\documentclass[aip,jcp,reprint,noshowkeys]{revtex4-1}
\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable}

\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}}}

\usepackage{hyperref}
\hypersetup{
    colorlinks=true,
    linkcolor=blue,
    filecolor=blue,      
    urlcolor=blue,
    citecolor=blue
}
\newcommand{\cdash}{\multicolumn{1}{c}{---}}
\newcommand{\mc}{\multicolumn}
\newcommand{\fnm}{\footnotemark}
\newcommand{\fnt}{\footnotetext}
\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
\newcommand{\mr}{\multirow}
\newcommand{\SI}{\textcolor{blue}{supporting information}}

\newcommand{\br}{\mathbf{r}}
	
% energies
\newcommand{\EHF}{E_\text{HF}}
\newcommand{\Ec}{E_\text{c}}
\newcommand{\EPT}{E_\text{PT2}}
\newcommand{\EFCI}{E_\text{FCI}}
\newcommand{\EsCI}{E_\text{sCI}}
\newcommand{\EDMC}{E_\text{DMC}}
\newcommand{\EexFCI}{E_\text{exFCI}}
\newcommand{\EexDMC}{E_\text{exDMC}}
\newcommand{\Ead}{\Delta E_\text{ad}}

\newcommand{\ex}[4]{$^{#1}#2_{#3}^{#4}$}
\newcommand{\ra}{\rightarrow}

% units
\newcommand{\IneV}[1]{#1 eV}
\newcommand{\InAU}[1]{#1 a.u.}
\newcommand{\InAA}[1]{#1 \AA}

\newcommand{\pis}{\pi^\star}
\newcommand{\si}{\sigma}
\newcommand{\sis}{\sigma^\star}



\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}

\begin{document}	

\title{G2 Atomization Energies With Chemical Accuracy}

\author{Bath\'elemy Pradines}
\affiliation{\LCPQ}
\author{Anthony Scemama}
\affiliation{\LCPQ}
\author{Julien Toulouse}
\affiliation{\LCT}
\author{Pierre-Fran\c{c}ois Loos}
\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr}
\affiliation{\LCPQ}
\author{Emmanuel Giner}
\affiliation{\LCT}

\begin{abstract}
\end{abstract}

\maketitle

%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%
\section{Theory}
%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The DFT basis-set correction in a nutshell}
The basis-set correction investigated here proposes to use the RSDFT formalism to capture a part of the short-range correlation effects missing in a finite one-electron basis-set.  
In a nutshell, this formalism relies on 1) the definition of a complementary density functional aiming at describing the correlation effects absent in a finite basis-set, 2) the definition of an \textit{effective non divergent interaction} as the real-space representation of the coulomb operator projected in a finite basis-set, 
3) the fit of such an effective interaction with a long-range interaction through the definition of a \textit{range-separation parameter varying in space}, 4) the use of a correlation functional from RSDFT with a \textit{multi-determinant} reference evaluated with the range-separation parameter varying in space.  
More details can be found in \cite{GinPraFerAssSavTou-JCP-18}. 

\subsubsection{Definition of basis-set dependent complementary functional}
The 

%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results}
%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{The case of C$_2$ and the comparison with the F$_{12}$ methods.}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table*}
\caption{Dissociation energy ($D_e$) in kcal/mol of the C$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F$_{12}$, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets.}
\begin{ruledtabular}
\begin{tabular}{lccccccc}
%\hline
                & FCIQMC    & CIPSI             & FCIQMC+F$_{12}$     & CIPSI+LDA$_{\text{HF}}$  & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$  & CIPSI+PBE${_\text{HF-val}}$     \\
\hline                                                                                                                                                          
V2Z             & 130.0     &  132.0            & 142.3               &  141.9                   & 142.9                       &  142.7                   & 145.6                          \\
V3Z             & 139.9     &  140.3            & 145.3               &  142.8                   & 145.5                       &  142.7                   & 146.7                          \\
V4Z             &   -       &  143.6            & -                   &  145.8                   & 146.2                       &  145.3                   & 147.0                          \\
V5Z             &   -       &  144.3            & -                   &  145.1                   & 146.1                       &  144.9                   & 146.5                          \\
%\hline
 & \multicolumn{5}{c}{Estimated exact} \\
 & \multicolumn{5}{c}{ 146.9} \\
\end{tabular}
\end{ruledtabular}
\label{conv_He_table}
\end{table*}
%
\bibliography{G2-srDFT}

\end{document}