Electrostatic Interaction and Steric Repulsion

When the two systems A and B are brought from infinity to their equilibrium postions, the wavefunctions FA and TB of the subsystems will be overlapping. The Pauli principle is obeyed by explicitly antisymmetrizing (operator A) and renormalizing (factor N) the product wavefunction  

The A operator in this case is just (1 12)5 with P12 the permutation operator. Equation [12] demonstrates that p° is different from pA + pB = l pAl2 + l pBl2. The first two terms show that the density at A and B is actually the original density enhanced by a factor 1/(1 - S2) 1. The last term in the expression for p° on the last line of Eq. [12] shows that this enhancement is effected by a depletion of density from the overlap region, where both (pA and pB, hence the product tpA(pB have sizable values. 

The energy change from A + B to E° can be written as the electrostatic interaction defined above, plus all other effects lumped together into the Pauli repulsion term AEPauli  

It is always possible to write the energy corresponding to a wavefunction as the sum of the kinetic energy (the expectation value of the kinetic energy operator) and of the potential energy, which is the expectation value of all Coulombic operators, so we write A ° as the sum of kinetic and potential energy differences, 

Let us consider the simple case that cpA and (pB are symmetry equivalent (e.g., the Is orbitals of He2 or triplet H2). The well-known MOs 

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