No abstract

A general theoretical framework for introducing many-body or lattice effects into gas/solid scattering is presented. The theory is presently restricted to classical scattering off harmonic lattices but is otherwise completely general. It is nonperturbative and valid for arbitrary lattice temperature. The theory is based on a formulation of lattice dynamics suggested by and related to the Kubo–Mori theory of generalized Brownian motion. This formulation leads to a generalized Langevin equation (GLE) in which only the coordinates of the gas atom and the n∼1–6 surface atoms directly struck by the gas atom appear explicitly. The remainder of the lattice, which functions as a harmonic heat bath, affects the collision through a friction kernel and a Gaussian random force appearing in the GLE. The GLE can be solved in terms of a tractable number of (n+1) -particle gas–surface trajectories using approximate stochastic techniques. Stochastic solution yields thermally averaged temporal gas particle probability distribution functions (pdf). From the long time limit of these pdf’s all temperature dependent gas–surface cross sections can be found. In the limit of zero friction, the theory gives a convenient method for calculating atom–oscillator thermally averaged cross sections which circumvents laborious Monte Carlo classical trajectory sampling and which can be generalized to treat other gas phase collision problems.

A new Monte Carlo simulation procedure is developed which is expected to produce more rapid convergence than the standard Metropoli~ method. The trial particle moves are chosen in accord with a Brownian dynamics algorithm rather than at random. For two model systems, a string of point masses joined by harmonic springs and a cluster of charged soft spheres, the new procedure is compared to the standard one and shown to manifest a more rapid convergence rate for some important energetic and structural properties.