Propagation of uncertainty in experiment: structures of Ni (II) coordination complexes.

Accurate experimental XAFS (X-ray absorption fine-structure) data including uncertainties are required during analysis for valid comparison of results and conclusions of hypothesis testing on structural determinations. Here an approach is developed to investigate data without standard interpolation of experimental data and with minimal loss of information content in the raw data. Nickel coordination complexes bis(i-n-propylsalicylaldiminato)nickel(II) (i-pr) and bis(N-n-propylsalicylaldiminato)nickel(II) (n-pr) are investigated. The additional physical insight afforded by the correct propagation of experimental uncertainty is used to determine newly refined structures for the innermost co-ordination shell. Two sets of data are investigated for each complex; one optimized for high point accuracy and one optimized for high point density. Clearly both are important and in this investigation the quality of the physical insight from each is directly provided by measured and propagated uncertainties to fairly represent the relevant accuracies. The results provide evidence for an approximate tetrahedral geometry for the i-pr Ni complex that is more symmetric than previously concluded, with our high point accuracy data yielding ligand lengths of 2.017 ± 0.006 Å and 2.022 ∓ 0.006 Å for Ni-N and Ni-O bonds, respectively, and an even more skewed square-planar (i.e. rhombohedral) arrangement for the n-pr complex with corresponding bond lengths of 2.133 ± 0.004 Å and 1.960 ∓ 0.003 Å. The ability to distinguish using hypothesis testing between the subtle differences in XAFS spectra arising from the approximate local tetrahedral and square-planar geometries of the complexes is also highlighted. The effect of standard interpolation on experimental XAFS spectra prior to fitting with theoretical model structures is investigated. While often performed as a necessary step for Fourier transformation into position space, this will nonetheless skew the fit away from actual data taken, and fails to preserve the information content within the data uncertainty. The artificial effects that interpolation imposes on χr2 are demonstrated. Finally, a method for interpolation is introduced which locally preserves the χr2 and thus information content, when a regular grid is required, e.g for further analysis in r-space.