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

The exchange energy of Random Phase Approximation is exact for a many-body ground state, but the correlation energy is often overestimated in magnitude. This error comes from a poor description of the short-range correlation. RPA+ largely reduces the error by adding a local or semi-local correction [1]. RPA+, on the other hand, is accurate for the total energies of atoms and binding energies. However, RPA+ fails to provide much improvement over RPA for single-election systems like the stretched H₂⁺ and systems where spin-polarization plays a significant role such as atomization energies. Within this work, we have introduced a simple correction to the RPA+ correlation energy (mgRPA+) to make it exact for a single-electron system [2,3]. We then investigated how this approximation works for atomization energies, ionization energies, electron affinities and the dissociation of H₂⁺ and He₂⁺. We found that with little extra computational cost mgRPA+ outperforms RPA+ in all the tests we have considered.

[1] Z. Yan, J.P. Perdew, S. Kurth, Phys. Rev. B 61, 16430 (2000)
[2] T. Gould, A. Ruzsinszky, J.P. Perdew, Phys. Rev. A, 100, 022515 (2019), Phys. Rev. A 2020, 101, 059902 (2020)
[3] S. Ruan, X. Ren, T. Gould, A. Ruzsinszky, submitted.