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Manu: saving work in the discussion

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Emmanuel Fromager 2020-03-11 18:09:00 +01:00
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Manuscript/eDFT.tex
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@ -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