1784 lines
89 KiB
TeX
1784 lines
89 KiB
TeX
\documentclass[aip,jcp,reprint,onecolumn,noshowkeys]{revtex4-1}
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,float}
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% energies
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\newcommand{\EHF}{E_\text{HF}}
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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{\CEISAM}{Laboratoire CEISAM (UMR 6230), CNRS, Universit\'e de Nantes, Nantes, France}
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\begin{document}
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\title{Supplementary Material for ``Reference Energies for Double Excitations''}
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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{Martial Boggio-Pasqua}
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\affiliation{\LCPQ}
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\author{Anthony Scemama}
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\affiliation{\LCPQ}
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\author{Michel Caffarel}
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\affiliation{\LCPQ}
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\author{Denis Jacquemin}
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\affiliation{\CEISAM}
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\begin{abstract}
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\end{abstract}
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\maketitle
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\tableofcontents
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Geometries}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Below are given the cartesian coordinates of the compounds investigated in this study.
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These are provided in atomic units (bohr) and they have been obtained at the CC3(full)/aug-cc-pVTZ level of theory, except for hexatriene where the geometry has been optimized at the CCSD(T)/aug-cc-pVTZ level.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Acrolein}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C -1.11645072 -0.68348783 0.00000000
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C 1.20647847 0.83714564 0.00000000
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C 3.46831059 -0.28872636 0.00000000
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O -3.23666415 0.19187203 0.00000000
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H -0.80613858 -2.74747338 0.00000000
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H 0.98699813 2.86613511 0.00000000
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H 5.20930864 0.77443560 0.00000000
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H 3.60951559 -2.33000749 0.00000000
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Benzene}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 0.00000000 2.63144965 0.00000000
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C -2.27890225 1.31572483 0.00000000
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C -2.27890225 -1.31572483 0.00000000
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C 0.00000000 -2.63144965 0.00000000
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C 2.27890225 -1.31572483 0.00000000
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C 2.27890225 1.31572483 0.00000000
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H -4.04725813 2.33668557 0.00000000
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H -4.04725813 -2.33668557 0.00000000
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H 0.00000000 -4.67337115 0.00000000
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H 4.04725813 -2.33668557 0.00000000
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H 4.04725813 2.33668557 0.00000000
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H 0.00000000 4.67337115 0.00000000
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Butadiene}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 1.14656244 0.00000000 0.75468820
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C -1.14656244 0.00000000 -0.75468820
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C 3.48132647 0.00000000 -0.22482805
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C -3.48132647 0.00000000 0.22482805
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H 0.90770978 0.00000000 2.78883925
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H -0.90770978 0.00000000 -2.78883925
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H 3.77525814 0.00000000 -2.24895470
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H -3.77525814 0.00000000 2.24895470
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H 5.13664967 0.00000000 0.96861890
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H -5.13664967 0.00000000 -0.96861890
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Carbon dimer}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 0.00000000 0.00000000 1.17922927
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C 0.00000000 0.00000000 -1.17922927
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Carbon trimer}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 0.00000000 0.00000000 0.00000000
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C 0.00000000 0.00000000 2.45345613
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C 0.00000000 0.00000000 -2.45345613
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Ethylene}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 0.00000000 1.26026583 0.00000000
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C 0.00000000 -1.26026583 0.00000000
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H 0.00000000 2.32345976 1.74287672
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H 0.00000000 -2.32345976 1.74287672
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H 0.00000000 2.32345976 -1.74287672
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H 0.00000000 -2.32345976 -1.74287672
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Formaldehyde}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 0.00000000 0.00000000 -1.13947666
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O 0.00000000 0.00000000 1.14402883
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H 0.00000000 1.76627623 -2.23398653
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H 0.00000000 -1.76627623 -2.23398653
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Glyoxal}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 1.21360282 0.75840215 0.00000000
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C -1.21360282 -0.75840215 0.00000000
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O 3.25581408 -0.26453186 0.00000000
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O -3.25581408 0.26453186 0.00000000
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H 0.96135276 2.81883243 0.00000000
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H -0.96135276 -2.81883243 0.00000000
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Hexatriene}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C -0.0002476 1.2717818 0.0000000
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C 0.0002476 -1.2717818 0.0000000
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C 2.2709215 2.7978697 0.0000000
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C -2.2709215 -2.7978697 0.0000000
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C 2.2709215 5.3313687 0.0000000
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C -2.2709215 -5.3313687 0.0000000
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H -1.7938035 2.2677902 0.0000000
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H 1.7938035 -2.2677902 0.0000000
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H 4.0548550 1.7921594 0.0000000
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H -4.0548550 -1.7921594 0.0000000
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H 0.5178662 6.3842559 0.0000000
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H -0.5178662 -6.3842559 0.0000000
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H 4.0110587 6.3968755 0.0000000
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H -4.0110587 -6.3968755 0.0000000
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Nitrosomethane}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C -1.78426612 0.00000000 -1.07224050
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N -0.00541753 0.00000000 1.08060391
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O 2.18814985 0.00000000 0.43452135
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H -0.77343975 0.00000000 -2.86415606
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H -2.97471478 1.66801808 -0.86424584
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H -2.97471478 -1.66801808 -0.86424584
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Nitroxyl}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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O 0.21099695 0.00000000 2.15462460
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N -0.44776863 0.00000000 -0.03589263
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H 1.18163475 0.00000000 -1.17386890
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Pyrazine}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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N -2.66620111 0.00000000 0.00000000
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N 2.66620111 0.00000000 0.00000000
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C -1.31510863 2.13188686 0.00000000
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C -1.31510863 -2.13188686 0.00000000
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C 1.31510863 2.13188686 0.00000000
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C 1.31510863 -2.13188686 0.00000000
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H -2.35234226 3.88751412 0.00000000
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H -2.35234226 -3.88751412 0.00000000
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H 2.35234226 3.88751412 0.00000000
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H 2.35234226 -3.88751412 0.00000000
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Tetrazine}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 0.00000000 0.00000000 1.26054332
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C 0.00000000 0.00000000 -1.26054332
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N 0.00000000 1.19421138 0.66133002
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N 0.00000000 -1.19421138 0.66133002
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N 0.00000000 1.19421138 -0.66133002
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N 0.00000000 -1.19421138 -0.66133002
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H 0.00000000 0.00000000 2.33817427
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H 0.00000000 0.00000000 -2.33817427
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Energetics of EOM-CC calculations}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%------------------------------
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\subsection{Acrolein}
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%------------------------------
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%%% ACROLEIN %%%
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\begin{table}[H]
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\caption{
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\label{tab:acrolein_CC}
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Energies (in hartree) and transition energies $\Delta E$ (in eV) of acrolein for various methods and basis sets.
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}
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\begin{ruledtabular}
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\begin{tabular}{llldddddd}
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Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{\pi}{\pis}}
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& \mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 3\,\ex{1}{A}{}{'}: \tr{\pi,\pi}{\pis,\pis}} \\
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\cline{4-6} \cline{7-9}
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& & & \mcc{1\,\ex{1}{A}{}{'}} & \mcc{2\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$}
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& \mcc{1\,\ex{1}{A}{}{'}} & \mcc{3\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$} \\
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\hline
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Acrolein & CC3 & 6-31+G* & -191.370\,506 & -191.119\,437 & 6.83
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& -191.370\,506 & -191.068\,953 & 8.21 \\
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& & AVDZ & -191.445\,933 & -191.200\,748 & 6.67
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& -191.445\,933 & -191.148\,026 & 8.11 \\
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& & AVTZ & -191.613\,332 & -191.368\,842 & 6.65
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& -191.613\,332 & -191.316\,467 & 8.08 \\
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% & EOM-CCSDT & 6-31+G* & & & \\
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% & & AVDZ & & & \\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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%------------------------------
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\subsection{Benzene}
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%------------------------------
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%%% BENZENE %%%
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\begin{table}[H]
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\caption{
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\label{tab:benzene_CC}
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Energies (in hartree) and transition energies $\Delta E$ (in eV) of benzene for various methods and basis sets.
