Analytic Interatomic Forces in the Random Phase Approximation

TL;DR

This paper derives compact equations for interatomic forces within the RPA framework, enabling efficient calculations of molecular dynamics, phonons, and structural relaxations with potential extensions to advanced correlation methods.

Contribution

It introduces a concise derivation of RPA interatomic forces, incorporating position-dependent operators and implementing them in the PAW formalism for various applications.

Findings

Successfully implemented RPA forces in PAW formalism

Demonstrated applications in molecular dynamics and phonon calculations

Established a framework extendable to advanced correlation energy approximations

Abstract

We discuss that in the random phase approximation (RPA) the first derivative of the energy with respect to the Green's function is the self-energy in the GW approximation. This relationship allows us to derive compact equations for the RPA interatomic forces. We also show that position dependent overlap operators are elegantly incorporated in the present framework. The RPA force equations have been implemented in the projector augmented wave formalism, and we present illustrative applications, including ab initio molecular dynamics simulations, the calculation of phonon dispersion relations for diamond and graphite, as well as structural relaxations for water on boron nitride. The present derivation establishes a concise framework for forces within perturbative approaches and is also applicable to more involved approximations for the correlation energy.