\documentclass[aip,jcp,reprint,onecolumn,noshowkeys]{revtex4-1} \usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable,float} \usepackage{natbib} \bibliographystyle{achemso} \AtBeginDocument{\nocite{achemso-control}} \usepackage{mathpazo,libertine} \usepackage{hyperref} \hypersetup{ colorlinks=true, linkcolor=blue, filecolor=blue, urlcolor=blue, citecolor=blue } \newcommand{\alert}[1]{\textcolor{red}{#1}} \definecolor{darkgreen}{HTML}{009900} \usepackage[normalem]{ulem} \newcommand{\titou}[1]{\textcolor{black}{#1}} \newcommand{\jt}[1]{\textcolor{purple}{#1}} \newcommand{\manu}[1]{\textcolor{darkgreen}{#1}} \newcommand{\toto}[1]{\textcolor{brown}{#1}} \newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}} \newcommand{\trashJT}[1]{\textcolor{purple}{\sout{#1}}} \newcommand{\trashMG}[1]{\textcolor{darkgreen}{\sout{#1}}} \newcommand{\trashAS}[1]{\textcolor{brown}{\sout{#1}}} \newcommand{\MG}[1]{\manu{(\underline{\bf MG}: #1)}} \newcommand{\JT}[1]{\juju{(\underline{\bf JT}: #1)}} \newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}} \newcommand{\AS}[1]{\toto{(\underline{\bf TOTO}: #1)}} \usepackage{hyperref} \hypersetup{ colorlinks=true, linkcolor=blue, filecolor=blue, urlcolor=blue, citecolor=blue } \newcommand{\mc}{\multicolumn} \newcommand{\fnm}{\footnotemark} \newcommand{\fnt}{\footnotetext} \newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} \newcommand{\SI}{\textcolor{blue}{supporting information}} \newcommand{\QP}{\textsc{quantum package}} % second quantized operators \newcommand{\ai}[1]{\hat{a}_{#1}} \newcommand{\aic}[1]{\hat{a}^{\dagger}_{#1}} % units \newcommand{\IneV}[1]{#1 eV} \newcommand{\InAU}[1]{#1 a.u.} \newcommand{\InAA}[1]{#1 \AA} \newcommand{\kcal}{kcal/mol} % methods \newcommand{\D}{\text{D}} \newcommand{\T}{\text{T}} \newcommand{\Q}{\text{Q}} \newcommand{\X}{\text{X}} \newcommand{\UEG}{\text{UEG}} \newcommand{\HF}{\text{HF}} \newcommand{\ROHF}{\text{ROHF}} \newcommand{\LDA}{\text{LDA}} \newcommand{\PBE}{\text{PBE}} \newcommand{\FCI}{\text{FCI}} \newcommand{\CBS}{\text{CBS}} \newcommand{\exFCI}{\text{exFCI}} \newcommand{\CCSDT}{\text{CCSD(T)}} \newcommand{\lr}{\text{lr}} \newcommand{\sr}{\text{sr}} \newcommand{\Ne}{N} \newcommand{\NeUp}{\Ne^{\uparrow}} \newcommand{\NeDw}{\Ne^{\downarrow}} \newcommand{\Nb}{N_{\Bas}} \newcommand{\Ng}{N_\text{grid}} \newcommand{\nocca}{n_{\text{occ}^{\alpha}}} \newcommand{\noccb}{n_{\text{occ}^{\beta}}} \newcommand{\n}[2]{n_{#1}^{#2}} \newcommand{\Ec}{E_\text{c}} \newcommand{\E}[2]{E_{#1}^{#2}} \newcommand{\DE}[2]{\Delta E_{#1}^{#2}} \newcommand{\bE}[2]{\Bar{E}_{#1}^{#2}} \newcommand{\DbE}[2]{\Delta \Bar{E}_{#1}^{#2}} \newcommand{\bEc}[1]{\Bar{E}_\text{c,md}^{#1}} \newcommand{\e}[2]{\varepsilon_{#1}^{#2}} \newcommand{\be}[2]{\Bar{\varepsilon}_{#1}^{#2}} \newcommand{\bec}[1]{\Bar{e}^{#1}} \newcommand{\wf}[2]{\Psi_{#1}^{#2}} \newcommand{\W}[2]{W_{#1}^{#2}} \newcommand{\w}[2]{w_{#1}^{#2}} \newcommand{\hn}[2]{\Hat{n}_{#1}^{#2}} \newcommand{\rsmu}[2]{\mu_{#1}^{#2}} \newcommand{\V}[2]{V_{#1}^{#2}} \newcommand{\SO}[2]{\phi_{#1}(\br{#2})} \newcommand{\tX}{\text{X}} % basis sets \newcommand{\Bas}{\mathcal{B}} \newcommand{\BasFC}{\mathcal{A}} \newcommand{\FC}{\text{FC}} \newcommand{\occ}{\text{occ}} \newcommand{\virt}{\text{virt}} \newcommand{\val}{\text{val}} \newcommand{\Cor}{\mathcal{C}} % operators \newcommand{\hT}{\Hat{T}} \newcommand{\hWee}[1]{\Hat{W}_\text{ee}^{#1}} \newcommand{\updw}{\uparrow\downarrow} \newcommand{\f}[2]{f_{#1}^{#2}} \newcommand{\Gam}[2]{\Gamma_{#1}^{#2}} % coordinates \newcommand{\br}[1]{\mathbf{r}_{#1}} \newcommand{\dbr}[1]{d\br{#1}} \newcommand{\ra}{\rightarrow} % frozen core \newcommand{\WFC}[2]{\widetilde{W}_{#1}^{#2}} \newcommand{\fFC}[2]{\widetilde{f}_{#1}^{#2}} \newcommand{\rsmuFC}[2]{\widetilde{\mu}_{#1}^{#2}} \newcommand{\nFC}[2]{\widetilde{n}_{#1}^{#2}} % energies \newcommand{\EHF}{E_\text{HF}} \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{\Eabs}{\Delta E_\text{abs}} \newcommand{\ex}[4]{$^{#1}#2_{#3}^{#4}$} \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 (UMR 7616), Universit\'e Pierre et Marie Curie, Sorbonne Universit\'e, CNRS, Paris, France} \begin{document} \title{Supporting Information for ``Chemically-Accurate Excitation Energies With Small Basis Sets''} \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} \end{abstract} \maketitle %\tableofcontents %%%%%%%%%%%%%%%%%%%%%%%% \section{Geometries} \label{sec:intro} %%%%%%%%%%%%%%%%%%%%%%%% Below are given the cartesian coordinates of the compounds investigated in this study. These are provided in Angstroms (\AA) and they have been obtained at the CC3(full)/aug-cc-pVTZ level of theory, \cite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19} except for methylene where the FCI/TZVP geometries have been extracted from Ref.~\onlinecite{SheLeiVanSch-JCP-98}. %%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Ammonia} %%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{verbatim} N 0.067759 0.000000 0.000000 H -0.313823 0.468746 -0.811891 H -0.313823 -0.937491 0.000000 H -0.313823 0.468746 0.811891 \end{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Carbon dimer} %%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{verbatim} C 0.000000 0.000000 0.624021 C 0.000000 0.000000 -0.624021 \end{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Carbon monoxyde} %%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{verbatim} C 0.000000 0.000000 -1.249421 0 0.000000 0.000000 0.892667 \end{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Ethylene} %%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{verbatim} C 0.000000 0.666904 0.000000 C 0.000000 -0.666904 0.000000 H 0.000000 1.229522 0.922291 H 0.000000 -1.229522 0.922291 H 0.000000 1.229522 -0.922291 H 0.000000 -1.229522 -0.922291 \end{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Methylene} %%%%%%%%%%%%%%%%%%%%%%%%%%% %============================== \subsubsection{$1\,{}^3 B_1$ state} %============================== \begin{verbatim} C 0.000000 0.000000 0.000000 H 0.000000 0.000000 1.077500 H -0.784304 0.000000 -0.738832 \end{verbatim} %============================== \subsubsection{$1\,{}^1 A_1$ state} %============================== \begin{verbatim} C 0.000000 0.000000 0.000000 H 0.000000 0.000000 1.108900 H -1.085109 0.000000 -0.228470 \end{verbatim} %============================== \subsubsection{$1\,{}^1 B _1$ state} %============================== \begin{verbatim} C 0.000000 0.000000 0.000000 H 0.000000 0.000000 1.074800 H -0.668198 0.000000 -0.841847 \end{verbatim} %============================== \subsubsection{$2\,{}^1A_1$ state} %============================== \begin{verbatim} C 0.000000 0.000000 0.000000 H 0.000000 0.000000 1.067800 H -0.183953 0.000000 -1.051836 \end{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Water} %%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{verbatim} O 0.000000 0.000000 -0.069903 H 0.000000 0.757532 0.518435 H 0.000000 -0.757532 0.518435 \end{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Total energies} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The exFCI total energies can be found in the {\SI} of Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19}. Here, we report the absolute energetic corrections for each state of each molecule obtained with the three short-range correlation functionals considered in the present study (i.e., LDA, PBE and PBEot). %%% TABLE 1 %%% \begin{squeezetable} \begin{table*}[h] \caption{ Total energies (in hartree) of excited states of methylene for various methods and basis sets. The value in parenthesis is an estimate on the last digit of the extrapolation error.} \label{tab:CH2} \begin{ruledtabular} \begin{tabular}{lldddd} & & \mc{4}{c}{States} \\ \cline{3-6} Method & Basis set & \tabc{$1\,^{3}B_1$} & \tabc{$1\,^{1}A_1$} & \tabc{$1\,^{1}B_1$} & \tabc{$2\,^{1}A_1$} \\ \hline exFCI & AVDZ & -39.04846(1) & -39.03225(1) & -38.99203(1) & -38.95076(1) \\ & AVTZ & -39.08064(3) & -39.06565(2) & -39.02833(1) & -38.98709(1) \\ & AVQZ & -39.08854(1) & -39.07402(2) & -39.03711(1) & -38.99607(1) \\ & AV5Z & -39.09079(1) & -39.07647(1) & -39.03964(3) & -38.99867(1) \\ & CBS & -39.09141 & -39.07715 & -39.04034 & -38.99939 \\ \\ exFCI+PBEot & AVDZ & -39.06924(1) & -39.05651(1) & -39.01777(1) & -38.97698(1) \\ & AVTZ & -39.08805(3) & -39.07430(2) & -39.03742(1) & -38.99652(1) \\ & AVQZ & -39.09189(1) & -39.07795(2) & -39.04124(1) & -39.00044(1) \\ \\ exFCI+PBE & AVDZ & -39.07282(1) & -39.06150(1) & -39.02181(1) & -38.97873(1) \\ & AVTZ & -39.08948(3) & -39.07639(2) & -39.03911(1) & -38.99724(1) \\ & AVQZ & -39.09247(1) & -39.07885(2) & -39.04193(1) & -39.00066(1) \\ \\ exFCI+LDA & AVDZ & -39.07450(1) & -39.06213(1) & -39.02233(1) & -38.97946(1) \\ & AVTZ & -39.09099(3) & -39.07779(2) & -39.04051(1) & -38.99859(1) \\ & AVQZ & -39.09319(1) & -39.07959(2) & -39.04267(1) & -39.00135(1) \\ \\ SHCI\fnm[1] & AVQZ & -39.08849(1) & -39.07404(1) & -39.03711(1) & -38.99603(1) \\ CR-EOMCC (2,3)D\fnm[2]& AVQZ& -39.08817 & -39.07303 & -39.03450 & -38.99457 \\ FCI\fnm[3] & TZ2P & -39.066738 & -39.048984 & -39.010059 & -38.968471 \\ \end{tabular} \end{ruledtabular} \fnt[1]{Semistochastic heat-bath CI (SHCI) calculations from Ref.~\onlinecite{ChiHolAdaOttUmrShaZim-JPCA-18}.} \fnt[2]{Completely-renormalized equation-of-motion coupled cluster (CR-EOMCC) calculations from Refs.~\onlinecite{SheLeiVanSch-JCP-98, JenBun-JCP-88}.} \fnt[3]{Reference \onlinecite{SheLeiVanSch-JCP-98}.} \end{table*} \end{squeezetable} %%% %%% %%% %%% %%% TABLE 2 %%% \begin{turnpage} \begin{squeezetable} \begin{table*}[h] \caption{ Basis set energetic corrections (in hartree) on absorption energies for excited states of ammonia, carbon dimer, water and ethylene for various methods and basis sets.