Abstract
We describe methods for constructing a Maximum Entropy X-ray electron density map in crystallography that fits certain amplitudes and phases uniquely subject to a squared residual constraint. The calculations use a free energy analogue, or statistical potential that derives from the grand partition function of the maximum entropy problem in Fourier space. It is a function of the statistical forces, the Lagrangian multipliers of the entropy. Three new functions Y, G and Ψ allow us to fit the data with predetermined accuracy, and to avoid divergences which would otherwise occur. The method is able to handle physically realistic and elaborate models: cells with fixed density regions, several types of scattering atom, anomalous dispersion. The control algorithm, and the relation between the domains of the force and probability variables are outlined.
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© 1989 Springer Science+Business Media Dordrecht
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McLachlan, A.D. (1989). A Statistical Potential for Modelling X-ray Electron Density Maps with Known Phases. In: Skilling, J. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7860-8_23
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DOI: https://doi.org/10.1007/978-94-015-7860-8_23
Publisher Name: Springer, Dordrecht
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