Electron density distribution Mulliken population analysis

An analysis of the electronic density distribution (Mulliken analysis of the valence orbital population [147]) has shown the bonding in the 6d element compounds to be dominated by a large participation of both the 6d3/2 and 6dsn orbitals (e.g., 70% in DbCls) and is typical of d-element compounds [148]. The 7s, as well as both the 6pi/2 and 6ps/2 orbitals, each contribute about 15 % to the bonding. The most important conclusion for the chemical experiment was, therefore, that the 6d elements are close homologs of the 5d elements and should exhibit similar chemical properties. 

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. 

Electron distributions are ascertained by means of a Mulliken population analysis of the ir-electron atomic populations (in the case of complete n-delocalization, each atom in the 67r-electron five-membered ring would have 1.20 7r-electrons associated with it) by determining the spatial extent of the localized orbitals of both the out-of-plane lone pair of the heteroatom and the C=C double bonds as well as through comparing the total electron density plots in planes parallel to the molecular plane. 

A simple and robust quantitative MO-type approach (as opposed to density approaches) is the ubiquitous Mulliken population analysis [40]. The key concept of this easily programmed and fast method is the distribution of electrons based on occupations of atomic orbitals. The atomic populations do not, however, include electrons from the overlap populations, which are divided exactly in the middle of the bonds, regardless of the bonding type and the electronegativity. As a consequence, differences of atom types are not properly accommodated and the populations per orbital can be larger than 2, which is a violation of the Pauli principle a simple remedy for this error is a Lowdin population analysis that... 

For a characterization of the electronic structure, the spatial electron density distributions, the bond order between atoms and ionicities of each atom in the cluster are estimated according to the Mulliken population analysis [35]. The overlap population, (2 ., of electrons between two atoms v and v is defined as,... 

The results, in fact, are often quite informative. His group has attempted to get some idea of the charge distribution by using a Mulliken population analysis to determine the charges associated with the atoms. However, because of certain arbitrary features in the Mulliken scheme, a charge density plot is probably a more satisfactory way of looking at molecular charge distribution. A recent compilation of such electron density plots has been published by Streitwieser and Owens. ... 

The valence electron density distributions of cristobalite, stishovite, spinel and perovskite are shown in Figure 1 (the electron distribution of quartz, which is not shown, is essentially identical to that of cristobalite). The non-spherical distortions are significant, and agree well with the results of crystalline Hartree-Fock calculations [47]. In general, there are approximately 0.3-0.5 electrons in the bonding regions, by Mulliken population analysis. 

Density contour maps, like those of Fig. 1 (Sect. 2.3) for the nitrogen molecule or Fig. 2 (Sect. 4.2) for ethylene give a complete picture of the electronic distribution in a molecule. However, it is more convenient, especially for comparative studies, to describe the electronic structure by a set of single numbers rather than by maps, even if this involves the loss of much information. This is why indices summarizing the form of the electron distribution in the neighborhood of an atom or a bond have been defined by quantum chemists. Following Mulliken, the assignment of a set of such indices to a molecule may be called its population analysis. 

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