The mean square variation of multiple scattering path length by molecular dynamics simulation

Approximations in the treatment of Debye–Waller factors in multiple scattering calculations are one of the principal remaining uncertainties in XAFS calculations. The amplitude of each path varies as a function of the mean square variation in path length. This quantity depends on the many-body correlations involving atoms in the path, as well as the mean square displacement of individual atoms. The correlations normal as well as parallel to interatomic vectors are required, and the effects of anharmonicity must be taken into account. Although difficult to calculate accurately, these quantities can be extracted directly from molecular dynamics (MD) simulations. Here we present temperature dependent results for copper, using a semiempirical potential based on a tight-binding model, from which the cumulants of the variation in path length as well as the correlation functions are derived. XAFS calculations based on extracted parameters are compared with those calculated directly from the MD atomic coordinates, and with results using Debye model and lattice dynamic calculations.