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

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-interactioncorrected (GIC) range-separated ensemble density-functional theory (eDFT) for excited states. While standard extrapolations rely on energies that decay as µ −2 in the large range-separation-parameter µ limit, we show analytically that (approximate) range-separated GIC ensemble energies converge more rapidly (as µ −3 ) towards their pure wavefunction theory values (µ → +∞ 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) µ 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 Σ + 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.

A weight-dependent local correlation density-functional approximation for ensembles

“…As readily seen from Eq. ( 34), inserting the ensemble density matrix into the HF interaction energy functional introduces unphysical ghost-interaction errors 61,69,70,74,104 as well as curvature: 69,70…”

Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems

“…In practice, the use of such a decomposition might be problematic as inserting an ensemble density into E H [n] causes the infamous ghost-interaction error. 51,60,68,69,74 The latter should in principle be removed by the exchange component of the ensemble xc functional…”

Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer

“…which, in practice, can induce substantial ghost interaction errors [26,27,28,29]. In the exact theory, the latter are removed by the weight-dependent exchange and correlation functionals.…”

“…the weighted sum of ground-and excited-state densities). This issue is actually related to the proper description of the weight dependence in the exchange energy [27,28,29].…”