A simple self-Interaction correction to the RPA+ correlation energy

The exchange energy of the Random Phase Approximation is exact for a many-body ground state, but the correlation energy is often overestimated. The error comes from the poor description of the short-range correlation. The RPA+ approximation ^[1] largely reduces this error for atoms, for the jellium surface and for the uniform electron gas by adding a local or semi-local correction. While the RPA+ is accurate for the total energies of atoms, it fails for single-electron systems like stretched H²⁺, and systems where spin-polarization plays a significant role such as ionization energies, electron affinities, and atomization energies. In this work, we have introduced a simple correction to the RPA+ correlation energy to make the new gRPA+ ^[2] approximation exact for single-electron systems. We are assessing this computationally feasible approximation beyond RPA for various molecular test sets and we analyze the impact of self-interaction correction.

[1] S. Kurth and J. P. Perdew, Phys. Rev. B 59, 10461 (1999).
[2] T. Gould, A. Ruzsinszky, J.P. Perdew, Phys. Rev. A 100, 022515 (2019)