Excitation energies from G{\"o}rling-Levy perturbation theory along the range-separated adiabatic connection

TL;DR

This paper evaluates a G{"o}rling-Levy perturbation theory along the range-separated adiabatic connection for calculating electronic excitation energies, showing improved accuracy for Rydberg states over previous methods.

Contribution

It introduces and assesses a G{"o}rling-Levy based perturbation approach that maintains constant ground-state density, improving excitation energy predictions for Rydberg states.

Findings

More accurate Rydberg state excitation energies with GL-based perturbation.

Similar valence state excitation energies compared to RS-based perturbation.

No density-functional approximations used in calculations.

Abstract

A G{\"o}rling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schr{\"o}dinger (RS)-based perturbation theory introduced in a previous work [E. Rebolini, J. Toulouse, A. M. Teale, T. Helgaker, A. Savin, Mol. Phys. 113, 1740 (2015)], this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionization energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.