AB-INITIO STRUCTURE DETERMINATION BY THE MAXIMUM ENTROPY AND LIKELIHOOD METHOD USING POWDER DIFFRACTION DATA AND THE CONCEPT OF HYPEROCTANT PHASE ANGLES. W. Dong and C. J. Gilmore, Department of Chemistry, University of Glasgow, G12 8QQ, UK.

The problem of reflection overlap in powder diffraction is the factor which most limits our ability to solve crystal structures ab initio from such data. The conventional multiplicity weighted eqi-partition of the intensity among the overlapped reflections is often much too crude to make structure solution possible with conventional methods. In the maximum entropy - likelihood approach (Bricogne, Acta Cryst. (1991), A47, 803-829) as programmed in the MICE program (Gilmore, Henderson & Bricogne (1991). Acta Cryst. A47, 830-841; Shankland, Gilmore, Bricogne & Hashizume (1993). Acta Cryst. A49, 493-501) partitioning the intensity of overlapped reflections is carried out by the concept of a hyperoctant phase permutation. Each overlap has associated with it the phase angles of the reflections comprising it plus one or more angles which define the intensity partitioning. These hyperoctant angles are permuted as normal phases and used to build the nodes of a phasing tree, which are then subjected to entropy maximisation. Following this, each node has a likelihood measure associated with it. We have now established a statistical method of analysing such likelihoods to determine both the phase angles and the intensities for strong overlaps, and have applied the technique successfully to organic molecules and zeolites with a mixture of laboratory and synchrotron data. It is a significant step forward in our goal to make the MICE program totally automatic.

This work is supported by the EPSRC and Eastman Kodak Ltd.