Joint X-ray and neutron data refinement of structural and charge density parameters

A procedure for joint refinement of X-ray and neutron data is described in which structural, charge density and extinction parameters are adjusted simultaneously in order to arrive at the best least-squares solution with respect to all available diffraction data. This X + N refinement is applied to previously collected low-temperature data on oxalic acid dihydrate, C₂H₂O₄.2H₂O, and results are compared with the X-ray-only refinement, and an X-ray refinement with neutron values for the hydrogen structural parameters. The X + N model deformation density shows higher peak heights in the lone-pair regions than the X- ray-only model density and resembles more closely the X-N deformation maps. Though the X + N maps are more strongly model dependent, they contain less noise, provide an analytical description of the deformation density and, unlike the X-N density, can be obtained in principle with a less than complete data set. The estimate of the goodness-of-fit for each of the data sets requires an apportioning of the joint parameters, which in this study is based on the relative magnitude of the least-squares derivatives.