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 intensities I derived via the background-peak-background procedure. Least-squares optimizations reveal differences between the low-order (0 < s < 0.7 Angstrom (-1)) and high-order (0.7 < s < 1.0 Angstrom (-1)) structure models. The scale factors indicate discrepancies of up to 10% between the low-order and high-order reflection intensities. This observation is compound independent. It reflects the scan-angle-induced truncation error., because the applied 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 asymmetric unit. Our selection of observed intensities (I > 3 sigma) stresses that 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 thus a more robust structure we decided to exploit background modelling. We described the background intensities B( (H) over right arrow) with an 11th degree polynomial in theta. This function predicts the local background b at each position (H) over right arrow and defines the counting statistical distribution 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 this framework we reanalysed the structure of the copper(II) derivative. Background modelling resulted in a structure model with an improved internal consistency. At the same time the unweighted R value based on all observations decreased from 10.6 to 8.4%. A redetermination of the structure at 120 K concluded the analysis.