From 3db515af30fd8b714ff19f8a935aafd81ae9e174 Mon Sep 17 00:00:00 2001 From: Emmanuel Fromager Date: Wed, 11 Mar 2020 23:11:54 +0100 Subject: [PATCH] Manu: done with the conclusion --- Manuscript/eDFT.tex | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/Manuscript/eDFT.tex b/Manuscript/eDFT.tex index d72b486..3bc5a1e 100644 --- a/Manuscript/eDFT.tex +++ b/Manuscript/eDFT.tex @@ -1561,7 +1561,7 @@ again that the usage of equal weights has the benefit of significantly reducing A local and ensemble-weight-dependent correlation density-functional approximation (eLDA) has been constructed in the context of GOK-DFT for spin-polarized triensembles in -1D. The approach is actually general and can be extended to real +1D. The approach is general and can be extended to real (three-dimensional) systems~\cite{Loos_2009,Loos_2009c,Loos_2010,Loos_2010d,Loos_2017a} and larger ensembles in order to @@ -1570,20 +1570,20 @@ progress in this direction. Unlike any standard functional, eLDA incorporates derivative discontinuities through its weight dependence. The latter originates -from the finite uniform electron gas \titou{on which} eLDA is -(partially) based on. The KS-eLDA scheme, where exact exchange is -combined with eLDA, delivers accurate excitation energies for both +from the finite uniform electron gas on which eLDA is +(partially) based. The KS-eLDA scheme, where exact \manu{individual +exchange energies are} +combined with \manu{the eLDA correlation functional}, delivers accurate excitation energies for both single and double excitations, especially when an equiensemble is used. In the latter case, the same weights are assigned to each state belonging to the ensemble. The improvement on the excitation energies brought by the KS-eLDA scheme is particularly impressive in the strong correlation regime where usual methods, such as TDLDA, fail. -We have observed that, although the ensemble correlation discontinuity has a +We have observed that, although the correlation ensemble derivative has a non-negligible effect on the excitation energies (especially for the single excitations), its magnitude can be significantly reduced by performing equiweight calculations instead of zero-weight calculations. -Let us finally stress that the present methodology can be extended -straightforwardly to other types of ensembles like, for example, the +Let us finally stress that the present methodology can be extended to other types of ensembles like, for example, the $\nEl$-centered ones, \cite{Senjean_2018,Senjean_2020} thus allowing for the design of a LDA-type functional for the calculation of ionization potentials, electron affinities, and fundamental gaps.