Electron density distributions topological analysis

Iversen, B.B., Larsen, F.K., Figgis, B.N. and Reynolds, P.A. (1997) X-N study ofthe electron density distribution in tra s-tetraammine-dinitronickel(II) at 9K transition metal bonding and topological analysis, J. Chem. Soc., Dalton Trans. 2227-2240. 

In the following chapter we show how the topology of an important function of p, the Laplacian, enables us to obtain additional information from the analysis of the electron density distribution. 

E. Espinosa et al., From weak to strong interactions A comparative analysis of the topological and energetic properties of the electron density distribution involving X-F-F-Y systems. J. Chem. Phys. 117, 5529-5543 (2001)... 

The stereochemical shape concept covers a wide range of possible resolutions, from the details of electron density distributions between pairs of nuclei in relatively small molecules to the structural organization of the tertiary structure of proteins [201-203], the architecture of supramolecular assemblies [204-230], the problems of shape selectivity in reactions of large molecules [231-233], and the intriguing shape features of self-replicating chemical systems [234-239]. In the following chapters we shall discuss various topological shape analysis techniques, suitable for the relevant level of resolution. 

The spectroscopic properties of M-SiO and M-(SiO)2 (1-1 and 1-2 complexes with M = Cu, Ag, or An) have been theoretically studied. It has been shown that both M-SiO and M-(SiO)2 compounds in their ground state are bent with a metal-Si bonded structure. The calculated M(ns) spin density agrees well with the ESR experimental data. iFrom a topological analysis of the electron density distribution it has been found that the M-Si bond enei correlates with the electron density located at the M-Sl bond path (bond critical point). Audenies fortuna juvat... 

Because of the nonquantitative nature of A/o(r) maps , the X-ray diffraction data recorded for coesite was used to genraate a total electron density distribution, p(r), for the mineral. In an analysis of the bond critical point properties of the distribution, Downs located the critical points along each of its Si—O bonds, determined the value of the electron density and the Laplacian of /o(r) at each of these critical points, V pfr, ), and mapped —V p(r) over the domain of each of its Si—O—Si skeletal units. A mapping of the total electron density distribution and its topological properties has a distinct advantage over a mapping of the deformation density in that The derivation of a unique and physically meaningful difference (deformation) electron density is a problem that cannot be solved since the choice of the promolecular reference density always implies some... 

Nowadays, this view of electron density has been refined and extended by more sophisticated topological analysis. Modem methods are based on accurate experimental (or calculated) electron density distributions. Hansen and Coppens developed the finite multipole expansion (multipole model, MM) [40], which partitions... 

Now that we have seen how eleetron densities can be determined by high-angle X-ray diffraction, it is time to discuss methods for extracting chemically relevant information from the electron density distribution in three dimensions. The topological analysis of electron density was first mentioned in Section 2.4 in a more general context, and it should be stressed here that the mathematical tools to be discussed in this section can be applied equally to electron density distributions determined experimentally or derived quantum mechanically (Section 3.6). This direct link between theory and experiment therefore offers a unique way to view details of the electronic stmcture of chemical systems and to inspect structural details that lie beyond the standard viewpoint of three-dimensional molecular structure defined purely by the positions of atomic nuclei. In this... 

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