Memory function parametrization in the GLE-Ghost atom formalism: A microscopic approach

The memory function used in the GLE approach to solid atom motion is modeled as a generalization of the position autocorrelation function for a multidimensional Brownian oscillator. The exact microscopic memory function and the assumed form are required to agree in two limits: at short times and for the low frequency density of states. This suffices to specify all the parameters, including those which control the memory of correlated motion between primary zone atoms as mediated by the rest of the solid. Determination of these parameters utilizes as the fundamental input the frequency matrix for the solid. An example is presented for various fcc solid surfaces assuming Lennard-Jones (12, 6) forces between the solid atoms. The approach is capable, in principle, of treating such interesting structures as high Miller index surfaces, molecular solids and adsorbed species while retaining only a small number of primary zone atoms.