Multiple-scattering x-ray-absorption fine-structure Debye-Waller factor calculations

An efficient local equation-of-motion method is introduced for calculations of the mean-square half-path-length fluctuations ${\sigma }_j^2$ in multiple-scattering x-ray-absorption fine-structure Debye-Waller factors in aperiodic systems. Given a few local force constants, the method yields ${\sigma }_j^2$ via projected densities of modes or via the displacement-displacement correlation function in real time, over a few vibration cycles. The calculation scales linearly with the system size and does not rely on any symmetry considerations. Sample applications are presented for crystalline Cu and Ge, and zinc tetraimidazole.