The use of structural information in the estimation of crystal-structure phase invariants

Abstract

Recent developments in translation-function methods have secured a priori estimates of the imaginary component of molecular transform products, which are here shown to permit improved estimates of crystal- structure phase invariants when the orientations, but not the positions, of conformationally known structural fragments are available. Trial calculations indicate that the values of the triple-phase invariants computed from the phases of the oriented molecular transform products are indistinguishable from values of these invariants computed with the various oriented molecular structures at their true locations in the unit cell, provided that the fragments comprise half or more of the contents of the asymmetric unit. The Σ1 phases calculated for such structures are equal to the phases produced by the various properly positioned fragments of the partial structure. These results imply that a unique direct-methods solution to determine the positions of the fragments is virtually guaranteed for partial structures of this size or larger. The accuracy of the computed triple invariants for smaller fragments, comprising about one quarter or less of the contents of the asymmetric unit, remains sufficiently better than the corresponding ab initio direct-methods estimates, and should provide a more reliable basis for determining the positions of the fragments by multi-solution procedures. Computed phase-invariant procedures should possess an important advantage over translation-function methods in applications which involve multiple fragments of known orientation.