188 lines
9.5 KiB
TeX
188 lines
9.5 KiB
TeX
\documentclass[aip,jcp,reprint,noshowkeys]{revtex4-1}
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable}
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\usepackage{mathpazo,libertine}
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\usepackage[normalem]{ulem}
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\newcommand{\alert}[1]{\textcolor{red}{#1}}
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\definecolor{darkgreen}{RGB}{0, 180, 0}
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\newcommand{\beurk}[1]{\textcolor{darkgreen}{#1}}
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\newcommand{\trash}[1]{\textcolor{red}{\sout{#1}}}
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\usepackage{hyperref}
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\hypersetup{
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colorlinks=true,
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linkcolor=blue,
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filecolor=blue,
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urlcolor=blue,
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citecolor=blue
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}
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\newcommand{\cdash}{\multicolumn{1}{c}{---}}
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\newcommand{\mc}{\multicolumn}
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\newcommand{\fnm}{\footnotemark}
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\newcommand{\fnt}{\footnotetext}
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\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
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\newcommand{\mr}{\multirow}
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\newcommand{\SI}{\textcolor{blue}{supporting information}}
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\newcommand{\br}{\mathbf{r}}
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% energies
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\newcommand{\EHF}{E_\text{HF}}
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\newcommand{\Ec}{E_\text{c}}
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\newcommand{\EPT}{E_\text{PT2}}
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\newcommand{\EFCI}{E_\text{FCI}}
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\newcommand{\EsCI}{E_\text{sCI}}
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\newcommand{\EDMC}{E_\text{DMC}}
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\newcommand{\EexFCI}{E_\text{exFCI}}
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\newcommand{\EexDMC}{E_\text{exDMC}}
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\newcommand{\Ead}{\Delta E_\text{ad}}
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\newcommand{\ex}[4]{$^{#1}#2_{#3}^{#4}$}
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\newcommand{\ra}{\rightarrow}
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% units
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\newcommand{\IneV}[1]{#1 eV}
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\newcommand{\InAU}[1]{#1 a.u.}
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\newcommand{\InAA}[1]{#1 \AA}
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\newcommand{\pis}{\pi^\star}
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\newcommand{\si}{\sigma}
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\newcommand{\sis}{\sigma^\star}
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\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
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\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique, Universit\'e Pierre et Marie Curie, Sorbonne Universit\'e, CNRS, Paris, France}
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\begin{document}
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\title{G2 Atomization Energies With Chemical Accuracy}
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\author{Bath\'elemy Pradines}
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\affiliation{\LCPQ}
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\author{Anthony Scemama}
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\affiliation{\LCPQ}
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\author{Julien Toulouse}
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\affiliation{\LCT}
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\author{Pierre-Fran\c{c}ois Loos}
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\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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\author{Emmanuel Giner}
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\affiliation{\LCT}
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\begin{abstract}
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\end{abstract}
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\maketitle
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Introduction}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Theory}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{The DFT basis-set correction in a nutshell}
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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.
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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,
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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.
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More details can be found in \cite{GinPraFerAssSavTou-JCP-18}.
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\subsubsection{Definition of basis-set dependent complementary functional}
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The
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Results}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{The case of C$_2$ and the comparison with the F$_{12}$ methods.}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{table*}
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\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. $^a$ Results from Ref\cite{BytLaiRuedenJCP05} }
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\begin{ruledtabular}
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\begin{tabular}{lccccccc}
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%\hline
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& FCIQMC & CIPSI & FCIQMC+F$_{12}$ & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
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\hline
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V2Z & 130.0 & 132.0 & 142.3 & 141.9 & 142.9 & 142.7 & 143.3 \\
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V3Z & 139.9 & 140.3 & 145.3 & 142.8 & 145.5 & 142.7 & 144.7 \\
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V4Z & - & 143.6 & - & 145.8 & 146.2 & 145.3 & 145.7 \\
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V5Z & - & 144.3 & - & 145.1 & 146.1 & 144.9 & 145.6 \\
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%\hline
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& \multicolumn{5}{c}{Estimated exact $^a$} \\
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& \multicolumn{5}{c}{ 146.9} \\
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\end{tabular}
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\end{ruledtabular}
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\label{conv_He_table}
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\end{table*}
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\begin{table*}
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\caption{Dissociation energy ($D_e$) in kcal/mol of the N$_2$ 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. }
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\begin{ruledtabular}
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\begin{tabular}{lccccc}
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%\hline
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& CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
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\hline
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V2Z & 200.9 & 216.3 & 218.2 & 222.3 & 224.8 \\
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V3Z & 217.1 & 223.1 & 225.8 & 224.6 & 226.7 \\
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V4Z & 223.5 & 227.9 & 228.8 & 227.7 & 228.3 \\
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V5Z & 225.7 & 227.9 & 228.4 & 227.7 & 228.3 \\
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%\hline
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& \multicolumn{5}{c}{Estimated exact} \\
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& \multicolumn{5}{c}{228.5$^a$ } \\
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\end{tabular}
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\end{ruledtabular}
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\label{conv_He_table}
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\end{table*}
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\begin{table*}
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\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. }
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\begin{ruledtabular}
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\begin{tabular}{lccccc}
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%\hline
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& CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
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\hline
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V2Z & 27.5 & 30.8 & 31.1 & 32.1 & 32.4 \\
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V3Z & 35.4 & 37.0 & 37.5 & 37.5 & 37.8 \\
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V4Z & 37.5 & 38.7 & 38.8 & 38.7 & 38.8 \\
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V5Z & 38.0 & 38.7 & 38.8 & 38.7 & 38.8 \\
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%\hline
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& \multicolumn{5}{c}{Estimated exact} \\
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& \multicolumn{5}{c}{ 38.2$^a$} \\
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\end{tabular}
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\end{ruledtabular}
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\label{conv_He_table}
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\end{table*}
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\begin{table*}
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\caption{Dissociation energy ($D_e$) in kcal/mol of the O$_2$ 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. }
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\begin{ruledtabular}
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\begin{tabular}{lccccc}
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%\hline
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& CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
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\hline
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V2Z & 105.3 & 111.8 & 112.5 & 115.0 & 116.1 \\
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V3Z & 114.6 & 117.2 & 118.5 & 118.4 & 119.4 \\
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V4Z & 118.0 & 120.0 & 120.2 & 120.2 & 120.5 \\
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V5Z & & & & & \\
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%\hline
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& \multicolumn{5}{c}{Estimated exact} \\
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& \multicolumn{5}{c}{120.2 $^a$} \\
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\end{tabular}
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\end{ruledtabular}
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\label{conv_He_table}
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\end{table*}
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%
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\bibliography{G2-srDFT}
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\end{document}
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