loos/srDFT_G2
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

new graph

Browse Source
This commit is contained in:
Pierre-Francois Loos 2019-04-13 21:49:32 +02:00
parent 8414bf42de
commit 57157bf151
4 changed files with 183 additions and 89 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
Data/N2_VXZ.dat
View File

@ -1,6 +1,6 @@
exFCI 201.1 217.1 223.5 225.7 227.8 exFCI 201.1 217.1 223.5 225.7 227.8
exFCI+LDA 217.9 225.9 228.0 228.6 227.8 exFCI+LDA 217.9 225.9 228.0 228.6 227.8
exFCI+PBE 227.7 227.8 228.3 228.5 227.8 exFCI+PBE 227.7 227.8 228.3 228.5 227.8
CCSD(T) 199.9 216.3 222.8 225.0 227.8 CCSD(T) 199.9 216.3 222.8 225.0 227.2
CCSD(T)+LDA 216.3 224.8 227.2 227.8 227.8 CCSD(T)+LDA 216.3 224.8 227.2 227.8 227.2
CCSD(T)+PBE 225.9 226.7 227.5 227.8 227.8 CCSD(T)+PBE 225.9 226.7 227.5 227.8 227.2

6
Data/O2_VXZ.dat
View File

@ -1,6 +1,6 @@
exFCI 105.2 114.5 118.0 119.1 120.0 exFCI 105.2 114.5 118.0 119.1 120.0
exFCI+LDA 112.4 118.4 120.2 120.4 120.0 exFCI+LDA 112.4 118.4 120.2 120.4 120.0
exFCI+PBE 117.2 119.4 120.3 120.4 120.0 exFCI+PBE 117.2 119.4 120.3 120.4 120.0
CCSD(T) 103.9 113.6 117.1 118.6 120.0 CCSD(T) 103.9 113.6 117.1 118.6 119.6
CCSD(T)+LDA 110.6 117.2 119.2 119.8 120.0 CCSD(T)+LDA 110.6 117.2 119.2 119.8 119.6
CCSD(T)+PBE 115.1 118.0 119.3 119.8 120.0 CCSD(T)+PBE 115.1 118.0 119.3 119.8 119.6

72
Manuscript/G2-srDFT.tex
View File

@ -440,56 +440,20 @@ iii) vanishes in the limit of a complete basis set, hence guaranteeing an unalte
\section{Results} \section{Results}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
%%% TABLE I %%% %%% FIGURE 1 %%%
\begin{table*} \begin{figure*}
\includegraphics[width=0.33\linewidth]{C2_VXZ}
\hspace{1cm}
\includegraphics[width=0.33\linewidth]{O2_VXZ}
\\
\includegraphics[width=0.33\linewidth]{N2_VXZ}
\hspace{1cm}
\includegraphics[width=0.33\linewidth]{F2_VXZ}
\caption{ \caption{
\label{tab:diatomics} 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.
Dissociation energy ($\De$) in {\kcal} of \ce{C2}, \ce{O2}, \ce{N2} and \ce{F2} computed with various methods and basis sets. See {\SI} for raw data.
