THE SAS MAXIMAL PRINCIPLE. Herbert Hauptman, Hauptman-Woodward Medical Research Institute, Inc., 73 High Street, Buffalo, New York 14203-1196 USA

When SAS diffraction data are available, the phase problem may be formulated as one of global optimization. Although the objective function has a myriad of local maxima, its global maxima, no more than two, are readily found by means of the newly derived SAS tangent formula. The initial applications show that the method is capable of producing, ab initio, the values of thousands of phases with acceptable average errors (< 50deg.) and interpretable maps, even with experimental data at a resolution of about 2.5Å.

The method described here also solves the associated redundant system of linear congruences, an alternative formulation of the phase problem when SAS data are available.

This work is supported by NIH Grant No. PO1 GM46733.