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Emmanuel Giner 2019-03-25 20:02:28 +01:00
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Manuscript/G2-srDFT.tex
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@ -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*}
%