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% second quantized operators
\newcommand { \ai } [1]{ \hat { a} _ { #1} }
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% units
\newcommand { \IneV } [1]{ #1 eV}
\newcommand { \InAU } [1]{ #1 a.u.}
\newcommand { \InAA } [1]{ #1 \AA }
\newcommand { \kcal } { kcal/mol}
% methods
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\newcommand { \Q } { \text { Q} }
\newcommand { \X } { \text { X} }
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% energies
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\newcommand { \EsCI } { E_ \text { sCI} }
\newcommand { \EDMC } { E_ \text { DMC} }
\newcommand { \EexFCI } { E_ \text { exFCI} }
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\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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\subsection{Carbon monoxyde}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\begin{verbatim}
%C 0.000000 0.000000 -1.249421
%0 0.000000 0.000000 0.892667
%\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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 \, { } ^ 1 A _ 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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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The exFCI total energies can be found in the { \SI } of Refs.~\onlinecite { LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19} .
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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).
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%%% 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}
%%% %%% %%% %%%
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%%% 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
\\
\\
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% Carbon monoxyde & $1\,^{1}\Sigma^+$
% & -0.074\,328 & -0.031\,117 & -0.015\,510
% & -0.084\,655 & -0.035\,318 & -0.017\,142
% & -0.076\,668 & -0.077\,437 & -0.018\,768
% \\
% & $1\,^{1}\Pi$
% & -0.075\,790 & -0.031\,456 & -0.016\,083
% & -0.085\,494 & -0.035\,255 & -0.017\,182
% & -0.036\,301 & -0.036\,359 & -0.018\,855
% \\
% \\
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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 _ { 1 g } $
& -0.057\, 559 & -0.022\, 007 &
& -0.066\, 251 & -0.024\, 599 &
& -0.065\, 343 & -0.027\, 274 &
\\
& $ 1 \, ^ { 1 } B _ { 3 u } $
& -0.054\, 862 & -0.020\, 972 &
& -0.063\, 185 & -0.023\, 501 &
& -0.061\, 786 & -0.025\, 978 &
\\
& $ 1 \, ^ { 1 } B _ { 1 u } $
& -0.057\, 591 & -0.022\, 249 &
& -0.064\, 517 & -0.023\, 971 &
& -0.063\, 619 & -0.026\, 561 &
\\
& $ 1 \, ^ { 1 } B _ { 1 g } $
& -0.054\, 995 & -0.020\, 994 &
& -0.063\, 386 & -0.023\, 564 &
& -0.061\, 978 & -0.026\, 087 &
\\
& $ 1 \, ^ { 3 } B _ { 1 u } $
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& -0.056\, 056 & -0.020\, 862 &
& -0.063\, 499 & -0.023\, 241 &
& -0.063\, 304 & -0.025\, 971 &
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\\
& $ 1 \, ^ { 3 } B _ { 3 u } $
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& -0.054\, 752 & -0.020\, 441 &
& -0.062\, 078 & -0.022\, 891 &
& -0.060\, 894 & -0.025\, 249 &
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\\
& $ 1 \, ^ { 3 } B _ { 1 g } $
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& -0.054\, 924 & -0.020\, 480 &
& -0.062\, 306 & -0.022\, 962 &
& -0.061\, 089 & -0.025\, 334 &
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\\
\\
\end { tabular}
\end { ruledtabular}
\end { table*}
\end { squeezetable}
\end { turnpage}
%%% %%% %%%
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\bibliography { ../Ex-srDFT,../Ex-srDFT-control}
\end { document}
