A mathematical analysis of the GW0 method for computing electronic excited energies of molecules

TL;DR

This paper provides a rigorous mathematical analysis of the GW0 method for calculating electronic excited energies, establishing a framework and proving the existence and uniqueness of solutions in a perturbative setting.

Contribution

It introduces a formal mathematical framework for the GW method and proves the well-posedness of GW0 equations, which was previously lacking.

Findings

Established a mathematical framework for one-body operators in many-body perturbation theory.

Proved existence and uniqueness of solutions to GW0 equations in a perturbative regime.

Provided insights into the mathematical properties of the GW method.

Abstract

This paper analyses the GW method for finite electronic systems. In a first step, we provide a mathematical framework for the usual one-body operators that appear naturally in many-body perturbation theory. We then discuss the GW equations which construct an approximation of the one-body Green's function, and give a rigorous mathematical formulation of these equations. Finally, we study the well-posedness of the GW0 equations, proving the existence of a unique solution to these equations in a perturbative regime.