Experimental charge-density studies: data reduction and model quality: the more the better?

Abstract

In this review, recent developments concerning data and model quality in experimental charge-density investigations from a personal view-point are described. Data quality is not only achieved by the high resolution, high I/σ(I) values, low merging R values and high multiplicity. The quality of the innermost reflections especially is crucial for mapping the density distribution of the outermost valence electrons and can be monitored by (I/σ). New detector technologies seem to be promising improvements. Empirical corrections to correct for low-energy contamination of mirror-focused X-ray data and for resolution- and temperature-dependent errors caused by factors such as thermal diffuse scattering are described. Shashlik-like residual density patterns can indicate the need for an anharmonic description of the thermal motion of individual atoms. The physical reliability of the derived model must be thoroughly analysed. The derived probability density functions for the mean-squared atomic vibrational displacements especially should have only small negative values. The treatment of H atoms has been improved by methods to estimate anisotropic thermal motion. For very high resolution data, the polarization of the core density cannot be neglected. Several tools to detect systematic errors are described. A validation tool is presented that easily detects when the refinement of additional parameters yields a real improvement in the model or simply overfits the given data. In all investigated structures, it is proved that the multipole parameters of atoms with a comparable chemical environment should be constrained to be identical. The use of restraints could be a promising alternative.

Experimental X-ray Electron Density Study of Atomic Charges, Oxidation States, and Inverted Ligand Field in Cu(CF3)4–

“…The κ and κ′ parameters of hydrogen atoms were fixed to a value of 1.2. Crystallographic output and a detailed evaluation of the fit are given in Figures S1–S4 in the Supporting Information.…”

“…Considering that the oxidation state of Cu and the associated valence electron count of the CF 3 ligands are strongly related to the electron density distribution (EDD), it is surprising that the latter has not seized a more prominent role in the many experimental and theoretical contributions. The fact is that the EDD is obtainable from accurate single-crystal X-ray diffraction experiments using a multipole model and has been used in numerous studies to provide insight into the question of molecular reactivity, bonding analysis, aromaticity, etc. − The core of the approach is the fitting of population parameters related to atom-centered spherical harmonic functions, as proposed by Hansen and Coppens, and this advanced modeling requires data of the utmost quality. ,, …”

Ground-State Charge-Density Distribution in a Crystal of the Luminescent ortho-Phenylenediboronic Acid Complex with 8-Hydroxyquinoline

“…Multipole refinements for all data sets were carried out using the MOPRO suite , combined with the current version of the University at Buffalo Data Bank (UBDB), which employs the Hansen–Coppens multipole model . Full details are present in the Supporting Information. ,− Despite the relatively low extreme values in the residual density and quite satisfactory R -factors, inspection of the residual density distribution revealed some systematic effects in the solvent molecule fragment, namely around the O4 oxygen atom (Figure a). Careful examination indicated that mostly the high-angle data are responsible for the presence of these spurious features suggesting that the observed model deficiencies are related to some inappropriate thermal motion description of this atom.…”

X-ray Charge Density Study of the Drug Methimazole with Z′ = 2: Differences in the Electronic Structure of the Thiourea Core due to Crystal Packing Effects

“…Total PDF and its anharmonic part for sulfur atoms S(1a) and S(1b) are shown in Figure S6. Refinement of thermal motion anharmonicity was justified by meeting certain conditions described in the literature; 58 namely, the R values dropped quite considerably, and, for both sulfur atoms, some of the coefficients were at least three times larger than their esd. One of the most important validation criteria, namely, the coherence of topological analysis of the experimental ED modeled, is further discussed in detail.…”