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@ -364,7 +364,7 @@ makes the ensemble much more linear (see Fig.~\ref{fig:Ew_H2}), and the excitati
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As readily seen from Eq.~\eqref{eq:Cxw}, $\Cx{\ew{}}$ reduces to $\Cx{}$ for $\ew{} = 0$.
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As readily seen from Eq.~\eqref{eq:Cxw}, $\Cx{\ew{}}$ reduces to $\Cx{}$ for $\ew{} = 0$.
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Note that we are not only using data from $\ew{} = 0$ to $\ew{} = 1/2$, but we also consider $1/2 < \ew{} \le 1$.
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Note that we are not only using data from $\ew{} = 0$ to $\ew{} = 1/2$, but we also consider $1/2 < \ew{} \le 1$.
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We ensure that the weight-dependent functional does not affect the two ghost-interaction-free limit at $\ew{} = 0$ and $1$.
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We ensure that the weight-dependent functional does not affect the two ghost-interaction-free limit at $\ew{} = 0$ and $1$.
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It is interesting to note that, around $\ew{} = 0$, the behavior of Eq.~\eqref{eq:Cxw} is linear
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\begin{figure}
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\begin{figure}
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\includegraphics[width=0.8\linewidth]{Cx_H2}
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\includegraphics[width=0.8\linewidth]{Cx_H2}
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\caption{
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\caption{
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@ -373,7 +373,7 @@ We ensure that the weight-dependent functional does not affect the two ghost-int
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}
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}
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\end{figure}
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\end{figure}
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In a third time, we add up correlation via the VWN5 local correlation functional. \cite{Vosko_1980}
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Third, we add up correlation via the VWN5 local correlation functional. \cite{Vosko_1980}
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For the sake of clarity, the explicit expression of the VWN5 functional is not reported here but it can be found in Ref.~\onlinecite{Vosko_1980}.
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For the sake of clarity, the explicit expression of the VWN5 functional is not reported here but it can be found in Ref.~\onlinecite{Vosko_1980}.
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The combination of the Slater and VWN5 functionals (SVWN5) yield a highly non-linear ensemble energy (as shown in Fig.~\ref{fig:Ew_H2}), while the combination of the MSFL and VWN5 functionals exhibit a small curvature and improved excitation energies, especially at small weights.
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The combination of the Slater and VWN5 functionals (SVWN5) yield a highly non-linear ensemble energy (as shown in Fig.~\ref{fig:Ew_H2}), while the combination of the MSFL and VWN5 functionals exhibit a small curvature and improved excitation energies, especially at small weights.
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@ -608,14 +608,14 @@ $\pdv{\E{\xc}{(1-\xi,\xi)}[\n{}{}]}{\xi}$ dans l'intégrale, non ? Can it be :
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%%% TABLE I %%%
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%%% TABLE I %%%
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\begin{table*}
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\begin{table*}
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\caption{
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\caption{
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Excitation energies (in eV) of \ce{H2} with $\RHH = 1.4$ bohr for various methods and basis sets.
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Excitation energies (in eV) associated with the lowest double excitation of \ce{H2} with $\RHH = 1.4$ bohr for various methods and basis sets.
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\label{tab:Energies}
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\label{tab:Energies}
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}
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}
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\begin{ruledtabular}
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\begin{ruledtabular}
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\begin{tabular}{llccccc}
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\begin{tabular}{llccccc}
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\mc{2}{c}{xc functional} \\
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\mc{2}{c}{xc functional} & & \mc{2}{c}{GOK} \\
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\cline{1-2}
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\cline{1-2} \cline{4-5}
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exchange & correlation & Basis & GOK($\ew{} = 0$) & GOK($\ew{} = 1/2$) & LIM & MOM \\
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exchange & correlation & Basis & $\ew{} = 0$ & $\ew{} = 1/2$ & LIM & MOM \\
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\hline
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\hline
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HF & & aug-cc-pVDZ & 38.52 & 30.86 & 34.55 & 28.65 \\
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HF & & aug-cc-pVDZ & 38.52 & 30.86 & 34.55 & 28.65 \\
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& & aug-cc-pVTZ & 38.58 & 35.82 & 35.68 & 28.65 \\
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& & aug-cc-pVTZ & 38.58 & 35.82 & 35.68 & 28.65 \\
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