| The EXAFS Debye-Waller factor is an essential term appearing in the EXAFS equation that accounts for the disorder of a given sample. Single and multiple scattering Debye-Waller factors must be known accurately to obtain quantitative agreement with experimental data. Since the total number of fit parameters that can be varied is limited, data cannot support fitting of all relevant multiple-scattering Debye-Waller factors. Calculation of the Debye-Waller factors is typically done by the Feff6 program, using the correlated Debye approximation, where a single parameter (Debye Temperature) is varied. This clearly cannot account in general for Debye-Waller factors in materials with heterogeneous bond strengths, such as biomolecules. As an alternative, in this work, I calculate them ab initio directly from the known or hypothetical 3D structure. Analytical expressions for multiple scattering Debye-Waller factors, based on the plane wave approach, are derived. Semi-empirical Hamiltonians (AM1, MNDO) and the ab initio Density Functional Method (DFT) are used to calculate the normal mode eigenfrequencies and eigenvectors. These data are used to calculate all single and multiple scattering Debye-Waller factors with up to eight legs for a two and three atom cluster and up to five legs for a four atom cluster. The relative importance of a variety of multiple-scattering paths is examined. Using these Debye-Waller factors, theoretical {dollar}chi(k){dollar} data are compared with experimental infrared, Raman and EXAFS spectra. DFT provides very good results for all materials tested, and the methods developed are practical and accurate for the molecular systems studied. |
