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Some years ago the direct-methods origin-free modulus sum function (S) was adapted to the processing of intensity data from density functions with positive and negative peaks [Rius, Miravitlles & Allmann (1996). Acta Cryst. A52, 634-639]. That implementation used phase relationships explicitly. Although successfully applied to different situations where the number of reflections was small, its generalization to larger problems required avoiding the time-consuming manipulation of quartet terms. To circumvent this limitation, a modification of the recently introduced S-FFT algorithm (that maximizes S with only Fourier transforms) is presented here. The resulting S2-FFT algorithm is highly effective for crystal structures with at least one moderate scatterer in the unit cell. Test calculations have been performed on conventional single-crystal X-ray diffraction data, on neutron diffraction data of compounds with negative scatterers and on intensities of superstructure reflections to solve difference structures.

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