The deviations with respect to the corresponding CBS values are reported in parenthesis. \label{fig:diatomics}}
} \end{figure*}
\begin{ruledtabular}
\begin{tabular}{llddddd}
& & \mc{4}{c}{Dunning's basis set}
\\
\cline{3-6}
Molecule & Method & \tabc{$\X = \D$} & \tabc{$\X = \T$} & \tabc{$\X = \Q$} & \tabc{$\X = 5$} & \tabc{CBS}
\\
\hline
\ce{C2} & exFCI\fnm[1] & 132.0 (-13.7 ) & 140.3 (-5.4 ) & 143.6 (-2.1 ) & 144.7 (-1.0 ) & 145.7 \\
(cc-pVXZ) & exFCI+LDA\fnm[1] & 141.3 (-4.4 ) & 145.1 (-0.6 ) & 146.4 (+0.7 ) & 146.3 (+0.6 ) & \\
& exFCI+PBE\fnm[1] & 145.7 (+0.0 ) & 145.7 (+0.0 ) & 146.3 (+0.6 ) & 146.2 (+0.5 ) & \\
& CCSD(T)\fnm[1] & 129.2 (-16.2 ) & 139.1 (-6.3 ) & 143.0 (-2.4 ) & 144.2 (-1.2 ) & 145.4 \\
& CCSD(T)+LDA\fnm[1] & 139.1 (-6.3 ) & 143.7 (-1.7 ) & 145.9 (+0.5 ) & 145.9 (+0.5 ) & \\
& CCSD(T)+PBE\fnm[1] & 142.8 (-2.6 ) & 144.2 (-1.2 ) & 145.9 (+0.5 ) & 145.8 (+0.4 ) & \\ \\
\ce{C2} & exFCI\fnm[2] & 131.0 (-16.1 ) & 141.5 (-5.6 ) & 145.1 (-2.0 ) & 146.1 (-1.0 ) & 147.1 \\
(cc-pCVXZ) & exFCI+LDA\fnm[2] & 141.4 (-5.7 ) & 146.7 (-0.4 ) & 147.8 (+0.7 ) & 147.6 (+0.5 ) & \\
& exFCI+PBE\fnm[2] & 145.1 (-2.0 ) & 147.0 (-0.1 ) & 147.7 (+0.6 ) & 147.5 (+0.4 ) & \\ \\
\ce{N2} & exFCI\fnm[1] & 201.1 (-26.7 ) & 217.1 (-10.7 ) & 223.5 (-4.3 ) & 225.7 (-2.1 ) & 227.8 \\
(cc-pVXZ) & exFCI+LDA\fnm[1] & 217.9 (-9.9 ) & 225.9 (-1.9 ) & 228.0 (+0.2 ) & 228.6 (+0.8 ) & \\
& exFCI+PBE\fnm[1] & 227.7 (-0.1 ) & 227.8 (+0.0 ) & 228.3 (+0.5 ) & 228.5 (+0.7 ) & \\
& CCSD(T)\fnm[1] & 199.9 (-27.3 ) & 216.3 (-10.9 ) & 222.8 (-4.4 ) & 225.0 (-2.2 ) & 227.2 \\
& CCSD(T)+LDA\fnm[1] & 216.3 (-10.9 ) & 224.8 (-2.4 ) & 227.2 (-0.0 ) & 227.8 (+0.6 ) & \\
& CCSD(T)+PBE\fnm[1] & 225.9 (-1.3 ) & 226.7 (-0.5 ) & 227.5 (+0.3 ) & 227.8 (+0.6 ) & \\ \\
\ce{N2} & exFCI\fnm[2] & 202.2 (-26.6 ) & 218.5 (-10.3 ) & 224.4 (-4.4 ) & 226.6 (-2.2 ) & 228.8 \\
(cc-pCVXZ) & exFCI+LDA\fnm[2] & 218.0 (-10.8 ) & 226.8 (-2.0 ) & 229.1 (+0.3 ) & 229.4 (+0.6 ) & \\
& exFCI+PBE\fnm[2] & 226.4 (-2.4 ) & 228.2 (-0.6 ) & 229.1 (+0.3 ) & 229.2 (+0.4 ) & \\ \\
\ce{O2} & exFCI\fnm[1] & 105.2 (-14.8 ) & 114.5 (-5.5 ) & 118.0 (-2.0 ) & 119.1 (-0.9 ) & 120.0 \\
(cc-pVXZ) & exFCI+LDA\fnm[1] & 112.4 (-7.6 ) & 118.4 (-1.6 ) & 120.2 (+0.2 ) & 120.4 (+0.4 ) & \\
& exFCI+PBE\fnm[1] & 117.2 (-2.8 ) & 119.4 (-0.6 ) & 120.3 (+0.3 ) & 120.4 (+0.4 ) & \\
& CCSD(T)\fnm[1] & 103.9 (-16.1 ) & 113.6 (-6.0 ) & 117.1 (-2.5 ) & 118.6 (-1.0 ) & 119.6 \\
& CCSD(T)+LDA\fnm[1] & 110.6 (-9.0 ) & 117.2 (-2.4 ) & 119.2 (-0.4 ) & 119.8 (+0.2 ) & \\
& CCSD(T)+PBE\fnm[1] & 115.1 (-4.5 ) & 118.0 (-1.6 ) & 119.3 (-0.3 ) & 119.8 (+0.2 ) & \\ \\
