An ab initio equation of motion method is introduced to calculate the temperature-dependent mean-square vibrational amplitudes ${\sigma }^2$ which appear in the Debye-Waller factors in x-ray absorption, x-ray scattering, and related spectra. The approach avoids explicit calculations of phonon modes, and is based instead on calculations of the displacement-displacement time correlation function from ab initio density functional theory molecular dynamics simulations. The method also yields the vibrational density of states and thermal quantities such as the lattice free energy. Illustrations of the method are presented for a number of systems and compared with other methods and experiment.

• Received 30 August 2011

DOI:https://doi.org/10.1103/PhysRevB.85.024303