On the use of many-body perturbation theory and quantum-electrodynamics in molecular electronic structure theory

Abstract

Many-body perturbation theory is firmly established in molecular electronic structure studies both as a method of calculation in its own right and in underpinning other approaches to the electron correlation problem, such as coupled electron pair approximations and various cluster expansions. The central pillar of the many-body perturbation theory is the linked diagram theorem obtained by Goldstone using the method of Feynman graphs to enumerate the terms of the perturbation series. Feynman had introduced his graphs in his formulation of quantum electrodynamics. Goldstone restricted his analysis to the non-relativistic many-body problem, so that interactions were taken to be instantaneous and the effects of relativity were ignored. In recent years, the growing interest in the treatment of relativistic and quantum electrodynamic effects in atoms and molecules has necessitated the re-introduction of physics that has been known for over forty years. A key to this development for molecular systems is a rigorous and robust implementation of the algebraic approximation for Dirac and Dirac-like equations. The algebraic approximation provides a representation of both the positive-energy and the negative-energy branches of the Dirac spectrum. Relativistic many-body perturbation theory, relativistic coupled pair approximations and relativistic coupled cluster theories can be formulated within the ‘no-virtual-pair’ approximation. Such formulations are restricted to the positive energy branch of the spectrum. However, the negative energy states make an essential contribution to the description of atomic and molecular electronic structure. The investigation of this contribution is facilitated by proper implementation of the algebraic approximation using formulations which are amenable to systematic refinement.