Perturbation theories for the calculation of molecular interaction energies. I. General formalism

In the calculation of the interaction energy of two atoms, it is particularly convenient to take the zero order Hamiltonian H(0) to be the sum of the atomic Hamiltonians. Then H(0) does not reflect the full permutational symmetry of the exact Hamiltonian H. Many different perturbation expansions with such a ``nonsymmetric'' H(0) have been proposed. In this paper, these expansions are reviewed and classified within a very general perturbation framework. Also, a new ``optimized'' method is proposed which, by virtue of the Rayleigh-Ritz variational principle, is guaranteed to give better results than any of the previously suggested methods. For simplicity the analysis is restricted to the case that the spin-free zero order function φ(0) and the spin-free exact wavefunction ψ are both nondegenerate. As an example, the construction of the first order wavefunction in each method is discussed in detail for the simple case of a single symmetry operation.