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.

Topological analysis of the electron density in hydrogen bonds

“…Furthermore, the phase problem, which is mainly important when non-centrosymmetric space groups are involved, is another implicit source of inaccuracy. Even if the multipolar models of &(r) permit a much better description of phases than the spherical-atom model ( Souhassou et al, 1991), the results have to be analysed critically (El Haouzi et al, 1996;Spackman & Byrom, 1997; Pe  re Á s et al, 1999): atomic constraints must be applied in some cases and several re®nement strategies must be tested to drive the convergence to the most realistic minima. Finally, it is noteworthy that in the intermolecular regions on which this study is focused features in &(r) are of much lower magnitude than those around atomic positions, and thus they can be more sensitive to small variations induced by different experiments, methods, models and strategies.…”

Evaluation of the Solid State Dipole Moment and Pyroelectric Coefficient of Phosphangulene by Multipolar Modeling of X-ray Structure Factors

“…For this reason the method of singular value decomposition (SVD) [8,9,32] was introduced for solving the normal equations. Eigenvalues less than 5 Â 10 À8 times the largest eigenvalue of the normal matrix were set to zero.…”

“…Phosphangulene represents a challenge because it crystallizes in the noncentrosymmetric high symmetry space group R3m, with five of the eight atoms on special positions in the asymmetric unit. [7,8] However, obtaining pyroelectric coefficients from diffraction data has advantages. First of all, the testing of a newly synthesized material requires solving the crystal structure anyway.…”

Experimental and theoretical electronic charge densities in molecular crystals

“…However, determination of polarizability from X-ray diffraction requires careful handling of data. Many of the studies on NLO crystals using charge density concentrate merely on the accurate extraction of phases associated with the structure factors [75][76][77][78],…”