Direct methods and isomorphous replacement. The triplet invariant estimate when heavy atoms are located

The probabilistic theory of the three-phase structure invariants for isomorphous pairs has been generalized to the case in which a heavy-atom structure model is available. The rigorous method of joint probability distributions has been applied: it is able to handle errors in measurements and in the heavy-atom structure model, as well as the lack of isomorphism. The conclusive formulas have been successfully applied to experimental data.