New Formulation and Solution of the Phase Problem in X-Ray Analysis of Noncentric Crystals Containing Anomalous Scatterers

Use of anomalous dispersion in x-ray analyses of noncentric crystals reduces the problem of phase determination for any given structure factor to the choice between two possible roots of two simultaneous quadratic equations. This assumes that anomalous scatterer positions have been established by classical techniques. Selection of the correct root is aided by: the $P_s\left(\mathrm{u}\right)$ function of Okaya, Saito, and Pepinsky; heavy atom or isomorphous replacement techniques; or the linear inequalities of Okaya. Given moderately accurate structure factor amplitudes $\left|F\mathrm{h}\right|$ and $|F-\mathrm{h}|$, the phase problem is solved for noncentric crystals containing anomalous scatterers; and the absolute configuration of the structure is obtained as a by-product of the direct analysis.