Electronic distribution overlap populations

Mulliken population analysis. This treatment shows how a molecule under investigation distributes electrons according to the atomic orbital occupancy. Note that the overlap population between two atoms is divided evenly between them without consideration of possible differences in atom types, electronegativities, and so on. 

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... 

The MOs in the diatomic molecules discussed above have only two coefficients, so their chemical interpretation poses few problems. The situation becomes slightly more complicated when the molecule is polyatomic or when each atom uses more than one AO. Overlap population and net atomic charges can then be used to give a rough idea of the electronic distribution in the molecule. 

Molecular orbitals are characterized by energies and amplitudes expressing the distribution of electron density over the nuclear framework (1-3). In the linear combination of atomic orbital (LCAO) approximation, the latter are expressed in terms of AO coefficients which in turn can be processed using the Mulliken approach into atomic and overlap populations. These in turn are related to relative charge distribution and atom-atom bonding interactions. Although in principle all occupied MOs are required to describe an observable molecular property, in fact certain aspects of structure and reactivity correlate rather well with the nature of selected filled and unfilled MOs. In particular, the properties of the highest occupied MO (HOMO) and lowest unoccupied MO (LUMO) permit the rationalization of trends in structural and reaction properties (28). A qualitative predictor of stability or, alternatively, a predictor of electron... 

Rearrangements of the electronic structure during inversion may be studied by computing the Mulliken atomic and overlap polulations 174>. Atomic populations describe the electronic distribution and the charges... 

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 DV X a-method has been first proposed and formulated more than 25 years ago by Ellis and Painter at Northwestern University. This method allows to calculate relatively large systems with medium accuracy. However the knowledge of energy eigenvalues, electron distributions, effective charges or overlap populations etc. are a valid tool for physical and chemical interpretations. 

The reason for these problems is the imbalance of overlap populations and the net atomic populations, and this imbalance is due primarily to the arbitrary equal distribution of the overlap population between atoms involved. In spite of these two problems, which have to be remembered when analyzing populations of orbitals and atoms, MPA is still frequently used for electron population analysis. 

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