Open AccessNovel treatment of the experimental data in the application of the maximum‐entropy method to the determination of the electron‐density distribution from X‐ray experiments
Author(s) -
De Vries R. Y.,
Briels W. J.,
Feil D.
Publication year - 1994
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
eISSN - 1600-5724
pISSN - 0108-7673
DOI - 10.1107/s0108767393012802
Subject(s) - principle of maximum entropy , entropy maximization , maximum entropy probability distribution , mathematics , entropy (arrow of time) , maximization , electron density , distribution (mathematics) , electron , statistical physics , mathematical analysis , physics , statistics , mathematical optimization , thermodynamics , quantum mechanics
The maximum-entropy method (MEM) has been tested on a limited set of noisy Fourier data from a known electron-density distribution (EDD). It is shown that maximizing the entropy of the EDD under the usual condition of fitting the variance of the data set does not necessarily lead to a satisfactory error distribution of the calculated reflections. The MEM property of producing the flattest EDD consistent with the data causes the calculated values of strong reflections to deviate systematically as much as possible from their measured values. Calculated values of strong reflections are usually smaller than their measured values. The use of a novel constraint on the entropy maximization greatly improves the form of the error distribution and also the calculated EDD