ON INTEGRATING DIRECT-METHODS AND ISOMORPHOUS REPLACEMENT TECHNIQUES - THE FORMULA P-10

The joint probability distribution of ten pairs of isomorphous structu re factors has been derived. Their indices correspond to the reflexion s contained in the second phasing shell of the triplet invariant, as d escribed by the theory of representations [Giacovazzo (1977). Acta Cry st. A33, 934-944; Giacovazzo (1980). Acta Cryst. A36, 362-373]. The co nclusive formula allows the estimation of triplet invariants via a sec ond representation formula, called the P-10 formula, which is more acc urate than the traditional formula of Giacovazzo, Cascarano & Zheng [A cta Cryst. (1988), A44, 45-51]. The procedure is also able to take int o consideration the prior information on the heavy-atom structure, whe n available.