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}
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\begin{ruledtabular}
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\begin{tabular}{lllddd}
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Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{E}{2g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
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\cline{4-6}
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& & & \mcc{1\,\ex{1}{A}{1g}{}} & \mcc{1\,\ex{1}{E}{2g}{}} & \mcc{$\Delta E$} \\
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\hline
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Benzene & CC3 & 6-31+G* & -231.537\,359 & -231.224\,840 & 8.50 \\
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& & AVDZ & -231.615\,828 & -231.305\,692 & 8.44 \\
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& & AVTZ & -231.823\,303 & -231.515\,298 & 8.38 \\
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& EOM-CCSDT & 6-31+G* & -231.544\,019 & -231.234\,416 & 8.42 \\
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% & & AVDZ & & & \\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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%------------------------------
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\subsection{Beryllium}
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%------------------------------
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%%% BERYLLIUM
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\begin{table}[H]
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\caption{
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\label{tab:Be_CC}
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Energies (in hartree) and transition energies $\Delta E$ (in eV) of beryllium for various methods and basis sets.
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}
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\begin{ruledtabular}
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\begin{tabular}{lllddd}
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Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{S}{}{} $\ra$ 1\,\ex{1}{D}{}{}: \tr{2s^2}{2p^2}} \\
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\cline{4-6}
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& & & \mcc{1\,\ex{1}{S}{}{}} & \mcc{1\,\ex{1}{D}{}{}} & \mcc{$\Delta E$} \\
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\hline
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Beryllium & CC3 & 6-31+G* & -14.615\,618 & -14.320\,113 & 8.04 \\
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& & AVDZ & -14.617\,469 & -14.617\,469 & 7.23 \\
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& & AVTZ & -14.624\,384 & -14.361\,336 & 7.16 \\
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& & AVQZ & -14.640\,094 & -14.378\,479 & 7.12 \\
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& EOM-CCSDT & 6-31+G* & -14.615\,628 & -14.320\,223 & 8.04 \\
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& & AVDZ & -14.617\,474 & -14.351\,962 & 7.22 \\
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& & AVTZ & -14.624\,415 & -14.361\,571 & 7.15 \\
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& & AVQZ & -14.640\,163 & -14.378\,990 & 7.11 \\
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& EOM-CCSDTQ & 6-31+G* & -14.615\,630 & -14.320\,232 & 8.04 \\
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& & AVDZ & -14.617\,476 & -14.351\,972 & 7.23 \\
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& & AVTZ & -14.624\,424 & -14.361\,624 & 7.15 \\
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& & AVQZ & -14.640\,171 & -14.379\,038 & 7.11 \\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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%------------------------------
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\subsection{Butadiene}
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%------------------------------
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%%% BUTADIENE %%%
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\begin{table}[H]
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\caption{
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\label{tab:butadiene_CC}
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Energies (in hartree) and transition energies $\Delta E$ (in eV) of butadiene for various methods and basis sets.
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}
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\begin{ruledtabular}
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\begin{tabular}{lllddd}
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Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
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\cline{4-6}
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& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
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\hline
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Butadiene & CC3 & 6-31+G* & -155.492\,606 & -155.245\,263 & 6.73 \\
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& & AVDZ & -155.563\,604 & -155.318\,201 & 6.68 \\
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& & AVTZ & -155.707\,377 & -155.462\,232 & 6.67 \\
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& & AVQZ & -155.746\,249 & -155.501\,078 & 6.67 \\
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& EOM-CCSDT & 6-31+G* & -155.498\,045 & -155.254\,297 & 6.63 \\
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& & AVDZ & -155.563\,681 & -155.321\,535 & 6.59 \\
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& & AVTZ & -155.706\,231 & & \\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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%------------------------------
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\subsection{Carbon dimer}
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%------------------------------
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%%% CARBON DIMER %%%
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\begin{table}[H]
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\caption{
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\label{tab:C2_CC}
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Energies (in hartree) and transition energies $\Delta E$ (in eV) of the carbon dimer for various methods and basis sets.
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}
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\begin{ruledtabular}
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\begin{tabular}{llldddddd}
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Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}
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& \mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}} \\
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\cline{4-6} \cline{7-9}
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& & & \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{2\,\ex{1}{\Sigma}{g}{+}} & \mcc{$\Delta E$}
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& \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{1\,\ex{1}{\Delta}{g}{}} & \mcc{$\Delta E$} \\
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\hline
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Carbon dimer& CC3 & 6-31+G* & -75.726\,283 & -75.612\,374 & 3.10 & -75.726\,283 & -75.607\,558 & 3.23 \\
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& & AVDZ & -75.734\,267 & -75.620\,083 & 3.11 & -75.734\,267 & -75.613\,622 & 3.28 \\
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& & AVTZ & -75.787\,555 & -75.675\,376 & 3.05 & -75.787\,555 & -75.667\,882 & 3.25 \\
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& & AVQZ & -75.803\,550 & -75.692\,215 & 3.03 & -75.803\,550 & -75.684\,510 & 3.24 \\
|
|
& EOM-CCSDT & 6-31+G* & -75.724\,387 & -75.625\,387 & 2.69 & -75.724\,387 & -75.619\,114 & 2.86 \\
|
|
& & AVDZ & -75.732\,355 & -75.635\,647 & 2.63 & -75.732\,355 & -75.626\,726 & 2.87 \\
