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Manuscript/C2_CVXZ.pdf
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Manuscript/C2_CVXZ.pdf
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Manuscript/C2_VXZ.pdf
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Manuscript/F2_VXZ.pdf
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@ -441,19 +441,20 @@ iii) vanishes in the limit of a complete basis set, hence guaranteeing an unalte
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%% FIGURE 1 %%%
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%%% FIGURE 1 %%%
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\begin{figure*}
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\begin{figure}
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\includegraphics[width=0.33\linewidth]{C2_VXZ}
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\includegraphics[width=0.49\linewidth]{C2_VXZ}
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\hspace{1cm}
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% \hspace{1cm}
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\includegraphics[width=0.33\linewidth]{O2_VXZ}
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\includegraphics[width=0.49\linewidth]{O2_VXZ}
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\\
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\\
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\includegraphics[width=0.33\linewidth]{N2_VXZ}
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\includegraphics[width=0.49\linewidth]{N2_VXZ}
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\hspace{1cm}
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% \hspace{1cm}
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\includegraphics[width=0.33\linewidth]{F2_VXZ}
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\includegraphics[width=0.49\linewidth]{F2_VXZ}
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\caption{
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\caption{
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Deviation (in \kcal) from CBS atomization energies of \ce{C2} (top left), \ce{O2} (top right), \ce{N2} (bottom left) and \ce{F2} (bottom right) obtained with various methods and basis sets.
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Deviation (in \kcal) from CBS atomization energies of \ce{C2} (top left), \ce{O2} (top right), \ce{N2} (bottom left) and \ce{F2} (bottom right) obtained with various methods and basis sets.
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The green region corresponds to chemical accuracy (i.e.~error below 1 {\kcal}).
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See {\SI} for raw data.
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See {\SI} for raw data.
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\label{fig:diatomics}}
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\label{fig:diatomics}}
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\end{figure*}
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\end{figure}
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%%% TABLE II %%%
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%%% TABLE II %%%
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\begin{table}
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\begin{table}
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@ -461,6 +462,7 @@ iii) vanishes in the limit of a complete basis set, hence guaranteeing an unalte
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Statistical analysis (in \kcal) of the G2 correlation energies depicted in Fig.~\ref{fig:G2_Ec}.
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Statistical analysis (in \kcal) of the G2 correlation energies depicted in Fig.~\ref{fig:G2_Ec}.
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Mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX) with respect to the CCSD(T)/CBS reference correlation energies.
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Mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX) with respect to the CCSD(T)/CBS reference correlation energies.
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CA corresponds to the number of correlation energies (out of 55) obtained with chemical accuracy.
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CA corresponds to the number of correlation energies (out of 55) obtained with chemical accuracy.
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See {\SI} for raw data.
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\label{tab:stats}}
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\label{tab:stats}}
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\begin{ruledtabular}
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\begin{ruledtabular}
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\begin{tabular}{ldddd}
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\begin{tabular}{ldddd}
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@ -490,6 +492,7 @@ iii) vanishes in the limit of a complete basis set, hence guaranteeing an unalte
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\caption{
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\caption{
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Deviation (in \kcal) from CCSD(T)/CBS reference correlation energies obtained with various methods with the cc-pVDZ (top), cc-pVTZ (center) and cc-pVQZ (bottom) basis sets.
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Deviation (in \kcal) from CCSD(T)/CBS reference correlation energies obtained with various methods with the cc-pVDZ (top), cc-pVTZ (center) and cc-pVQZ (bottom) basis sets.
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The green region corresponds to chemical accuracy (i.e.~error below 1 {\kcal}).
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The green region corresponds to chemical accuracy (i.e.~error below 1 {\kcal}).
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See {\SI} for raw data.
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\label{fig:G2_Ec}}
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\label{fig:G2_Ec}}
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\end{figure*}
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\end{figure*}
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@ -514,10 +517,12 @@ Frozen core calculations are defined as such: an \ce{He} core is frozen from \ce
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In the context of the basis set correction, the set of spinorbitals $\BasFC$ involved in the definition of the effective interaction refers to the non-frozen spinorbitals.
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In the context of the basis set correction, the set of spinorbitals $\BasFC$ involved in the definition of the effective interaction refers to the non-frozen spinorbitals.
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The FC density-based correction was used consistently when the FC approximation was applied in WFT methods.
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The FC density-based correction was used consistently when the FC approximation was applied in WFT methods.
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In order to estimate the complete basis set (CBS) limit for each model, we employed the two-point extrapolation proposed in Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98} for the correlation energies, and we refer to these as $\CBS$.
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In order to estimate the complete basis set (CBS) limit for each model, we employed the two-point extrapolation proposed in Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98} for the correlation energies, and we refer to these as $\CBS$.
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\titou{What about the HF energies?}
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%\subsection{Convergence of the atomization energies with the WFT models }
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%\subsection{Convergence of the atomization energies with the WFT models }
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As the exFCI calculations were converged with a precision of about 0.1 {\kcal}, we can consider these atomization energies as near-FCI values.
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As the exFCI calculations were converged with a precision of about 0.1 {\kcal}, we can consider these atomization energies as near-FCI values, and they will be our references for \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2}.
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They will be our references for \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2} in a given basis, and the results for these diatomics are reported in Table \ref{tab:diatomics}.
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The results for these diatomics are reported in Fig.~\ref{fig:diatomics}.
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The corresponding numerical data can be found as {\SI}.
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As one can see, the convergence of the exFCI atomization energies is, as expected, slow with respect to the basis set: chemical accuracy (error below 1 {\kcal}) is barely reached for \ce{C2}, \ce{O2} and \ce{F2} even with a cc-pV5Z basis set.
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As one can see, the convergence of the exFCI atomization energies is, as expected, slow with respect to the basis set: chemical accuracy (error below 1 {\kcal}) is barely reached for \ce{C2}, \ce{O2} and \ce{F2} even with a cc-pV5Z basis set.
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Also, the atomization energies are consistently underestimated, reflecting that, in a given basis, the atom is always better described than the molecule due to the larger number of interacting electron pairs in the molecular system.
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Also, the atomization energies are consistently underestimated, reflecting that, in a given basis, the atom is always better described than the molecule due to the larger number of interacting electron pairs in the molecular system.
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A similar trend holds for CCSD(T).
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A similar trend holds for CCSD(T).
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@ -549,7 +554,7 @@ Therefore, similar to F12 methods, \cite{TewKloNeiHat-PCCP-07} we can safely cla
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{Supporting information}
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\section*{Supporting information}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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See {\SI} for raw data associated with the G2-1 correlation energies.
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See {\SI} for raw data associated with the atomization energies of the four diatomics and the G2-1 correlation energies.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{acknowledgements}
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\begin{acknowledgements}
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