Figures of merit in direct methods: a new point of view

Abstract

The probabilistic approach has been extensively used for analysing the statistical meanings of some traditional figures of merit. New figures of merit have also been introduced; some exploit one-phase and two-phase structure seminvariants of the first rank, the expected negative and/or enantiomorph-sensitive triplet invariants, and the expected negative and/or enantiomorph-sensitive quartets. Other figures of merit exploit the distribution of statistical parameters connected with PSI(0) and active triplets. A new combined figure of merit is shown to be a powerful tool for selecting the correct solutions among the various sets output by multisolution methods.