Beyond the Random Phase Approximation for the Electron Correlation Energy: The Importance of Single Excitations

TL;DR

This paper shows that including single excitation contributions or using self-consistent Hartree-Fock energies significantly improves the accuracy of RPA-based methods for electron correlation energies in molecules and solids.

Contribution

It introduces the importance of single excitation contributions to correct the systematic underbinding in RPA calculations within density-functional theory.

Findings

Adding SE contributions achieves chemical accuracy in benchmark tests.

Replacing non-self-consistent exchange with self-consistent Hartree-Fock improves results.

Both methods correct the underbinding issue of standard RPA schemes.

Abstract

The random phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange energy, represents the state-of-the-art exchange-correlation functional within density-functional theory (DFT). However, the standard RPA practice -- evaluating both the exact-exchange and the RPA correlation energy using local or semilocal Kohn-Sham (KS) orbitals -- leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior is largely corrected by adding a "single excitation" (SE) contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent exact-exchange total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using Kohn-Sham orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of non-covalent intermolecular interactions.