diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex index fbb5a3a..fc8469e 100644 --- a/Manuscript/G2-srDFT.tex +++ b/Manuscript/G2-srDFT.tex @@ -156,6 +156,7 @@ \newcommand{\IneV}[1]{#1 eV} \newcommand{\InAU}[1]{#1 a.u.} \newcommand{\InAA}[1]{#1 \AA} +\newcommand{\kcal}{kcal.mol$^{-1}$} % methods @@ -659,6 +660,40 @@ Therefore, we propose the following valence-only approximations for the compleme \section{Results} %%%%%%%%%%%%%%%%%%%%%%%% +\begin{table} + \caption{ + Statistical analysis (in \kcal) of the G2 atomization energies depicted in Fig.~\ref{fig:G2_AE}. + Mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX) with respect to the CCSD(T)/CBS reference data. + \label{tab:stats}} + \begin{ruledtabular} + \begin{tabular}{lddd} + Method & \tabc{MAD} & \tabc{RMSD} & \tabc{MAX} \\ + \hline + CCSD(T)/cc-pVDZ & 22.81 & 25.82 & 72.08 \\ + CCSD(T)/cc-pVTZ & 7.95 & 8.99 & 25.99 \\ + CCSD(T)/cc-pVQZ & 3.24 & 3.67 & 11.66 \\ + CCSD(T)/cc-pV5Z & 1.39 & 1.54 & 3.46 \\ + \\ + CCSD(T)+LDA/cc-pVDZ & 11.75 & 13.99 & 54.88 \\ + CCSD(T)+LDA/cc-pVTZ & 3.11 & 3.94 & 16.77 \\ + CCSD(T)+LDA/cc-pVQZ & 0.87 & 1.36 & 6.22 \\ + \\ + CCSD(T)+PBE/cc-pVDZ & 8.68 & 10.92 & 45.81 \\ + CCSD(T)+PBE/cc-pVTZ & 2.66 & 3.52 & 14.73 \\ + CCSD(T)+PBE/cc-pVQZ & 0.88 & 1.36 & 5.96 \\ + \end{tabular} + \end{ruledtabular} +\end{table} + +\begin{figure*} + \includegraphics[width=\linewidth]{VDZ} + \includegraphics[width=\linewidth]{VTZ} + \includegraphics[width=\linewidth]{VQZ} + \caption{ + Deviation (in \kcal) from CCSD(T)/CBS reference atomization energies obtained with various methods with the cc-pVDZ (top), cc-pVTZ (center) and cc-pVQZ (bottom) basis sets. + \label{fig:G2_AE}} +\end{figure*} + \subsection{Comparison between the CIPSI and CCSD(T) models in the case of C$_2$, N$_2$, O$_2$, F$_2$} 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$_2$ and F$_2$ homo-nuclear diatomic molecules in the Dunning cc-pVXZ and cc-pCVXZ in the case of N$_2$ (X=D,T,Q,5) using both the CIPSI algorithm and the CCSD(T). N$_2$, O$_2$ and F$_2$ belong to the G2 set and can be considered as weakly correlated, whereas C$_2$ contains already a non negligible non dynamic correlation component. @@ -678,36 +713,23 @@ Also, the values obtained with the largest basis sets tends to converge toward a \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. + Dissociation energy ($\De$) in {\kcal} of the \ce{C2}, \ce{O2}, \ce{N2} and \ce{F2} molecules computed with various methods and basis