Second-order perturbative correlation energy functional in the ensemble density-functional theory

TL;DR

This paper develops a second-order perturbation theory for ensemble correlation energy in density-functional theory and evaluates its effectiveness in calculating excitation energies for model systems and atoms.

Contribution

It introduces a PT2 approximation for ensemble correlation energy in EDFT and assesses its performance on excitation energies in various systems.

Findings

PT2 improves excitation energies in 1D models for most cases.

PT2 worsens excitation energies for atoms due to functional inconsistencies.

Convergence behavior of PT2 depends on the number of unoccupied orbitals.

Abstract

We derive the second-order approximation (PT2) to the ensemble correlation energy functional by applying the G\"{o}rling-Levy perturbation theory on the ensemble density-functional theory (EDFT). Its performance is checked by calculating excitation energies with the direct ensemble correction method in 1D model systems and 3D atoms using numerically exact Kohn-Sham orbitals and potentials. Comparing with the exchange-only approximation, the inclusion of the ensemble PT2 correlation improves the excitation energies in 1D model systems in most cases, including double excitations and charge-transfer excitations. However, the excitation energies for atoms are generally worse with PT2. We find that the failure of PT2 in atoms is due to the two contributions of an orbital-dependent functional to excitation energies being inconsistent in the calculations. We also analyze the convergence of PT2 excitation energies with respect to the number of unoccupied orbitals.