\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} \newcommand{\De}{D_\text{e}} % 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 F12 methods.} \begin{table*} \caption{Dissociation energy ($D_e$) in kcal/mol of the F$_2$ 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. $^a$ Results from Ref\cite{PetTouUmr-JCP-12} taking into account the ZPE correction. } \begin{ruledtabular} \begin{tabular}{lccccc} %\hline & CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\ \hline V2Z & 27.5 & 30.8 & 31.1 & 32.1 & 32.4 \\ V3Z & 35.4 & 37.0 & 37.5 & 37.5 & 37.8 \\ V4Z & 37.5 & 38.7 & 38.8 & 38.7 & 38.8 \\ V5Z & 38.0 & 38.7 & 38.8 & 38.7 & 38.8 \\ %\hline & \multicolumn{5}{c}{Estimated exact} \\ & \multicolumn{5}{c}{ 38.2$^a$} \\ \end{tabular} \end{ruledtabular} \label{conv_He_table} \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} & & \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{Exp.} \\ \hline \ce{C2} & FCIQMC & 130.0(1) & 139.9(3) & 143.3(2) & & 146.9(5)\fnm[1] \\ & FCIQMC+F12 & 142.3 & 145.3 & & & \\ \hline & exFCI & 132.0 & 140.3 & 143.6 & 144.3 & \\ \hline & exFCI+LDA & 141.9 & 142.8 & 145.8 & 146.2 & \\ & exFCI+LDA(FC) & 142.9 & 145.5 & 146.2 & 146.1 & \\ \hline & exFCI+PBE & 146.1 & 143.9 & 145.9 & 145.12 & \\ & exFCI+PBE (FC) & 147.7 & 146.3 & 146.4 & 146.0 & \\ \hline & exFCI+PBE-on-top& 142.7 & 142.7 & 145.3 & 144.9 & \\ & exFCI+PBE-on-top(FC) & 143.3 & 144.7 & 145.7 & 145.6 & \\ \\ \ce{N2} & exFCI & 200.9 & 217.1 & 223.5 & 225.7 & 228.5\fnm[2] \\ \hline & exFCI+LDA & 216.3 & 223.1 & 227.9 & 227.9 & \\ & exFCI+LDA(FC) & 218.2 & 225.8 & 228.8 & 228.4 & \\ \hline & exFCI+PBE & 225.3 & 225.6 & 228.2 & 227.9 & \\ & exFCI+PBE (FC) & 228.6 & 228.1 & 228.9 & 228.6 & \\ \hline & exFCI+PBE-on-top& 222.3 & 224.6 & 227.7 & 227.7 & \\ & exFCI+PBE-on-top(FC) & 224.8 & 226.7 & 228.3 & 228.3 & \\ \\ \ce{O2} & exFCI & 105.3 & 114.6 & 118.0 &119.1 & 120.2\fnm[2] \\ \hline & exFCI+LDA & 111.8 & 117.2 & 120.0 &119.9 & \\ & exFCI+LDA(FC) & 112.5 & 118.5 & 120.2 & 120.2 & \\ \hline & exFCI+PBE & 115.9 & 118.4 & 120.1 &119.9 & \\ & exFCI+PBE (FC) & 117.5 & 119.5 & 120.4 &120.3 & \\ \hline & exFCI+PBE-on-top& 115.0 & 118.4 & 120.2 & & \\ & exFCI+PBE-on-top(FC) & 116.1 & 119.4 & 120.5 & & \\ \\ \ce{F2} & exFCI & 27.5 & 35.4 & 37.5 & 38.0 & 38.2\fnm[2] \\ \hline & exFCI+LDA & 30.8 & 37.0 & 38.7 & 38.7 & \\ & exFCI+LDA(FC) & 31.1 & 37.5 & 38.8 & 38.8 & \\ \hline & exFCI+PBE & 33.3 & 37.8 & 38.8 & 38.7 & \\ & exFCI+PBE (FC) & 33.9 & 38.2 & 39.0 & 38.8 & \\ \hline & exFCI+PBE-on-top& 32.1 & 37.5 & 38.7 & 38.7 & \\ & exFCI+PBE-on-top(FC) & 32.4 & 37.8 & 38.8 & 38.8 & \\ \end{tabular} \end{ruledtabular} \fnt[1]{Results from Ref.~\onlinecite{BytLaiRuedenJCP05}.} \fnt[2]{Results from Ref.~\onlinecite{PetTouUmr-JCP-12}.} \end{table*} % \bibliography{G2-srDFT} \end{document}