A probabilistic theory of two-phase seminvariants of first rank via the method of representations. IV. Practical aspects and applications

An algorithm is devised to calculate the expected values of two-phase seminvariants of first rank in space groups up to orthorhombic. This algorithm is based on the probabilistic theory [Giacovazzo (1979). Acta Cryst. A35, 296-305]. The method has been tested on several known structures using the probabilistic formulae obtained via the Gram-Charlier expansion of the characteristic function. We report here the results of the calculations which show how the method can secure a good estimate of a limited number of two-phase seminvariants. These estimates can certainly be of great help in the initial stages of phase determination. In addition, the estimated values of the two-phase seminvariants can be used as a figure of merit to discriminate among the several sets of phases generated in a multisolution process. The use of two-phase seminvariants for enantiomorph discrimination in space groups of class 222 is also illustrated. A detailed comparison with the coincidence method shows the noticeable improvement attained by the present algorithm.