diff --git a/Manuscript/G2-srDFT.pdf b/Manuscript/G2-srDFT.pdf index c14b048..c0e444d 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 fca1722..1ec6246 100644 --- a/Manuscript/G2-srDFT.tex +++ b/Manuscript/G2-srDFT.tex @@ -52,6 +52,7 @@ \newcommand{\EsCI}{E_\text{sCI}} \newcommand{\EDMC}{E_\text{DMC}} \newcommand{\EexFCI}{E_\text{exFCI}} +\newcommand{\EexFCIbasis}{E_\text{exFCI}^{\basis}} \newcommand{\EexDMC}{E_\text{exDMC}} \newcommand{\Ead}{\Delta E_\text{ad}} \newcommand{\efci}[0]{E_{\text{FCI}}^{\basis}} @@ -452,7 +453,20 @@ Therefore, we propose the following valence-only approximations for the compleme \section{Results} %%%%%%%%%%%%%%%%%%%%%%%% -\subsection{The case of C$_2$, F$_2$, O$_2$, F$_2$ and the impact of the lack of basis functions adapted to core correlation } +\subsection{The case of C$_2$, N$_2$, O$_2$, F$_2$ and the impact of the lack of basis functions adapted to core correlation } +We begin the investigation of the behavior of the basis-set correction by the study of the atomization energies of the C$_2$, N$_2$, O$_2$, F$_2$ homo-nuclear diatomic molecules in the Dunning cc-pVXZ and cc-pCVXZ (X=D,T,Q,5) using the CIPSI algorithm to obtain reliable estimate of $\efci$ and $\denfci$. +\subsubsection{CIPSI calculations } +All CIPSI calculations were performed in two steps. First, a CIPSI calculation was performed until the zeroth-order wave function reaches $10^6$ Slater determinants, from which we extracted the natural orbitals. From this set of natural orbitals, we performed CIPSI calculations until the $\EexFCIbasis$ reaches about $0.1$ mH convergence for each systems. Such convergence criterion is more than sufficient for the CIPSI densities $\dencipsi$. +Therefore, from now on, we assume that +\begin{equation} + \efci \approx \EexFCIbasis +\end{equation} +and that +\begin{equation} + \denrfci \approx \dencipsi. +\end{equation} +Regarding the wave function chosen to define the local range-separation parameter $\mur$, we take a single Slater determinant built with the natural orbitals of the first CIPSI calculation. +\subsubsection{Treating the valence electrons} \begin{table*} \caption{ @@ -462,10 +476,12 @@ Therefore, we propose the following valence-only approximations for the compleme \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)\fnm[1] \\ & FCIQMC+F12 & 142.3 & 145.3 & & & \\ @@ -480,8 +496,37 @@ Therefore, we propose the following valence-only approximations for the compleme \hline & exFCI+PBE-on-top& 142.7 & 142.7 & 145.3 & 144.9 & \\ & exFCI+PBE-on-top-val & 143.3 & 144.7 & 145.7 & 145.6 & \\ + \\ + \cline{3-6} + & & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{ } + \\ + \\ + \hline + & ex (FC)FC-FCI & 130.5 & 140.5 & 143.8 & 144.9 & \\ + \hline + & ex (FC)FCI+LDA & 140.9 & 145.7 & 146.6 & 146.4 & \\ + & ex (FC)FCI+LDA-val & 141.3 & 145.6 & 146.5 & 146.4 & \\ + \hline + & ex (FC)FCI+PBE & 144.5 & 145.9 & 146.4 & 146.3 & \\ + & ex (FC)FCI+PBE -val & 145.2 & 145.9 & 146.4 & 146.3 & \\ + + & ex FC-FCI & 131.0 & 141.5 & 145.1 & ----- & \\ + \hline + & ex FCI+LDA & 141.4 & 146.7 & 147.8 & ----- & \\ + & ex FCI+LDA-val & 141.8 & 146.6 & 147.7 & ----- & \\ + \hline + & ex FCI+PBE & 145.1 & 147.0 & 147.7 & ----- & \\ + & ex FCI+PBE -val & 145.7 & 147.0 & 147.6 & ----- & \\ + \\ + \\ + & & \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.