Acta Crystallographica Section B

Structural Science

Volume 57, Part 4 (August 2001)

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 [bold 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 [bold 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 [bold 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 [bold sigma] ²(I) = I so that the error (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.

Online 24 July 2001


	Structure factor file (CIF format) (193.1 kbytes) Contains datablock Cu294K

	Structure factor file (CIF format) (199.3 kbytes) Contains datablock Cu120K

	Structure factor file (CIF format) (253.0 kbytes) Contains datablock Mn

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