On Integrating Direct Methods and Isomorphous Replacement Techniques. The Formula P₁₀

Abstract

The joint probability distribution of ten pairs of isomorphous structure factors has been derived. Their indices correspond to the reflexions contained in the second phasing shell of the triplet invariant, as described by the theory of representations [Giacovazzo (1977). Acta Cryst. A33, 934-944; Giacovazzo (1980). Acta Cryst. A36, 362-373]. The conclusive formula allows the estimation of triplet invariants via a second representation formula, called the P10 formula, which is more accurate than the traditional formula of Giacovazzo, Cascarano & Zheng [Acta Cryst. (1988), A44, 45-51]. The procedure is also able to take into consideration the prior information on the heavy-atom structure, when available.