} + \\ \\ \ce{N2} & exFCI & 200.9 & 217.1 & 223.5 & 225.7 & 228.5\fnm[2] \\ + \\ \hline & exFCI+LDA & 216.3 & 223.1 & 227.9 & 227.9 & \\ & exFCI+LDA-val & 217.8 & 225.9 & 228.1 & 228.5 & \\ @@ -491,6 +536,43 @@ Therefore, we propose the following valence-only approximations for the compleme \hline & exFCI+PBE-on-top& 222.3 & 224.6 & 227.7 & 227.7 & \\ & exFCI+PBE-on-top-val & 224.8 & 226.7 & 228.3 & 228.3 & \\ + \cline{3-6} + \\ + & & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{ } + \\ + \\ + & ex (FC)FCI & 201.6 & 217.9 & 223.7 & 226.0 & \\ + \hline + & ex (FC)FCI+LDA & 217.4 & 226.2 & 228.4 & 228.7 & \\ + & ex (FC)FCI+LDA-val & 218.7 & 226.3 & 228.5 & 228.7 & \\ + \hline + & ex (FC)FCI+PBE & 225.8 & 227.6 & 228.4 & 228.6 & \\ + & ex (FC)FCI+PBE -val & 228.0 & 227.8 & 228.5 & 228.6 & \\ + & ex FCI & 202.0 & 218.5 & 224.3 & ----- & \\ + \hline + & ex FCI+LDA & 217.8 & 226.8 & 229.0 & ----- & \\ + & ex FCI+LDA-val & 218.8 & 226.9 & 229.0 & ----- & \\ + \hline + & ex FCI+PBE & 226.2 & 228.2 & 229.0 & ----- & \\ + & ex FCI+PBE -val & 227.8 & 228.2 & 229.0 & ----- & \\ + \\ + \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{ + \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} + \\ + \cline{3-6} + Molecule & Method & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z} & \tabc{Exp.} \\ \ce{O2} & exFCI & 105.3 & 114.6 & 118.0 &119.1 & 120.2\fnm[2] \\ \hline @@ -521,58 +603,6 @@ Therefore, we propose the following valence-only approximations for the compleme \end{table*} -\begin{table*} - \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} - \\ - \cline{3-6} - Molecule & Method & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{Exp.} - \\ - \hline - \ce{C2} & ex (FC)FC-FCI & 130.5 & 140.5 & 143.8 & 144.9 &146.9(5)\fnm \\ - \hline - & ex (FC)FCI+LDA & 140.9 & 145.7 & 146.6 & 146.4 & \\ - & ex (FC)FCI+LDA-val & 141.3 & 145.6 & 146.5 & 146.4 & \\ - \hline - & ex (FC)FCI+PBE & 144.5 & 145.9 & 146.4 & 146.3 & \\ - & ex (FC)FCI+PBE -val & 145.2 & 145.9 & 146.4 & 146.3 & \\ - - \ce{C2} & ex FC-FCI & 131.0 & 141.5 & 145.1 & ----- & \\ - \hline - & ex FCI+LDA & 141.4 & 146.7 & 147.8 & ----- & \\ - & ex FCI+LDA-val & 141.8 & 146.6 & 147.7 & ----- & \\ - \hline - & ex FCI+PBE & 145.1 & 147.0 & 147.7 & ----- & \\ - & ex FCI+PBE -val & 145.7 & 147.0 & 147.6 & ----- & \\ - \\ - \ce{N2} & ex (FC)FCI & 201.6 & 217.9 & 223.7 & 226.0 & 228.5\fnm[2] \\ - \hline - & ex (FC)FCI+LDA & 217.4 & 226.2 & 228.4 & 228.7 & \\ - & ex (FC)FCI+LDA-val & 218.7 & 226.3 & 228.5 & 228.7 & \\ - \hline - & ex (FC)FCI+PBE & 225.8 & 227.6 & 228.4 & 228.6 & \\ - & ex (FC)FCI+PBE -val & 228.0 & 227.8 & 228.5 & 228.6 & \\ - \ce{N2} & ex FCI & 202.0 & 218.5 & 224.3 & ----- & 228.5\fnm[2] \\ - \hline - & ex FCI+LDA & 217.8 & 226.8 & 229.0 & ----- & \\ - & ex FCI+LDA-val & 218.8 & 226.9 & 229.0 & ----- & \\ - \hline - & ex FCI+PBE & 226.2 & 228.2 & 229.0 & ----- & \\ - & ex FCI+PBE -val & 227.8 & 228.2 & 229.0 & ----- & \\ - \\ - - \end{tabular} - \end{ruledtabular} - \fnt[1]{Results from Ref.~\onlinecite{BytLaiRuedenJCP05}.} - \fnt[2]{Results from Ref.~\onlinecite{PetTouUmr-JCP-12}.} -\end{table*} - - %