Stereochemical analysis of ferrocene and the uncertainty of fluorescence XAFS data

Methods for the quantification of statistically valid measures of the uncertainties associated with X-ray absorption fine structure (XAFS) data obtained from dilute solutions using fluorescence measurements are developed. Experimental data obtained from 10 mM solutions of the organometallic compound ferrocene, Fe(C₅H₅)₂, are analysed within this framework and, following correction for various electronic and geometrical factors, give robust estimates of the standard errors of the individual measurements. The reliability of the refinement statistics of standard current XAFS structure approaches that do not include propagation of experimental uncertainties to assess subtle structural distortions is assessed in terms of refinements obtained for the staggered and eclipsed conformations of the C₅H₅ rings of ferrocene. Standard approaches (XFIT, IFEFFIT) give refinement statistics that appear to show strong, but opposite, preferences for the different conformations. Incorporation of experimental uncertainties into an IFEFFIT-like analysis yield refinement statistics for the staggered and eclipsed forms of ferrocene which show a far more realistic preference for the eclipsed form which accurately reflects the reliability of the analysis. Moreover, the more strongly founded estimates of the refined parameter uncertainties allow more direct comparison with those obtained by other techniques. These XAFS-based estimates of the bond distances have accuracies comparable with those obtained using single-crystal diffraction techniques and are superior in terms of their use in comparisons of experimental and computed structures.