From f665a87bf6a200e95c5126693be049285403aa08 Mon Sep 17 00:00:00 2001 From: Emmanuel Fromager Date: Wed, 11 Mar 2020 18:09:00 +0100 Subject: [PATCH] Manu: saving work in the discussion --- Manuscript/eDFT.tex | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/Manuscript/eDFT.tex b/Manuscript/eDFT.tex index a34ca86..6d1fb6a 100644 --- a/Manuscript/eDFT.tex +++ b/Manuscript/eDFT.tex @@ -1273,8 +1273,13 @@ drastically. %drives the all thing.\\} It is important to note that, even though the GIC removes the explicit quadratic terms from the ensemble energy, a non-negligible curvature -remains in the GIC-eLDA ensemble energy due to the optimization of the -ensemble KS orbitals in the presence of ghost-interaction error {[see Eqs.~\eqref{eq:min_with_HF_ener_fun} and \eqref{eq:Ew-eLDA}]}. +remains in the GIC-eLDA ensemble energy. \manu{This might be due to +\textit{(i)} the correlation eLDA +functional, which induces linear or quadratic weight dependencies of 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}]}}. %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