Structures of copper(II) and manganese(II) di(hydrogen malonate) dihydrate; effects of intensity profile truncation...

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 A(-1)) and high-order (0.7 < s < 1.0 A(-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-I-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 by that pseudo-symmetry. 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-->) with an 11th degree polynomial in straight theta. This function predicts the local background b at each position H--> 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)/P(B) and thus I = R - b and sigma(2)(I) = I so that the error sigma(I) 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.