Rayleigh-Schrodinger perturbation theory third-order energy

Even-order Invariants for Rayleigh-Schrodinger Perturbation Theory. Full fourth-order correlation energy calculations are now possible and it is, therefore, important to have fourth-order forms which share the invariance properties of the [2/1] Pade approximants in third-order. The expression... 

On taking the Rayleigh-Schrodinger perturbation expansion for the energy beyond second-order, we find that so-called renormalization terms appear. In third-order Rayleigh-Schrodinger perturbation theory, the energy coefficient can be written in the form... 

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... 

Fig. 8. Theoretical and experimental low-lying spectrum for 0 obtained with the Bonn A potential defined in Table A.l of Ref. [7], using both a HO basis and a BHF basis. The terms H f, and denote the effective interaction through first, second and third order in Rayleigh-Schrodinger (RS) perturbation theory. All energies in MeV. Taken from Ref. [53].

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