\ce{F2} & exFCI\fnm[1] & 26.7 (-12.3 ) & 35.1 (-3.9 ) & 37.1 (-1.9 ) & 38.0 (-1.0 ) & 39.0 \\
(cc-pVXZ) & exFCI+LDA\fnm[1] & 30.4 (-8.6 ) & 37.2 (-1.8 ) & 38.4 (-0.6 ) & 38.9 (-0.1 ) & \\
& exFCI+PBE\fnm[1] & 33.1 (-5.9 ) & 37.9 (-1.1 ) & 38.5 (-0.5 ) & 38.9 (-0.1 ) & \\
& CCSD(T)\fnm[1] & 25.7 (-12.5 ) & 34.4 (-3.8 ) & 36.5 (-1.7 ) & 37.4 (-0.8 ) & 38.2 \\
& CCSD(T)+LDA\fnm[1] & 29.2 (-9.0 ) & 36.5 (-1.7 ) & 37.2 (-1.0 ) & 38.2 (+0.0 ) & \\
& CCSD(T)+PBE\fnm[1] & 31.5 (-6.7 ) & 37.1 (-1.1 ) & 37.8 (-0.4 ) & 38.2 (+0.0 ) & \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Frozen 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*}
%%% TABLE II %%% %%% TABLE II %%%
\begin{table} \begin{table}
@ -518,7 +482,7 @@ iii) vanishes in the limit of a complete basis set, hence guaranteeing an unalte
\end{ruledtabular} \end{ruledtabular}
\end{table} \end{table}
%%% FIGURE 1 %%% %%% FIGURE 2 %%%
\begin{figure*} \begin{figure*}
\includegraphics[width=\linewidth]{VDZ} \includegraphics[width=\linewidth]{VDZ}
\includegraphics[width=\linewidth]{VTZ} \includegraphics[width=\linewidth]{VTZ}
@ -532,16 +496,16 @@ iii) vanishes in the limit of a complete basis set, hence guaranteeing an unalte
%\subsection{Comparison between the CIPSI and CCSD(T) models in the case of C$_2$, N$_2$, O$_2$, F$_2$} %\subsection{Comparison between the CIPSI and CCSD(T) models in the case of C$_2$, N$_2$, O$_2$, F$_2$}
We begin our investigation of the performance of the basis set correction by computing the atomization energies of \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2} obtained with Dunning's cc-pVXZ basis sets (X $=$ D, T, Q and 5). We begin our investigation of the performance of the basis set correction by computing the atomization energies of \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2} obtained with Dunning's cc-pVXZ basis sets (X $=$ D, T, Q and 5).
In the case of \ce{C2} and \ce{N2}, we also perform calculations with the cc-pCVXZ family. In the case of \ce{C2} and \ce{N2}, we also perform calculations with the cc-pCVXZ family.
\ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2-1 set, whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11} \ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2-1 set \cite{CurRagTruPop-JCP-91} (see below), whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11}
In a second time, we compute the entire correlation energies of the G2-1 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family of basis sets. In a second time, we compute the entire correlation energies of the G2-1 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family of basis sets.