sets. + The deviation with respect to the CBS values are reported in square brackets. } \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{$D_e^{Q5Z}$} + Molecule & Method & \tabc{X=D} & \tabc{X=T} & \tabc{X=Q} & \tabc{X=5} & \tabc{CBS} \\ - \\ - %\hline - %\ce{C2} & (FC)FCIQMC & 130.0(1) & 139.9(3) & 143.3(2) & & 144.9 \\ - % & (FC)FCIQMC+F12 & 142.3 & 145.3 & & & \\ \hline - \ce{C2} & ex (FC)FCI & 132.0 & 140.3 & 143.6 & 144.7 & 145.7 \\ - \hline - & ex (FC)FCI+LDA-val & 141.3 & 145.1 & 146.4 & 146.3 & \\ - & ex (FC)FCI+PBE-val & 145.7 & 145.7 & 146.3 & 146.2 & \\ - \hline - \hline - & (FC)CCSD(T) & 129.2 & 139.1 & 143.0 & 144.2 & 145.4 \\ - \hline - & (FC)CCSD(T)+LDA-val & 139.1 & 143.7 & 145.9 & 145.9 & \\ - & (FC)CCSD(T)+PBE-val & 142.8 & 144.2 & 145.9 & 145.8 & \\ - \hline - \\ - \cline{3-6} - & & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{ $D_e^{C(Q5)Z}$ } - \\ + \ce{C2} & exFCI\fnm[1] & 132.0 & 140.3 & 143.6 & 144.7 & 145.7 \\ + (cc-pVXZ) & exFCI+LDA\fnm[1] & 141.3 & 145.1 & 146.4 & 146.3 & \\ + & exFCI+PBE\fnm[1] & 145.7 & 145.7 & 146.3 & 146.2 & \\ + & CCSD(T)\fnm[1] & 129.2 & 139.1 & 143.0 & 144.2 & 145.4 \\ + & CCSD(T)+LDA\fnm[1] & 139.1 & 143.7 & 145.9 & 145.9 & \\ + & CCSD(T)+PBE\fnm[1] & 142.8 & 144.2 & 145.9 & 145.8 & \\ \\ % \hline %%%%%%%% & ex (FC)FC-FCI & 130.5 & 140.5 & 143.8 & 144.9 & 147.1 \\ @@ -718,45 +740,25 @@ Also, the values obtained with the largest basis sets tends to converge toward a %%%%%%%% & 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 & \\ - \hline - & ex FCI & 131.0 & 141.5 & 145.1 & 146.1 & 147.1 \\ - \hline - & ex FCI+LDA & 141.4 & 146.7 & 147.8 & 147.6 & \\ + \ce{C2} & exFCI\fnm[2] & 131.0 & 141.5 & 145.1 & 146.1 & 147.1 \\ + (cc-pCVXZ) & exFCI+LDA\fnm[2] & 141.4 & 146.7 & 147.8 & 147.6 & \\ %%%%%%%% & ex FCI+LDA-val & 141.8 & 146.6 & 147.7 & 147.6 & \\ - \hline - & ex FCI+PBE & 145.1 & 147.0 & 147.7 & 147.5 & \\ + & exFCI+PBE\fnm[2] & 145.1 & 147.0 & 147.7 & 147.5 & \\ %%%%%%%% & ex FCI+PBE-val & 145.7 & 147.0 & 147.6 & 147.5 & \\ \\ - \\ - & & \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{$D_e^{Q5Z}$} - \\ - \\ - \ce{N2} & ex (FC)FCI & 201.1 & 217.1 & 223.5 & 225.7 & 227.8 \\ - \hline - & ex (FC)FCI+LDA-val & 217.9 & 225.9 & 228.0 & 228.6 & \\ - & ex (FC)FCI+PBE-val & 227.7 & 227.8 & 228.3 & 228.5 & \\ + \ce{N2} & exFCI\fnm[1] & 201.1 & 217.1 & 223.5 & 225.7 & 227.8 \\ + (cc-pVXZ) & exFCI+LDA\fnm[1] & 217.9 & 225.9 & 228.0 & 228.6 & \\ + & exFCI+PBE\fnm[1] & 227.7 & 227.8 & 228.3 & 228.5 & \\ % & exFCI+PBE-on-top-val & 224.8 & 226.7 & 228.3 & 228.3 & \\ - \hline - \hline - & (FC)CCSD(T) & 199.9 & 216.3 & 222.8 & 225.0 & 227.2 \\ - \hline + & CCSD(T)\fnm[1] & 199.9 & 216.3 & 222.8 & 225.0 & 227.2 \\ %%%%%%%%& ex (FC)CCSD(T)+LDA & 214.7 & 221.9 & ----- & ----- & \\ %%%%%%%%& ex (FC)CCSD(T)+PBE & 223.4 & 224.3 & ----- & ----- & \\ - & (FC)CCSD(T)+LDA-val & 216.3 & 224.8 & 227.2 & 227.8 & \\ - & (FC)CCSD(T)+PBE-val & 225.9 & 226.7 & 227.5 & 227.8 & \\ - \hline + & CCSD(T)+LDA\fnm[1] & 216.3 & 224.8 & 227.2 & 227.8 & \\ + & CCSD(T)+PBE\fnm[1] & 225.9 & 226.7 & 227.5 & 227.8 & \\ + \\ %%%%%%%%& ex (FC)FCI+LDA & 216.4 & 223.1 & 227.9 & 228.1 & \\ %%%%%%%%& ex (FC)FCI+PBE & 225.4 & 225.6 & 228.2 & 227.9 & \\ %%%%%%%% & exFCI+PBE-on-top& 222.3 & 224.6 & 227.7 & 227.7 & \\ - \\ - \\ - \cline{3-6} - & & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{$D_e^{Q5Z}$} - \\ - \\ %%%%%%%% & ex (FC)FCI & 201.7 & 217.9 & 223.7 & 225.7 & 228.8 \\ %%%%%%%%\hline %%%%%%%% & ex (FC)FCI+LDA & 217.5 & 226.2 & 228.4 & 228.5 & \\ @@ -764,70 +766,41 @@ Also, the values obtained with the largest basis sets tends to converge toward a %%%%%%%%\hline %%%%%%%% & ex (FC)FCI+PBE & 225.8 & 227.6 & 228.4 & 228.3 & \\ %%%%%%%% & ex (FC)FCI+PBE-val & 227.5 & 227.7 & 228.4 & 228.0 & \\ - \hline - & ex FCI & 202.2 & 218.5 & 224.4 & 226.6 & 228.8 \\ - \hline - & ex FCI+LDA & 218.0 & 226.8 & 229.1 & 229.4 & \\ - %%%%%%%% & ex FCI+LDA-val & 219.1 & 226.9 & 229.0 & 228.9 & \\ - \hline - & ex FCI+PBE & 226.4 & 228.2 & 229.1 & 229.2 & \\ - %%%%%%%% & ex FCI+PBE-val & 228.0 & 228.2 & 229.1 & 228.9 & \\ + \ce{N2} & exFCI\fnm[2] & 202.2 & 218.5 & 224.4 & 226.6 & 228.8 \\ + (cc-pCVXZ) & exFCI+LDA\fnm[2] & 218.0 & 226.8 & 229.1 & 229.4 & \\ + %%%%%%%% & ex FCI+LDA-val & 219.1 & 226.9 & 229.0 & 228.9 & \\ + & exFCI+PBE\fnm[2] & 226.4 & 228.2 & 229.1 & 229.2 & \\ + %%%%%%%% & ex FCI+PBE-val & 228.0 & 228.2 & 229.1 & 228.9 & \\ \\ - \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{$D_e^{Q5Z}$} - \\ - \ce{O2} & exFCI & 105.2 & 114.5 & 118.0 &119.1 & 120.0 \\ - \hline + \ce{O2} & exFCI\fnm[1] & 105.2 & 114.5 & 118.0 &119.1 & 120.0 \\ %%%%%%%% & exFCI+LDA & 111.8 & 117.2 & 120.0 &119.9 & \\ - & exFCI+LDA-val & 112.4 & 118.4 & 120.2 &120.4 & \\ + (cc-pVXZ) & exFCI+LDA\fnm[1] & 112.4 & 118.4 & 120.2 &120.4 & \\ %%%%%%%%\hline %%%%%%%% & exFCI+PBE & 115.9 & 118.4 & 120.1 &119.9 & \\ - & exFCI+PBE-val & 117.2 & 119.4 & 120.3 &120.4 & \\ - \hline - \hline - & (FC)CCSD(T) & 103.9 & 113.6 & 117.1 & 118.6 & 120.0 \\ - & (FC)CCSD(T)+LDA-val & 110.6 & 117.2 & 119.2 & 119.8 & \\ - & (FC)CCSD(T)+PBE-val & 115.1 & 118.0 & 119.3 & 119.8 & \\ - \hline + & exFCI+PBE\fnm[1] & 117.2 & 119.4 & 120.3 &120.4 & \\ + & CCSD(T)\fnm[1] & 103.9 & 113.6 & 117.1 & 118.6 & 120.0 \\ + & CCSD(T)+LDA\fnm[1] & 110.6 & 117.2 & 119.2 & 119.8 & \\ + & CCSD(T)+PBE\fnm[1] & 115.1 & 118.0 & 119.3 & 119.8 & \\ %%%%%%%% & exFCI+PBE-on-top & 115.0 & 118.4 & 120.2 & & \\ %%%%%%%% & exFCI+PBE-on-top-val & 116.1 & 119.4 & 120.5 & & \\ \\ - Molecule & Method & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z} & \tabc{$D_e^{Q5Z}$} - \\ - \ce{F2} & exFCI & 26.7 & 35.1 & 37.1 & 38.0 & 39.0 \\ - \hline + \ce{F2} & exFCI\fnm[1] & 26.7 & 35.1 & 37.1 & 38.0 & 39.0 \\ %%%%%%%% & exFCI+LDA & 30.8 & 37.0 & 38.7 & 38.7 & \\ - & exFCI+LDA-val & 30.4 & 37.2 & 38.4 & 38.9 & \\ + (cc-pVXZ) & exFCI+LDA\fnm[1] & 30.4 & 37.2 & 38.4 & 38.9 & \\ %%%%%%%% \hline %%%%%%%% & exFCI+PBE & 33.3 & 37.8 & 38.8 & 38.7 & \\ - & exFCI+PBE -val & 33.1 & 37.9 & 38.5 & 38.9 & \\ + & exFCI+PBE\fnm[1] & 33.1 & 37.9 & 38.5 & 38.9 & \\ %%%%%%%% & exFCI+PBE-on-top& 32.1 & 37.5 & 38.7 & 38.7 & \\ %%%%%%%% & exFCI+PBE-on-top-val & 32.4 & 37.8 & 38.8 & 38.8 & \\ - \hline - \hline - & (FC)CCSD(T) & 25.7 & 34.4 & 36.5 & 37.4 & 38.2 \\ - & (FC)CCSD(T)+LDA-val & 29.2 & 36.5 & 37.2 & 38.2 & \\ - & (FC)CCSD(T)+PBE-val & 31.5 & 37.1 & 37.8 & 38.2 & \\ + & CCSD(T)\fnm[1] & 25.7 & 34.4 & 36.5 & 37.4 & 38.2 \\ + & CCSD(T)+LDA\fnm[1] & 29.2 & 36.5 & 37.2 & 38.2 & \\ + & CCSD(T)+PBE\fnm[1] & 31.5 & 37.1 & 37.8 & 38.2 & \\ \end{tabular} \end{ruledtabular} - \fnt[1]{Results from Ref.~\onlinecite{BytLaiRuedenJCP05}.} - \fnt[2]{Results from Ref.~\onlinecite{PetTouUmr-JCP-12}.} + \fnt[1]{Fronzen core calculations. Only valence spinorbitals are taken into account in the basis set correction.} + \fnt[2]{``Full'' calculation, i.e., all electrons are correlated. All spinorbitals are taken into account in the basis set correction.} \end{table*} diff --git a/Manuscript/VDZ.pdf b/Manuscript/VDZ.pdf index c0ff876..21cf038 100644 Binary files a/Manuscript/VDZ.pdf and b/Manuscript/VDZ.pdf differ diff --git a/Manuscript/VQZ.pdf b/Manuscript/VQZ.pdf index 4044d35..11de9a1 100644 Binary files a/Manuscript/VQZ.pdf and b/Manuscript/VQZ.pdf differ diff --git a/Manuscript/VTZ.pdf b/Manuscript/VTZ.pdf index 8c3910b..34b670f 100644 Binary files a/Manuscript/VTZ.pdf and b/Manuscript/VTZ.pdf differ