Repulsive Interactions in Valence Bond Theory

the triplet repulsion arises due to the Pauli exclusion principle and is often referred to as Pauli repulsion. 

For a situation where we have four electrons on the two centers (10), VB theory predicts a doubling of the Pauli repulsion, and the following expression is obtained by complete analogy to qualitative MO theory  

One can in fact very simply generalize the rules for Pauli repulsion. Thus, the electronic repulsion in an AO-based determinant is equal to the quantity, 

Consider, for example, VB structures with three electrons on two centers, (A B) and (A B), each being described as a single AO-based determinant (see Exercise 3.3). The interaction energy that takes place between A and B in each one of these structures by itself (e.g., 11) is repulsive and following Equation 3.40 will be given by the Pauli repulsion term in Equation 3.41  

For an interacting system that is described by a VB structure involving more than one determinant (see Exercise 3.4), Equation 3.40 can still be applied in an approximate form if squared overlaps are neglected (i.e., S2 = 0)  

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