|
|
& & AVTZ & -75.784\,146 & -75.689\,819 & 2.57 & -75.784\,146 & -75.678\,992 & 2.86 \\
|
|
& & AVQZ & -75.799\,645 & -75.705\,297 & 2.57 & -75.799\,645 & -75.694\,314 & 2.87 \\
|
|
& EOM-CCSDTQ & 6-31+G* & -75.727\,010 & -75.641\,912 & 2.32 & -75.727\,010 & -75.634\,258 & 2.52 \\
|
|
& & AVDZ & -75.735\,284 & -75.652\,947 & 2.24 & -75.735\,284 & -75.642\,656 & 2.52 \\
|
|
& & AVTZ & -75.787\,747 & -75.709\,576 & 2.13 & -75.787\,747 & -75.697\,804 & 2.45 \\
|
|
& EOM-CCSDTQP & 6-31+G* & -75.727\,492 & -75.643\,261 & 2.29 & -75.727\,492 & -75.727\,492 & 2.51 \\
|
|
& & AVDZ & -75.735\,840 & -75.654\,491 & 2.21 & -75.735\,840 & -75.643\,803 & 2.50 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Carbon trimer}
|
|
%------------------------------
|
|
|
|
%%% CARBON TRIMER %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:C3_CC}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of the carbon trimer for various methods and basis sets.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{llldddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}
|
|
& \mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}} \\
|
|
\cline{4-6} \cline{7-9}
|
|
& & & \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{2\,\ex{1}{\Sigma}{g}{+}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{1\,\ex{1}{\Delta}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Carbon trimer & CC3 & 6-31+G* & -113.745\,261 & -113.500\,779 & 6.65 & -113.745\,261 & -113.480\,808 & 7.20 \\
|
|
& & AVDZ & -113.759\,083 & -113.514\,829 & 6.65 & -113.759\,083 & -113.494\,687 & 7.20 \\
|
|
& & AVTZ & -113.844\,068 & -113.598\,548 & 6.68 & -113.844\,068 & -113.578\,066 & 7.24 \\
|
|
& & AVQZ & -113.868\,492 & -113.623\,578 & 6.66 & -113.868\,492 & -113.603\,104 & 7.22 \\
|
|
& EOM-CCSDT & 6-31+G* & -113.741\,023 & -113.525\,900 & 5.85 & -113.741\,023 & -113.501\,431 & 6.52 \\
|
|
& & AVDZ & -113.755\,069 & -113.541\,328 & 5.82 & -113.755\,069 & -113.516\,450 & 6.49 \\
|
|
& & AVTZ & -113.838\,608 & -113.621\,830 & 5.90 & -113.838\,608 & -113.597\,120 & 6.57 \\
|
|
& & AVQZ & -113.862\,469 & -113.645\,020 & 5.92 & -113.862\,469 & -113.620\,516 & 6.58 \\
|
|
& EOM-CCSDTQ & 6-31+G* & -113.743\,343 & -113.546\,630 & 5.35 & -113.743\,343 & -113.522\,060 & 6.02 \\
|
|
& & AVDZ & -113.757\,672 & -113.562\,458 & 5.31 & -113.757\,672 & -113.537\,320 & 6.00 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Ethylene}
|
|
%------------------------------
|
|
|
|
%%% ETHYLENE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:ethylene_CC}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of ethylene for various methods and basis sets.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Ethylene & CC3 & 6-31+G* & -78.325\,158 & -77.817\,291 & 13.82 \\
|
|
& & AVDZ & -78.368\,712 & -77.870\,066 & 13.57 \\
|
|
& & AVTZ & -78.444\,299 & -77.951\,137 & 13.42 \\
|
|
& & AVQZ & -78.464\,260 & -77.984\,451 & 13.06\\
|
|
& EOM-CCSDT & 6-31+G* & -78.325\,466 & -77.829\,347 & 13.50 \\
|
|
& & AVDZ & -78.369\,061 & -77.883\,840 & 13.20 \\
|
|
% & & AVTZ & -78.444\,096 & & \\
|
|
& EOM-CCSDTQ & 6-31+G* & -78.325\,913 & -77.833\,839 & 13.39 \\
|
|
& & AVDZ & -78.369\,710 & -77.889\,453 & 13.07 \\
|
|
& EOM-CCSDTQP & 6-31+G* & -78.325\,962 & -77.834\,035 & 13.39 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Formaldehyde}
|
|
%------------------------------
|
|
|
|
%%% FORMALDEHYDE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:formaldehyde_CC}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of ethylene for various methods and basis sets.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{1}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{1}{}} & \mcc{3\,\ex{1}{A}{1}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Formaldehyde& CC3 & 6-31+G* & -114.196\,244 & -113.773\,939 & 11.49 \\
|
|
& & AVDZ & -114.245\,501 & -113.833\,222 & 11.22 \\
|
|
& & AVTZ & -114.344\,118 & -113.932\,524 & 11.20 \\
|
|
& & AVQZ & -114.373\,678 & -113.962\,323 & 11.19 \\
|
|
& EOM-CCSDT & 6-31+G* & -114.195\,911 & -113.787\,932 & 11.10 \\
|
|
& & AVDZ & -114.245\,054 & -113.848\,759 & 10.78 \\
|
|
& & AVTZ & -114.343\,049 & -113.946\,700 & 10.79 \\
|
|
& & AVQZ & -114.372\,366 & -113.975\,394 & 10.80 \\
|
|
& EOM-CCSDTQ & 6-31+G* & -114.196\,803 & -113.797\,250 & 10.87 \\
|
|
& & AVDZ & -114.246\,007 & -113.862\,524 & 10.44 \\
|
|
& EOM-CCSDTQP & 6-31+G* & -114.196\,855 & -113.797\,764 & 10.86 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Glyoxal}
|
|
%------------------------------
|
|
|
|
%%% GLYOXAL %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:glyoxal_CC}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of glyoxal for various methods and basis sets.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Glyoxal & CC3 & 6-31+G* & -227.236\,455 & -226.988\,947 & 6.74 \\
|
|
& & AVDZ & -227.317\,437 & -227.070\,979 & 6.71 \\
|
|
& & AVTZ & -227.507\,912 & -227.259\,369 & 6.76 \\
|
|
& & AVQZ & -227.566\,052 & -227.317\,664 & 6.76 \\
|
|
& EOM-CCSDT & 6-31+G* & -227.235\,215 & -227.005\,775 & 6.24 \\
|
|
& & AVDZ & -227.315\,943 & -227.087\,288 & 6.22 \\
|
|
& & AVTZ & -227.505\,065 & -227.271\,579 & 6.35 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Hexatriene}
|
|
%------------------------------
|
|
|
|
%%% HEXATRIENE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:hexatriene_CC}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of hexatriene for various methods and basis sets.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Hexatriene & CC3 & 6-31+G* & -232.661\,482 & -232.449\,077 & 5.78 \\
|
|
& & AVDZ & -232.759\,871 & -232.547\,649 & 5.77 \\
|
|
& & AVTZ & -232.971\,955 & -232.760\,024 & 5.77 \\
|
|
& EOM-CCSDT & 6-31+G* & -232.669\,310 & -232.462\,052 & 5.64 \\
|
|
& & AVDZ & -232.759\,513 & -232.551\,992 & 5.65 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Nitrosomethane}
|
|
%------------------------------
|
|
|
|
%%% NITROSOMETHANE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:nitrosomethane_CC}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of nitrosomethane for various methods and basis sets.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{}{'}} & \mcc{2\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Nitrosomethane & CC3 & 6-31+G* & -169.342\,484 & -169.131\,944 & 5.73 \\
|
|
& & AVDZ & -169.414\,755 & -169.203\,473 & 5.75 \\
|
|
& & AVTZ & -169.559\,567 & -169.347\,997 & 5.76 \\
|
|
& & AVQZ & -169.602\,537 & -169.391\,634 & 5.74 \\
|
|
& EOM-CCSDT & 6-31+G* & -169.342\,012 & -169.148\,711 & 5.26 \\
|
|
& & AVDZ & -169.414\,096 & -169.220\,885 & 5.26 \\
|
|
& & AVTZ & -169.557\,831 & -169.363\,318 & 5.29 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Nitroxyl}
|
|
%------------------------------
|
|
|
|
%%% NITRSOXYL %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:nitroxyl_CC}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of nitroxyl for various methods and basis sets.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{}{'}} & \mcc{2\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Nitroxyl& CC3 & 6-31+G* & -130.151\,876 & -129.957\,929 & 5.28 \\
|
|
& & AVDZ & -130.204\,169 & -130.011\,360 & 5.25 \\
|
|
& & AVTZ & -130.310\,876 & -130.117\,680 & 5.26 \\
|
|
& & AVQZ & -130.343\,921 & -130.151\,556 & 5.23 \\
|
|
& EOM-CCSDT & 6-31+G* & -130.151\,628 & -129.974\,547 & 4.82 \\
|
|
& & AVDZ & -130.203\,765 & -130.028\,985 & 4.76 \\
|
|
& & AVTZ & -130.309\,652 & -130.133\,807 & 4.79 \\
|
|
& & AVQZ & -130.342\,420 & -130.166\,137 & 4.80 \\
|
|
& EOM-CCSDTQ & 6-31+G* & -130.153\,185 & -129.986\,516 & 4.54 \\
|
|
& & AVDZ & -130.205\,384 & -130.042\,787 & 4.42 \\
|
|
& EOM-CCSDTQP & 6-31+G* & -130.153\,329 & -129.987\,473 & 4.51\\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Pyrazine}
|
|
%------------------------------
|
|
|
|
%%% PYRAZINE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:pyrazine_CC}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of pyrazine for various methods and basis sets.
|
|
Note the inversion of the two transitions compared to multiconfigurational calculations (see Table \ref{tab:pyrazine_CAS}).
