Quantitative local structure refinement from XANES: multi-dimensional interpolation approach

A new method to determine local structure in terms of a few structural parameters is proposed and realised in FitIt software. It is based on fitting of X-ray absorption near-edge structure (XANES) spectra using the combination of full multiple-scattering calculations, and multi-dimensional interpolation of spectra as a function of structural parameters. The procedure is divided into two steps: the construction of an interpolation polynomial, and the fitting of experimental spectra using the interpolation polynomial. During the construction of the polynomial, multiple-scattering calculations for certain sets of structural parameters are needed. The strategy for the selection of the most important expansion terms and corresponding sets of structural parameters is proposed. Fitting of the spectrum using multi-dimensional interpolation is very fast (a few seconds) because multiple-scattering calculations are unnecessary during this step. Also, this approach allows the development of a visual interface with the possibility of seeing the spectrum that corresponds to any set of structural parameters immediately. Thus, using a very limited number of multiple-scattering calculations, which are most time-consuming, it is possible to fit XANES. The interpolation polynomial construction procedure for three model molecules, FeS₄, FeO₆ and Ni(CN)₄, is demonstrated. An additional test has been performed for the latter most-complex example to check the assumption that a minimum of discrepancy between theoretical and experimental spectra corresponds only to the correct structure of the complex. A comparison with another XANES fitting software, MXAN, is given.