diff --git a/Manuscript/G2-srDFT.pdf b/Manuscript/G2-srDFT.pdf index b3ab7ca..22b678c 100644 Binary files a/Manuscript/G2-srDFT.pdf and b/Manuscript/G2-srDFT.pdf differ diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex index 5154725..5b2c14a 100644 --- a/Manuscript/G2-srDFT.tex +++ b/Manuscript/G2-srDFT.tex @@ -39,6 +39,7 @@ \newcommand{\ex}[4]{$^{#1}#2_{#3}^{#4}$} \newcommand{\ra}{\rightarrow} +\newcommand{\De}{D_\text{e}} % units \newcommand{\IneV}[1]{#1 eV} @@ -100,7 +101,10 @@ The \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} } + \caption{ + \label{tab:diatomics} + Dissociation energy ($\De$) in kcal/mol of the \ce{C2}, \ce{O2}, \ce{N2} and \ce{F2} molecules computed with various methods and basis sets. + } \begin{ruledtabular} \begin{tabular}{llddddd} & & \mc{4}{c}{Dunning's basis set} @@ -109,7 +113,7 @@ The 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) \\ + \ce{C2} & FCIQMC & 130.0(1) & 139.9(3) & 143.3(2) & & 146.9(5)\fnm[1] \\ & 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 & \\ @@ -117,19 +121,19 @@ The & 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 \\ + \ce{O2} & exFCI & 105.3 & 114.6 & 118.0 & & 120.2\fnm[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 \\ + \ce{N2} & exFCI & 200.9 & 217.1 & 223.5 & 225.7 & 228.5\fnm[2] \\ & 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 \\ + \ce{F2} & exFCI & 27.5 & 35.4 & 37.5 & 38.0 & 38.2\fnm[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 & & \\ @@ -137,84 +141,11 @@ The \end{tabular} \end{ruledtabular} + \fnt[1]{Results from Ref.~\onlinecite{BytLaiRuedenJCP05}.} + \fnt[2]{Results from Ref.~\onlinecite{PetTouUmr-JCP-12}.} \end{table*} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\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}{lccccccc} - & FCIQMC & CIPSI & FCIQMC+F12 & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\ -\hline -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 \\ -V4Z & - & 143.6 & - & 145.8 & 146.2 & 145.3 & 145.7 \\ -V5Z & - & 144.3 & - & 145.1 & 146.1 & 144.9 & 145.6 \\ - & \multicolumn{5}{c}{Estimated exact $^a$} \\ - & \multicolumn{5}{c}{ 146.9} \\ -\end{tabular} -\end{ruledtabular} -\label{conv_He_table} -\end{table*} - -\begin{table*} -\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{tabular}{lccccc} - & CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\ -\hline -V2Z & 200.9 & 216.3 & 218.2 & 222.3 & 224.8 \\ -V3Z & 217.1 & 223.1 & 225.8 & 224.6 & 226.7 \\ -V4Z & 223.5 & 227.9 & 228.8 & 227.7 & 228.3 \\ -V5Z & 225.7 & 227.9 & 228.4 & 227.7 & 228.3 \\ - & \multicolumn{5}{c}{Estimated exact} \\ - & \multicolumn{5}{c}{228.5$^a$ } \\ -\end{tabular} -\end{ruledtabular} -\label{conv_He_table} -\end{table*} - - -\begin{table*} -\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{tabular}{lccccc} -%\hline - & CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\ -\hline -V2Z & 27.5 & 30.8 & 31.1 & 32.1 & 32.4 \\ -V3Z & 35.4 & 37.0 & 37.5 & 37.5 & 37.8 \\ -V4Z & 37.5 & 38.7 & 38.8 & 38.7 & 38.8 \\ -V5Z & 38.0 & 38.7 & 38.8 & & 38.8 \\ -%\hline - & \multicolumn{5}{c}{Estimated exact} \\ - & \multicolumn{5}{c}{ 38.2$^a$} \\ -\end{tabular} -\end{ruledtabular} -\label{conv_He_table} -\end{table*} - - -\begin{table*} -\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{tabular}{lccccc} - & CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\ -\hline -V2Z & 105.3 & 111.8 & 112.5 & 115.0 & 116.1 \\ -V3Z & 114.6 & 117.2 & 118.5 & 118.4 & 119.4 \\ -V4Z & 118.0 & 120.0 & 120.2 & 120.2 & 120.5 \\ -V5Z & & & & & \\ - & \multicolumn{5}{c}{Estimated exact} \\ - & \multicolumn{5}{c}{120.2 $^a$} \\ -\end{tabular} -\end{ruledtabular} -\label{conv_He_table} -\end{table*} - - - %