Retrieval of Structure-Factor Phases in Non-centrosymmetric Space Groups. Model Studies Using Multipole Refinements

Abstract

Structure factors with known magnitude and phase are constructed for seven different molecular crystals in non-centrosymmetric space groups and used to calibrate the retrieval of structure-factor phase information with several different scattering factor models. Monopole models are confirmed to be inadequate, yielding poor estimates of phases and underestimating the Fourier deformation electron density by as much as 50%. Multipole models are generally successful, with the conspicuous exception of hexamethylenetetramine (HMT). The results confirm the known difficulty of phasing structure-factor magnitudes for HMT, but reveal a broad spectrum of behaviour of phase retrieval in various non-centrosymmetric space groups, depending partly on the number of reflections with restricted phases. For several systems (urea, hydrogen peroxide, L-alanine and borazine) the results confirm that multipole refinements of scattering factor models against experimental data are capable of yielding highly accurate phases and hence reliable electron distributions. For the exceptional case of HMT a simple eigenvalue filtering technique enables retrieval of phases and electron densities with an accuracy comparable to the best of the other non-centrosymmetric systems studied.