Abstract
A formula is derived for centrosymmetric crystals from fourth-order determinantal joint probability distributions that provides, for the triplet invariants, values of P+/P-, the ratio of the probability that an invariant has a plus sign associated with it to the probability that it has a minus sign. The formula makes use of the entire data set in the computations for each invariant. Test calculations indicate that many hundreds of invariants can be selected by use of the formula with essential certainty that their value is equal to zero. Several invariants whose value is equal to π can also be selected on occasion with very high reliability.
Keywords: crystal structure, phase determination, triplet selection, determinantal distributions
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Karle I. L., Gibson J. W., Karle J. The conformation and crystal structure of the cyclic polypeptide -gly-gly-D-ala-D-ala-gly-gly .3H2O. J Am Chem Soc. 1970 Jun 17;92(12):3755–3760. doi: 10.1021/ja00715a037. [DOI] [PubMed] [Google Scholar]
- Karle J. Joint probability distribution of the invariants comprising determinantal inequalities: Heuristic derivation. Proc Natl Acad Sci U S A. 1978 Jun;75(6):2545–2548. doi: 10.1073/pnas.75.6.2545. [DOI] [PMC free article] [PubMed] [Google Scholar]