} \begin{ruledtabular}{} \begin{tabular}{llddddddddd} & & \mc{9}{c}{Deviation with respect to TBE} \\ \cline{3-11} & & \mc{3}{c}{exFCI+PBEot} & \mc{3}{c}{exFCI+PBE} & \mc{3}{c}{exFCI+LDA} \\ \cline{3-5} \cline{6-8} \cline{9-11} Molecule & State & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ} & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ} & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ} \\ \hline Ammonia & $1\,^{1}A_{1}$ & -0.044\,635 & -0.016\,982 & -0.008\,134 & -0.051\,254 & -0.019\,468 & -0.008\,997 & -0.048\,544 & -0.020\,906 & -0.010\,081 \\ & $1\,^{1}A_{2}$ & -0.039\,461 & -0.014\,997 & -0.007\,039 & -0.047\,284 & -0.018\,061 & -0.008\,251 & -0.044\,515 & -0.019\,266 & -0.009\,218 \\ & $1\,^{1}E$ & -0.039\,392 & -0.014\,949 & -0.007\,017 & -0.047\,456 & -0.018\,077 & -0.008\,245 & -0.044\,860 & -0.019\,344 & -0.009\,222 \\ & $2\,^{1}A_{1}$ & -0.040\,071 & -0.014\,995 & -0.006\,988 & -0.047\,916 & -0.018\,163 & -0.008\,241 & -0.045\,561 & -0.019\,651 & -0.009\,258 \\ & $2\,^{1}A_{2}$ & -0.039\,483 & -0.014\,904 & -0.006\,961 & -0.047\,307 & -0.018\,019 & -0.008\,211 & -0.045\,008 & -0.019\,252 & -0.009\,175 \\ & $1\,^{3}A_{2}$ & -0.038\,969 & -0.014\,725 & -0.006\,828 & -0.047\,144 & -0.018\,010 & -0.008\,221 & -0.044\,361 & -0.019\,216 & -0.009\,181 \\ \\ Carbon dimer & $1\,^{1}\Sigma_g^+$ & -0.037\,716 & -0.014\,339 & -0.006\,758 & -0.050\,128 & -0.019\,217 & -0.008\,918 & -0.049\,570 & -0.021\,425 & -0.010\,307 \\ & $1\,^{1}\Delta_g$ & -0.042\,611 & -0.016\,313 & -0.007\,592 & -0.050\,686 & -0.019\,737 & -0.009\,079 & -0.049\,710 & -0.021\,590 & -0.010\,380 \\ & $2\,^{1}\Sigma_g^+$ & -0.042\,167 & -0.016\,136 & -0.00\,7567 & -0.050\,333 & -0.019\,473 & -0.00\,8978 & -0.049\,208 & -0.021\,292 & -0.01\,0257 \\ \\ Carbon monoxyde & $1\,^{1}\Sigma^+$ & & & & & & & & & \\ & $1\,^{1}\Pi$ & & & & & & & & & \\ \\ Water & $1\,^{1}A_1$ & -0.058\,765 & -0.024\,014 & -0.011\,990 & -0.066\,603 & -0.027\,236 & -0.013\,127 & -0.059\,660 & -0.027\,777 & -0.014\,274 \\ & $1\,^{1}B_1$ & -0.052\,137 & -0.021\,369 & -0.010\,611 & -0.061\,033 & -0.025\,180 & -0.012\,076 & -0.054\,803 & -0.025\,596 & -0.013\,154 \\ & $1\,^{1}A_2$ & -0.052\,102 & -0.021\,325 & -0.010\,591 & -0.061\,406 & -0.025\,263 & -0.012\,114 & -0.055\,215 & -0.025\,776 & -0.013\,270 \\ & $2\,^{1}A_1$ & -0.052\,995 & -0.021\,690 & -0.010\,852 & -0.061\,959 & -0.025\,457 & -0.012\,258 & -0.055\,301 & -0.025\,786 & -0.013\,304 \\ & $1\,^{3}B_1$ & -0.051\,161 & -0.020\,974 & -0.010\,117 & -0.057\,882 & -0.023\,791 & -0.011\,280 & -0.052\,744 & -0.024\,500 & -0.012\,358 \\ & $1\,^{3}A_2$ & -0.051\,244 & -0.020\,982 & -0.010\,115 & -0.058\,090 & -0.023\,847 & -0.011\,302 & -0.052\,729 & -0.024\,611 & -0.012\,398 \\ & $1\,^{3}A_1$ & -0.052\,193 & -0.021\,398 & -0.010\,401 & -0.059\,073 & -0.024\,272 & -0.011\,595 & -0.053\,409 & -0.024\,840 & -0.012\,699 \\ \\ Ethylene & $1\,^{1}A_{1g}$ & -0.057\,559 & -0.022\,007 & & -0.066\,251 & -0.024\,599 & & -0.065\,343 & -0.027\,274 & \\ & $1\,^{1}B_{3u}$ & -0.054\,862 & -0.020\,972 & & -0.063\,185 & -0.023\,501 & & -0.061\,786 & -0.025\,978 & \\ & $1\,^{1}B_{1u}$ & -0.057\,591 & -0.022\,249 & & -0.064\,517 & -0.023\,971 & & -0.063\,619 & -0.026\,561 & \\ & $1\,^{1}B_{1g}$ & -0.054\,995 & -0.020\,994 & & -0.063\,386 & -0.023\,564 & & -0.061\,978 & -0.026\,087 & \\ & $1\,^{3}B_{1u}$ & -0.055\,186 & -0.020\,862 & & -0.063\,076 & -0.023\,241 & & -0.062\,938 & -0.025\,971 & \\ & $1\,^{3}B_{3u}$ & -0.054\,356 & -0.020\,441 & & -0.062\,107 & -0.022\,891 & & -0.060\,879 & -0.025\,249 & \\ & $1\,^{3}B_{1g}$ & -0.054\,526 & -0.020\,480 & & -0.062\,333 & -0.022\,962 & & -0.061\,051 & -0.025\,334 & \\ \\ \end{tabular} \end{ruledtabular} \end{table*} \end{squeezetable} \end{turnpage} %%% %%% %%% \bibliography{../Ex-srDFT,../Ex-srDFT-control} \end{document}