• Herbert Hauptman

      Articles written in Journal of Chemical Sciences

    • The phase problem of x-ray crystallography

      Herbert Hauptman

      More Details Abstract Fulltext PDF

      Three major themes are developed:

      The fundamental principle of direct methods: The structure seminvanants link the observed magnitudes ¦E¦ with the desired phasesΦ of the normalized structure factorsE. Specifically, for fixed enantiomorph, the observed magnitudes ¦E¦ determine, in general, unique values for all the structure seminvariants; the latter, in turn, as certain well defined linear combinations of the phases, lead to unique values for the individual phases Φ.

      The neighbourhood principle. For fixed enantiomorph, the value of any structure seminvariantT is primarily determined, in favourable cases, by the values of one or more small sets of magnitudes ¦E¦, the neighbourhoods ofT, and is relatively insensitive to the great bulk of remaining magnitudes. The conditional probability distribution ofT, given the magnitudes in any of its neighbourhoods, yields an estimate forT which is particularly good in the favourable case that the variance of the distribution happens to be small.

      The extension concept: By embedding the structure seminvariantT and its symmetry related variants in suitable structure invariantsQ, one obtains the extensionsQ of the seminvariantT. In this way the probabilistic theory of the structure seminvariants is reduced to that of the structure invariants, which is well developed.

      Finally, the traditional techniques of direct methods are combined with isomorphous replacement and anomalous dispersion.

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