This chapter describes a range of methods for solving the phase problem when a structure that is similar to the one being analysed has already been determined. These methods generally rely on comparing the Patterson function of the unknown structure (calculated from its diffraction intensities) with that calculated from the known structure. For computational expedience, the comparison of the two Patterson functions is done in two stages known as the rotation function and the translation function. In the rotation function, the Patterson of the search model is rotated through various angles and compared with the target Patterson — the orientation which gives the highest correlation with the target Patterson indicates a likely solution. The correct position of the search model within the target unit cell can then be determined essentially by calculating the inter-molecular vectors at a series of trial positions and comparing them with the target Patterson — this is known as the translation function. The variables affecting these calculations are discussed and methods for verifying the results are described, as are recent developments in bioinformatics which can be exploited to optimise the search model.
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