Singles correlation energy contributions in solids

TL;DR

This paper investigates the role of singles contributions in the random phase approximation for solids, deriving new expressions and approximations to improve correlation energy calculations in condensed matter physics.

Contribution

It introduces a new derivation of singles contributions using a density-varying adiabatic connection and fluctuation dissipation theorem, and proposes a novel approximation based on the density matrix in RPA.

Findings

Singles contributions significantly affect correlation energies in weakly bonded systems.

New approximation improves accuracy of RPA for various solid state systems.

Analysis includes rare gas solids, ice, water adsorption, and covalent/metallic bonds.

Abstract

The random phase approximation to the correlation energy often yields highly accurate results for condensed matter systems. However, ways how to improve its accuracy are being sought and here we explore the relevance of singles contributions for prototypical solid state systems. We set out with a derivation of the random phase approximation using the adiabatic connection and fluctuation dissipation theorem, but contrary to the most commonly used derivation, the density is allowed to vary along the coupling constant integral. This yields results closely paralleling standard perturbation theory. We re-derive the standard singles of G\"orling-Levy perturbation theory [G\"orling and Levy, Phys. Rev. A {\bf 50}, 196 (1994)], highlight the analogy of our expression to the renormalized singles introduced by Ren and coworkers [Ren, Tkatchenko, Rinke, and Scheffler, Phys. Rev. Lett. {\bf 106}, 153003 (2011)], and introduce a new approximation for the singles using the density matrix in the random phase approximation. We discuss the physical relevance and importance of singles alongside illustrative examples of simple weakly bonded systems, including rare gas solids (Ne, Ar, Xe), ice, adsorption of water on NaCl, and solid benzene. The effect of singles on covalently and metallically bonded systems is also discussed.