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{llldddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}}
|
|
& \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{4-6} \cline{7-9}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{A}{g}{}} & \mcc{3\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Pyrazine & CC3 & 6-31+G* & -263.574\,080 & -263.247\,798 & 8.88 & -263.574\,080 & -263.233\,284 & 9.27 \\
|
|
& & AVDZ & -263.651\,711 & -263.329\,377 & 8.77 & -263.651\,711 & -263.314\,640 & 9.17 \\
|
|
& & AVTZ & -263.876\,837 & -263.557\,246 & 8.69 & -263.876\,837 & -263.539\,937 & 9.17 \\
|
|
% & & AVQZ & & & \\
|
|
% & EOM-CCSDT & 6-31+G* & & & \\
|
|
% & & AVDZ & & & \\
|
|
% & & AVTZ & & & \\
|
|
% & & AVQZ & & & \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
|
|
%------------------------------
|
|
\subsection{Tetrazine}
|
|
%------------------------------
|
|
|
|
%%% TETRAZINE %%%
|
|
\begin{squeezetable}
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:tetrazine_CC}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of tetrazine for various methods and basis sets.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddddddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{}: \tr{n,n}{\pis,\pis}}
|
|
& \mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2}}
|
|
& \mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{3}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2}} \\
|
|
\cline{4-6} \cline{7-9} \cline{10-12}
|
|
& & & \mcc{1\,\ex{1}{A}{1g}{}} & \mcc{2\,\ex{1}{A}{1g}{}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{A}{1g}{}} & \mcc{1\,\ex{1}{B}{3g}{}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{A}{1g}{}} & \mcc{1\,\ex{3}{B}{3g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Tetrazine & CC3 & 6-31+G* & 295.547\,380 & 295.318\,726 & 6.22
|
|
& 295.547\,380 & 295.266\,625 & 7.64
|
|
& 295.547\,380 & 295.277\,104 & 7.35 \\
|
|
& & AVDZ & 295.628\,264 & 295.399\,771 & 6.22
|
|
& 295.628\,264 & 295.348\,321 & 7.62
|
|
& 295.628\,264 & 295.358\,861 & 7.33 \\
|
|
& & AVTZ & 295.870\,425 & 295.642\,258 & 6.21
|
|
& 295.870\,425 & 295.590\,509 & 7.62
|
|
& 295.870\,425 & 295.600\,445 & 7.35 \\
|
|
& & AVQZ & 295.943\,553 & 295.716\,082 & 6.19
|
|
& 295.943\,553 & 295.664\,184 & 7.60
|
|
& 295.943\,553 & 295.673\,917 & 7.34 \\
|
|
& EOM-CCSDT & 6-31+G* & 295.543\,914 & 295.328\,716 & 5.86
|
|
% & & &
|
|
% & & & \\
|
|
& & AVDZ & 295.624\,243 & 295.408\,977 & 5.86
|
|
% & & &
|
|
% & & & \\
|
|
% & & AVTZ & & &
|
|
% & & &
|
|
% & & & \\
|
|
% & & AVQZ & & &
|
|
% & & &
|
|
% & & & \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
\end{squeezetable}
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\section{Energetics of multiconfigurational calculations}
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
%------------------------------
|
|
\subsection{Acrolein}
|
|
%------------------------------
|
|
|
|
%%% ACROLEIN %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:acrolein_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of acrolein for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
The $(4,4)$ active space contains the $\piCC$, $\piCO$, $\pisCC$ and $\pisCO$ orbitals.
|
|
The $(10,10)$ active space adds up the $\siCC$, $\siCO$, $\sisCC$ and $\sisCO$ orbitals.
|
|
The state-averaged (SA) CASSCF calculation is performed with $3$ states.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{llldddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{\pi}{\pis}}
|
|
& \mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 3\,\ex{1}{A}{}{'}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{4-6}\cline{7-9}
|
|
& & & \mcc{1\,\ex{1}{A}{}{'}} & \mcc{2\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{A}{}{'}} & \mcc{3\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Acrolein & SA-CASSCF(4,4) & 6-31+G* & -190.816\,793 & -190.494\,611 & 8.77 & -190.816\,793 & -190.527\,136 & 7.88 \\
|
|
& & AVDZ & -190.836\,891 & -190.519\,307 & 8.64 & -190.836\,891 & -190.547\,121 & 7.89 \\
|
|
& & AVTZ & -190.882\,696 & -190.565\,771 & 8.62 & -190.882\,696 & -190.593\,513 & 7.87 \\
|
|
& & AVQZ & -190.894\,452 & -190.577\,536 & 8.62 & -190.894\,452 & -190.605\,403 & 7.87 \\
|
|
& CASPT2(4,4) & 6-31+G* & -191.324\,307 & -191.047\,227 & 7.28 & -191.324\,307 & -191.020\,060 & 8.02 \\
|
|
& & AVDZ & -191.394\,637 & -191.121\,911 & 7.13 & -191.394\,637 & -191.092\,243 & 7.94 \\
|
|
& & AVTZ & -191.561\,092 & -191.291\,491 & 7.03 & -191.561\,092 & -191.258\,865 & 7.92 \\
|
|
& & AVQZ & -191.614\,759 & -191.345\,798 & 7.01 & -191.614\,759 & -191.311\,943 & 7.93 \\
|
|
& MS-CASPT2(4,4) & 6-31+G* & -191.315\,591 & -191.061\,210 & 6.92 & -191.315\,591 & -191.005\,163 & 8.45 \\
|
|
& & AVDZ & -191.385\,082 & -191.137\,241 & 6.74 & -191.385\,082 & -191.075\,842 & 8.41 \\
|
|
& & AVTZ & -191.551\,275 & -191.306\,016 & 6.67 & -191.551\,275 & -191.243\,026 & 8.39 \\
|
|
& & AVQZ & -191.604\,948 & -191.360\,303 & 6.66 & -191.604\,948 & -191.296\,011 & 8.41 \\
|
|
& XMS-CASPT2(4,4) & 6-31+G* & -191.314\,712 & -191.055\,201 & 7.06 & -191.314\,712 & -191.009\,976 & 8.29 \\
|
|
& & AVDZ & -191.384\,070 & -191.130\,132 & 6.91 & -191.384\,070 & -191.081\,589 & 8.23 \\
|
|
& & AVTZ & -191.550\,097 & -191.299\,092 & 6.83 & -191.550\,097 & -191.248\,936 & 8.20 \\
|
|
& & AVQZ & -191.603\,706 & -191.353\,389 & 6.81 & -191.603\,706 & -191.301\,988 & 8.21 \\
|
|
& PC-NEVPT2(4,4) & 6-31+G* & -191.324\,250 & -191.076\,946 & 6.73 & -191.324\,250 & -191.024\,801 & 8.15 \\
|
|
& & AVDZ & -191.393\,648 & -191.151\,487 & 6.59 & -191.393\,648 & -191.096\,983 & 8.07 \\
|
|
& & AVTZ & -191.559\,225 & -191.321\,416 & 6.47 & -191.559\,225 & -191.263\,015 & 8.06 \\
|
|
& & AVQZ & -191.612\,658 & -191.375\,778 & 6.45 & -191.612\,658 & -191.315\,961 & 8.07 \\
|
|
& SC-NEVPT2(4,4) & 6-31+G* & -191.323\,420 & -191.068\,805 & 6.93 & -191.323\,420 & -191.022\,315 & 8.19 \\
|
|
& & AVDZ & -191.392\,720 & -191.143\,095 & 6.79 & -191.392\,720 & -191.094\,153 & 8.12 \\
|
|
& & AVTZ & -191.558\,276 & -191.312\,963 & 6.68 & -191.558\,276 & -191.260\,162 & 8.11 \\
|
|
& & AVQZ & -191.611\,699 & -191.367\,369 & 6.65 & -191.611\,699 & -191.313\,100 & 8.13 \\
