On the Estimation of the Remainder Term in Møller-Plesset MP2 Theory from Limited Configuration Interaction

I Hubac,S Wilson

doi:10.3390/i3050570

Abstract

In a previous paper, we have avoided an infinite order perturbation expansion and obtained a closed expression which consists of the second-order Møller-Plesset energy component together with a remainder term. The applicabilty of second-order many-body perturbation theory with a Møller-Plesset reference hamiltonian then rests upon the magnitude of this remainder term rather than the behaviour of the higher order terms on the perturbation series. In the present work, we show how this remainder term can be estimated by limited configuration interaction.

Highlights

Many-body perturbation theory with a Møller-Plesset reference hamiltonian is the most widely used approach to the correlation problem in atomic and molecular systems
By employing a hybrid partitioning scheme based on both the Rayleigh-Schrodinger and the generalized Brillouin-Wigner approaches, it has been shown [5] that the electron correlation energy expression arising in the second-order many-body perturbation theory with a Møller-Plesset reference hamiltonian can be written as part of a closed expression consisting of the MP2 approximation to the correlation energy together with a remainder term, R
In previous work [28,29] we have shown how Brillouin-Wigner perturbation theory can be used to obtain a posteriori corrections to the method of limited configuration interaction which allow for the non-linear scaling with electron number

Summary

Introduction

Many-body perturbation theory with a Møller-Plesset reference hamiltonian is the most widely used approach to the correlation problem in atomic and molecular systems. By employing a hybrid partitioning scheme based on both the Rayleigh-Schrodinger and the generalized Brillouin-Wigner approaches, it has been shown [5] that the electron correlation energy expression arising in the second-order many-body perturbation theory with a Møller-Plesset reference hamiltonian can be written as part of a closed expression consisting of the MP2 approximation to the correlation energy together with a remainder term, R. This is followed by a brief discussion

The remainder term in MP2 theory

Estimation of the remainder term from limited configuration interaction

Discussion