221 lines
7.2 KiB
TeX
221 lines
7.2 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{Excitation Energies Near The Complete Basis Set Limit}
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\author{Emmanuel Giner}
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\affiliation{\LCT}
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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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\begin{abstract}
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By combining extrapolated selected configuration interaction (sCI) calculations performed with the CIPSI algorithm with the recently proposed short-range density-functional functional correction for basis set incompleteness [\href{https://doi.org/10.1063/1.5052714}{Giner et al., J.~Chem.~Phys.~149, 194301 (2018)}], we show that one can obtain vertical and adiabatic excitation energies with chemical accuracy with a small basis set.
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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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\label{sec:intro}
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%%%%%%%%%%%%%%%%%%%%%%%%
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One of the most fundamental problem of conventional electronic structure methods is their slow energy convergence with respect to the size of the one-electron basis set.
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This problem was already noticed thirty years ago by Kutzelnigg \cite{Kutzelnigg_1985} who proposed to introduce explicitly the correlation between electrons via the introduction of the interelectronic distance $r_{12} = \abs{\br_1 - \br_2}$ as a basis function. \cite{Kutzelnigg_1991, Termath_1991, Klopper_1991a, Klopper_1991b, Noga_1994}
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This yields a prominent improvement of the energy convergence from $O(L^{-3})$ to $O(L^{-7})$ (where $L$ is the maximum angular momentum of the one-electron basis).
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This idea was later generalised to more accurate correlation factors $f_{12} \equiv f(r_{12})$. \cite{Persson_1996, Persson_1997, May_2004, Tenno_2004b, Tew_2005, May_2005}
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The resulting F12 methods achieve chemical accuracy for small organic molecules with relatively small Gaussian basis sets. \cite{Tenno_2012a, Tenno_2012b, Hattig_2012, Kong_2012}
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For example, as illustrated by Tew and coworkers, one can obtain, at the CCSD(T) level, quintuple-zeta quality correlation energies with a triple-zeta basis. \cite{Tew_2007b}
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In the present study, we rely on the recently proposed short-range density-functional functional correction for basis set incompleteness. \cite{Giner_2018}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Computational details}
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\label{sec:compdetails}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Results}
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\label{sec:res}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%=======================
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\subsection{Water}
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\label{sec:H2O}
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%=======================
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%=======================
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\subsection{Formaldehyde}
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\label{sec:CH2O}
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%=======================
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%=======================
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\subsection{Methylene}
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\label{sec:CH2}
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%=======================
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%%% TABLE 1 %%%
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\begin{squeezetable}
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\begin{table*}
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\caption{
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Total energies $E$ (in hartree) and adiabatic transition energies $\Ead$ (in eV) of excited states of methylene for various methods and basis sets.}
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\begin{ruledtabular}{}
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\begin{tabular}{llddddddd}
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& & \mc{1}{c}{$1\,^{3}B_1$}
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& \mc{2}{c}{$1\,^{3}B_1 \ra 1\,^{1}A_1$}
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& \mc{2}{c}{$1\,^{3}B_1 \ra 1\,^{1}B_1$}
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& \mc{2}{c}{$1\,^{3}B_1 \ra 2\,^{1}A_1$} \\
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\cline{3-3} \cline{4-5}
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\cline{6-7} \cline{8-9}
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Method & Basis set & \tabc{$E$ (a.u.)}
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& \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)}
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& \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)}
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& \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)} \\
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\hline
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exFCI & AVDZ & -39.04846(1)
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& -39.03225(1) & 0.441
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& -38.99203(1) & 1.536
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& -38.95076(1) & 2.659 \\
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& AVTZ & -39.08064(3)
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& -39.06565(2) & 0.408
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& -39.02833(1) & 1.423
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& -38.98709(1) & 2.546 \\
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& AVQZ & -39.08854(1)
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& -39.07402(2) & 0.395
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& -39.03711(1) & 1.399
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& -38.99607(1) & 2.516 \\
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& AV5Z & -39.09079(1)
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& -39.07647(1) & 0.390
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& -39.03964(3) & 1.392
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& -38.99867(1) & 2.507 \\
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exFCI+srLDA & AVDZ &
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& & 0.347
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& & 1.431
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& & 2.590 \\
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& AVTZ &
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& & 0.360
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& & 1.377
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& & 2.513 \\
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& AVQZ &
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& & 0.371
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& & 1.376
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& & 2.498 \\
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exFCI+srPBE & AVDZ &
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& & 0.358
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& & 1.420
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& & 2.529 \\
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& AVTZ &
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& & 0.373
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& & 1.383
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& & 2.496 \\
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& AVQZ &
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& & 0.380
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& & 1.381
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& & 2.492 \\
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HBCI & AVQZ & -39.08849(1)
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& -39.07404(1) & 0.393
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& -39.03711(1) & 1.398
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& -38.99603(1) & 2.516 \\
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CR-EOMCC (2,3)D& AVQZ & -39.08817
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& -39.07303 & 0.412
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& -39.03450 & 1.460
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& -38.99457 & 2.547 \\
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FCI & TZ2P & -39.066738
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& -39.048984 & 0.483
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& -39.010059 & 1.542
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& -38.968471 & 2.674 \\
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DMC & &
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& & 0.406
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& & 1.416
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& & 2.524 \\
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Exp. & &
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& & 0.400
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& & 1.411
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\end{tabular}
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\end{ruledtabular}
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\end{table*}
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\end{squeezetable}
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%%% %%% %%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Conclusion}
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\label{sec:ccl}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{Supporting Information}
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See {\SI} for geometries and additional information (including total energies).
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%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{acknowledgements}
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This work was performed using HPC resources from
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i) GENCI-TGCC (Grant No. 2018-A0040801738),
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ii) CALMIP (Toulouse) under allocations 2018-0510 and 2018-12158.
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\end{acknowledgements}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\bibliography{Ex-srDFT}
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\end{document}
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