|
|
& SA-CASSCF(10,10) & 6-31+G* & -190.901\,844 & -190.604\,891 & 8.52 & -190.901\,844 & -190.588\,596 & 8.08 \\
|
|
& & AVDZ & -190.922\,572 & -190.627\,675 & 8.48 & -190.922\,572 & -190.610\,975 & 8.02 \\
|
|
& & AVTZ & -190.969\,088 & -190.674\,144 & 8.45 & -190.969\,088 & -190.658\,408 & 8.03 \\
|
|
& & AVQZ & -190.981\,013 & -190.686\,066 & 8.45 & -190.981\,013 & -190.670\,433 & 8.03 \\
|
|
& CASPT2(10,10) & 6-31+G* & -191.317\,112 & -191.048\,898 & 7.30 & -191.317\,112 & -191.025\,543 & 7.93 \\
|
|
& & AVDZ & -191.386\,586 & -191.125\,107 & 7.12 & -191.386\,586 & -191.095\,164 & 7.93 \\
|
|
& & AVTZ & -191.550\,979 & -191.292\,124 & 7.04 & -191.550\,979 & -191.262\,481 & 7.85 \\
|
|
& & AVQZ & -191.603\,845 & -191.345\,407 & 7.03 & -191.603\,845 & -191.315\,601 & 7.84 \\
|
|
& MS-CASPT2(10,10) & 6-31+G* & -191.317\,379 & -191.064\,112 & 6.89 & -191.317\,379 & -191.010\,063 & 8.36 \\
|
|
& & AVDZ & -191.386\,909 & -191.138\,090 & 6.77 & -191.386\,909 & -191.081\,858 & 8.30 \\
|
|
& & AVTZ & -191.551\,428 & -191.307\,080 & 6.65 & -191.551\,428 & -191.247\,076 & 8.28 \\
|
|
& & AVQZ & -191.604\,360 & -191.361\,127 & 6.62 & -191.604\,360 & -191.299\,366 & 8.30 \\
|
|
& XMS-CASPT2(10,10) & 6-31+G* & -191.317\,068 & -191.054\,948 & 7.13 & -191.317\,068 & -191.016\,423 & 8.18 \\
|
|
& & AVDZ & -191.386\,545 & -191.129\,376 & 7.00 & -191.386\,545 & -191.088\,046 & 8.12 \\
|
|
& & AVTZ & -191.550\,964 & -191.297\,066 & 6.91 & -191.550\,964 & -191.254\,533 & 8.07 \\
|
|
& & AVQZ & -191.603\,851 & -191.350\,762 & 6.89 & -191.603\,851 & -191.307\,168 & 8.07 \\
|
|
& PC-NEVPT2(10,10) & 6-31+G* & -191.306\,884 & -191.042\,313 & 7.20 & -191.306\,884 & -191.016\,252 & 7.91 \\
|
|
& & AVDZ & -191.373\,865 & -191.117\,154 & 6.99 & -191.373\,865 & -191.082\,430 & 7.93 \\
|
|
& & AVTZ & -191.535\,396 & -191.281\,326 & 6.91 & -191.535\,396 & -191.247\,069 & 7.85 \\
|
|
& & AVQZ & -191.587\,434 & -191.333\,787 & 6.90 & -191.587\,434 & -191.299\,435 & 7.84 \\
|
|
& SC-NEVPT2(10,10) & 6-31+G* & -191.301\,553 & -191.029\,383 & 7.41 & -191.301\,553 & -191.004\,556 & 8.08 \\
|
|
& & AVDZ & -191.368\,122 & -191.102\,474 & 7.23 & -191.368\,122 & -191.070\,989 & 8.09 \\
|
|
& & AVTZ & -191.529\,364 & -191.266\,222 & 7.16 & -191.529\,364 & -191.235\,143 & 8.01 \\
|
|
& & AVQZ & -191.581\,316 & -191.318\,611 & 7.15 & -191.581\,316 & -191.287\,313 & 8.00 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Benzene}
|
|
%------------------------------
|
|
|
|
%%% BENZENE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:benzene_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of benzene for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
The $(6,6)$ active space contains the $\piCC$ and $\pisCC$ orbitals.
|
|
The state-averaged (SA) CASSCF calculations for the 1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{E}{2g}{} and 1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{} transition are performed with $3$ and $4$ states, respectively.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{llldddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{E}{2g}{}: \tr{\pi,\pi}{\pis,\pis}}
|
|
& \mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{4-6} \cline{7-9}
|
|
& & & \mcc{1\,\ex{1}{A}{1g}{}} & \mcc{1\,\ex{1}{E}{2g}{}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{A}{1g}{}} & \mcc{2\,\ex{1}{A}{1g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Benzene & SA-CASSCF(6,6) & 6-31+G* & -230.777\,109 & -230.478\,032 & 8.14 & -230.775\,595 & -230.352\,550 & 11.51 \\
|
|
& & AVDZ & -230.794\,127 & -230.495\,900 & 8.12 & -230.792\,529 & -230.371\,597 & 11.45 \\
|
|
& & AVTZ & -230.847\,275 & -230.549\,481 & 8.10 & -230.845\,668 & -230.425\,112 & 11.44 \\
|
|
& & AVQZ & -230.860\,443 & -230.562\,744 & 8.10 & -230.858\,833 & -230.438\,347 & 11.44 \\
|
|
& CASPT2(6,6) & 6-31+G* & -231.454\,277 & -231.144\,541 & 8.43 & -231.454\,825 & -231.067\,472 & 10.54 \\
|
|
& & AVDZ & -231.526\,608 & -231.218\,048 & 8.40 & -231.527\,187 & -231.145\,592 & 10.38 \\
|
|
& & AVTZ & -231.732\,461 & -231.426\,037 & 8.34 & -231.733\,152 & -231.355\,298 & 10.28 \\
|
|
& & AVQZ & -231.797\,381 & -231.490\,833 & 8.34 & -231.798\,119 & -231.420\,880 & 10.27 \\
|
|
& MS-CASPT2(6,6) & 6-31+G* & -231.454\,293 & -231.144\,525 & 8.43 & -231.464\,691 & -231.057\,606 & 11.08 \\
|
|
& & AVDZ & -231.526\,628 & -231.218\,028 & 8.40 & -231.538\,479 & -231.134\,299 & 11.00 \\
|
|
& & AVTZ & -231.732\,486 & -231.426\,013 & 8.34 & -231.745\,669 & -231.342\,781 & 10.96 \\
|
|
& & AVQZ & -231.797\,406 & -231.490\,808 & 8.34 & -231.811\,068 & -231.407\,931 & 10.97 \\
|
|
& XMS-CASPT2(6,6) & 6-31+G* & -231.454\,271 & -231.144\,528 & 8.43 & -231.454\,496 & -231.058\,586 & 10.77 \\
|
|
& & AVDZ & -231.526\,602 & -231.218\,033 & 8.40 & -231.526\,893 & -231.135\,964 & 10.64 \\
|
|
& & AVTZ & -231.732\,455 & -231.426\,021 & 8.34 & -231.733\,000 & -231.345\,434 & 10.55 \\
|
|
& & AVQZ & -231.797\,374 & -231.490\,817 & 8.34 & -231.798\,070 & -231.410\,862 & 10.54 \\
|
|
& PC-NEVPT2(6,6) & 6-31+G* & -231.469\,185 & -231.153\,743 & 8.58 & -231.469\,458 & -231.089\,140 & 10.35 \\
|
|
& & AVDZ & -231.541\,157 & -231.226\,445 & 8.56 & -231.541\,534 & -231.167\,452 & 10.18 \\
|
|
& & AVTZ & -231.746\,700 & -231.433\,880 & 8.51 & -231.747\,162 & -231.379\,842 & 10.00 \\
|
|
& & AVQZ & -231.811\,494 & -231.498\,524 & 8.52 & & & \\
|
|
& SC-NEVPT2(6,6) & 6-31+G* & -231.468\,398 & -231.151\,496 & 8.62 & -231.468\,632 & -231.077\,860 & 10.63 \\
|
|
& & AVDZ & -231.468\,398 & -231.224\,034 & 8.61 & -231.540\,646 & -231.155\,560 & 10.48 \\
|
|
& & AVTZ & -231.745\,845 & -231.431\,454 & 8.56 & -231.746\,267 & -231.364\,760 & 10.38 \\
|
|
& & AVQZ & -231.810\,639 & -231.496\,111 & 8.56 & -231.811\,095 & -231.430\,238 & 10.36 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Beryllium}
|
|
%------------------------------
|
|
|
|
%%% BERYLLIUM
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:Be_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of beryllium for various methods and basis sets.
|
|
In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
Similarly, PC-NEVPT2 and SC-NEVPT2 yield undistinguishable results.
