Structures of copper(II) and manganese(II) di(hydrogen malonate) dihydrate; effects of intensity profile truncation and background modelling on structure models

The crystal structures of the title compounds were determined with net inte nsities I derived via the background-peak-background procedure. Least-squar es optimizations reveal differences between the low-order (0 < s < 0.7 Angs trom (-1)) and high-order (0.7 < s < 1.0 Angstrom (-1)) structure models. T he scale factors indicate discrepancies of up to 10% between the low-order and high-order reflection intensities. This observation is compound indepen dent. It reflects the scan-angle-induced truncation error., because the app lied scan angle (0.8 + 2.0 tan theta)degrees underestimates the wavelength dispersion in the monochromated X-ray beam. The observed crystal structures show pseudo-l-centred sublattices for three of its non-H atoms in the asym metric unit. Our selection of observed intensities (I > 3 sigma) stresses t hat pseudo-symmetry. Model refinements on individual data sets with (h + k + l) = 2n and (h + k + l) = 2n + 1 illustrate the lack of model robustness caused bv that pseudosymmetry. To obtain a better balanced data set and thu s a more robust structure we decided to exploit background modelling. We de scribed the background intensities B( (H) over right arrow) with an 11th de gree polynomial in theta. This function predicts the local background b at each position (H) over right arrow and defines the counting statistical dis tribution P(B), in which b serves as average and variance. The observation R defines P(R). This leads to P(I) = P(R)IP(B) and thus I = R - b and sigma (2)(I) = I So that the error sigma (l) is background independent. Within t his framework we reanalysed the structure of the copper(II) derivative. Bac kground modelling resulted in a structure model with an improved internal c onsistency. At the same time the unweighted R value based on all observatio ns decreased from 10.6 to 8.4%. A redetermination of the structure at 120 K concluded the analysis.