described within the semiclassical percolation picture of the QHE. We investigate a number of random potentials with finite correlation length. Coupling to higher Landau levels leads to damped cyclotron oscillations in the velocity correlation. Besides that, we observe a long time tail Φ(t)∼t−κ with κ≈2.3 for all potential ranges investigated. Within the statistical uncertainty and the time interval considered, this power law is consistent with the semiclassical result obtained by averaging over all cluster sizes. Our findings imply detectable deviations from Drude's law for the AC conductivity.

We demonstrate that the vibrational excitation in the NO/diamond(110) system can be explained purely mechanically by the compression of the interatomic spring during the collision at a corrugated surface. The substrate phonons are taken into account in the soft-cube model reproducing the observed surface temperature effect by weighting the phonons with the appropriate Boltzmann factor. As for the translational degree of freedom the diamond surface in our model acts as an almost rigid surface exchanging nearly no energy with the molecule. This is in agreement with the experimental data for high incident energy, but at variance for low incident energy possibly due to multiple scattering events and trapping-desorption processes which are not contained in our model.

The excited vibrational states of adsorbed hydrogen on metals are usually delocalized. As a consequence the inelastic e-scattering signal is strongly broadened. At high coverage the phonon dispersion is superimposed on this broadening. We apply the random phase approximation to this situation. As long as the vibrational ground state has negligible band width the broadening and dispersion turn out to be independent. Within tight binding approximation for the excited vibrational states the dispersion can be calculated from standard lattice dynamics, although for the excited states the concept of a displacement coordinate cannot be used. Experimental dispersion curves for hydrogen on Ni(110) can be fitted using a model with first-, second- and third-nearest-neighbor forces. The dependence of force constants on distance turns out to be unusual, indicating strong indirect interactions and probably even non-central forces.