Merge branch 'master' of https://github.com/pfloos/srDFT
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Emmanuel Giner
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\newcommand{\SI}{\textcolor{blue}{supporting information}}
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\newcommand{\EexFCI}{E_\text{exFCI}}
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\newcommand{\EexDMC}{E_\text{exDMC}}
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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{Prout}
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\title{Excitation Energies Near The Complete Basis Set Limit}
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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{Anthony Scemama}
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%\affiliation{\LCPQ}
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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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\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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\begin{table*}
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\caption{
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Total energies (in hartree) and adiabatic transition energies (in eV) of excited states of methylene for various methods and basis sets.}
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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}{lccdd}
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Method & Basis set & State & \mcc{Total energy (a.u.)} & \mcc{Excitation energy (eV)} \\
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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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CIPSI & AVDZ & $1\,^{3}B_1$ & -39.04846(1) & \\
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& & $1\,^{1}A_1$ & -39.03225(1) & 0.441 \\
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& & $1\,^{1}B_1$ & -38.99203(1) & 1.536 \\
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& & $2\,^{1}A_1$ & -38.95076(1) & 2.659 \\
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CIPSI & AVTZ & $1\,^{3}B_1$ & -39.08064(3) & \\
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& & $1\,^{1}A_1$ & -39.06565(2) & 0.408 \\
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& & $1\,^{1}B_1$ & -39.02833(1) & 1.423 \\
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& & $2\,^{1}A_1$ & -38.98709(1) & 2.546 \\
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CIPSI & AVQZ & $1\,^{3}B_1$ & -39.08854(1) & \\
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& & $1\,^{1}A_1$ & -39.07402(2) & 0.395 \\
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& & $1\,^{1}B_1$ & -39.03711(1) & 1.399 \\
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& & $2\,^{1}A_1$ & -38.99607(1) & 2.516 \\
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CIPSI & AV5Z & $1\,^{3}B_1$ & -39.09079(1) & \\
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& & $1\,^{1}A_1$ & -39.07647(1) & 0.390 \\
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& & $1\,^{1}B_1$ & -39.03964(3) & 1.392 \\
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& & $2\,^{1}A_1$ & -38.99867(1) & 2.507 \\
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CIPSI+srLDA & AVDZ & $1\,^{3}B_1$ & & \\
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& & $1\,^{1}A_1$ & & 0.347 \\
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& & $1\,^{1}B_1$ & & 1.431 \\
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& & $2\,^{1}A_1$ & & 2.590 \\
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CIPSI+srLDA & AVTZ & $1\,^{3}B_1$ & & \\
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& & $1\,^{1}A_1$ & & 0.360 \\
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& & $1\,^{1}B_1$ & & 1.377 \\
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& & $2\,^{1}A_1$ & & 2.513 \\
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CIPSI+srLDA & AVQZ & $1\,^{3}B_1$ & & \\
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& & $1\,^{1}A_1$ & & 0.371 \\
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& & $1\,^{1}B_1$ & & 1.376 \\
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& & $2\,^{1}A_1$ & & 2.498 \\
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CIPSI+srPBE & AVDZ & $1\,^{3}B_1$ & & \\
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& & $1\,^{1}A_1$ & & 0.358 \\
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& & $1\,^{1}B_1$ & & 1.420 \\
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& & $2\,^{1}A_1$ & & 2.529 \\
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CIPSI+srPBE & AVTZ & $1\,^{3}B_1$ & & \\
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& & $1\,^{1}A_1$ & & 0.373 \\
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& & $1\,^{1}B_1$ & & 1.383 \\
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& & $2\,^{1}A_1$ & & 2.496 \\
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CIPSI+srPBE & AVQZ & $1\,^{3}B_1$ & & \\
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& & $1\,^{1}A_1$ & & 0.380 \\
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& & $1\,^{1}B_1$ & & 1.381 \\
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& & $2\,^{1}A_1$ & & 2.492 \\
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SHCI & AVQZ & $1\,^{3}B_1$ & -39.08849(1) & \\
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& & $1\,^{1}A_1$ & -39.07404(1) & 0.393 \\
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& & $1\,^{1}B_1$ & -39.03711(1) & 1.398 \\
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& & $2\,^{1}A_1$ & -38.99603(1) & 2.516 \\
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CR-EOMCC (2,3)D& AVQZ & $1\,^{3}B_1$ & -39.08817 & \\
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& & $1\,^{1}A_1$ & -39.07303 & 0.412 \\
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& & $1\,^{1}B_1$ & -39.03450 & 1.460 \\
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& & $2\,^{1}A_1$ & -38.99457 & 2.547 \\
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FCI & TZ2P & $1\,^{3}B_1$ & -39.066738 & \\
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& & $1\,^{1}A_1$ & -39.048984 & 0.483 \\
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& & $1\,^{1}B_1$ & -39.010059 & 1.542 \\
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& & $2\,^{1}A_1$ & -38.968471 & 2.674 \\
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DMC & & $1\,^{3}B_1$ & & \\
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& & $1\,^{1}A_1$ & & 0.406 \\
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& & $1\,^{1}B_1$ & & 1.416 \\
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& & $2\,^{1}A_1$ & & 2.524 \\
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Exp. & & $1\,^{3}B_1$ & & \\
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& & $1\,^{1}A_1$ & & 0.400 \\
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& & $1\,^{1}B_1$ & & 1.411 \\
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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{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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%%%%%%%%%%%%%%%%%%%%%%%%
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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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