Past, present and future of charge density and density matrix refinements

International audienceBasic theoretical and some practical aspects of the interpretation of X-ray scattering experiments are described. Our focus is on model building and refinement associated with retrieving information related to electron density matrices from the measured data. The ill-posed nature of this inverse problem is emphasised and the physical significance, reliability and reproducibility of the properties obtained by data fitting are discussed through representative examples taken from recent studies. A special attention is devoted to the pseudoatom formalism widely used to interpret high-resolution single-crystal X-ray diffraction data to map the static electron distribution in solids. © Springer Science+Business Media B.V. 2012

Topological Analysis of the Experimental Electron Densities of Amino Acids. 1. D,L\mathrm{_{D,L}}-Aspartic Acid at 20 K

High-resolution X-ray diffraction data collected at 20 K are interpreted in terms of the rigid-pseudoatom formalism to derive the electron density and related properties, such as the electrostatic potential and electric moments, of the crystalline d,l-aspartic acid. The refinement models applied are restricted via rigid-bond type constraints to reduce possible bias in the mean-square displacement amplitudes due to inadequacies in the thermal deconvolution. The density and its Laplacian extracted from the data is analyzed in terms of the topological properties of covalent bonds and nonbonded interactions. The results are compared to those calculated at the Hartree−Fock level of theory and to those obtained experimentally for analogous molecules. The comparison must consider the differences in the locations of the bond critical points of the densities in question, that is, how the bond polarity manifests itself in the distribution of charge obtained by different methods. One of the key questions to the reliability of experimental pseudoatomic densities seems to be whether the treatment of the X-ray data can be standardized so as to reduce model inadequacies, especially those related to the derivation of monopole populations

Electron density studies on complexes of 18-crown-6

Abstract -Electron density studies on 18 -crown -6 x 2 cyanamide as well as 18 -crown-6 x KN3 x H20 show, that the chemistry of crownethers obviously is characterized by highly sophisticated electrostatic interactions, which can be formed as a consequence of a very symmetric and flexible arrangement of electron density. As a consequence the electrostatic interactions, which mainly describe the binding situation, are overlayed by dipole-dipole interactions and dispersive interactions respectively. Detailed measurements show, that strong polarisation effects in the lone pair region of the oxygens play an important role

Accurate Experimental Electronic Properties of DL-Proline Monohydrate Obtained Within 1 Day

A 1-day x-ray diffraction experiment on DL-proline monohydrate was performed at 100 kelvin with synchrotron radiation and a charge-coupled device area detection technique. The accuracy of the charge density distribution and of the related electronic properties extracted from these data is comparable or even superior to the accuracy obtained from a 6-week experiment on DL-aspartic acid with conventional x-ray diffraction methods. A data acquisition time of 1 day is comparable to the time needed for an ab initio calculation on the isolated molecules. This technique renders larger molecular systems of biological importance accessible to charge density experiments

Experimental charge density studies of disordered N-phenylpyrrole and N-(4-fluorophenyl)pyrrole.

The static electron densities of the title compounds were extracted from high-resolution X-ray diffraction data using the nucleus-centered finite multipole expansion technique. The interpretation of the data collected for the N-phenylpyrrole crystal revealed a static disorder that could be successfully resolved within the aspherical-atom formalism. The local and integrated topological properties of the density obtained via a constrained multipole refinement are in statistical agreement with those calculated at the B3LYP/cc-pVTZ level of theory for the isolated molecule and for those derived from the experimental density of the para-fluorinated derivative N-(4-fluorophenyl)pyrrole. The topological analysis of the densities indicates neither pyramidal character of the pyrrole N-atom nor a quinoidal structure of the phenyl rings in either molecule. The fluorine substitution appears to have only a minor effect on the density of the remaining constituents but it results in markedly different features of the electrostatic potential of the two compounds, The consistency of the multipole refinement is validated by residual density analysis