Localised molecular orbital approximation

In the complex electrostatic field of a molecule, it is usually impracticable to obtain accurate molecular orbitals, so it is customary to express them approximately as linear combinations of atomic orbitals belonging to the constituent atoms. This is called the linear combination of atomic orbital or LCAO form. Although they are only approximate, the LOAO functions do show most of the properties of the precise orbitals. Both molecular and localised equivalent orbitals can be expressed in this manner. 

The main result that emerges from the discussions of particular eases is that it has proved possible to give a description of a molecule in terms of equivalent orbitals which are approximately localised, but which can be-transformed into delocalised molecular orbitals without any change in the value of the total wave function. The equivalent orbitals are closely associated with the interpretation of a chemical bond in the theory, for, in a saturated molecule, the equivalent orbitals are mainly localised about two atoms, or correspond to lone-pair electrons. Double and triple bonds in molecules such as ethylene and acetylene are represented as bent single bonds, although the rather less localised o-n description is equally valid. 

It seems clear from results of many workers ) that as a consequence of the above overlap properties, the mainly metal ajg molecular orbital is essentially localised on the metal with the 3 orbital contributing approximately 95% to the molecular orbital. In contrast the metal ejg and orbitals are considerably more mixed in their respective molecular orbitals, with the extent of involvement varying between 50 and 90% depending on the rings. 

A chemist also wants to know the gross populations on each atom. The gross population on A or B certainly includes the respective net population, but for each atom one must also include a part of the overlap population. The simplest procedure is to proportion the two parts equally to A and B, even when a and b are unequal i.e., Nab(< >A < >B) to eadi atom. Adding this to the net population of either atom gives a gross population N(A) or N(B), such that N(A) + N(B) = N. Therefore, a specific molecular orbital can be described as nonbonding either because N(A) N i.e., it is localised almost exclusively on one centre, or N(A) and N(B) are both significant but the overlap population 2 Nab ( >A ( >B) is approximately equal to zero. 

When the Mossbauer nucleus is surrounded by a set of localised charges, the above equations can be used to calculate the EFG directly, and this is the basis of one approximate treatment. More rigorously, the charges must be treated as electron density associated with atomic or molecular orbitals. The geometrical terms must then be replaced by the appropriate expectation values, giving EFG components such as... 

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