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Emmanuel Giner
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@ -52,6 +52,7 @@
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\newcommand{\EsCI}{E_\text{sCI}}
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\newcommand{\EsCI}{E_\text{sCI}}
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\newcommand{\EDMC}{E_\text{DMC}}
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\newcommand{\EDMC}{E_\text{DMC}}
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\newcommand{\EexFCI}{E_\text{exFCI}}
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\newcommand{\EexFCI}{E_\text{exFCI}}
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\newcommand{\EexFCIbasis}{E_\text{exFCI}^{\basis}}
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\newcommand{\EexDMC}{E_\text{exDMC}}
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\newcommand{\EexDMC}{E_\text{exDMC}}
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\newcommand{\Ead}{\Delta E_\text{ad}}
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\newcommand{\Ead}{\Delta E_\text{ad}}
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\newcommand{\efci}[0]{E_{\text{FCI}}^{\basis}}
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\newcommand{\efci}[0]{E_{\text{FCI}}^{\basis}}
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@ -452,7 +453,20 @@ Therefore, we propose the following valence-only approximations for the compleme
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\section{Results}
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\section{Results}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\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 }
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\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 }
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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 $\denfci$.
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\subsubsection{CIPSI calculations }
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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 $\dencipsi$.
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Therefore, from now on, we assume that
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\begin{equation}
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\efci \approx \EexFCIbasis
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\end{equation}
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and that
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\begin{equation}
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\denrfci \approx \dencipsi.
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\end{equation}
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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.
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\subsubsection{Treating the valence electrons}
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\begin{table*}
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\begin{table*}
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\caption{
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\caption{
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@ -462,10 +476,12 @@ Therefore, we propose the following valence-only approximations for the compleme
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\begin{ruledtabular}
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\begin{ruledtabular}
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\begin{tabular}{llddddd}
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\begin{tabular}{llddddd}
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& & \mc{4}{c}{Dunning's basis set}
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& & \mc{4}{c}{Dunning's basis set}
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\\
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\\
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\\
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\cline{3-6}
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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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Molecule & Method & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z} & \tabc{Exp.}
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\\
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\\
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\\
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\hline
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\hline
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\ce{C2} & FCIQMC & 130.0(1) & 139.9(3) & 143.3(2) & & 146.9(5)\fnm[1] \\
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\ce{C2} & FCIQMC & 130.0(1) & 139.9(3) & 143.3(2) & & 146.9(5)\fnm[1] \\
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& FCIQMC+F12 & 142.3 & 145.3 & & & \\
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& FCIQMC+F12 & 142.3 & 145.3 & & & \\
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@ -480,8 +496,37 @@ Therefore, we propose the following valence-only approximations for the compleme
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\hline
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\hline
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& exFCI+PBE-on-top& 142.7 & 142.7 & 145.3 & 144.9 & \\
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& exFCI+PBE-on-top& 142.7 & 142.7 & 145.3 & 144.9 & \\
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& exFCI+PBE-on-top-val & 143.3 & 144.7 & 145.7 & 145.6 & \\
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& exFCI+PBE-on-top-val & 143.3 & 144.7 & 145.7 & 145.6 & \\
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\\
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\cline{3-6}
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& & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{ }
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\\
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\\
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\hline
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& ex (FC)FC-FCI & 130.5 & 140.5 & 143.8 & 144.9 & \\
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\hline
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& ex (FC)FCI+LDA & 140.9 & 145.7 & 146.6 & 146.4 & \\
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& ex (FC)FCI+LDA-val & 141.3 & 145.6 & 146.5 & 146.4 & \\
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\hline
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& ex (FC)FCI+PBE & 144.5 & 145.9 & 146.4 & 146.3 & \\
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& ex (FC)FCI+PBE -val & 145.2 & 145.9 & 146.4 & 146.3 & \\
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& ex FC-FCI & 131.0 & 141.5 & 145.1 & ----- & \\
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\hline
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& ex FCI+LDA & 141.4 & 146.7 & 147.8 & ----- & \\
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& ex FCI+LDA-val & 141.8 & 146.6 & 147.7 & ----- & \\
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\hline
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& ex FCI+PBE & 145.1 & 147.0 & 147.7 & ----- & \\
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& ex FCI+PBE -val & 145.7 & 147.0 & 147.6 & ----- & \\
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\\
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\\
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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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\\
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\\
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\ce{N2} & exFCI & 200.9 & 217.1 & 223.5 & 225.7 & 228.5\fnm[2] \\
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\ce{N2} & exFCI & 200.9 & 217.1 & 223.5 & 225.7 & 228.5\fnm[2] \\
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\\
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\hline
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\hline
