Atomic forces from correlation energy functionals based on the adiabatic-connection fluctuation-dissipation theorem

TL;DR

This paper develops and implements analytical atomic forces within the RPA framework based on the adiabatic-connection fluctuation-dissipation theorem, enabling accurate geometry and vibrational property calculations for molecules and solids.

Contribution

It introduces the first implementation of analytical atomic forces in RPA using plane waves and pseudopotentials, improving computational accuracy and efficiency.

Findings

RPA forces are of excellent numerical quality.

Self-consistency has negligible impact on geometries and vibrational frequencies.

RPA and RPAx outperform PBE and achieve accuracy comparable to wavefunction methods.

Abstract

We extend the capabilities of correlation energy functionals based on the adiabatic-connection fluctuation-dissipation theorem by implementing the analytical atomic forces within the random phase approximation (RPA), in the context of plane waves and pseudopotentials. Forces are calculated at self-consistency through the optimized effective potential method and the Hellmann-Feynman theorem. In addition, non-self-consistent RPA forces, starting from the PBE generalized gradient approximation, are evaluated using density functional perturbation theory. In both cases, we find forces of excellent numerical quality. Furthermore, for most molecules and solids studied, self-consistency is found to have a negligible impact on the computed geometries and vibrational frequencies. The RPA is shown to systematically improve over PBE and, by including the exact-exchange kernel within RPA + exchange (RPAx), through finite-difference total energy calculations, we obtain an accuracy comparable to advanced wavefunction methods. Finally, we estimate the anharmonic shift and provide accurate theoretical references based on RPA and RPAx for the zone-center optical phonon of diamond, silicon, and germanium.