ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
A general method for phase extension and refinement is described. It consists of minimizing a conveniently defined functional {\tt M} by the steepest-descent or conjugate-gradient techniques. This functional consists of a term R = ½ Σ (|F| - |Fobs|)2 plus any given number of constraint equations selected according to the requirements of the particular problem considered. Several examples of the introduction of constraints are described in detail, both in direct and reciprocal space, and a few one-dimensional tests provide insight in the behavior of the different alternatives. Also, some general features that the calculated electron density function should fulfil, such as positivity and boundness, are directly introduced without the need of terms other than R in the functional {\tt M}. The connection between this approach and the ones which use the principle of maximum entropy is discussed. A critical analysis shows that those methods are just different ways of minimizing R with the constraints of positivity.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0108767383001294
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