This molecular set has been exhausively studied in the last 20 years (see, for example, Refs.~\onlinecite{FelPetDix-JCP-08,Gro-JCP-09,FelPet-JCP-09,NemTowNee-JCP-10,FelPetHil-JCP-11,PetTouUmr-JCP-12,FelPet-JCP-13,KesSylKohTewMar-JCP-18}). This molecular set has been exhausively studied in the last 20 years (see, for example, Refs.~\onlinecite{FelPetDix-JCP-08, Gro-JCP-09, FelPet-JCP-09, NemTowNee-JCP-10, FelPetHil-JCP-11, HauKlo-JCP-12, PetTouUmr-JCP-12, FelPet-JCP-13, KesSylKohTewMar-JCP-18}).
%The reference values for the atomization energies are extracted from Ref.~\onlinecite{HauKlo-JCP-12} and corresponds to frozen-core non-relativistic atomization energies obtained at the CCSD(T)(F12)/cc-pVQZ-F12 level of theory corrected for higher-excitation contributions ($E_\text{CCSDT(Q)/cc-pV(D+d)Z} - E_\text{CCSD(T)/cc-pV(D+d)Z})$. %The reference values for the atomization energies are extracted from Ref.~\onlinecite{HauKlo-JCP-12} and corresponds to frozen-core non-relativistic atomization energies obtained at the CCSD(T)(F12)/cc-pVQZ-F12 level of theory corrected for higher-excitation contributions ($E_\text{CCSDT(Q)/cc-pV(D+d)Z} - E_\text{CCSD(T)/cc-pV(D+d)Z})$.
As a method $\modY$ we employ either CCSD(T) or exFCI. As a method $\modY$ we employ either CCSD(T) or exFCI.
Here, exFCI stands for extrapolated FCI energies computed with the CIPSI algorithm. \cite{HurMalRan-JCP-73, GinSceCaf-CJC-13, GinSceCaf-JCP-15} Here, exFCI stands for extrapolated FCI energies computed with the CIPSI algorithm. \cite{HurMalRan-JCP-73, GinSceCaf-CJC-13, GinSceCaf-JCP-15}
We refer the interested reader to Refs.~\onlinecite{HolUmrSha-JCP-17, SceGarCafLoo-JCTC-18, LooSceBloGarCafJac-JCTC-18, SceBenJacCafLoo-JCP-18, LooBogSceCafJAc-JCTC-19} for more details. We refer the interested reader to Refs.~\onlinecite{HolUmrSha-JCP-17, SceGarCafLoo-JCTC-18, LooSceBloGarCafJac-JCTC-18, SceBenJacCafLoo-JCP-18, LooBogSceCafJAc-JCTC-19} for more details.
In the case of the CCSD(T) calculations, we have $\modZ = \HF$ as we use the restricted open-shell HF (ROHF) one-electron density to compute the complementary energy. In the case of the CCSD(T) calculations, we have $\modZ = \HF$ as we use the restricted open-shell HF (ROHF) one-electron density to compute the complementary energy.
\titou{For exFCI, we use the density of a converged variational wave function. For exFCI, the one-electron density is computed from a very large CIPSI expansion containing several million determinants.
For the definition of the interaction, we use a single Slater determinant built in the ROHF basis for the CCSD(T) calculation, and built with the natural orbitals of the converged variational wave function for the exFCI calculations.} %For the definition of the interaction, we use a single Slater determinant built in the ROHF basis for the CCSD(T) calculation, and built with the natural orbitals of the converged variational wave function for the exFCI calculations.
