Atomic population definition

Vicinity index. One such measure of separation is based on an exact upper bound for two-electron integrals of model wavefunctions which remains almost always valid for realistic LCAO orbitals, as well. The vicinity index [30, 31] of two MOs (pi and (pj fits well into framework of population localization, as it uses the atomic population definitions QlA and QJA of the orbitals defined by (14). The quantity... 

The earliest definition of atomic charges is related to Mulliken s population analysis [24] and assumes equipartition of overlap populations between the relevant atoms, yielding the gross atomic populations ... 

In MO theory, the Mulliken population analysis [149], where the population of the MOs is decomposed into atomic populations and diatomic overlap populations, considerably influenced the formulation of bonding concepts, although it does not describe a bond order per se. On the basis of the Mulliken population analysis, Mayer introduced a popular definition of the number of bonds between two centers A and B originally formulated for one-determinant wave functions [142-144, 150],... 

The quantum mechanical theory of AIMs affords a straightforward definition of the atomic population, ... 

From the intuitive point of view, the concept of bond order is somewhat more ambiguous than that of atomic population. Whereas A a is usually construed as the number of electrons ascribed to an atom A, the bond order Bab niay be interpreted as a measure of bond strength, bond multiplicity, or the number of electron pairs involved in covalent interactions between A and B. Most of the currently known definitions of Bab stem from the last of these interpretations. Accordingly, they begin with the extraction of the exchange correlation term from the two-electron reduced density matrix y(ri, T2, r, rj). 

Population Analyses Population analyses are used to gain a detailed understanding of the electronic properties of a molecule. A common feature of most of these analytic tools is the definition of atomic charges. Because there is no... 

If population analysis is not synonymous with the concept of an AIM, it becomes necessary to introduce a proper set of requirements before one can speak of an AIM. An AIM is a quantum object and as such has an electron density of its own. This atomic electron density must obviously be positive definite and the sum of these atomic densities must equal the molecular density. Each atomic density pA(r) can be obtained from the molecular density p(r) in the following way ... 

In Section 3.1., we shall show that the dynamic model leads to an unambiguous determination of the type of nonbonded interactions involved while the static model may lead to erroneous predictions as a result of an ambiguous definition of the nature of a nonbonded interaction. The superiority of the dynamic model is due to the fact that nonbonded interactions affect bonded interactions and, thus, the change in an overall overlap population rather than the change of a specific overlap population between nonbonded atoms or groups is the most appropriate index of a nonbonded interaction. Accordingly, we shall employ the dynamic model in all subsequent discussions of molecular structure, unless otherwise stated. 

Introduction. This is a method of naming, commonly used for organic compounds, in which names are based on that of an individual parent hydride, usually ending in-ane. -ene or -yne. The hydride name is understood to signify a definite fixed population of hydrogen atoms attached to a skeletal structure. 

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