|
|
The $(2,12)$ active space contains the two valence electrons and the $2s$, $2p$, $3p$ and $3d$ orbitals.
|
|
The state-averaged (SA) CASSCF calculation is performed with $3$ states.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{S}{}{} $\ra$ 1\,\ex{1}{D}{}{}: \tr{2s^2}{2p^2}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{S}{}{}} & \mcc{1\,\ex{1}{D}{}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Beryllium & SA-CASSCF(2,12) & 6-31+G* & -14.612\,854 & -14.318\,502 & 8.01 \\
|
|
& & AVDZ & -14.615\,325 & -14.350\,722 & 7.20 \\
|
|
& & AVTZ & -14.615\,469 & -14.354\,014 & 7.11 \\
|
|
& & AVQZ & -14.615\,734 & -14.354\,812 & 7.10 \\
|
|
& CASPT2(2,12) & 6-31+G* & -14.614\,869 & -14.320\,023 & 8.02 \\
|
|
& & AVDZ & -14.616\,802 & -14.351\,933 & 7.21 \\
|
|
& & AVTZ & -14.622\,901 & -14.361\,341 & 7.12 \\
|
|
& & AVQZ & -14.637\,040 & -14.375\,999 & 7.10 \\
|
|
& NEVPT2(2,12) & 6-31+G* & -14.614\,901 & -14.320\,403 & 8.01 \\
|
|
& & AVDZ & -14.616\,757 & -14.352\,020 & 7.20 \\
|
|
& & AVTZ & -14.623\,028 & -14.361\,559 & 7.11 \\
|
|
& & AVQZ & -14.637\,151 & -14.376\,228 & 7.10 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
|
|
%------------------------------
|
|
\subsection{Butadiene}
|
|
%------------------------------
|
|
|
|
%%% BUTADIENE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:butadiene_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of butadiene for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
The $(4,4)$ active space includes the $\piCC$ and $\pisCC$ orbitals while the $(10,10)$ active space adds the $\siCC$ and $\sisCC$ orbitals.}
|
|
The state-averaged (SA) CASSCF calculation is performed with $2$ states.
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Butadiene & SA-CASSCF(4,4) & 6-31+G* & -154.973\,885 & -154.729\,068 & 6.66 \\
|
|
& & AVDZ & -154.987\,684 & -154.743\,317 & 6.65 \\
|
|
& & AVTZ & -155.026\,077 & -154.782\,092 & 6.64 \\
|
|
& & AVQZ & -155.035\,161 & -154.791\,236 & 6.64 \\
|
|
& CASPT2(4,4) & 6-31+G* & -155.429\,138 & -155.178\,472 & 6.82 \\
|
|
& & AVDZ & -155.493\,427 & -155.243\,990 & 6.79 \\
|
|
& & AVTZ & -155.637\,204 & -155.388\,901 & 6.76 \\
|
|
& & AVQZ & -155.681\,619 & -155.433\,024 & 6.76 \\
|
|
& MS-CASPT2(4,4) & 6-31+G* & -155.429\,142 & -155.178\,468 & 6.82 \\
|
|
& & AVDZ & -155.493\,429 & -155.243\,989 & 6.79 \\
|
|
& & AVTZ & -155.637\,207 & -155.388\,898 & 6.76 \\
|
|
& & AVQZ & -155.681\,624 & -155.433\,019 & 6.76 \\
|
|
& XMS-CASPT2(4,4) & 6-31+G* & -155.429\,147 & -155.178\,464 & 6.82 \\
|
|
& & AVDZ & -155.493\,431 & -155.243\,985 & 6.79 \\
|
|
& & AVTZ & -155.637\,212 & -155.388\,892 & 6.76 \\
|
|
& & AVQZ & -155.681\,629 & -155.433\,013 & 6.77 \\
|
|
& PC-NEVPT2(4,4) & 6-31+G* & -155.437\,512 & -155.183\,695 & 6.91 \\
|
|
& & AVDZ & -155.501\,541 & -155.248\,495 & 6.89 \\
|
|
& & AVTZ & -155.645\,027 & -155.393\,039 & 6.86 \\
|
|
& & AVQZ & -155.689\,335 & -155.437\,062 & 6.86 \\
|
|
& SC-NEVPT2(4,4) & 6-31+G* & -155.437\,070 & -155.182\,225 & 6.93 \\
|
|
& & AVDZ & -155.501\,076 & -155.246\,822 & 6.92 \\
|
|
& & AVTZ & -155.644\,552 & -155.391\,318 & 6.89 \\
|
|
& & AVQZ & -155.688\,858 & -155.435\,387 & 6.90 \\
|
|
& SA-CASSCF(10,10)& 6-31+G* & -155.046\,301 & -154.789\,097 & 7.00 \\
|
|
& & AVDZ & -155.060\,856 & -154.803\,483 & 7.00 \\
|
|
& & AVTZ & -155.100\,013 & -154.843\,143 & 6.99 \\
|
|
& & AVQZ & -155.109\,236 & -154.852\,461 & 6.99 \\
|
|
& CASPT2(10,10) & 6-31+G* & -155.433\,830 & -155.184\,024 & 6.80 \\
|
|
& & AVDZ & -155.498\,365 & -155.249\,091 & 6.78 \\
|
|
& & AVTZ & -155.640\,528 & -155.392\,682 & 6.74 \\
|
|
& & AVQZ & -155.684\,195 & -155.436\,216 & 6.75 \\
|
|
& MS-CASPT2(10,10)& 6-31+G* & -155.433\,839 & -155.184\,016 & 6.80 \\
|
|
& & AVDZ & -155.498\,370 & -155.249\,086 & 6.78 \\
|
|
& & AVTZ & -155.640\,537 & -155.392\,673 & 6.74 \\
|
|
& & AVQZ & -155.684\,206 & -155.436\,205 & 6.75 \\
|
|
& XMS-CASPT2(10,10)& 6-31+G* & -155.433\,843 & -155.184\,013 & 6.80 \\
|
|
& & AVDZ & -155.498\,372 & -155.249\,085 & 6.78 \\
|
|
& & AVTZ & -155.640\,541 & -155.392\,670 & 6.74 \\
|
|
& & AVQZ & -155.684\,210 & -155.436\,202 & 6.75 \\
|
|
& PC-NEVPT2(10,10)& 6-31+G* & -155.423\,461 & -155.175\,243 & 6.75 \\
|
|
& & AVDZ & -155.485\,031 & -155.237\,429 & 6.74 \\
|
|
& & AVTZ & -155.623\,947 & -155.377\,725 & 6.70 \\
|
|
& & AVQZ & -155.666\,748 & -155.420\,408 & 6.70 \\
|
|
& SC-NEVPT2(10,10)& 6-31+G* & -155.418\,966 & -155.167\,964 & 6.83 \\
|
|
& & AVDZ & -155.480\,099 & -155.229\,526 & 6.82 \\
|
|
& & AVTZ & -155.618\,701 & -155.369\,542 & 6.78 \\
|
|
& & AVQZ & -155.661\,442 & -155.412\,153 & 6.78 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
|
|
%------------------------------
|
|
\subsection{Carbon dimer}
|
|
%------------------------------
|
|
|
|
%%% CARBON DIMER %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:C2_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of the carbon dimer for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
The $(8,8)$ active space contains all the valence electrons and orbitals.
