Identification of systematically aberrant phase relationships arising from structural regularity

In many crystals the asymmetric unit is composed largely of repeating structural fragments all having the same orientation. This situation occurs in crystals of organic compounds containing fused benzene ring systems, for example. In the direct determination of such crystal structures approximate values for the phase-angle sums of certain triplets of strong reflections whose indices sum to zero can be predicted from the Fourier transform of a single fragment in its proper orientation. We describe a method for determining this orientation by fitting the square of the transform of the fragment to the intensity data and indicate how information derived from the oriented transform may be applied to the direct solution of crystal structures. An application of the method to the determination of the crystal structure of the plant pigment methoxydalrubone (C₂₀H₂₀O₅; P, Z = 2) is given.