diff --git a/Manuscript/FarDFT.tex b/Manuscript/FarDFT.tex index 3cf5ea3..fe787c9 100644 --- a/Manuscript/FarDFT.tex +++ b/Manuscript/FarDFT.tex @@ -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 %%% %%%%%%%%%%%%%%% diff --git a/Manuscript/fig/EnsembleEnergy_wHF_wLDA_weLDA_wHFbarre_wLDAbarre_weLDAbarre_R=1.4.pdf b/Manuscript/fig/EnsembleEnergy_wHF_wLDA_weLDA_wHFbarre_wLDAbarre_weLDAbarre_R=1.4.pdf new file mode 100644 index 0000000..258f332 Binary files /dev/null and b/Manuscript/fig/EnsembleEnergy_wHF_wLDA_weLDA_wHFbarre_wLDAbarre_weLDAbarre_R=1.4.pdf differ diff --git a/Manuscript/fig/ExcitationEnergyExact_wHF_wLDA_weLDA_w=0etw=0.5.pdf b/Manuscript/fig/ExcitationEnergyExact_wHF_wLDA_weLDA_w=0etw=0.5.pdf new file mode 100644 index 0000000..adf4c87 Binary files /dev/null and b/Manuscript/fig/ExcitationEnergyExact_wHF_wLDA_weLDA_w=0etw=0.5.pdf differ diff --git a/Manuscript/fig/GSetDES_exact_HF_LDA_eLDA.pdf b/Manuscript/fig/GSetDES_exact_HF_LDA_eLDA.pdf new file mode 100644 index 0000000..15475aa Binary files /dev/null and b/Manuscript/fig/GSetDES_exact_HF_LDA_eLDA.pdf differ