|
|
The state-averaged (SA) CASSCF calculations for the 1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+} and 1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{} transitions are performed with $2$ and $3$ states, respectively.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{llldddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}
|
|
& \mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}} \\
|
|
\cline{4-6} \cline{7-9}
|
|
& & & \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{2\,\ex{1}{\Sigma}{g}{+}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{1\,\ex{1}{\Delta}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Carbon dimer& SA-CASSCF(8,8) & 6-31+G* & -75.611\,462 & -75.505\,844 & 2.87 & -75.606\,326 & -75.511\,554 & 2.58 \\
|
|
& & AVDZ & -75.615\,948 & -75.510\,158 & 2.88 & -75.610\,186 & -75.516\,995 & 2.54 \\
|
|
& & AVTZ & -75.629\,954 & -75.525\,529 & 2.84 & -75.623\,869 & -75.532\,462 & 2.49 \\
|
|
& & AVQZ & -75.634\,302 & -75.529\,926 & 2.84 & -75.628\,160 & -75.536\,889 & 2.48 \\
|
|
& CASPT2(8,8) & 6-31+G* & -75.712\,841 & -75.616\,625 & 2.62 & -75.712\,081 & -75.624\,016 & 2.40 \\
|
|
& & AVDZ & -75.720\,037 & -75.622\,541 & 2.65 & -75.718\,980 & -75.632\,150 & 2.36 \\
|
|
& & AVTZ & -75.771\,020 & -75.677\,915 & 2.53 & -75.770\,442 & -75.688\,258 & 2.24 \\
|
|
& & AVQZ & -75.788\,081 & -75.696\,113 & 2.50 & -75.787\,711 & -75.706\,614 & 2.21 \\
|
|
& MS-CASPT2(8,8) & 6-31+G* & -75.713\,015 & -75.616\,451 & 2.63 & -75.712\,081 & -75.624\,016 & 2.40 \\
|
|
& & AVDZ & -75.720\,227 & -75.622\,351 & 2.66 & -75.718\,980 & -75.632\,150 & 2.36 \\
|
|
& & AVTZ & -75.771\,335 & -75.677\,601 & 2.55 & -75.770\,442 & -75.688\,258 & 2.24 \\
|
|
& & AVQZ & -75.788\,434 & -75.695\,760 & 2.52 & -75.787\,711 & -75.706\,614 & 2.21 \\
|
|
& XMS-CASPT2(8,8) & 6-31+G* & -75.712\,895 & -75.616\,452 & 2.62 & -75.712\,081 & -75.624\,016 & 2.40 \\
|
|
& & AVDZ & -75.720\,084 & -75.622\,349 & 2.66 & -75.718\,980 & -75.632\,150 & 2.36 \\
|
|
& & AVTZ & -75.771\,145 & -75.677\,625 & 2.54 & -75.770\,442 & -75.688\,258 & 2.24 \\
|
|
& & AVQZ & -75.788\,231 & -75.695\,795 & 2.52 & -75.787\,711 & -75.706\,614 & 2.21 \\
|
|
& PC-NEVPT2(8,8) & 6-31+G* & -75.705\,939 & -75.612\,560 & 2.54 & -75.705\,885 & -75.620\,265 & 2.33 \\
|
|
& & AVDZ & -75.711\,503 & -75.618\,073 & 2.54 & -75.711\,303 & -75.628\,447 & 2.25 \\
|
|
& & AVTZ & -75.759\,612 & -75.670\,557 & 2.42 & -75.759\,837 & -75.681\,954 & 2.12 \\
|
|
& & AVQZ & -75.775\,832 & -75.688\,105 & 2.39 & -75.776\,239 & -75.699\,658 & 2.08 \\
|
|
& SC-NEVPT2(8,8) & 6-31+G* & -75.703\,755 & -75.608\,773 & 2.58 & -75.703\,208 & -75.616\,965 & 2.35 \\
|
|
& & AVDZ & -75.709\,115 & -75.613\,713 & 2.60 & -75.708\,307 & -75.624\,464 & 2.28 \\
|
|
& & AVTZ & -75.757\,077 & -75.666\,007 & 2.48 & -75.756\,627 & -75.677\,825 & 2.14 \\
|
|
& & AVQZ & -75.773\,268 & -75.683\,471 & 2.44 & -75.772\,982 & -75.695\,459 & 2.11 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
|
|
%------------------------------
|
|
\subsection{Carbon trimer}
|
|
%------------------------------
|
|
|
|
%%% CARBON TRIMER %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:C3_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of the carbon trimer for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
The $(12,12)$ active space contains all the valence electrons and orbitals.
|
|
The state-averaged (SA) CASSCF calculations for the 1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+} and 1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{} transitions are performed with $2$ and $3$ states, respectively.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{llldddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}
|
|
& \mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}} \\
|
|
\cline{4-6} \cline{7-9}
|
|
& & & \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{2\,\ex{1}{\Sigma}{g}{+}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{1\,\ex{1}{\Delta}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Carbon trimer& SA-CASSCF(12,12) & 6-31+G* & -113.547\,179 & -113.332\,694 & 5.84 & -113.543\,499 & -113.360\,079 & 4.99 \\
|
|
& & AVDZ & -113.554\,346 & -113.340\,290 & 5.82 & -113.550\,471 & -113.367\,517 & 4.98 \\
|
|
& & AVTZ & -113.576\,466 & -113.361\,965 & 5.84 & -113.572\,398 & -113.389\,220 & 4.98 \\
|
|
& & AVQZ & -113.582\,463 & -113.368\,153 & 5.83 & -113.578\,357 & -113.395\,436 & 4.98 \\
|
|
& CASPT2(12,12) & 6-31+G* & -113.716\,995 & -113.501\,672 & 5.86 & -113.715\,833 & -113.527\,402 & 5.13 \\
|
|
& & AVDZ & -113.728\,453 & -113.514\,880 & 5.81 & -113.727\,030 & -113.540\,997 & 5.06 \\
|
|
& & AVTZ & -113.810\,722 & -113.596\,829 & 5.82 & -113.809\,454 & -113.622\,903 & 5.08 \\
|
|
& & AVQZ & -113.837\,431 & -113.623\,512 & 5.82 & -113.836\,208 & -113.649\,414 & 5.08 \\
|
|
& MS-CASPT2(12,12) & 6-31+G* & -113.716\,996 & -113.501\,671 & 5.86 & -113.715\,833 & -113.527\,402 & 5.13 \\
|
|
& & AVDZ & -113.728\,454 & -113.514\,879 & 5.81 & -113.727\,030 & -113.540\,997 & 5.06 \\
|
|
& & AVTZ & -113.810\,722 & -113.596\,828 & 5.82 & -113.809\,454 & -113.622\,903 & 5.08 \\
|
|
& & AVQZ & -113.837\,431 & -113.623\,511 & 5.82 & -113.836\,208 & -113.649\,414 & 5.08 \\
|
|
& XMS-CASPT2(12,12) & 6-31+G* & -113.716\,997 & -113.501\,671 & 5.86 & -113.715\,833 & -113.527\,402 & 5.13 \\
|
|
& & AVDZ & -113.728\,456 & -113.514\,879 & 5.81 & -113.727\,030 & -113.540\,997 & 5.06 \\
|
|
& & AVTZ & -113.810\,725 & -113.596\,828 & 5.82 & -113.809\,454 & -113.622\,903 & 5.08 \\
|
|
& & AVQZ & -113.837\,433 & -113.623\,511 & 5.82 & -113.836\,208 & -113.649\,414 & 5.08 \\
|
|
& PC-NEVPT2(12,12) & 6-31+G* & -113.711\,719 & -113.492\,466 & 5.97 & -113.711\,402 & -113.518\,270 & 5.26 \\
|
|
& & AVDZ & -113.722\,348 & -113.502\,996 & 5.97 & -113.721\,864 & -113.529\,435 & 5.24 \\
|
|
& & AVTZ & -113.800\,831 & -113.580\,845 & 5.99 & -113.800\,484 & -113.607\,374 & 5.25 \\
|
|
& & AVQZ & -113.826\,452 & -113.606\,310 & 5.99 & -113.826\,144 & -113.632\,678 & 5.26 \\
|
|
& SC-NEVPT2(12,12) & 6-31+G* & -113.705\,615 & -113.485\,949 & 5.98 & -113.704\,595 & -113.513\,036 & 5.21 \\
|
|
& & AVDZ & -113.715\,356 & -113.495\,802 & 5.97 & -113.714\,109 & -113.523\,345 & 5.19 \\
|
|
& & AVTZ & -113.793\,489 & -113.573\,267 & 5.99 & -113.792\,375 & -113.600\,931 & 5.21 \\
|
|
& & AVQZ & -113.819\,136 & -113.598\,720 & 6.00 & -113.818\,079 & -113.626\,223 & 5.22 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Ethylene}
|
|
%------------------------------
|
|
|
|
%%% ETHYLENE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:ethylene_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of ethylene for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
The $(2,2)$ active space includes the $\piCC$ and $\pisCC$ orbitals while the $(4,4)$ active space adds the $\siCC$ and $\sisCC$ orbitals.}
|
|
The state-averaged (SA) CASSCF calculation is performed with $2$ states.
