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Julien Toulouse 2020-01-28 10:39:58 +01:00
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Manuscript/srDFT_SC.tex
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@ -281,9 +281,6 @@
\author{Emmanuel Giner} \author{Emmanuel Giner}
\email{emmanuel.giner@lct.jussieu.fr} \email{emmanuel.giner@lct.jussieu.fr}
\affiliation{\LCT} \affiliation{\LCT}
\author{Barth\'el\'emy Pradines}
\affiliation{\LCT}
\affiliation{\ISCD}
\author{Anthony Scemama} \author{Anthony Scemama}
\affiliation{\LCPQ} \affiliation{\LCPQ}
\author{Pierre-Fran\c{c}ois Loos} \author{Pierre-Fran\c{c}ois Loos}
@ -603,11 +600,6 @@ We then define three complementary functionals:
\label{eq:def_pbeueg_ii} \label{eq:def_pbeueg_ii}
\bar{E}^\Bas_{\pbeontXi} = \int \d\br{} \,\denr \ecmd(\argrpbeontXi), \bar{E}^\Bas_{\pbeontXi} = \int \d\br{} \,\denr \ecmd(\argrpbeontXi),
\end{equation} \end{equation}
%\item[iii)] $\pbeuegns$ which combines a zero spin polarization and the UEG on-top pair density of Eq.~\eqref{eq:def_n2ueg}:
%\begin{equation}
% \label{eq:def_pbeueg_iii}
% \bar{E}^\Bas_{\pbeuegns} = \int \d\br{} \,\denr \ecmd(\argrpbeuegns),
%\end{equation}
\item[iii)] $\pbeontns$ which combines a zero spin polarization and the on-top pair density of Eq.~\eqref{eq:def_n2extrap}: \item[iii)] $\pbeontns$ which combines a zero spin polarization and the on-top pair density of Eq.~\eqref{eq:def_n2extrap}:
\begin{equation} \begin{equation}
\label{eq:def_pbeueg_iv} \label{eq:def_pbeueg_iv}
@ -652,16 +644,8 @@ The performance of each of these functionals is tested in the following. Note th
\ce{H10} & cc-pVDZ & 622.1 [43.3] & 642.6 [22.8] & 649.2 [16.2] & 649.5 [15.9] \\ \ce{H10} & cc-pVDZ & 622.1 [43.3] & 642.6 [22.8] & 649.2 [16.2] & 649.5 [15.9] \\
& cc-pVTZ & 655.2 [10.2] & 661.9 [3.5] & 666.0 [-0.6] & 666.0 [-0.6] \\ & cc-pVTZ & 655.2 [10.2] & 661.9 [3.5] & 666.0 [-0.6] & 666.0 [-0.6] \\
& cc-pVQZ & 661.2 [4.2] & 664.1 [1.3] & 666.4 [-1.0] & 666.5 [-1.1] \\[0.1cm] & cc-pVQZ & 661.2 [4.2] & 664.1 [1.3] & 666.4 [-1.0] & 666.5 [-1.1] \\[0.1cm]
%\cline{2-6}
& &\multicolumn{4}{c}{Estimated exact:\fnm[1] 665.4} \\[0.2cm] & &\multicolumn{4}{c}{Estimated exact:\fnm[1] 665.4} \\[0.2cm]
\hline \hline
% & & \tabc{exFCI} & \tabc{exFCI+$\pbeuegXi$} & \tabc{exFCI+$\pbeontXi$} & \tabc{exFCI+$\pbeontns$}\\
%\hline
%\ce{C2} & aug-cc-pVDZ & 204.6 [29.5] & 218.0 [16.1] & 217.4 [16.7] & 217.0 [17.1] \\
% & aug-cc-pVTZ & 223.4 [10.9] & 228.1 [6.0] & 228.6 [5.5] & 226.5 [5.6] \\[0.1cm]
%\cline{2-6}
% & & \multicolumn{4}{c}{Estimated exact:\fnm[2] 234.1} \\[0.2cm]
%\hline
& & \tabc{exFCI} & \tabc{exFCI+$\pbeuegXi$} & \tabc{exFCI+$\pbeontXi$} & \tabc{exFCI+$\pbeontns$}\\ & & \tabc{exFCI} & \tabc{exFCI+$\pbeuegXi$} & \tabc{exFCI+$\pbeontXi$} & \tabc{exFCI+$\pbeontns$}\\
\hline \hline
\ce{N2} & aug-cc-pVDZ & 321.9 [40.8] & 356.2 [6.5] & 355.5 [7.2] & 354.6 [8.1] \\ \ce{N2} & aug-cc-pVDZ & 321.9 [40.8] & 356.2 [6.5] & 355.5 [7.2] & 354.6 [8.1] \\
@ -745,18 +729,6 @@ Analyzing more carefully the performance of the different types of approximate f
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure*}
% \includegraphics[width=0.45\linewidth]{data/C2/DFT_avdzE_relat.pdf}
% \includegraphics[width=0.45\linewidth]{data/C2/DFT_avdzE_relat_zoom.pdf}
% \includegraphics[width=0.45\linewidth]{data/C2/DFT_avtzE_relat.pdf}
% \includegraphics[width=0.45\linewidth]{data/C2/DFT_avtzE_relat_zoom.pdf}
% \caption{
% Potential energy curves of the \ce{C2} molecule calculated with exFCI and basis-set corrected exFCI using the aug-cc-pVDZ (top) and aug-cc-pVTZ (bottom) basis sets. The estimated exact energies are based on fit of experimental data and obtained from Ref.~\onlinecite{LieCle-JCP-74a}.
% \label{fig:C2}}
%\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*} \begin{figure*}
@ -775,21 +747,8 @@ The estimated exact energies are based on a fit of experimental data and obtaine
\end{figure*} \end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure*}
% \includegraphics[width=0.45\linewidth]{data/F2/DFT_vdzE_relat.pdf}
% \includegraphics[width=0.45\linewidth]{data/F2/DFT_vdzE_relat_zoom.pdf}
% \includegraphics[width=0.45\linewidth]{data/F2/DFT_vtzE_relat.pdf}
% \includegraphics[width=0.45\linewidth]{data/F2/DFT_vtzE_relat_zoom.pdf}
% \includegraphics[width=0.45\linewidth]{data/F2/DFT_vqzE_relat.pdf}
% \includegraphics[width=0.45\linewidth]{data/F2/DFT_vqzE_relat_zoom.pdf}
% \caption{
% Potential energy curves of the \ce{F2} molecule calculated with CEEIS$^1$ and basis-set corrected CEEIS$^1$ using the cc-pVDZ (top), cc-pVTZ (middle) and cc-pVQZ (bottom) basis sets.
% The estimated exact energies are based on a fit of the valence-only extrapolated CEEIS data extracted from Ref.~\onlinecite{BytNagGorRue-JCP-07}.
% \label{fig:F2}}
%\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*} \begin{figure*}
\subfigure[aug-cc-pVDZ]{ \subfigure[aug-cc-pVDZ]{
\includegraphics[width=0.45\linewidth]{data/F2/DFT_avdzE_relat.pdf} \includegraphics[width=0.45\linewidth]{data/F2/DFT_avdzE_relat.pdf}