Semiempirical implementations of SLG wave function

In this section, we consider a family of semiempirical implementations of the antisymmetrized product of the strictly local geminals (SLG). Quite naturally, this approach applies only to compounds (largely organic) with well localized two-center two-electron bonds. It had been originally developed for an old-fashioned MINDO/3 type of parametrization of the molecular Hamiltonian and then extended to the more contemporary NDDO family of parametrizations. First, the description of the wave function is given in detail and then the energy functional is described and analyzed. Its variation provides the equilibrium values of the electronic structure variables (ESVs) relevant for this method. 

Chemical bonds and lone pairs are described by singlet two-electron functions -geminals [135] taken in the form originally proposed by Weinbaum [136]. Using the second quantization notation they are written as  

The geminals defined in the carrier space spanned by HOs constructed by the above formulae are termed to be strictly local geminals (SLG). 

The wave function of electrons in the molecule is then taken as the antisymmetrized product of the geminals given by eqs. (2.60), (2.61)  

The Hamiltonian for a molecular system in a general semiempirical approximation can be represented as a sum of one- and two-center contributions  

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