\textit{Ab initio} X-Ray Absorption Fine Structure Cumulants*

Theoretical calculations of vibrational effects in x-ray absorption spectra typically employ semi-phenomenological models, e.g. empirical force constants or correlated Debye or Einstein models. Instead we introduce an efficient and generally applicable \textit{ab initio} approach based on electronic structure calculations of the dynamical matrix together with the Lanczos recursion algorithm [1] and relations between the cumulants. The approach yields 1) the thermal expansion coefficients (first cumulant of the vibrational distribution function); 2) correlated Debye-Waller factors (second cumulants) and 3) anharmonic contributions (third cumulants). Results are presented for crystalline (Cu, Au, Ge, GaAs) and molecular (GeCl$_4$, C$_6$H$_6$) systems. Our results for the Debye-Waller factors agree well with experiment. \\ \\ {[1]}H.J. Krappe and H.H. Rossner, Phys. Rev. B\textbf{70}, 104102 (2004).