On the application of phase relationships to complex structures. V. Finding the solution

Multisolution direct methods for solving crystal structures lead to many plausible sets of phases and some means of determining the correct set is necessary. For centrosymmetric structures, figures of merit are usually quite discriminating and the examination of only one or two E maps is necessary. For noncentrosymmetric structures, figures of merit are unreliable and the necessity of examining a large number of E maps can sometime prove to be an almost insuperable obstacle to finding the correct structure. A procedure is described for overcoming this difficulty. The Cooley-Tukey fast-Fourier-transform technique is used to compute E maps and all peaks greater than a certain height are located. A selection of the highest of these peaks, whose number is chosen by the program user, is then analysed with respect to bond lengths and angles. Favourable projections of coherent groups of peaks are output on the line printer in the form of integers representing the ranking order of the peaks and in positions which represent an undistorted projection of the group. Computing time is of the order of one minute per set of phases and the examination of a set of 32 maps and finding the correct solution takes about 30 minutes.