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Multipole Model (multipole + model)
Selected AbstractsA standard local coordinate system for multipole refinements of the estrogen core structureJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2003Kristin Kirschbaum A comparative charge density study on a series of estrogen derivatives has been initiated. The study utilizes the Hansen,Coppens atom-centred multipole model to describe the valence electron density distribution. Direct comparison of the population parameters for each estrogen after the respective multipole refinements requires standardization of the atom-centred local coordinate systems. Such a standard coordinate system for the common estrogen core is reported, taking advantage of the shape of those multipoles which have the spatial characteristics of sp2 and sp3 hybrid orbitals. Additionally, populating these principal multipoles at the beginning stage of the refinements improves the stability of these large highly correlated calculations. [source] Multipole electron-density modelling of synchrotron powder diffraction data: the case of diamondACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2010H. Svendsen Accurate structure factors are extracted from synchrotron powder diffraction data measured on crystalline diamond based on a novel multipole model division of overlapping reflection intensities. The approach limits the spherical-atom bias in structure factors extracted from overlapping powder data using conventional spherical-atom Rietveld refinement. The structure factors are subsequently used for multipole electron-density modelling, and both the structure factors and the derived density are compared with results from ab initio theoretical calculations. Overall, excellent agreement is obtained between experiment and theory, and the study therefore demonstrates that synchrotron powder diffraction can indeed provide accurate structure-factor values based on data measured in minutes with limited sample preparation. Thus, potential systematic errors such as extinction and twinning commonly encountered in single-crystal studies of small-unit-cell inorganic structures can be overcome with synchrotron powder diffraction. It is shown that the standard Hansen,Coppens multipole model is not flexible enough to fit the static theoretical structure factors, whereas fitting of thermally smeared structure factors has much lower residuals. If thermally smeared structure factors (experimental or theoretical) are fitted with a slightly wrong radial model (s2p2 instead of sp3) the radial scaling parameters (`,' parameters) are found to be inadequate and the `error' is absorbed into the atomic displacement parameter. This directly exposes a correlation between electron density and thermal parameters even for a light atom such as carbon, and it also underlines that in organic systems proper deconvolution of thermal motion is important for obtaining correct static electron densities. [source] On the origin of topological differences between experimental and theoretical crystal charge densitiesACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2000Anatoliy Volkov Topological analysis of experimental and theoretical (molecular and crystal) electron densities of p -nitroaniline and p -amino- p,-nitrobiphenyl reveals considerable discrepancies between experiment and theory for the bond critical points properties. Particularly large differences occur for the positive curvature along the bond path (,3). The differences become somewhat smaller when more extended basis sets and correlation effects are introduced in the theoretical calculations. The effect of the crystal matrix on the properties of bond critical points is evaluated for the p -nitroaniline molecule using the 6-21G** and 6-31G** basis sets. The differences between the isolated molecule and the molecule in the crystal are too small to explain the quantitative disagreement between the theoretical and experimental topologies reported in the literature and found in the current study. For most bonds, the observed changes in the properties of the electron density agree well for both basis sets but some discrepancies are found for changes in ,3 for N,H and aromatic C,C bonds. When the theoretical densities are projected into the multipole density functions through refinement of the theoretical structure factors, the topological properties change and differences between theory and experiment are reduced. The main origin of the observed discrepancies is attributed to the nature of the radial functions in the experimental multipole model. [source] Topological properties of hydrogen bonds and covalent bonds from charge densities obtained by the maximum entropy method (MEM)ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009Jeanette Netzel Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T, 20,K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (lmax = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C,C, C,N and C,O bonds, and for hydrogen bonds together with covalent C,H and N,H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H...O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997). An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds. [source] The experimental and theoretical QTAIMC study of the atomic and molecular interactions in dinitrogen tetroxideACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009Vladimir G. Tsirelson The atomic and molecular interactions in a crystal of dinitrogen tetraoxide, ,-N2O4, have been studied in terms of the quantum topological theory of molecular structure using high-resolution, low-temperature X-ray diffraction data. The experimental electron density and electrostatic potential have been reconstructed with the Hansen,Coppens multipole model. In addition, the three-dimensional periodic electron density of crystalline ,-N2O4 has been calculated at the B3LYP/cc-pVDZ level of theory with and without the geometry optimization. The application of the quantum theory of atoms in molecules and crystals (QTAIMC) recovered the two types of intermolecular bond paths between O atoms in crystalline ,-N2O4, one measuring 3.094, the other 3.116,Å. The three-dimensional distribution of the Laplacian of the electron density around the O atoms showed that the lumps in the negative Laplacian fit the holes on the O atoms in the adjacent molecules, both atoms being linked by the intermolecular bond paths. This shows that the Lewis-type molecular complementarity contributes significantly to intermolecular bonding in crystalline N2O4. Partial overlap of atomic-like basins created by zero-flux surfaces in both the electron density and the electrostatic potential show that attractive electrostatic interaction exists between O atoms even though they carry the same net formal charge. The exchange and correlation contributions to the potential energy density were also computed by means of the model functionals, which use the experimental electron density and its derivatives. It was found that the intermolecular interactions in ,-N2O4 are accompanied by the correlation energy-density `bridges' lowering the local potential energy along the intermolecular O...O bond paths in the electron density, while the exchange energy density governs the shape of bounded molecules. [source] Charge density and electrostatic potential analyses in paracetamolACTA CRYSTALLOGRAPHICA SECTION B, Issue 3 2009Nouzha Bouhmaida The electron density of monoclinic paracetamol was derived from high-resolution X-ray diffraction at 100,K. The Hansen,Coppens multipole model was used to refine the experimental electron density. The topologies of the electron density and the electrostatic potential were carefully analyzed. Numerical and analytical procedures were used to derive the charges integrated over the atomic basins. The highest charge magnitude (,1.2,e) was found for the N atom of the paracetamol molecule, which is in agreement with the observed nucleophilic attack occurring in the biological media. The electric field generated by the paracetamol molecule was used to calculate the atomic charges using the divergence theorem. This was simultaneously applied to estimate the total electrostatic force exerted on each atom of the molecule by using the Maxwell stress tensor. The interaction electrostatic energy of dimers of paracetamol in the crystal lattice was also estimated. [source] Accurate charge density of the tripeptide Ala-Pro-Ala with the maximum entropy method (MEM): influence of data resolutionACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2007Andreas Hofmann The accurate electron density of Ala-Pro-Ala is determined by the maximum entropy method (MEM), employing the same reflection data measured at 100,K which was used for a multipole refinement by Kalinowski et al. [(2007), Acta Cryst. Accepted for publication]. Properties of the electron density are compared with the corresponding properties of the static electron density from the multipole model and to the dynamic MEM electron density of trialanine at 20,K. It is thus shown that the increased thermal smearing at 100,K leads to lower electron densities in the bond critical points and atomic charges closer to zero for Ala-Pro-Ala than has been obtained for trialanine at 20,K. The influence of the resolution of the data is investigated by a series of MEM calculations. Atomic charges and atomic volumes are found not to depend on the resolution, but the charge density in the BCPs decreases with decreasing resolution of the dataset. The origin of this dependence is found to lie mostly in the more accurate estimate of the atomic displacement parameters (ADPs) for the higher-resolution datasets. If these effects are taken into account, meaningful information on chemical bonding can be obtained with data at a resolution better than dmin = 0.63,Å. Alternatively, low-resolution X-ray diffraction data can be used in accurate electron-density studies by the MEM, if another source of accurate values of the ADPs is available, e.g. from refinements with multipole parameters from a database of transferable multipole parameters. [source] Features of the electron density in magnesium diboride: reconstruction from X-ray diffraction data and comparison with TB-LMTO and FPLO calculationsACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2003S. Lee Features of the electron density in MgB2 reconstructed from room-temperature single-crystal X-ray diffraction intensities using a multipole model are considered. Topological analysis of the total electron density has been applied to characterize the atomic interactions in magnesium diboride. The shared-type B,B interaction in the B-atom layer reveals that both , and , components of the bonding are strong. A closed-shell-type weak B,B , interaction along the c axis of the unit cell has also been found. The Mg,B closed-shell interaction exhibits a bond path that is significantly curved towards the vertical Mg-atom chain ([110] direction). The latter two facts reflect two sorts of bonding interactions along the [001] direction. Integration of the electron density over the zero-flux atomic basins reveals a charge transfer of ,1.4,(1) electrons from the Mg atoms to the B-atom network. The calculated electric-field gradients at nuclear positions are in good agreement with experimental NMR values. The anharmonic displacement of the B atoms is also discussed. Calculations of the electron density by tight-binding linear muffin-tin orbital (TB-LMTO) and full-potential non-orthogonal local orbital (FPLO) methods confirm the results of the reconstruction from X-ray diffraction; for example, a charge transfer of 1.5 and 1.6 electrons, respectively, was found. [source] | ||||||||||