Ys. Liu et Nh. Hu, PROBABILISTIC ESTIMATION OF THE STRUCTURE SEMINVARIANTS IN THE MONOCLINIC AND ORTHORHOMBIC SYSTEMS WHEN ANOMALOUS SCATTERERS ARE PRESENT, Acta crystallographica. Section A, Foundations of crystallography, 50, 1994, pp. 595-601
The estimate formulas for the two-phase structure seminvariants (TPSSs
) in the presence of anomalous scattering are obtained from the estima
te of the two-phase structure invariants [Hauptman (1982). Acta Cryst.
A38, 632-641; Giacovazzo (1983). Acta Cryst. A39, 585-592] and the co
nditional probability distribution of the TPSSs is derived from the ne
ighborhood theory [Hauptman (1975). Acta Cryst. A31, 680-687]. A proce
dure for estimating the one-phase structure seminvariants near O or pi
(OPSSs) is proposed, based on the TPSS estimates. Test results for kn
own structures with error-free data show accurate estimates for the TP
SSs, even in the macromolecular case. For the OPSSs, the accuracy is r
elated to the strength of anomalous scattering by heavy atoms in the m
acromolecular case. The incorporation of the heavy-atom information im
proves the results.