\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} % 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{Excitation Energies Near The Complete Basis Set Limit} \author{Emmanuel Giner} \affiliation{\LCT} \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} \begin{abstract} 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. \end{abstract} \maketitle %%%%%%%%%%%%%%%%%%%%%%%% \section{Introduction} \label{sec:intro} %%%%%%%%%%%%%%%%%%%%%%%% 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. 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} 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). 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} 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} 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} In the present study, we rely on the recently proposed short-range density-functional functional correction for basis set incompleteness. \cite{Giner_2018} %%%%%%%%%%%%%%%%%%%%%%%% \section{Computational details} \label{sec:compdetails} %%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% \section{Results} \label{sec:res} %%%%%%%%%%%%%%%%%%%%%%%% %======================= \subsection{Water} \label{sec:H2O} %======================= %======================= \subsection{Formaldehyde} \label{sec:CH2O} %======================= %======================= \subsection{Methylene} \label{sec:CH2} %======================= %%% TABLE 1 %%% \begin{squeezetable} \begin{table*} \caption{ Total energies $E$ (in hartree) and adiabatic transition energies $\Ead$ (in eV) of excited states of methylene for various methods and basis sets.} \begin{ruledtabular}{} \begin{tabular}{llddddddd} & & \mc{1}{c}{$1\,^{3}B_1$} & \mc{2}{c}{$1\,^{3}B_1 \ra 1\,^{1}A_1$} & \mc{2}{c}{$1\,^{3}B_1 \ra 1\,^{1}B_1$} & \mc{2}{c}{$1\,^{3}B_1 \ra 2\,^{1}A_1$} \\ \cline{3-3} \cline{4-5} \cline{6-7} \cline{8-9} Method & Basis set & \tabc{$E$ (a.u.)} & \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)} & \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)} & \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)} \\ \hline exFCI & AVDZ & -39.04846(1) & -39.03225(1) & 0.441 & -38.99203(1) & 1.536 & -38.95076(1) & 2.659 \\ & AVTZ & -39.08064(3) & -39.06565(2) & 0.408 & -39.02833(1) & 1.423 & -38.98709(1) & 2.546 \\ & AVQZ & -39.08854(1) & -39.07402(2) & 0.395 & -39.03711(1) & 1.399 & -38.99607(1) & 2.516 \\ & AV5Z & -39.09079(1) & -39.07647(1) & 0.390 & -39.03964(3) & 1.392 & -38.99867(1) & 2.507 \\ exFCI+srLDA & AVDZ & & & 0.347 & & 1.431 & & 2.590 \\ & AVTZ & & & 0.360 & & 1.377 & & 2.513 \\ & AVQZ & & & 0.371 & & 1.376 & & 2.498 \\ exFCI+srPBE & AVDZ & & & 0.358 & & 1.420 & & 2.529 \\ & AVTZ & & & 0.373 & & 1.383 & & 2.496 \\ & AVQZ & & & 0.380 & & 1.381 & & 2.492 \\ HBCI & AVQZ & -39.08849(1) & -39.07404(1) & 0.393 & -39.03711(1) & 1.398 & -38.99603(1) & 2.516 \\ CR-EOMCC (2,3)D& AVQZ & -39.08817 & -39.07303 & 0.412 & -39.03450 & 1.460 & -38.99457 & 2.547 \\ FCI & TZ2P & -39.066738 & -39.048984 & 0.483 & -39.010059 & 1.542 & -38.968471 & 2.674 \\ DMC & & & & 0.406 & & 1.416 & & 2.524 \\ Exp. & & & & 0.400 & & 1.411 \end{tabular} \end{ruledtabular} \end{table*} \end{squeezetable} %%% %%% %%% %%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusion} \label{sec:ccl} %%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% \section*{Supporting Information} %%%%%%%%%%%%%%%%%%%%%%%% See {\SI} for geometries and additional information (including total energies). %%%%%%%%%%%%%%%%%%%%%%%% \begin{acknowledgements} This work was performed using HPC resources from i) GENCI-TGCC (Grant No. 2018-A0040801738), ii) CALMIP (Toulouse) under allocations 2018-0510 and 2018-12158. \end{acknowledgements} %%%%%%%%%%%%%%%%%%%%%%%% \bibliography{Ex-srDFT} \end{document}