The $GW$ Approximation: A Quantum Chemistry Perspective

TL;DR

This paper provides a comprehensive overview of the $GW$ approximation in quantum chemistry, detailing its theoretical foundations, practical implementation, and applications to different molecular systems.

Contribution

It offers a detailed explanation of the $GW$ method, including derivation, calculation steps, and applications to weakly and strongly correlated molecules, aiding wider adoption.

Findings

Numerical results for water and carbon dimer demonstrate the method's versatility.

Detailed step-by-step guide facilitates implementation in quantum chemistry.

Illustrative plots clarify physical quantities computed using $GW$.

Abstract

We provide an in-depth examination of the $GW$ approximation of Green's function many-body perturbation theory by detailing both its theoretical and practical aspects in the realm of quantum chemistry. First, the quasiparticle context is introduced before delving into the derivation of Hedin's equations. From these, we explain how to derive the well-known $GW$ approximation of the self-energy. In a second time, we meticulously explain each step involved in a $GW$ calculation and what type of physical quantities can be computed. To illustrate its versatility, we consider two contrasting systems: the water molecule, a weakly correlated system, and the carbon dimer, a strongly correlated system. Each stage of the process is thoroughly detailed and explained alongside numerical results and illustrative plots. We hope that the contribution will facilitate the dissemination and democratization of Green's function-based formalisms within the computational and theoretical quantum chemistry community.