A Proposal for a Modified Møller-Plesset Perturbation Theory

A modified version of the Møller-Plesset approach for obtaining the correlation energy associated to a Hartree-Fock ground state is proposed. The method is tested in a model of interacting fermions that allows for an exact solution. Using up to third order terms improved results are obtained, even in the limit of loosely bound particles. The study of molecules and larger systems is seriously constrained by their many body nature. Several approximation schemes have been devised over the years, among which the Hartree-Fock (HF) method is one of the oldest and most fruitful. Because it treats interactions in a mean field way particle correlations are left out, however, a shortcoming that can limit severely the validity of its results. One may improve over HF by treating correlations as a perturbation. In the so-called Møller-Plesset method, a Rayleigh-Schrödinger perturbative expansion that is naturally suggested by the same structure of the HF solution[1,2,3,4] is adopted. This formalism reduces the correlation energy to an infinite series in the perturbation, of which only the first few terms need to be computed in practice. This scheme has been used for a long time as a good starting point to study correlation effects in molecular systems. However, this method is useful only if the perturbation series is rapidly convergent, which is not always true[5]. Failures of the Møller-Plesset method have been documented even for small molecules [5,6,7]. In this paper we present a ∗ Corresponding author. E-mail: [email protected] Preprint submitted to Chemical Physics Letters 2 February 2008 variation of the Møller-Plesset approach that appears to give accurate results in low order perturbation schemes even when particles are loosely bound, such as in chemical bonds. Consider the many-particles Hamiltonian H = ∑