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& exFCI+LDA & 216.3 & 223.1 & 227.9 & 227.9 & \\
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& exFCI+LDA & 216.3 & 223.1 & 227.9 & 227.9 & \\
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& exFCI+LDA-val & 217.8 & 225.9 & 228.1 & 228.5 & \\
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& exFCI+LDA-val & 217.8 & 225.9 & 228.1 & 228.5 & \\
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@ -491,6 +536,43 @@ Therefore, we propose the following valence-only approximations for the compleme
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\hline
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\hline
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& exFCI+PBE-on-top& 222.3 & 224.6 & 227.7 & 227.7 & \\
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& exFCI+PBE-on-top& 222.3 & 224.6 & 227.7 & 227.7 & \\
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& exFCI+PBE-on-top-val & 224.8 & 226.7 & 228.3 & 228.3 & \\
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& exFCI+PBE-on-top-val & 224.8 & 226.7 & 228.3 & 228.3 & \\
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\cline{3-6}
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\\
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& & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{ }
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\\
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\\
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& ex (FC)FCI & 201.6 & 217.9 & 223.7 & 226.0 & \\
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\hline
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& ex (FC)FCI+LDA & 217.4 & 226.2 & 228.4 & 228.7 & \\
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& ex (FC)FCI+LDA-val & 218.7 & 226.3 & 228.5 & 228.7 & \\
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\hline
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& ex (FC)FCI+PBE & 225.8 & 227.6 & 228.4 & 228.6 & \\
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& ex (FC)FCI+PBE -val & 228.0 & 227.8 & 228.5 & 228.6 & \\
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& ex FCI & 202.0 & 218.5 & 224.3 & ----- & \\
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\hline
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& ex FCI+LDA & 217.8 & 226.8 & 229.0 & ----- & \\
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& ex FCI+LDA-val & 218.8 & 226.9 & 229.0 & ----- & \\
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\hline
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& ex FCI+PBE & 226.2 & 228.2 & 229.0 & ----- & \\
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& ex FCI+PBE -val & 227.8 & 228.2 & 229.0 & ----- & \\
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\\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Results from Ref.~\onlinecite{BytLaiRuedenJCP05}.}
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\fnt[2]{Results from Ref.~\onlinecite{PetTouUmr-JCP-12}.}
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\end{table*}
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\begin{table*}
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\caption{
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\label{tab:diatomics}
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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.
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}
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\begin{ruledtabular}
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\begin{tabular}{llddddd}
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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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\\
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\ce{O2} & exFCI & 105.3 & 114.6 & 118.0 &119.1 & 120.2\fnm[2] \\
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\ce{O2} & exFCI & 105.3 & 114.6 & 118.0 &119.1 & 120.2\fnm[2] \\
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\hline
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\hline
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@ -521,58 +603,6 @@ Therefore, we propose the following valence-only approximations for the compleme
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\end{table*}
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\end{table*}
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\begin{table*}
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\caption{
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\label{tab:diatomics}
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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.
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}
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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-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{Exp.}
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\\
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\hline
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\ce{C2} & ex (FC)FC-FCI & 130.5 & 140.5 & 143.8 & 144.9 &146.9(5)\fnm \\
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\hline
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& ex (FC)FCI+LDA & 140.9 & 145.7 & 146.6 & 146.4 & \\
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& ex (FC)FCI+LDA-val & 141.3 & 145.6 & 146.5 & 146.4 & \\
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\hline
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& ex (FC)FCI+PBE & 144.5 & 145.9 & 146.4 & 146.3 & \\
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& ex (FC)FCI+PBE -val & 145.2 & 145.9 & 146.4 & 146.3 & \\
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\ce{C2} & ex FC-FCI & 131.0 & 141.5 & 145.1 & ----- & \\
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\hline
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& ex FCI+LDA & 141.4 & 146.7 & 147.8 & ----- & \\
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& ex FCI+LDA-val & 141.8 & 146.6 & 147.7 & ----- & \\
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\hline
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& ex FCI+PBE & 145.1 & 147.0 & 147.7 & ----- & \\
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& ex FCI+PBE -val & 145.7 & 147.0 & 147.6 & ----- & \\
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\\
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\ce{N2} & ex (FC)FCI & 201.6 & 217.9 & 223.7 & 226.0 & 228.5\fnm[2] \\
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\hline
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& ex (FC)FCI+LDA & 217.4 & 226.2 & 228.4 & 228.7 & \\
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& ex (FC)FCI+LDA-val & 218.7 & 226.3 & 228.5 & 228.7 & \\
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\hline
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& ex (FC)FCI+PBE & 225.8 & 227.6 & 228.4 & 228.6 & \\
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& ex (FC)FCI+PBE -val & 228.0 & 227.8 & 228.5 & 228.6 & \\
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\ce{N2} & ex FCI & 202.0 & 218.5 & 224.3 & ----- & 228.5\fnm[2] \\
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\hline
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& ex FCI+LDA & 217.8 & 226.8 & 229.0 & ----- & \\
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& ex FCI+LDA-val & 218.8 & 226.9 & 229.0 & ----- & \\
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\hline
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& ex FCI+PBE & 226.2 & 228.2 & 229.0 & ----- & \\
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& ex FCI+PBE -val & 227.8 & 228.2 & 229.0 & ----- & \\
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\\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Results from Ref.~\onlinecite{BytLaiRuedenJCP05}.}
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\fnt[2]{Results from Ref.~\onlinecite{PetTouUmr-JCP-12}.}
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\end{table*}
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%
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%
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