Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states

TL;DR

This paper adapts an extrapolation technique to ghost-interaction-corrected range-separated ensemble DFT, achieving faster convergence of excitation energies and improving accuracy for excited states in small molecular systems.

Contribution

It introduces a modified extrapolation correction for GIC range-separated eDFT, demonstrating improved convergence rates and more accurate excitation energies for various molecular excitations.

Findings

GIC ensemble energies converge as μ^{-3} towards wavefunction theory values

Extrapolation improves excitation energy accuracy for small μ values

Method successfully applied to Rydberg, charge transfer, and double excitations

Abstract

The extrapolation technique of Savin [J. Chem. Phys. 140, 18A509 (2014)], which was initially applied to range-separated ground-state-density-functional Hamiltonians, is adapted in this work to ghost-interaction-corrected (GIC) range-separated ensemble density-functional theory (eDFT) for excited states. While standard extrapolations rely on energies that decay as $\mu^{-2}$ in the large range-separation-parameter $\mu$ limit, we show analytically that (approximate) range-separated GIC ensemble energies converge more rapidly (as $\mu^{-3}$) towards their pure wavefunction theory values ($\mu\rightarrow+\infty$ limit), thus requiring a different extrapolation correction. The purpose of such a correction is to further improve on the convergence and, consequently, to obtain more accurate excitation energies for a finite (and, in practice, relatively small) $\mu$ value. As a proof of concept, we apply the extrapolation method to He and small molecular systems (viz. H$_{2}$, HeH$^{+}$ and LiH), thus considering different types of excitations like Rydberg, charge transfer and double excitations. Potential energy profiles of the first three and four singlet $\Sigma^+$ excitation energies in HeH$^{+}$ and H$_{2}$, respectively, are studied with a particular focus on avoided crossings for the latter. Finally, the extraction of individual state energies from the ensemble energy is discussed in the context of range-separated eDFT, as a perspective.