The CCSD(T) calculations have been performed with Gaussian09 with standard threshold values. \cite{g09} The CCSD(T) calculations have been performed with Gaussian09 with standard threshold values. \cite{g09}
RS-DFT and exFCI calculations are performed with {\QP}. \cite{QP2} RS-DFT and exFCI calculations are performed with {\QP}. \cite{QP2}
For the numerical quadrature, we employ the SG-2 grid. \cite{DasHer-JCC-17} For the numerical quadrature, we employ the SG-2 grid. \cite{DasHer-JCC-17}

188
Manuscript/SI/G2_srDFT-SI.tex
View File

@ -1,26 +1,118 @@
\documentclass[aip,jcp,reprint,onecolumn,noshowkeys]{revtex4-1} \documentclass[aip,jcp,reprint,noshowkeys]{revtex4-1}
\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem} \usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable,xspace}
\usepackage{mathpazo,libertine} \usepackage{mathpazo,libertine}
\usepackage[normalem]{ulem}
\newcommand{\alert}[1]{\textcolor{red}{#1}}
\definecolor{darkgreen}{RGB}{0, 180, 0}
\newcommand{\beurk}[1]{\textcolor{darkgreen}{#1}}
\newcommand{\trash}[1]{\textcolor{red}{\sout{#1}}}
\newcommand{\cdash}{\multicolumn{1}{c}{---}} \usepackage{natbib}
\bibliographystyle{achemso}
\AtBeginDocument{\nocite{achemso-control}}
\newcommand{\alert}[1]{\textcolor{red}{#1}}
\definecolor{darkgreen}{HTML}{009900}
\usepackage[normalem]{ulem}
\newcommand{\titou}[1]{\textcolor{red}{#1}}
\newcommand{\juju}[1]{\textcolor{purple}{#1}}
\newcommand{\manu}[1]{\textcolor{darkgreen}{#1}}
\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}}
\newcommand{\trashJT}[1]{\textcolor{purple}{\sout{#1}}}
\newcommand{\trashMG}[1]{\textcolor{darkgreen}{\sout{#1}}}
\newcommand{\MG}[1]{\manu{(\underline{\bf MG}: #1)}}
\newcommand{\JT}[1]{\juju{(\underline{\bf JT}: #1)}}
\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}}
\usepackage{hyperref}
\hypersetup{
colorlinks=true,
linkcolor=blue,
filecolor=blue,
urlcolor=blue,
citecolor=blue
}
\newcommand{\mc}{\multicolumn} \newcommand{\mc}{\multicolumn}
\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
\newcommand{\fnm}{\footnotemark} \newcommand{\fnm}{\footnotemark}
\newcommand{\fnt}{\footnotetext} \newcommand{\fnt}{\footnotetext}
\newcommand{\mr}{\multirow} \newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
\newcommand{\SI}{\textcolor{blue}{supplementary material}} \newcommand{\SI}{\textcolor{blue}{supporting information}}
\newcommand{\kcal}{kcal/mol}
\newcommand{\QP}{\textsc{quantum package}} \newcommand{\QP}{\textsc{quantum package}}
% second quantized operators
\newcommand{\ai}[1]{\hat{a}_{#1}}
\newcommand{\aic}[1]{\hat{a}^{\dagger}_{#1}}
% units
\newcommand{\IneV}[1]{#1 eV}
\newcommand{\InAU}[1]{#1 a.u.}
\newcommand{\InAA}[1]{#1 \AA}
\newcommand{\kcal}{kcal/mol}
% methods
\newcommand{\D}{\text{D}}
\newcommand{\T}{\text{T}}
\newcommand{\Q}{\text{Q}}
\newcommand{\X}{\text{X}}
\newcommand{\UEG}{\text{UEG}}
\newcommand{\HF}{\text{HF}}
