A critical analysis of dipole-moment calculations as obtained from experimental and theoretical structure factors

Abstract

Three models of charge-density distribution - Hansen-Coppens multipolar, virtual atom and kappa - of different complexities, different numbers of refined parameters, and with variable levels of restraints, were tested against theoretical and high-resolution X-ray diffraction structure factors for 2-methyl-4-nitro-1-phenyl-1H-imidazole-5-carbonitrile. The influence of the model, refinement strategy, multipole level and treatment of the H atoms on the dipole moment was investigated. The dipole moment turned out to be very sensitive to the refinement strategy. Also, small changes in H-atom treatment can greatly influence the calculated magnitude and orientation of the dipole moment. The best results were obtained when H atoms were kept in positions determined by neutron diffraction and anisotropic displacement parameters (obtained by SHADE, in this case) were used. Also, constraints on kappa values of H atoms were found to be superior to the free refinement of these parameters. It is also shown that the over-parametrization of the multipolar model, although possibly leading to better residuals, in general gives worse dipole moments.

Statistical analysis of multipole-model-derived structural parameters and charge-density properties from high-resolution X-ray diffraction experiments

“…Importantly, the Shapiro-Wilk test is fulfilled showing the normal distribution of the observed dipole moment magnitudes across different measurements. This clearly indicates that the statistical variation is of the same range to the one observed from different multipolar refinements with respect to the same data set (Poulain-Paul et al, 2012;Bąk et al, 2011). This clearly indicates that the statistical variation is of the same range to the one observed from different multipolar refinements with respect to the same data set (Poulain-Paul et al, 2012;Bąk et al, 2011).…”

“…Recently, a number of studies explored the deficiencies of the multipole model (Bąk et al, 2009(Bąk et al, , 2011(Bąk et al, , 2012Poulain-Paul et al, 2012;Dittrich et al, 2012). Nevertheless, it should be noted that recorded diffracted-beam intensities also constitute a source of experimental errors, being further propagated across all stages of electron-density elucidation.…”

The generalized invariom database (GID)

“…Further studies are under way. Other properties, which are currently under critical study, include the electrostatic interaction energy (Abramov et al, 2000a,b;Li et al, 2002Li et al, , 2006Volkov, Koritsá nszky & Coppens, 2004;Spackman, 2007;Bouhmaida et al, 2009) and the molecular dipole moment (Spackman, 1992;Spackman et al, 2007;Poulain-Paul et al, 2012;). An open question is whether the approximations set in the HansenCoppens multipole model (frozen core, order of the expansion l max ¼ 4, m-independent radial functions) permit an accuracy to be reached that is high enough to obtain these properties from a reciprocal-space fit to structure factors in a reliable manner (Bąk et al, 2011;Jarzembska & Dominiak, 2012), and how modifications in the pseudoatom description can improve the situation.…”

The generalized invariom database (GID)

“…Further studies are under way. Other properties, which are currently under critical study, include the electrostatic interaction energy (Abramov et al, 2000a,b;Li et al, 2002Li et al, , 2006Volkov, Koritsá nszky & Coppens, 2004;Spackman, 2007;Bouhmaida et al, 2009) and the molecular dipole moment (Spackman, 1992;Spackman et al, 2007;Poulain-Paul et al, 2012;. An open question is whether the approximations set in the Hansen-Coppens multipole model (frozen core, order of the expansion l max ¼ 4, m-independent radial functions) permit an accuracy to be reached that is high enough to obtain these properties from a reciprocal-space fit to structure factors in a reliable manner (Bąk et al, 2011;Jarzembska & Dominiak, 2012), and how modifications in the pseudoatom description can improve the situation.…”