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Manu: fixing my corrections

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Emmanuel Fromager 2020-03-11 23:25:16 +01:00
parent 3db515af30
commit 9829dda6e0
1 changed files with 6 additions and 8 deletions
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Manuscript/eDFT.tex
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@ -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