Electronic structure variables ESV

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. 

The general scheme of the derivation of mechanistic models of PES from a QC description of molecular electronic structure reduces to the following moves. In the SLG based semiempirical QC there are the variables of two classes (electronic structure variables - ESV) geminal amplitudes and variables describing the HOs. ESVs of these classes must be (approximately) estimated, although the ESVs depend on molecular composition and geometry. 

As it is seen from the perturbative estimates, the density ESVs are not transferable and are rather sophisticated functions of those ESVs which define the shape and orientation of the hybridization tetrahedron on the donor atom. At this stage, it is possible to develop a mechanistic description which retains the variable x to keep track of details of the electronic structure. This picture is also suitable for constructing the QM/MM junctions. According to the perturbative estimates for the solutions of eq. (4.9) the equilibrium value of the y variable is always by one order of magnitude in (3Da smaller than x. Since only the combinations xy and y2 enter in the expression of the projection operator and thus in that for the energy, we may set y 0 without causing... 

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