new figs and tab

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Pierre-Francois Loos 2019-12-07 22:26:49 +01:00
parent 7b30e84c63
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@ -484,6 +484,59 @@ This embedding procedure can be theoretically justified by the generalised adiab
Within this in-principle-exact formalism, the (weight-dependent) xc energy of the ensemble is constructed from the (weight-independent) ground-state functional.
In the case of a homogeneous system (or equivalently within the LDA), substituting Eq.~\eqref{eq:dexcdw} into \eqref{eq:GACE} yields, in the case of a bi-ensemble, Eq.~\eqref{eq:eLDA}.
%%% TABLE I %%%
\begin{table*}
\caption{
Total energies (in hartree) and excitation energies (in \titou{hartree}) of \ce{H2} with $\RHH = 1.4$ bohr for various methods with the STO-3G minimal basis.
\label{tab:Energies}
}
\begin{ruledtabular}
\begin{tabular}{lddddddd}
Method & \tabc{$\E{}{(0)}$} & \tabc{$\E{}{(1)}$} & \tabc{$\Ex{}{(1)} = \E{}{(1)} - \E{}{(0)}$}
& \tabc{$\tE{}{\ew{} = 0}$} & \tabc{$\tEx{}{\ew{} = 0} = \left. \pdv{\tE{}{\ew{}}}{\ew{}} \right|_{\ew{} = 0}$}
& \tabc{$\tE{}{\ew{} = 1/2}$} & \tabc{$\tEx{}{\ew{} = 1/2} = \left. \pdv{\tE{}{\ew{}}}{\ew{}} \right|_{\ew{} = 1/2}$} \\
\hline
HF & -1.11671 & 0.460576 & 1.57729 & -1.11671 & -0.0981563 & -0.0981563 & 1.57729 \\
LDA & -1.12120 & 0.379745 & 1.50095 & -1.12120 & -0.370725 & -0.370725 & 1.50565 \\
eLDA & -1.12120 & 0.175337 & 1.29654 & -1.12120 & -0.462421 & -0.462421 & 1.30839 \\
CID & -1.13728 & 0.481138 & 1.61841 & \\
Exact\fnm[1] & & & & \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Reference \onlinecite{}.}
\end{table*}
%%% %%% %%% %%%
%%% FIG 1 %%%
\begin{figure}
\includegraphics[width=\linewidth]{fig/GSetDES_exact_HF_LDA_eLDA}
\caption{
Total energies (in hartree) of \ce{H2} as a function of $\RHH$ (in bohr) for various methods with the STO-3G minimal basis.
\label{tab:Energies}
}
\end{figure}
%%% %%% %%% %%%
%%% FIG 2 %%%
\begin{figure}
\includegraphics[width=\linewidth]{fig/ExcitationEnergyExact_wHF_wLDA_weLDA_w=0etw=0.5}
\caption{
Excitation energies (in hartree) of \ce{H2} as a function of $\RHH$ (in bohr) for various methods with the STO-3G minimal basis.
\label{tab:Energies}
}
\end{figure}
%%% %%% %%% %%%
%%% FIG 3 %%%
\begin{figure}
\includegraphics[width=\linewidth]{fig/EnsembleEnergy_wHF_wLDA_weLDA_wHFbarre_wLDAbarre_weLDAbarre_R=1.4}
\caption{
Ensemble energies (in hartree) of \ce{H2} with $\RHH = 1.4$ bohr as a function of the weight $\ew{}$ for various methods with the STO-3G minimal basis.
\label{tab:Energies}
}
\end{figure}
%%% %%% %%% %%%
%%%%%%%%%%%%%%%
%%% RESULTS %%%
%%%%%%%%%%%%%%%

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