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Pierre-Francois Loos 2020-03-07 13:07:07 +01:00
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Manuscript/eDFT.tex
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\begin{abstract} \begin{abstract}
We report a first generation of local, weight-dependent correlation density-functional approximations (DFAs) that incorporate information about both ground and excited states in the context of density-functional theory for ensembles (eDFT). We report a first generation of local, weight-dependent correlation density-functional approximations (DFAs) that incorporate information about both ground and excited states in the context of density-functional theory for ensembles (eDFT).
These density-functional approximations for ensembles (eDFAs) are specially designed for the computation of single and double excitations within eDFT, and can be seen as a natural extension of the ubiquitous local-density approximation for ensemble (eLDA). These density-functional approximations for ensembles (eDFAs) are specially designed for the computation of single and double excitations within \titou{Gross--Oliveira--Kohn (GOK) DFT (\textit{i.e.}, eDFT for excited states)}, and can be seen as a natural extension of the ubiquitous local-density approximation for ensemble (eLDA).
The resulting eDFAs, based on both finite and infinite uniform electron gas models, automatically incorporate the infamous derivative discontinuity contributions to the excitation energies through their explicit ensemble weight dependence. The resulting eDFAs, based on both finite and infinite uniform electron gas models, automatically incorporate the infamous derivative discontinuity contributions to the excitation energies through their explicit ensemble weight dependence.
Their accuracy is illustrated by computing single and double excitations in one-dimensional many-electron systems in the weak, intermediate and strong correlation regimes. Their accuracy is illustrated by computing single and double excitations in one-dimensional many-electron systems in the weak, intermediate and strong correlation regimes.
\titou{Although the present weight-dependent functional has been specifically designed for one-dimensional systems, the methodology proposed here is directly applicable to the construction of weight-dependent functionals for realistic three-dimensional systems, such as molecules and solids.} \titou{Although the present weight-dependent functional has been specifically designed for one-dimensional systems, the methodology proposed here is directly applicable to the construction of weight-dependent functionals for realistic three-dimensional systems, such as molecules and solids.}
@ -1231,15 +1231,16 @@ The effect on the double excitation is less pronounced.
Overall, one clearly sees that, with Overall, one clearly sees that, with
equal weights, KS-eLDA yields accurate excitation energies for both single and double excitations. equal weights, KS-eLDA yields accurate excitation energies for both single and double excitations.
This conclusion is verified for smaller and larger numbers of electrons This conclusion is verified for smaller and larger numbers of electrons
(see {\SI}).\\ (see {\SI}).
\manu{Manu: now comes the question that is, I believe, central in this %\\
work. How important are the %\manu{Manu: now comes the question that is, I believe, central in this
ensemble correlation derivatives $\partial \epsilon^\bw_{\rm %work. How important are the
c}(n)/\partial w_I$ that, unlike any functional %ensemble correlation derivatives $\partial \epsilon^\bw_{\rm
in the literature, the eLDA functional contains. We have to discuss this %c}(n)/\partial w_I$ that, unlike any functional
point... I now see, after reading what follows that this question is %in the literature, the eLDA functional contains. We have to discuss this
addressed later on. We should say something here and then refer to the %point... I now see, after reading what follows that this question is
end of the section, or something like that ...} %addressed later on. We should say something here and then refer to the
%end of the section, or something like that ...}
%%% FIG 4 %%% %%% FIG 4 %%%