Ab initiosingle- and multiple-scattering EXAFS Debye-Waller factors: Raman and infrared data

The extended x-ray-absorption fine structure (EXAFS) Debye-Waller factor is an essential term appearing in the EXAFS equation that accounts for the molecular structural and thermal disorder of a sample. Single- and multiple-scattering Debye-Waller factors must be known accurately to obtain quantitative agreement between theory and experiment. Since the total number of fitting parameters that can be varied is limited in general, data cannot support fitting of all relevant multiple-scattering Debye-Waller factors. Calculation of the Debye-Waller factors is typically done using the correlated Debye approximation, where a single parameter (Debye temperature) is varied. However, this procedure cannot account in general for Debye-Waller factors in materials with heterogeneous bond strengths, such as biomolecules. As an alternative procedure in this work, we calculate them ab initio directly from the known or hypothetical three-dimensional structure. In this paper we investigate the adequacy of various computational approaches for calculating vibrational structure within small molecules. Detailed EXAFS results will be presented in a subsequent paper. Analytical expressions are derived for multiple scattering Debye-Waller factors, based on the plane wave approximation. Semiempirical Hamiltonians and the ab initio density functional method are used to calculate the normal mode eigenfrequencies and eigenvectors. These data are used to calculate all single- and multiple-scattering Debye-Waller factors up to a four atom cluster. These ab initio Debye-Waller factors are compared to those calculated from experimental infrared and Raman frequencies. As an example comparison with experimental EXAFS data from ${\mathrm{GeCl}}_4,\hspace{0.5em}{\mathrm{GeH}}_3\mathrm{Cl}$ gases are also reported. Good agreement is observed for all cases tested.