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@ -97,20 +97,60 @@ The
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\section{Results}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{The case of C$_2$ and the comparison with the F$_{12}$ methods.}
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\subsection{The case of C$_2$ and the comparison with the F12 methods.}
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\begin{table*}
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\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} }
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\begin{ruledtabular}
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\begin{tabular}{llddddd}
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& & \mc{4}{c}{Dunning's basis set}
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\\
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\cline{3-6}
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Molecule & Method & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z} & \tabc{Exp.}
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\\
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\hline
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\ce{C2} & FCIQMC & 130.0(1) & 139.9(3) & 143.3(2) & & 146.9(5) \\
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& FCIQMC+F12 & 142.3 & 145.3 & & & \\
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& exFCI & 132.0 & 140.3 & 143.6 & 144.3 & \\
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& exFCI+LDA & 141.9 & 142.8 & 145.8 & 146.2 & \\
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& exFCI+LDA(FC) & 142.9 & 145.5 & 146.2 & 146.1 & \\
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& exFCI+PBE & 142.7 & 142.7 & 145.3 & 144.9 & \\
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& exFCI+PBE(FC) & 143.3 & 144.7 & 145.7 & 145.6 & \\
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\\
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\ce{O2} & exFCI & 105.3 & 114.6 & 118.0 & & 120.2 \\
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& exFCI+LDA & 111.8 & 117.2 & 120.0 & & \\
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& exFCI+LDA(FC) & 112.5 & 118.5 & 120.2 & & \\
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& exFCI+PBE & 115.0 & 118.4 & 120.2 & & \\
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& exFCI+PBE(FC) & 116.1 & 119.4 & 120.5 & & \\
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\\
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\ce{N2} & exFCI & 200.9 & 217.1 & 223.5 & 225.7 & 228.5 \\
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& exFCI+LDA & 216.3 & 223.1 & 227.9 & 227.9 & \\
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& exFCI+LDA(FC) & 218.2 & 225.8 & 228.8 & 228.4 & \\
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& exFCI+PBE & 222.3 & 224.6 & 227.7 & 227.7 & \\
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& exFCI+PBE(FC) & 224.8 & 226.7 & 228.3 & 228.3 & \\
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\\
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\ce{F2} & exFCI & 27.5 & 35.4 & 37.5 & 38.0 & 38.2 \\
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& exFCI+LDA & 30.8 & 37.0 & 38.7 & 38.7 & \\
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& exFCI+LDA(FC) & 31.1 & 37.5 & 38.8 & 38.8 & \\
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& exFCI+PBE & 32.1 & 37.5 & 38.7 & & \\
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& exFCI+PBE(FC) & 32.4 & 37.8 & 38.8 & 38.8 & \\
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\end{tabular}
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\end{ruledtabular}
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\end{table*}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{table*}
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\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} }
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\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} }
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\begin{ruledtabular}
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\begin{tabular}{lccccccc}
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%\hline
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& FCIQMC & CIPSI & FCIQMC+F$_{12}$ & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
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& FCIQMC & CIPSI & FCIQMC+F12 & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
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\hline
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V2Z & 130.0 & 132.0 & 142.3 & 141.9 & 142.9 & 142.7 & 143.3 \\
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V3Z & 139.9 & 140.3 & 145.3 & 142.8 & 145.5 & 142.7 & 144.7 \\
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V4Z & - & 143.6 & - & 145.8 & 146.2 & 145.3 & 145.7 \\
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V5Z & - & 144.3 & - & 145.1 & 146.1 & 144.9 & 145.6 \\
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%\hline
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& \multicolumn{5}{c}{Estimated exact $^a$} \\
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& \multicolumn{5}{c}{ 146.9} \\
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\end{tabular}
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@ -119,17 +159,15 @@ V5Z & - & 144.3 & - & 145.1
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\end{table*}
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\begin{table*}
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\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. }
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\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. }
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\begin{ruledtabular}
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\begin{tabular}{lccccc}
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%\hline
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& CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
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\hline
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V2Z & 200.9 & 216.3 & 218.2 & 222.3 & 224.8 \\
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V3Z & 217.1 & 223.1 & 225.8 & 224.6 & 226.7 \\
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V4Z & 223.5 & 227.9 & 228.8 & 227.7 & 228.3 \\
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V5Z & 225.7 & 227.9 & 228.4 & 227.7 & 228.3 \\
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%\hline
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& \multicolumn{5}{c}{Estimated exact} \\
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& \multicolumn{5}{c}{228.5$^a$ } \\
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\end{tabular}
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@ -139,7 +177,7 @@ V5Z & 225.7 & 227.9 & 228.4
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\begin{table*}
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\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. }
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\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. }
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\begin{ruledtabular}
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\begin{tabular}{lccccc}
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%\hline
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@ -159,17 +197,15 @@ V5Z & 38.0 & 38.7 & 38.8
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\begin{table*}
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\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. }
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\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. }
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\begin{ruledtabular}
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\begin{tabular}{lccccc}
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%\hline
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& CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
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\hline
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V2Z & 105.3 & 111.8 & 112.5 & 115.0 & 116.1 \\
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V3Z & 114.6 & 117.2 & 118.5 & 118.4 & 119.4 \\
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V4Z & 118.0 & 120.0 & 120.2 & 120.2 & 120.5 \\
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V5Z & & & & & \\
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%\hline
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& \multicolumn{5}{c}{Estimated exact} \\
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& \multicolumn{5}{c}{120.2 $^a$} \\
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\end{tabular}
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8274
srDFT_G2.nb
8274
srDFT_G2.nb
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