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Pierre-Francois Loos 2019-03-18 14:54:18 +01:00
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Data/.DS_Store vendored
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Manuscript/G2-srDFT.pdf
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Manuscript/G2-srDFT.tex
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@ -97,20 +97,60 @@ The
\section{Results} \section{Results}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The case of C$_2$ and the comparison with the F$_{12}$ methods.} \subsection{The case of C$_2$ and the comparison with the F12 methods.}
\begin{table*}
\caption{Dissociation energy ($D_e$) in kcal/mol of the C$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F12, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{BytLaiRuedenJCP05} }
\begin{ruledtabular}
\begin{tabular}{llddddd}
& & \mc{4}{c}{Dunning's basis set}
\\
\cline{3-6}
Molecule & Method & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z} & \tabc{Exp.}
\\
\hline
\ce{C2} & FCIQMC & 130.0(1) & 139.9(3) & 143.3(2) & & 146.9(5) \\
& FCIQMC+F12 & 142.3 & 145.3 & & & \\
& exFCI & 132.0 & 140.3 & 143.6 & 144.3 & \\
& exFCI+LDA & 141.9 & 142.8 & 145.8 & 146.2 & \\
& exFCI+LDA(FC) & 142.9 & 145.5 & 146.2 & 146.1 & \\
& exFCI+PBE & 142.7 & 142.7 & 145.3 & 144.9 & \\
& exFCI+PBE(FC) & 143.3 & 144.7 & 145.7 & 145.6 & \\
\\
\ce{O2} & exFCI & 105.3 & 114.6 & 118.0 & & 120.2 \\
& exFCI+LDA & 111.8 & 117.2 & 120.0 & & \\
& exFCI+LDA(FC) & 112.5 & 118.5 & 120.2 & & \\
& exFCI+PBE & 115.0 & 118.4 & 120.2 & & \\
& exFCI+PBE(FC) & 116.1 & 119.4 & 120.5 & & \\
\\
\ce{N2} & exFCI & 200.9 & 217.1 & 223.5 & 225.7 & 228.5 \\
& exFCI+LDA & 216.3 & 223.1 & 227.9 & 227.9 & \\
& exFCI+LDA(FC) & 218.2 & 225.8 & 228.8 & 228.4 & \\
& exFCI+PBE & 222.3 & 224.6 & 227.7 & 227.7 & \\
& exFCI+PBE(FC) & 224.8 & 226.7 & 228.3 & 228.3 & \\
\\
\ce{F2} & exFCI & 27.5 & 35.4 & 37.5 & 38.0 & 38.2 \\
& exFCI+LDA & 30.8 & 37.0 & 38.7 & 38.7 & \\
& exFCI+LDA(FC) & 31.1 & 37.5 & 38.8 & 38.8 & \\
& exFCI+PBE & 32.1 & 37.5 & 38.7 & & \\
& exFCI+PBE(FC) & 32.4 & 37.8 & 38.8 & 38.8 & \\
\end{tabular}
\end{ruledtabular}
\end{table*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table*} \begin{table*}
\caption{Dissociation energy ($D_e$) in kcal/mol of the C$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F$_{12}$, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{BytLaiRuedenJCP05} } \caption{Dissociation energy ($D_e$) in kcal/mol of the C$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F12, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{BytLaiRuedenJCP05} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lccccccc} \begin{tabular}{lccccccc}
%\hline & FCIQMC & CIPSI & FCIQMC+F12 & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
& FCIQMC & CIPSI & FCIQMC+F$_{12}$ & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
\hline \hline
V2Z & 130.0 & 132.0 & 142.3 & 141.9 & 142.9 & 142.7 & 143.3 \\ V2Z & 130.0 & 132.0 & 142.3 & 141.9 & 142.9 & 142.7 & 143.3 \\
V3Z & 139.9 & 140.3 & 145.3 & 142.8 & 145.5 & 142.7 & 144.7 \\ V3Z & 139.9 & 140.3 & 145.3 & 142.8 & 145.5 & 142.7 & 144.7 \\
V4Z & - & 143.6 & - & 145.8 & 146.2 & 145.3 & 145.7 \\ V4Z & - & 143.6 & - & 145.8 & 146.2 & 145.3 & 145.7 \\
V5Z & - & 144.3 & - & 145.1 & 146.1 & 144.9 & 145.6 \\ V5Z & - & 144.3 & - & 145.1 & 146.1 & 144.9 & 145.6 \\
%\hline
& \multicolumn{5}{c}{Estimated exact $^a$} \\ & \multicolumn{5}{c}{Estimated exact $^a$} \\
