Rayleigh-Schrodinger perturbation treatment

Note that the choice of non-orthogonal versus orthogonal basis functions has no consequence for the numerical variational solutions (cf. Coulson s treatment of He2, note 76), but it undermines the possibility of physical interpretation in perturbative terms. While a proper Rayleigh-Schrodinger perturbative treatment of the He- He interaction can be envisioned, it would not simply truncate at second order as assumed in the PMO analysis of Fig. 3.58. Note also that alternative perturbation-theory formulations that make no reference to an... 

The application of perturbation theory to many-body interactions leads to pairwise-additive and non-pairwise-additive contributions. For example, in the case of neutral, spherically symmetric systems which are separated by distances such that the orbital overlap can be neglected, the first non-pairwise-additive term appears at third order of the Rayleigh-Schrodinger perturbation treatment and corresponds to the dispersion energy which results from the induced-dipole-induced-dipole-induced-dipole78 interaction... 

Claverie P (1971) Theory of intermolecular forces. I. On the inadequacy of the usual Rayleigh-Schrodinger perturbation method for the treatment of intermolecular forces. Int J Quantum Chem 5 273-296... 

It is this effective Hamiltonian which semiempirical methods try to approximate more or less successfully. Therefore, an ab initio evaluation of is certainly desirable for an analysis of semiempirical methods. The computational implementation of Eqs. (7)-(9) requires a number of approximations [103] Use of a large but finite basis set, a Rayleigh-Schrodinger perturbation expansion of the inverse matrix in Eq. (9) around zero-order energies, and a quasidegenerate perturbation treatment through second or third order. This leads to an energy-independent Hamiltonian which includes nonclassical effective many-... 

In spite of this progress, problems remain and the description of electron correlation in molecules will remain an active field of research in the years ahead. The most outstanding problem is the development of robust theoretical apparatus for handling multi-reference treatments. Methods based on Rayleigh-Schrodinger perturbation theory suffer from the so-called intruder state problem. In recent years, it has been recognized that Brillouin-Wigner perturbation theory shows promise as a robust technique for the multi-reference problem which avoids the intruder state problem. 

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