Locating symmetry elements in Patterson superposition maps

Abstract

Abstract A reciprocal space technique for determining the location of symmetry elements in Patterson superposition maps has been developed. The overlap of the superposition map with a copy of the map generated by the placement of the symmetry element at an arbitrary position is calculated using the Fourier transform coefficients of the original map. When the overlap is maximized, the symmetry element has been placed in the correct position. An alternate expression, which minimizes the phase differences in the Fourier coefficients, is also described. Expressions are developed for constraining the positions of different symmetry elements to meet space group constraints. For superposition maps containing predominantly one image of the structure, the phases of the Fourier coefficients can be modified, using the locations of the symmetry elements, to provide approximate phases for the observed structure factors.