& \multicolumn{5}{c}{ 146.9} \\ & \multicolumn{5}{c}{ 146.9} \\
\end{tabular} \end{tabular}
@ -119,17 +159,15 @@ V5Z & - & 144.3 & - & 145.1
\end{table*} \end{table*}
\begin{table*} \begin{table*}
\caption{Dissociation energy ($D_e$) in kcal/mol of the N$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F$_{12}$, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{PetTouUmr-JCP-12} taking into account the ZPE correction. } \caption{Dissociation energy ($D_e$) in kcal/mol of the N$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F12, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{PetTouUmr-JCP-12} taking into account the ZPE correction. }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lccccc} \begin{tabular}{lccccc}
%\hline
& CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\ & CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
\hline \hline
V2Z & 200.9 & 216.3 & 218.2 & 222.3 & 224.8 \\ V2Z & 200.9 & 216.3 & 218.2 & 222.3 & 224.8 \\
V3Z & 217.1 & 223.1 & 225.8 & 224.6 & 226.7 \\ V3Z & 217.1 & 223.1 & 225.8 & 224.6 & 226.7 \\
V4Z & 223.5 & 227.9 & 228.8 & 227.7 & 228.3 \\ V4Z & 223.5 & 227.9 & 228.8 & 227.7 & 228.3 \\
V5Z & 225.7 & 227.9 & 228.4 & 227.7 & 228.3 \\ V5Z & 225.7 & 227.9 & 228.4 & 227.7 & 228.3 \\
%\hline
& \multicolumn{5}{c}{Estimated exact} \\ & \multicolumn{5}{c}{Estimated exact} \\
& \multicolumn{5}{c}{228.5$^a$ } \\ & \multicolumn{5}{c}{228.5$^a$ } \\
\end{tabular} \end{tabular}
@ -139,7 +177,7 @@ V5Z & 225.7 & 227.9 & 228.4
\begin{table*} \begin{table*}
\caption{Dissociation energy ($D_e$) in kcal/mol of the F$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F$_{12}$, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{PetTouUmr-JCP-12} taking into account the ZPE correction. } \caption{Dissociation energy ($D_e$) in kcal/mol of the F$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F12, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{PetTouUmr-JCP-12} taking into account the ZPE correction. }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lccccc} \begin{tabular}{lccccc}
%\hline %\hline
@ -159,17 +197,15 @@ V5Z & 38.0 & 38.7 & 38.8
\begin{table*} \begin{table*}
\caption{Dissociation energy ($D_e$) in kcal/mol of the O$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F$_{12}$, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{PetTouUmr-JCP-12} taking into account the ZPE correction. } \caption{Dissociation energy ($D_e$) in kcal/mol of the O$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F12, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{PetTouUmr-JCP-12} taking into account the ZPE correction. }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lccccc} \begin{tabular}{lccccc}
%\hline
& CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\ & CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
\hline \hline
V2Z & 105.3 & 111.8 & 112.5 & 115.0 & 116.1 \\ V2Z & 105.3 & 111.8 & 112.5 & 115.0 & 116.1 \\
V3Z & 114.6 & 117.2 & 118.5 & 118.4 & 119.4 \\ V3Z & 114.6 & 117.2 & 118.5 & 118.4 & 119.4 \\
V4Z & 118.0 & 120.0 & 120.2 & 120.2 & 120.5 \\ V4Z & 118.0 & 120.0 & 120.2 & 120.2 & 120.5 \\
V5Z & & & & & \\ V5Z & & & & & \\
%\hline
& \multicolumn{5}{c}{Estimated exact} \\ & \multicolumn{5}{c}{Estimated exact} \\
& \multicolumn{5}{c}{120.2 $^a$} \\ & \multicolumn{5}{c}{120.2 $^a$} \\
\end{tabular} \end{tabular}

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srDFT_G2.nb
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