Extended M{\o}ller-Plesset perturbation theory for dynamical and static correlations

TL;DR

This paper introduces an extended Møller-Plesset perturbation theory that effectively captures both static and dynamical electron correlations, improving accuracy in molecular energy calculations while maintaining computational efficiency.

Contribution

It develops a novel perturbative correction to spin-extended Hartree-Fock, combining static and dynamical correlation treatments within a single framework.

Findings

Significant improvements in molecular energy predictions.

Enhanced accuracy in excited state and singlet-triplet splitting calculations.

Comparable computational cost to standard MP2.

Abstract

We present a novel method that appropriately handles both dynamical and static electron correlation in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order M{\o}ller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter.