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Pierre-Francois Loos 2020-04-09 16:27:21 +02:00
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commit 146e37e928

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@ -283,7 +283,7 @@ The latters are determined by solving the ensemble KS equation
where $\hHc(\br{}) = -\nabla^2/2 + \vne(\br{})$, and where $\hHc(\br{}) = -\nabla^2/2 + \vne(\br{})$, and
\begin{equation} \begin{equation}
\fdv{\E{\Hxc}{\bw}[\n{}{}]}{\n{}{}(\br{})} \fdv{\E{\Hxc}{\bw}[\n{}{}]}{\n{}{}(\br{})}
= \fdv{\E{\Ha}{\bw}[\n{}{}]}{\n{}{}(\br{})} + \fdv{\E{\xc}{\bw}[\n{}{}]}{\n{}{}(\br{})} = \fdv{\E{\Ha}{}[\n{}{}]}{\n{}{}(\br{})} + \fdv{\E{\xc}{\bw}[\n{}{}]}{\n{}{}(\br{})}
\end{equation} \end{equation}
is the Hxc potential, with is the Hxc potential, with
\begin{subequations} \begin{subequations}
@ -670,117 +670,79 @@ Excitation energies (in eV) associated with the lowest double excitation of \ce{
& & aug-cc-pVTZ & 28.90 & 27.16 & 27.64 & 27.34 \\ & & aug-cc-pVTZ & 28.90 & 27.16 & 27.64 & 27.34 \\
& & aug-cc-pVQZ & 28.89 & 27.16 & 27.65 & 27.34 \\ & & aug-cc-pVQZ & 28.89 & 27.16 & 27.65 & 27.34 \\
\\ \\
B & LYP & aug-mcc-pV8Z\fnm[1] & & & & 28.42\fnm[2] \\ B & LYP & aug-mcc-pV8Z & & & & 28.42 \\
B3 & LYP & aug-mcc-pV8Z\fnm[1] & & & & 27.77\fnm[2] \\ B3 & LYP & aug-mcc-pV8Z & & & & 27.77 \\
HF & LYP & aug-mcc-pV8Z\fnm[1] & & & & 29.18\fnm[2] \\ HF & LYP & aug-mcc-pV8Z & & & & 29.18 \\
HF & & aug-mcc-pV8Z\fnm[1] & & & & 28.65\fnm[2] \\ HF & & aug-mcc-pV8Z & & & & 28.65 \\
\\ \\
HF & FCI & aug-mcc-pV8Z\fnm[1] & & & & 28.75\fnm[2] \\ \hline
\mc{5}{l}{Accurate (FCI/aug-mcc-pV8Z)\fnm[1]} & 28.75 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\fnt[1]{Reference \onlinecite{Mielke_2005}.} \fnt[1]{Reference \onlinecite{Barca_2018a}.}
\fnt[2]{Reference \onlinecite{Barca_2018a}.}
\end{table*} \end{table*}
%%% %%% %%% %%% %%% %%% %%% %%%
%%% TABLE I %%% %%% TABLE I %%%
\begin{table*} \begin{table}
\caption{ \caption{
Excitation energies (in eV) associated with the lowest double excitation of \ce{H2} with $\RHH = 3.7$ bohr for various methods, combinations of xc functionals, and basis sets. Excitation energies (in eV) associated with the lowest double excitation of \ce{H2} with $\RHH = 3.7$ bohr obtained with the aug-cc-pVTZ basis set for various methods and combinations of xc functionals.
\label{tab:BigTab_H2st} \label{tab:BigTab_H2st}
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{llccccc} \begin{tabular}{llcccc}
\mc{2}{c}{xc functional} & & \mc{2}{c}{GOK} \\ \mc{2}{c}{xc functional} & \mc{2}{c}{GOK} \\
\cline{1-2} \cline{4-5} \cline{1-2} \cline{3-4}
exchange & correlation & Basis & $\ew{} = 0$ & $\ew{} = 1/2$ & LIM & MOM \\ exchange & correlation & $\ew{} = 0$ & $\ew{} = 1/2$ & LIM & MOM \\
\hline \hline
HF & & aug-cc-pVDZ & 19.08 & 6.58 & 12.92 & 6.52 \\ HF & & 19.09 & 6.59 & 12.92 & 6.52 \\
& & aug-cc-pVTZ & 19.09 & 6.59 & 12.92 & 6.52 \\ S & & 5.31 & 5.60 & 5.46 & 5.56 \\
\\ S & VWN5 & 5.34 & 5.57 & 5.46 & 5.52 \\
S & & aug-cc-pVDZ & 5.31 & 5.60 & 5.46 & 5.56 \\ S & eVWN5 & 5.53 & 5.76 & 5.56 & 5.72 \\
& & aug-cc-pVTZ & 5.31 & 5.60 & 5.46 & 5.56 \\ GIC-S & & 5.55 & 5.56 & 5.56 & 5.56 \\
\\ GIC-S & VWN5 & 5.58 & 5.53 & 5.57 & 5.52 \\
S & VWN5 & aug-cc-pVDZ & 5.34 & 5.57 & 5.46 & 5.53 \\ GIC-S & eVWN5 & 5.77 & 5.72 & 5.66 & 5.72 \\
& & aug-cc-pVTZ & 5.34 & 5.57 & 5.46 & 5.52 \\ B & LYP & & & & 5.28 \\
\\ B3 & LYP & & & & 5.55 \\
S & eVWN5 & aug-cc-pVDZ & 5.53 & 5.76 & 5.56 & 5.72 \\ HF & LYP & & & & 6.68 \\
& & aug-cc-pVTZ & 5.53 & 5.76 & 5.56 & 5.72 \\ \hline
& & aug-cc-pVQZ & & & & \\ \mc{5}{l}{Accurate (FCI/aug-cc-pV5Z)\fnm[1]} & 8.69 \\
\\
GIC-S & & aug-cc-pVDZ & 5.56 & 5.56 & 5.56 & 5.56 \\
& & aug-cc-pVTZ & 5.55 & 5.56 & 5.56 & 5.56 \\
\\
GIC-S & VWN5 & aug-cc-pVDZ & 5.59 & 5.53 & 5.57 & 5.53 \\
& & aug-cc-pVTZ & 5.58 & 5.53 & 5.57 & 5.52 \\
\\
GIC-S & eVWN5 & aug-cc-pVDZ & 5.78 & 5.72 & 5.66 & 5.72 \\
& & aug-cc-pVTZ & 5.77 & 5.72 & 5.66 & 5.72 \\
\\
B & LYP & aug-cc-pVTZ & & & & 5.28 \\
B3 & LYP & aug-cc-pVTZ & & & & 5.55 \\
HF & LYP & aug-cc-pVTZ & & & & 6.68 \\
\\
% HF & FCI & aug-cc-pVDZ & & & & 8.78 \\
% HF & FCI & aug-cc-pVTZ & & & & 8.71 \\
% HF & FCI & aug-cc-pVQZ & & & & 8.70 \\
HF & FCI & aug-cc-pV5Z & & & & 8.69 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table*} \fnt[1]{FCI calculations performed with QUANTUM PACKAGE. \cite{QP2}}
\end{table}
%%% %%% %%% %%% %%% %%% %%% %%%
%%% TABLE I %%% %%% TABLE I %%%
\begin{table*} \begin{table}
\caption{ \caption{
Excitation energies (in hartree) associated with the lowest double excitation of \ce{He} for various methods, combinations of xc functionals, and basis sets. Excitation energies (in hartree) associated with the lowest double excitation of \ce{He} obtained with the d-aug-cc-pVQZ basis set for various methods and combinations of xc functionals.
\label{tab:BigTab_He} \label{tab:BigTab_He}
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{llccccc} \begin{tabular}{llcccc}
\mc{2}{c}{xc functional} & & \mc{2}{c}{GOK} \\ \mc{2}{c}{xc functional} & \mc{2}{c}{GOK} \\
\cline{1-2} \cline{4-5} \cline{1-2} \cline{3-4}
exchange & correlation & Basis & $\ew{} = 0$ & $\ew{} = 1/2$ & LIM & MOM \\ exchange & correlation & $\ew{} = 0$ & $\ew{} = 1/2$ & LIM & MOM \\
\hline \hline
HF & & d-aug-cc-pVDZ & 1.897 & 2.209 & 2.078 & 2.143 \\ HF & & 1.874 & 2.212 & 2.080 & 2.142 \\
& & d-aug-cc-pVTZ & 1.874 & 2.213 & 2.080 & 2.143 \\ S & & 1.062 & 2.056 & 1.547 & 2.030 \\
& & d-aug-cc-pVQZ & 1.874 & 2.212 & 2.080 & 2.142 \\ S & VWN5 & 1.163 & 2.104 & 1.612 & 2.079 \\
\\ S & eVWN5 & 1.174 & 2.108 & 1.615 & 2.083 \\
S & & d-aug-cc-pVDZ & 1.075 & 2.055 & 1.546 & 2.030 \\ GIC-S & & 1.996 & 2.044 & 1.988 & 2.030 \\
& & d-aug-cc-pVTZ & 1.062 & 2.057 & 1.547 & 2.031 \\ GIC-S & VWN5 & 2.107 & 2.097 & 2.060 & 2.079 \\
& & d-aug-cc-pVQZ & 1.062 & 2.056 & 1.547 & 2.030 \\ GIC-S & eVWN5 & 2.118 & 2.100 & 2.063 & 2.083 \\
\\ B & LYP & & & & 2.147 \\
S & VWN5 & d-aug-cc-pVDZ & 1.172 & 2.102 & 1.612 & \\ B3 & LYP & & & & 2.150 \\
& & d-aug-cc-pVTZ & 1.163 & & & \\ HF & LYP & & & & 2.171 \\
& & d-aug-cc-pVQZ & & & & \\ \hline
\\ \mc{5}{l}{Exact (explicitly-correlated method)\fnm[1] } & 2.126 \\
S & eVWN5 & d-aug-cc-pVDZ & & & & \\
& & d-aug-cc-pVTZ & & & & \\
& & d-aug-cc-pVQZ & & & & \\
\\
GIC-S & & d-aug-cc-pVDZ & & & & \\
& & d-aug-cc-pVTZ & & & & \\
& & d-aug-cc-pVQZ & & & & \\
\\
GIC-S & VWN5 & d-aug-cc-pVDZ & & & & \\
& & d-aug-cc-pVTZ & & & & \\
& & d-aug-cc-pVQZ & & & & \\
\\
GIC-S & eVWN5 & d-aug-cc-pVDZ & & & & \\
& & d-aug-cc-pVTZ & & & & \\
& & d-aug-cc-pVQZ & & & & \\
\\
B & LYP & d-aug-cc-pVQZ & & & & \\
B3 & LYP & d-aug-cc-pVQZ & & & & \\
HF & LYP & d-aug-cc-pVQZ & & & & \\
\\
\mc{2}{l}{Exact} & & & & & 2.126\fnm[1] \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\fnt[1]{Reference \onlinecite{Burges_1995}} \fnt[1]{Reference \onlinecite{Burges_1995}.}
\end{table*} \end{table}
%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%
%%% CONCLUSION %%% %%% CONCLUSION %%%