Transferable Hirshfeld atom model for rapid evaluation of aspherical atomic form factors.

Form factors based on aspherical models of atomic electron density have brought great improvement in the accuracies of hydrogen atom parameters derived from X-ray crystal structure refinement. Today, two main groups of such models are available, the banks of transferable atomic densities parametrized using the Hansen-Coppens multipole model which allows for rapid evaluation of atomic form factors and Hirshfeld atom refinement (HAR)-related methods which are usually more accurate but also slower. In this work, a model that combines the ideas utilized in the two approaches is tested. It uses atomic electron densities based on Hirshfeld partitions of electron densities, which are precalculated and stored in a databank. This model was also applied during the refinement of the structures of five small molecules. A comparison of the resulting hydrogen atom parameters with those derived from neutron diffraction data indicates that they are more accurate than those obtained with the Hansen-Coppens based databank, and only slightly less accurate than those obtained with a version of HAR that neglects the crystal environment. The advantage of using HAR becomes more noticeable when the effects of the environment are included. To speed up calculations, atomic densities were represented by multipole expansion with spherical harmonics up to l = 7, which used numerical radial functions (a different approach to that applied in the Hansen-Coppens model). Calculations of atomic form factors for the small protein crambin (at 0.73 Šresolution) took only 68 s using 12 CPU cores.

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

A comprehensive analysis of various properties derived from multiple high-resolution X-ray diffraction experiments is reported. A total of 13 charge-density-quality data sets of α-oxalic acid dihydrate (C2H2O4·2H2O) were subject to Hansen-Coppens-based modelling of electron density. The obtained parameters and properties were then statistically analysed yielding a clear picture of their variability across the different measurements. Additionally, a computational approach (CRYSTAL and PIXEL programs) was utilized to support and examine the experimental findings. The aim of the study was to show the real accuracy and interpretation limits of the charge-density-derived data. An investigation of raw intensities showed that most of the reflections (60-70%) fulfil the normality test and the lowest ratio is observed for weak reflections. It appeared that unit-cell parameters are determined to the order of 10(-3) Š(for cell edges) and 10(-2) ° (for angles), and compare well with the older studies of the same compound and with the new 100 K neutron diffraction data set. Fit discrepancy factors are determined within a 0.5% range, while the residual density extrema are about ±0.16 (3) e Å(-3). The geometry is very well reproducible between different data sets. Regarding the multipole model, the largest errors are present on the valence shell charge-transfer parameters. In addition, symmetry restrictions of multipolar parameters, with respect to local coordinate systems, are well preserved. Standard deviations for electron density are lowest at bond critical points, being especially small for the hydrogen-bonded contacts. The same is true for kinetic and potential energy densities. This is also the case for the electrostatic potential distribution, which is statistically most significant in the hydrogen-bonded regions. Standard deviations for the integrated atomic charges are equal to about 0.1 e. Dipole moments for the water molecule are comparable with the ones presented in various earlier studies. The electrostatic energies should be treated rather qualitatively. However, they are quite well correlated with the PIXEL results.

An experimental charge density of HEPES.

We report the experimental charge density of HEPES [4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid], which is a common buffering agent. The structure was refined using the Hansen-Coppens formalism. The ability of the HEPES molecule to form stable intermolecular interactions and intermolecular hydrogen bonds in the crystal structure is discussed in terms of its buffering properties. The protonation mode observed in the crystal structure is different from that expected in solution, suggesting that additional factors must be taken into consideration in order to explain the solution properties of the compound. As ordered HEPES molecules are found in the active sites of proteins in several protein crystal structures, our results will allow for quantitative analysis of the electrostatic potential of the interacting surfaces of those proteins.

Determination of experimental charge density in model nickel macrocycle: [3,11-bis(methoxycarbonyl)-1,5,9,13-tetraazacyclohexadeca-1,3,9,11-tetraenato-(2-)-kappa(4)N]nickel(II).

Experimental and theoretical atomic charges and d-orbital populations were obtained for [3,11-bis(methoxycarbonyl)-1,5,9,13-tetraazacyclohexadeca-1,3,9,11-tetraenato(2-)-kappa(4)N]nickel(II) monocrystal (16Ni) using the Hansen and Coppens formalism. Several models of this structure were tested as a function of quality of the fit, convergence of the refinement, value of residual peaks and holes, and Hirshfeld's rigid-bond test. The models with Ni-atomic scattering factors applied for the metal center are significantly better than those with the Ni-ionic scattering factors. The properties of the final electron density distributions are very consistent and similar for all of the models tested. The values of the d-orbital populations for Ni roughly agree with the occupation order of the d-electron levels for square-planar complexes derived from crystal field theory and are comparable with those obtained by the natural population analysis method. Experimental atoms-in-molecules charges calculated for four different models agree quite well for models with different symmetry restrictions and the same scattering factor for the Ni. Both experimental and theoretical methods predict relatively high negative values of charges for the nitrogen and oxygen atoms and also a quite high positive charge for the C(7) atom. The values of rho(r(BCP)) for the Ni-N bonds are in the range from 0.60 up to 0.75e A(-3), with positive laplacian values indicating noncovalent bonding. For the laplacian of the electron density evaluated in the plane of the macrocyclic ring, a typical map for a square-planar complex was obtained with four charge concentrations--3d(xy) orbitals--pointing toward the regions between the M-N bonds and charge depletions directed toward the (3,-1) critical points of the negative laplacian for the nitrogen atoms.