Non-orthogonality and short-range effects

First we note that the partitioning method used in obtaining the energy expression (14.3.12) for a wavefunction (14.1.2) is substantially unchanged for functions that are neither orthogonal nor normalized (Problem 2.27) the result becomes 

It should be noted that, since Eq and Ek are energies of AB relative to the reference level E + , Eq approaches zero at long range while E becomes an electronic excitation energy for a— a, b- b. Since excitation energies are usually of the order of a few electron volts, the overlap corrections in the denominator (which are of the order of van der Waals interactions) can safely be neglected while in the numerators 

Eo (— jnt) appears with an overlap factor and is small compared with the term which contains the interaction of two charge densities in close proximity. Consequently, the polarization and dispersion energies associated with the second-order sum in (14.5.4) cannot be greatly influenced by non-orthogonality effects. There is thus a certain formal justification for the common practice of estimating the neglected (repulsive) terms in (14.3.12), whether empirically or by calculation, as if Aey were quite independent of those already discussed. 

To proceed, we must evaluate the matrix elements. We use the functions 

To indicate the reduction, it will be sufficient to consider the non-orthogonality integral in (14.5.4). Thus 

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