The application of direct methods to difference structures. Non-centrosymmetric structures containing heavy atoms. III. Enantiomorph and origin fixation

Abstract

Direct methods are applied to the difference structure factors for a non-centrosymmetric structure containing one or more heavy atoms in known positions, such that the known atoms form either a centro-symmetric arrangement, or a translational subcell, or both. The present procedure is initiated by subtracting the known heavy-atom contribution from the observed structure factor (assuming that the observed and calculated structure factors have the same phase) to obtain approximate values of the magnitude and phase of the light-atom contribution. Either about ten reflections, which are most inconsistent with respect to the Σ2 formula, are selected as 'enantiomorph discriminating' reflections, or about ten reflections which are 'subcell' extinct are selected as (enantiomorph and) origin choices and symbols are assigned to these reflections. The Σ2 phase relationship is used to find relations between the symbols. The analysis of the symbols, together with one or more arbitrary choices to fix the enantiomorph and/or the origin, will lead to a unique solution of the symbols in terms of numerical values. Further refinement of the difference structure factors by the conventional DIRDIF procedure followed by a Fourier synthesis leads to an electron density map where the additional heavy-atom symmetry has been destroyed.