Dynamics of gas–surface interactions: 3D generalized Langevin model applied to fcc and bcc surfaces

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Abstract
A three dimensional generalized Langevin formalism is presented and applied to Ar and Xe interactions with Pt (111). Approximations for the random force and friction terms are proposed which permit realistic description of the motion and response of the surface atoms, including proper correlations among neighboring atoms. A ’’ghost atom’’ technique is developed which provides convenient numerical solution of the generalized Langevin equations in such a way that the fluctuation–dissipation theorem relating the random force and friction is satisfied rigorously. A simple prescription for determining parameters in the random force and friction is outlined. The prescription is applied to a four‐atom active zone to obtain explicit relationships for all parameters, depending only on the bulk and surface Debye frequencies, for fcc (100), (110), and (111), and bcc (100) and (110) surfaces. Calculations of energy accommodation, sticking probabilities, and thermal desorption rates are reported for Ar and Xe on Pt(111). The sensitivity of these properties on the parameters of the random force and friction, i.e., on the phonon spectrum, is examined. The dependence is found to be sufficiently weak to demonstrate convincingly that the generalized Langevin approach with relatively simple parameterization is capable of describing gas–surface dynamics with high accuracy.