International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 15.2, pp. 326-327
Section 15.2.3.3. General treatment of the structure-factor distribution
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Department of Haematology, University of Cambridge, Wellcome Trust Centre for Molecular Mechanisms in Disease, CIMR, Wellcome Trust/MRC Building, Hills Road, Cambridge CB2 2XY, England |
The Wilson, Sim, Luzzati and variable-error distributions have very similar forms, because they are all Gaussians arising from the application of the central limit theorem. The central limit theorem is valid under many circumstances; even when there are errors in position, scattering factor and B factor, as well as missing atoms, a similar distribution still applies. As long as these sources of error are independent, the true structure factor will have a Gaussian distribution centred on (Fig. 15.2.3.2), where D now includes effects of all sources of error, as well as compensating for errors in the overall scale and B factor (Read, 1990). in the acentric case, where , ɛ is the expected intensity factor and is the Wilson distribution parameter for the model.
Schematic illustration of the general structure-factor distribution, relevant in the case of any set of independent random errors in the atomic model. |
For centric reflections, the scattering differences are distributed along a line, so the probability distribution is a one-dimensional Gaussian.
References
Read, R. J. (1990). Structure-factor probabilities for related structures. Acta Cryst. A46, 900–912.Google Scholar