Wheland-Mulliken approximation

Formally, these equations are similar to the SCF LCAO MO equations. Thus, a good definition of //effective may yield satisfactory solutions, without the tedious iteration procedure of the SCF method. In practice, two calculation procedures have evolved from these equations, the Hiickel approximation and the Wheland-Mulliken approximation. Neither of them specifies the analytical form of H, but instead treats some of the matrix elements H,. as adjustable parameters. Their main difference resides in the neglect (Hiickel) or non-neglect (Wheland-Mulliken) of overlap. Their common feature is the tight-binding approximation, namely the neglect of all matrix elements which involve non-bonded atoms. 

In the spirit of the Huckel-Wheland theory, the Mulliken approximation for electron repulsion integrals 53) is used in the maximization of the localization sum (Eq. (28)). The details of the calculations are reported elsewhere. S4)... 

The interconnections of the two approximations have been extensively discussed. From a theoretical point of view, calculations without overlap (Hiickel type) can be considered as a way to reproduce with less labor the results of the calculations with overlap (Wheland-Mulliken type) provided that the quantities are interpreted as bearing over an orthogonalized basis. Thus, in practice, the Hiickel approximation is used most frequently with parameters H = a, and = f rs along each pair of adjacent atoms. These parameters are all expressed in terms of the corresponding values a and p for a standard carbon compound which need not be explicited until the end of the calculation. The individual energies of the electrons are finally obtained in the form... 

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