\newcommand{\LDA}{\text{LDA}}
\newcommand{\PBE}{\text{PBE}}
\newcommand{\FCI}{\text{FCI}}
\newcommand{\CBS}{\text{CBS}}
\newcommand{\exFCI}{\text{exFCI}}
\newcommand{\CCSDT}{\text{CCSD(T)}}
\newcommand{\lr}{\text{lr}}
\newcommand{\sr}{\text{sr}}
\newcommand{\Ne}{N}
\newcommand{\NeUp}{\Ne^{\uparrow}}
\newcommand{\NeDw}{\Ne^{\downarrow}}
\newcommand{\Nb}{N_{\Bas}}
\newcommand{\Ng}{N_\text{grid}}
\newcommand{\nocca}{n_{\text{occ}^{\alpha}}}
\newcommand{\noccb}{n_{\text{occ}^{\beta}}}
\newcommand{\n}[2]{n_{#1}^{#2}}
\newcommand{\Ec}{E_\text{c}}
\newcommand{\E}[2]{E_{#1}^{#2}}
\newcommand{\bE}[2]{\Bar{E}_{#1}^{#2}}
\newcommand{\bEc}[1]{\Bar{E}_\text{c}^{#1}}
\newcommand{\e}[2]{\varepsilon_{#1}^{#2}}
\newcommand{\be}[2]{\Bar{\varepsilon}_{#1}^{#2}}
\newcommand{\bec}[1]{\Bar{e}^{#1}}
\newcommand{\wf}[2]{\Psi_{#1}^{#2}}
\newcommand{\W}[2]{W_{#1}^{#2}}
\newcommand{\w}[2]{w_{#1}^{#2}}
\newcommand{\hn}[2]{\Hat{n}_{#1}^{#2}}
\newcommand{\rsmu}[2]{\mu_{#1}^{#2}}
\newcommand{\V}[2]{V_{#1}^{#2}}
\newcommand{\SO}[2]{\phi_{#1}(\br{#2})}
\newcommand{\modY}{Y}
\newcommand{\modZ}{Z}
% basis sets
\newcommand{\Bas}{\mathcal{B}}
\newcommand{\BasFC}{\Bar{\mathcal{B}}}
\newcommand{\FC}{\text{FC}}
\newcommand{\occ}{\text{occ}}
\newcommand{\virt}{\text{virt}}
\newcommand{\val}{\text{val}}
\newcommand{\Cor}{\mathcal{C}}
% operators
\newcommand{\hT}{\Hat{T}}
\newcommand{\hWee}[1]{\Hat{W}_\text{ee}^{#1}}
\newcommand{\updw}{\uparrow\downarrow}
\newcommand{\f}[2]{f_{#1}^{#2}}
\newcommand{\Gam}[2]{\Gamma_{#1}^{#2}}
% coordinates
\newcommand{\br}[1]{\mathbf{r}_{#1}}
\newcommand{\dbr}[1]{d\br{#1}}
\newcommand{\ra}{\rightarrow}
\newcommand{\De}{D_\text{e}}
\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} \newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique, Universit\'e Pierre et Marie Curie, Sorbonne Universit\'e, CNRS, Paris, France} \newcommand{\LCT}{Laboratoire de Chimie Th\'eorique, Sorbonne Universit\'e, CNRS, Paris, France}
\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France}
\begin{document} \begin{document}
@ -43,30 +135,68 @@
\maketitle \maketitle
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% TABLE I %%%
%\section{Computational details} \begin{table*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \caption{
%All the geometries have been extracted from Ref.~\onlinecite{HauJanScu-JCP-2009} and have performed at the B3LYP/6-31G(2df,p) level of theory. \label{tab:diatomics}
%The CCSD(T) calculations have been performed with Gaussian09 with standard threshold values. \cite{g09} Atomization energies (in {\kcal}) of \ce{C2}, \ce{O2}, \ce{N2} and \ce{F2} computed with various methods and basis sets.
%Frozen core calculations are defined as such: a \ce{He} core is frozen from \ce{B} to \ce{Mg}, while a \ce{Ne} core is frozen from \ce{Al} to \ce{Xe}. The deviations with respect to the corresponding CBS values are reported in parenthesis.
