Acta Crystallographica Section B

Structural Science

Volume 57, Part 4 (August 2001)

research papers

Acta Cryst. (2001). B57, 497-506 [ doi:10.1107/S0108768101004050 ]

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

A. T. H. Lenstra and O. N. Kataeva

Abstract: 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 Å^-1) and high-order (0.7 < s < 1.0 Å^-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] )° 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( $\displaystyle\mathrel{\mathop H^{\rightharpoonup}}$ ) with an 11th degree polynomial in [theta] . This function predicts the local background b at each position $\displaystyle\mathrel{\mathop H^{\rightharpoonup}}$ 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.

Keywords: structure models; spectral truncation; pseudo-symmetry; background modelling.