From 9829dda6e05a433afddfca766f1469ba16db0955 Mon Sep 17 00:00:00 2001 From: Emmanuel Fromager Date: Wed, 11 Mar 2020 23:25:16 +0100 Subject: [PATCH] Manu: fixing my corrections --- Manuscript/eDFT.tex | 14 ++++++-------- 1 file changed, 6 insertions(+), 8 deletions(-) diff --git a/Manuscript/eDFT.tex b/Manuscript/eDFT.tex index 3bc5a1e..b6051ce 100644 --- a/Manuscript/eDFT.tex +++ b/Manuscript/eDFT.tex @@ -121,9 +121,7 @@ \begin{document} -\title{Weight-dependent local density-functional \manu{approximation to -ensemble correlation energies}} -%\title{Weight-dependent local density-functional approximations for ensembles} +\title{A weight-dependent local correlation density-functional approximation for ensembles} \author{Pierre-Fran\c{c}ois Loos} \email{loos@irsamc.ups-tlse.fr} @@ -1272,16 +1270,16 @@ drastically. %when looking at your curves, this assumption cannot be made when the %correlation is strong. It is not clear to me which integral ($W_{01}?$) %drives the all thing.\\} -It is important to note that, even though the GIC removes the explicit -quadratic \manu{Hx} terms from the ensemble energy, a non-negligible curvature -remains in the GIC-eLDA ensemble energy \manu{when the electron -correlation is strong}. \manu{This is due to +It is important to note that, even though the GIC removes the explicitly +quadratic Hx terms from the ensemble energy, a non-negligible curvature +remains in the GIC-eLDA ensemble energy when the electron +correlation is strong. This is due to \textit{(i)} the correlation eLDA functional, which contributes linearly (or even quadratically) to the individual energies [see Eqs.~\eqref{eq:Taylor_exp_ind_corr_ener_eLDA} and \eqref{eq:Taylor_exp_DDisc_term}], and \textit{(ii)} the optimization of the ensemble KS orbitals in the presence of ghost-interaction errors {[see -Eqs.~\eqref{eq:min_with_HF_ener_fun} and \eqref{eq:WHF}]}}. +Eqs.~\eqref{eq:min_with_HF_ener_fun} and \eqref{eq:WHF}]}. %However, this orbital-driven error is small (in our case at %least) \trashEF{as the correlation part of the ensemble KS potential $\delta %\E{c}{\bw}[\n{}{}] /\delta \n{}{}(\br{})$ is relatively small compared