%RS-DFT calculations are performed with {\QP}. \cite{QP2} }
%For the quadrature grid, we employ ... radial and angular points. \begin{ruledtabular}
%The reference values for the atomization energies are extracted from Ref.~\onlinecite{HauKlo-JCP-12} and corresponds to frozen-core non-relativistic atomization energies obtained at the CCSD(T)(F12)/cc-pVQZ-F12 level of theory corrected for higher-excitation contributions ($E_\text{CCSDT(Q)/cc-pV(D+d)Z} - E_\text{CCSD(T)/cc-pV(D+d)Z})$). \begin{tabular}{llddddd}
& & \mc{4}{c}{Dunning's basis set}
\\
\cline{3-6}
Molecule & Method & \tabc{$\X = \D$} & \tabc{$\X = \T$} & \tabc{$\X = \Q$} & \tabc{$\X = 5$} & \tabc{CBS}
\\
\hline
\ce{C2} & exFCI\fnm[1] & 132.0 (-13.7 ) & 140.3 (-5.4 ) & 143.6 (-2.1 ) & 144.7 (-1.0 ) & 145.7 \\
(cc-pVXZ) & exFCI+LDA\fnm[1] & 141.3 (-4.4 ) & 145.1 (-0.6 ) & 146.4 (+0.7 ) & 146.3 (+0.6 ) & \\
& exFCI+PBE\fnm[1] & 145.7 (+0.0 ) & 145.7 (+0.0 ) & 146.3 (+0.6 ) & 146.2 (+0.5 ) & \\
& CCSD(T)\fnm[1] & 129.2 (-16.2 ) & 139.1 (-6.3 ) & 143.0 (-2.4 ) & 144.2 (-1.2 ) & 145.4 \\
& CCSD(T)+LDA\fnm[1] & 139.1 (-6.3 ) & 143.7 (-1.7 ) & 145.9 (+0.5 ) & 145.9 (+0.5 ) & \\
& CCSD(T)+PBE\fnm[1] & 142.8 (-2.6 ) & 144.2 (-1.2 ) & 145.9 (+0.5 ) & 145.8 (+0.4 ) & \\ \\
\ce{C2} & exFCI\fnm[2] & 131.0 (-16.1 ) & 141.5 (-5.6 ) & 145.1 (-2.0 ) & 146.1 (-1.0 ) & 147.1 \\
(cc-pCVXZ) & exFCI+LDA\fnm[2] & 141.4 (-5.7 ) & 146.7 (-0.4 ) & 147.8 (+0.7 ) & 147.6 (+0.5 ) & \\
& exFCI+PBE\fnm[2] & 145.1 (-2.0 ) & 147.0 (-0.1 ) & 147.7 (+0.6 ) & 147.5 (+0.4 ) & \\ \\
\ce{N2} & exFCI\fnm[1] & 201.1 (-26.7 ) & 217.1 (-10.7 ) & 223.5 (-4.3 ) & 225.7 (-2.1 ) & 227.8 \\
(cc-pVXZ) & exFCI+LDA\fnm[1] & 217.9 (-9.9 ) & 225.9 (-1.9 ) & 228.0 (+0.2 ) & 228.6 (+0.8 ) & \\
& exFCI+PBE\fnm[1] & 227.7 (-0.1 ) & 227.8 (+0.0 ) & 228.3 (+0.5 ) & 228.5 (+0.7 ) & \\
& CCSD(T)\fnm[1] & 199.9 (-27.3 ) & 216.3 (-10.9 ) & 222.8 (-4.4 ) & 225.0 (-2.2 ) & 227.2 \\
& CCSD(T)+LDA\fnm[1] & 216.3 (-10.9 ) & 224.8 (-2.4 ) & 227.2 (-0.0 ) & 227.8 (+0.6 ) & \\
& CCSD(T)+PBE\fnm[1] & 225.9 (-1.3 ) & 226.7 (-0.5 ) & 227.5 (+0.3 ) & 227.8 (+0.6 ) & \\ \\
\ce{N2} & exFCI\fnm[2] & 202.2 (-26.6 ) & 218.5 (-10.3 ) & 224.4 (-4.4 ) & 226.6 (-2.2 ) & 228.8 \\
(cc-pCVXZ) & exFCI+LDA\fnm[2] & 218.0 (-10.8 ) & 226.8 (-2.0 ) & 229.1 (+0.3 ) & 229.4 (+0.6 ) & \\
