The estimation of the one-phase structure seminvariants of first rank by means of their first and second representations

The estimation of the one-phase structure seminvariants of first rank is carried out in any centrosymmetric or non-centrosymmetric space group. Representations theory [Giacovazzo (1977), Acta Cryst. A33, 933-944] is suitably associated to the joint probability distribution method: the diffraction magnitudes belonging to the first and second phasing shells of any seminvariant are exploited in order to give probabilistic estimates of the seminvariant cosines. Probabilistic formulae are also derived via the method of complementary invariants.