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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.

ELMAM2 is a generalized and improved library of experimentally derived multipolar atom types. The previously published ELMAM database is restricted mostly to protein atoms. The current database is extended to common functional groups encountered in organic molecules and is based on optimized local axes systems taking into account the local pseudosymmetry of the molecular fragment. In this approach, the symmetry-restricted multipoles have zero populations, while others take generally significant values. The various applications of the database are described. The deformation electron densities, electrostatic potentials and interaction energies calculated for several tripeptides and aromatic molecules are calculated using ELMAM2 electron-density parameters and compared with the former ELMAM database and density functional theory calculations., (© 2012 International Union of Crystallography)

The existing pseudoatom databases (ELMAM, Invariom, UBDB and ELMAM2) enable structure refinement to be performed with the use of aspherical scattering factors computed from the transferable aspherical atom model (TAAM) as an alternative to independent atom model refinement. In addition, electrostatic properties can be estimated with the help of the databases. The quality of the structural and electrostatic properties obtained from the individual databases was tested. On the basis of a 100 K high-resolution single-crystal X-ray diffraction experiment on L-His-L-Ala dihydrate and 23 K high-resolution data for L-Ala [Destro & Marsh (1988). J. Phys. Chem. 92, 966-973], the structural properties, electron-density distributions and molecular electrostatic potentials obtained from different TAAMs were compared to each other and to reference models. Experimental multipolar models and theoretical models refined against theoretical structure factors computed from periodic density functional theory (DFT) calculations were compared to the TAAMs in order to determine which model best describes the crystal-field effect. Unperturbed wavefunctions based on the MP2 and DFT calculations and properties obtained directly from these were used as a reference to judge how properly the databases reproduce the properties of isolated molecules. For Gly-L-His dihydrate, D,L-His and the above-mentioned two crystal structures, deviations of the molecular dipole moments and Coulombic intermolecular interaction energies from the reference values were examined. Root-mean-square deviations (RMSDs) and correlation coefficients were used as a quantitative measure of the quality of the analysed properties. TAAM refinements reproduce X-H bond lengths optimized in theoretical periodic calculations. Structural properties obtained from different database models are similar to each other. The anisotropic displacement parameters from TAAMs are similar to the results of experimental multipolar refinement; differences are about 0.5 and 2.5% for high-resolution and low-resolution data, respectively. Differences in dipole-moment magnitudes calculated from database models are about 5%, and directions differ by up to 30°. The values of electrostatic interaction energies estimated from the individual TAAMs differ greatly from each other and from the reference values. RMSDs are about 9-15 and 22-33 kJ mol(-1) for UBDB and the other database models, respectively.

With an increasing number of biomacromolecular crystal structures being measured to ultra-high resolution, it has become possible to extend to large systems experimental charge-density methods that are usually applied to small molecules. A library has been built of average multipole populations describing the electron density of chemical groups in all 20 amino acids found in proteins. The library uses the Hansen & Coppens multipolar pseudo-atom model to derive molecular electron density and electrostatic potential distributions. The library values are obtained from several small peptide or amino acid crystal structures refined against ultra-high-resolution X-ray diffraction data. The library transfer is applied automatically in the MoPro software suite to peptide and protein structures measured at atomic resolution. The transferred multipolar parameters are kept fixed while the positional and thermal parameters are refined. This enables a proper deconvolution of thermal motion and valence-electron-density redistributions, even when the diffraction data do not extend to subatomic resolution. The use of the experimental library multipolar atom model (ELMAM) also has a major impact on crystallographic structure modelling in the case of small-molecule crystals at atomic resolution. Compared to a spherical-atom model, the library transfer results in a more accurate crystal structure, notably in terms of thermal displacement parameters and bond distances involving H atoms. Upon transfer, crystallographic statistics of fit are improved, particularly free R factors, and residual electron-density maps are cleaner.

The differences between two databases describing the polypeptide main chain in terms of charge-density parameters, directly usable in protein structure refinements, are discussed. These databases contain averaged multipole populations of peptide pseudo-atoms obtained from refinement against theoretical simulated data and against high-resolution experimental data on small peptide or amino acid molecules. The main discrepancy becomes apparent when electrostatic properties are calculated.

The normal matrix in the least-squares refinement of macromolecules is very sparse when the resolution reaches atomic and subatomic levels. The elements of the normal matrix, related to coordinates, thermal motion and charge-density parameters, have a global tendency to decrease rapidly with the interatomic distance between the atoms concerned. For instance, in the case of the protein crambin at 0.54 A resolution, the elements are reduced by two orders of magnitude for distances above 1.5 A. The neglect a priori of most of the normal-matrix elements according to a distance criterion represents an approximation in the refinement of macromolecules, which is particularly valid at very high resolution. The analytical expressions of the normal-matrix elements, which have been derived for the coordinates and the thermal parameters, show that the degree of matrix sparsity increases with the diffraction resolution and the size of the asymmetric unit.