Electron density distributions multipole analysis

A recent detailed X-ray diffraction study of the experimental electron density distribution in Fe(TTP)OCH3 has allowed the evaluation of the electron occupancies of the five 3d orbitals of the iron(III) ion (Lecomte, Chadwick, Coppens Stevens, 1983). A multipole population analysis gave the results presented in Table 3.11 and indicated a net charge of +2.5(2) on the iron ion, in good agreement with the expected oxidation... 

A reliable way to obtain such distributed multipole models is the distributed multipole analysis (DMA) method[8]. This takes advantage of the special properties of the Gaussian basis functions which are used in almost all modern wavefunction calculations. The electron density is a sum of products of such functions, and ai product of Gaussian functions can be represented as a Gaussian centred at some intermediate point[4l] ... 

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... 

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

Most of the relevant features of the charge density distribution can be elegantly elucidated by means of the topological analysis of the total electron density [43] nevertheless, electron density deformation maps are still a very effective tool in charge density studies. This is especially true for all densities that are not specified via a multipole model and whose topological analysis has to be performed from numerical values on a grid. 

The electrostatic term (Eei) describes the electrostatic energy between molecules A and B with nondeformed electronic structure. Using classical electrostatics, the electron density of a molecule can be expanded in a series of multipoles centered on one point, usually the center of mass of the molecule [1], For quantitative studies, where more accuracy is required, the multipole expansion is done on all atoms of the interacting molecules (the so-called distributed multipole expansion [29]). However, for qualitative analysis, the central multipole expansion provides sufficient accuracy. One then uses the multipole values found in the literature for isolated molecules [1], The electrostatic energy in the central multipole expansion can be written as a series, whose leading terms up to the dipole level are ... 

Bianchi et al retrieved the experimental electron density of Mn2(CO)io fi om a multipole analysis of accurate X-ray diffraction data at 120 K. A BP connects the two Mn atoms, but no cross BP was found between one Mn and the equatorial carbonyls of the other. The distribution of indicated closed-shell interactions for the metallic Mn-Mn bond and the dative Mn-CO bonds. An extensive analysis of the electron density, its Laplacian, a kinetic energy density G, the potential energy density V and the total energy density (= G + V), all evaluated at the BCP, leads to a classification. The Laplacian around the CO ligands shows that the carbon centroids of negative charge move toward the Mn atom indicating the polarization sense of the CO molecules. 

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