& exFCI+PBE\fnm[2] & 226.4 (-2.4 ) & 228.2 (-0.6 ) & 229.1 (+0.3 ) & 229.2 (+0.4 ) & \\ \\
\ce{O2} & exFCI\fnm[1] & 105.2 (-14.8 ) & 114.5 (-5.5 ) & 118.0 (-2.0 ) & 119.1 (-0.9 ) & 120.0 \\
(cc-pVXZ) & exFCI+LDA\fnm[1] & 112.4 (-7.6 ) & 118.4 (-1.6 ) & 120.2 (+0.2 ) & 120.4 (+0.4 ) & \\
& exFCI+PBE\fnm[1] & 117.2 (-2.8 ) & 119.4 (-0.6 ) & 120.3 (+0.3 ) & 120.4 (+0.4 ) & \\
& CCSD(T)\fnm[1] & 103.9 (-16.1 ) & 113.6 (-6.0 ) & 117.1 (-2.5 ) & 118.6 (-1.0 ) & 119.6 \\
& CCSD(T)+LDA\fnm[1] & 110.6 (-9.0 ) & 117.2 (-2.4 ) & 119.2 (-0.4 ) & 119.8 (+0.2 ) & \\
& CCSD(T)+PBE\fnm[1] & 115.1 (-4.5 ) & 118.0 (-1.6 ) & 119.3 (-0.3 ) & 119.8 (+0.2 ) & \\ \\
\ce{F2} & exFCI\fnm[1] & 26.7 (-12.3 ) & 35.1 (-3.9 ) & 37.1 (-1.9 ) & 38.0 (-1.0 ) & 39.0 \\
(cc-pVXZ) & exFCI+LDA\fnm[1] & 30.4 (-8.6 ) & 37.2 (-1.8 ) & 38.4 (-0.6 ) & 38.9 (-0.1 ) & \\
& exFCI+PBE\fnm[1] & 33.1 (-5.9 ) & 37.9 (-1.1 ) & 38.5 (-0.5 ) & 38.9 (-0.1 ) & \\
& CCSD(T)\fnm[1] & 25.7 (-12.5 ) & 34.4 (-3.8 ) & 36.5 (-1.7 ) & 37.4 (-0.8 ) & 38.2 \\
& CCSD(T)+LDA\fnm[1] & 29.2 (-9.0 ) & 36.5 (-1.7 ) & 37.2 (-1.0 ) & 38.2 (+0.0 ) & \\
& CCSD(T)+PBE\fnm[1] & 31.5 (-6.7 ) & 37.1 (-1.1 ) & 37.8 (-0.4 ) & 38.2 (+0.0 ) & \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Frozen 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*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Computational details}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{turnpage} \begin{turnpage}
\begin{squeezetable} \begin{squeezetable}
\begin{table} \begin{table}
\caption{ \caption{
\label{tab:AE} \label{tab:AE}
Deviation from the reference CBS atomization energies ($\Delta \text{AE}$) in {\kcal} for various methods.} Deviation from the reference CBS correlation energies (in {\kcal}) for various methods and basis sets.}
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lddddddddddd} \begin{tabular}{lddddddddddd}
& &
& \mc{10}{c}{Deviation from CBS atomization energies} \\ & \mc{10}{c}{Deviation from CBS correlation energies} \\
\cline{3-12} \cline{3-12}
& & \mc{4}{c}{CCSD(T)} & \mc{3}{c}{CCSD(T)+LDA} & \mc{3}{c}{CCSD(T)+PBE} \\ & & \mc{4}{c}{CCSD(T)} & \mc{3}{c}{CCSD(T)+LDA} & \mc{3}{c}{CCSD(T)+PBE} \\
\cline{3-6} \cline{7-9} \cline{10-12} \cline{3-6} \cline{7-9} \cline{10-12}