Quantifying Intuition: Bayesian Approach to Figures of Merit in EXAFS Analysis of Magic Size Clusters

Abstract: Analysis of the extended X-ray absorption fine structure (EXAFS) can yield local structural information in magic size clusters even when other structural methods (such as X-ray diffraction) fail, but typically requires an initial guess -- an atomistic model. Model comparison is thus one of the most crucial steps in establishing atomic structure of nanoscale systems and relies critically on the corresponding figures of merit (delivered by the data analysis) to make a decision on the most suitable model of atomic arrangements. However, none of the currently used statistical figures of merit take into account such significant factor as parameter correlations. Here we show that ignoring such correlations may result in a selection of an incorrect structural model. We then report on a new metric based on Bayes theorem that addresses this problem. We show that our new metric is superior to the currently used in EXAFS analysis as it reliably yields correct structural models even in cases when other statistical criteria may fail. We then demonstrate the utility of the new figure of merit in comparison of structural models for CdS magic-size clusters using EXAFS data.