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srDFT_G2/Manuscript/G2-srDFT.tex
eginer dc2368a6ae updated Manuscript
2019-03-21 17:29:12 +01:00

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\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}
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\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}
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