Some ideas on the deconvolution of the Patterson function
G. Germain, Michael Mark Woolfson · Acta Crystallographica · 1966
If a minimum function is computed from overlap on a single-weight peak in the Patterson function, the resultant map will, ideally, show a single image of the structure. However it is difficult to locate single-weight peaks in practice and overlap on a multiple peak produces several heavily-overlapped parallel images of the structure. The procedure described in this paper is as follows: (i) A minimum function is constructed from a multiple peak. (ii) The Fourier coefficients of the minimum function are found and, from these and the observed intensities, a map is computed which shows by what vectors the several images in the maximum function are displaced. (iii) The minimum function is displaced by the vectors found in (ii) and the minimum function of the result gives an approximation to the structure. An application to a model structure is described and possible developments of the method are indicated.