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A priori structural information is incorporated into determinantal phasing techniques to improve phase prediction accuracy in resolution ranges where atomic or isotropic group-scatterer assumptions are not valid. For this purpose a conditional joint probability distribution to triplet order for any set of normalized structure factors of space groups P1 and P
is derived. The covariance of two normalized structure factors from the original set is calculated. A more general conditional joint probability distribution, involving covariance matrices of any order, is further derived. Numerical tests are performed employing ideal models consisting of several atomic groups of known stereochemistry but with random positions and orientations. The results indicate that the inclusion of stereochemical information improves the accuracy of phase prediction. The relative merit of this strategy in either one of or both normalization and covariance calculations for different resolutions is discussed.
is derived. The covariance of two normalized structure factors from the original set is calculated. A more general conditional joint probability distribution, involving covariance matrices of any order, is further derived. Numerical tests are performed employing ideal models consisting of several atomic groups of known stereochemistry but with random positions and orientations. The results indicate that the inclusion of stereochemical information improves the accuracy of phase prediction. The relative merit of this strategy in either one of or both normalization and covariance calculations for different resolutions is discussed.
