Applications of leverage analysis in structure refinement

Abstract

Leverages measure the influence that observations (intensity data and restraints) have on the fit obtained in crystal structure refinement. Further analysis enables the influence that observations have on specific parameters to be measured. The results of leverage analyses are discussed in the context of the amino acid alanine and an incomplete high-pressure data set of the complex bis(salicylaldoximato)copper(II). Leverage analysis can reveal situations where weak data are influential and allows an assessment of the influence of restraints. Analysis of the high-pressure refinement of the copper complex shows that the influence of the highest-leverage intensity observations increases when completeness is reduced, but low leverages stay low. The influence of restraints, notably those applying the Hirshfeld rigid-bond criterion, also increases dramatically. In alanine the precision of the Flack parameter is determined by medium-resolution data with moderate intensities. The results of a leverage analysis can be incorporated into a weighting scheme designed to optimize the precision of a selected parameter. This was applied to absolute structure refinement of light-atom crystal structures. The standard uncertainty of the Flack parameter could be reduced to around 0.1 even for a hydrocarbon.