Acta Cryst. (1981). A37, 857-863 Joint X-ray and Neutron Data Refinement of Structural and Charge Density Parameters* BY P. COPPENS, R. BOEHME, P. F. PRICE AND E. D. STEVENS Chemistry Department, State University of New York at Buffalo, Buffalo, New York 14214, USA (Received 24 October 1980; accepted 22 April 1981) 857 Abstract A procedure for joint refinement of X-ray and neutron data is described in whichstructural, 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 refinementis applied to previously collected low- temperature data on oxalic acid dihydrate, C2H2Oa.2H20, 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 analyticaldescription 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. Introduction Several formalisms are presently being used for an analytical description of the electron distribution in a crystal. The most widely appliedof these use atom- centered non-spherical density functionswith adjust- able population and radial dependence (i.e. Hirshfeld, 1977; Stewart, 1976; Hansen & Coppens, 1978). The methods suffer from the drawback of cor- relation between structural and charge density param- eters. The occupancy of a dipolar density function, for example, tends to correlate with positional parameters * Electron Population Analysis of Accurate Diffraction Data. X. Part IX: Coppens, Moss & Hansen (1980). In Computing in Crystallography, edited by R. Diamond, S. Ramaseshan & K. Venkatesan. Bangalore: Indian Academy of Sciences. of the atom on which it is centered, and the same is true for quadrupole functions and anisotropic thermal parameters. The extent of this correlation depends on the data cut off and will be less severewhen large numbers of high-orderreflections, which contain a relatively small contribution from the valence electrons, are available. This correlation is especially pronounced for hydrogen atoms which scatter only weakly in the high-order region. When neutron diffraction data are available, a procedure is often adoptedin which hydrogen-atom parameters are kept constant at their neutron values. An alternative explored here is the simultaneous refinement of X-ray and neutron data in order to arrive at the best solution with regard to all diffraction data. The least-squares program M A U D Y writtenfor this purpose allows adjustment of structural, charge density and extinction parameters and is an extension of the previously described program for refinement of X-ray data only (Hansen & Coppens, 1978). Combining two data sets Severalissues arise which are relatedto the simul- taneous use of data sets from different origins. They are discussed below. 1. Differences in data collection temperature Systematic differences betweenspherical-atom X- ray and neutrondiffraction temperature factors have been traced to bias in the X-ray results resulting from the spherical-atom approximation. Such differences were especially pronounced in early studies which did not include many high-order reflections(Coppens, 1968); but should be less severe for extended data sets. Nevertheless, several more recent studies have shown discrepancies between X-ray and neutron atomic vibrationaltensors. These are probably due to dif- ferences in either data collection temperatureor differences in the background correction applied in the two experiments. The latter possibility, which includes 0567-7394/81/060857-07501.00 © 1981 International Union of Crystallography