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Ethylene & SA-CASSCF(2,2) & 6-31+G* & -78.050\,262 & -77.512\,725 & 14.63 \\
|
|
& & AVDZ & -78.057\,788 & -77.523\,386 & 14.54 \\
|
|
& & AVTZ & -78.078\,753 & -77.544\,816 & 14.53 \\
|
|
& & AVQZ & -78.083\,447 & -77.549\,521 & 14.53 \\
|
|
& CASPT2(2,2) & 6-31+G* & -78.288\,566 & -77.793\,374 & 13.47 \\
|
|
& & AVDZ & -78.327\,262 & -77.842\,617 & 13.19 \\
|
|
& & AVTZ & -78.403\,843 & -77.921\,305 & 13.13 \\
|
|
& & AVQZ & -78.427\,094 & -77.944\,614 & 13.13 \\
|
|
& MS-CASPT2(2,2) & 6-31+G* & -78.290\,306 & -77.791\,633 & 13.57 \\
|
|
& & AVDZ & -78.329\,197 & -77.840\,682 & 13.29 \\
|
|
& & AVTZ & -78.406\,016 & -77.919\,132 & 13.25 \\
|
|
& & AVQZ & -78.429\,366 & -77.942\,342 & 13.25 \\
|
|
& PC-NEVPT2(2,2) & 6-31+G* & -78.292\,578 & -77.793\,016 & 13.59 \\
|
|
& & AVDZ & -78.331\,562 & -77.851\,953 & 13.05 \\
|
|
& & AVTZ & -78.407\,808 & -77.937\,524 & 12.80 \\
|
|
& & AVQZ & -78.430\,942 & -77.964\,042 & 12.70 \\
|
|
& SC-NEVPT2(2,2) & 6-31+G* & -78.292\,491 & -77.792\,730 & 13.60 \\
|
|
& & AVDZ & -78.331\,469 & -77.851\,664 & 13.06 \\
|
|
& & AVTZ & -78.407\,725 & -77.937\,244 & 12.80 \\
|
|
& & AVQZ & -78.430\,856 & -77.963\,758 & 12.71 \\
|
|
& SA-CASSCF(4,4) & 6-31+G* & -78.074\,309 & -77.552\,058 & 14.21 \\
|
|
& & AVDZ & -78.082\,060 & -77.562\,851 & 14.13 \\
|
|
& & AVTZ & -78.103\,340 & -77.584\,460 & 14.12 \\
|
|
& & AVQZ & -78.108\,098 & -77.589\,227 & 14.12 \\
|
|
& CASPT2(4,4) & 6-31+G* & -78.290\,576 & -77.794\,942 & 13.49 \\
|
|
& & AVDZ & -78.329\,298 & -77.843\,094 & 13.23 \\
|
|
& & AVTZ & -78.405\,586 & -77.921\,465 & 13.17 \\
|
|
& & AVQZ & -78.428\,668 & -77.944\,571 & 13.17 \\
|
|
& MS-CASPT2(4,4) & 6-31+G* & -78.291\,055 & -77.794\,463 & 13.51 \\
|
|
& & AVDZ & -78.329\,856 & -77.842\,536 & 13.26 \\
|
|
& & AVTZ & -78.406\,272 & -77.920\,779 & 13.21 \\
|
|
& & AVQZ & -78.429\,409 & -77.943\,830 & 13.21 \\
|
|
& XMS-CASPT(4,4) & 6-31+G* & -78.290\,264 & -77.794\,002 & 13.50 \\
|
|
& & AVDZ & -78.328\,964 & -77.842\,084 & 13.25 \\
|
|
& & AVTZ & -78.405\,304 & -77.920\,370 & 13.20 \\
|
|
& & AVQZ & -78.428\,415 & -77.943\,434 & 13.20 \\
|
|
& PC-NEVPT2(4,4) & 6-31+G* & -78.289\,445 & -77.761\,980 & 14.35 \\
|
|
& & AVDZ & -78.327\,336 & -77.834\,250 & 13.42 \\
|
|
& & AVTZ & -78.402\,555 & -77.920\,807 & 13.11 \\
|
|
& & AVQZ & -78.425\,291 & -77.946\,194 & 13.04 \\
|
|
& SC-NEVPT2(4,4) & 6-31+G* & -78.287\,620 & -77.788\,941 & 13.57 \\
|
|
& & AVDZ & -78.325\,393 & -77.835\,389 & 13.33 \\
|
|
& & AVTZ & -78.400\,680 & -77.913\,304 & 13.26 \\
|
|
& & AVQZ & -78.423\,404 & -77.936\,130 & 13.26 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
|
|
%------------------------------
|
|
\subsection{Formaldehyde}
|
|
%------------------------------
|
|
|
|
%%% FORMALDEHYDE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:formaldehyde_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of formaldehyde for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
The $(4,3)$ active space contains the $\piCO$, $\pisCO$ orbitals and the lone pair on the oxygen atom $\nO$, while the $(6,5)$ active space adds up the $\siCO$ and $\sisCO$ orbitals.
|
|
The state-averaged (SA) CASSCF calculation is performed with $3$ states.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{llldddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi}{\pis}}
|
|
& \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{4-6}\cline{7-9}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{3\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Formaldehyde& SA-CASSCF(4,3) & 6-31+G* & -113.888\,047 & -113.459\,444 & 11.66 & -113.888\,047 & -113.434\,017 & 12.35 \\
|
|
& & AVDZ & -113.901\,336 & -113.480\,975 & 11.44 & -113.901\,336 & -113.458\,501 & 12.05 \\
|
|
& & AVTZ & -113.929\,392 & -113.510\,948 & 11.39 & -113.929\,392 & -113.486\,477 & 12.05 \\
|
|
& & AVQZ & -113.936\,772 & -113.518\,386 & 11.38 & -113.936\,772 & -113.493\,946 & 12.05 \\
|
|
& CASPT2(4,3) & 6-31+G* & -114.173\,092 & -113.809\,464 & 9.89 & -114.173\,092 & -113.780\,818 & 10.67 \\
|
|
& & AVDZ & -114.219\,234 & -113.862\,472 & 9.71 & -114.219\,234 & -113.842\,350 & 10.26 \\
|
|
& & AVTZ & -114.317\,115 & -113.964\,834 & 9.59 & -114.317\,115 & -113.943\,362 & 10.17 \\
|
|
& & AVQZ & -114.349\,288 & -113.997\,944 & 9.56 & -114.349\,288 & -113.975\,898 & 10.16 \\
|
|
& MS-CASPT2(4,3) & 6-31+G* & -114.174\,654 & -113.808\,721 & 9.96 & -114.174\,654 & -113.779\,999 & 10.74 \\
|
|
& & AVDZ & -114.221\,059 & -113.861\,959 & 9.77 & -114.221\,059 & -113.841\,038 & 10.34 \\
|
|
& & AVTZ & -114.319\,457 & -113.963\,748 & 9.68 & -114.319\,457 & -113.942\,106 & 10.27 \\
|
|
& & AVQZ & -114.351\,896 & -113.996\,538 & 9.67 & -114.351\,896 & -113.974\,697 & 10.26 \\
|
|
& XMS-CASPT2(4,3) & 6-31+G* & -114.172\,660 & -113.809\,912 & 9.87 & -114.172\,660 & -113.779\,080 & 10.71 \\
|
|
& & AVDZ & -114.218\,915 & -113.863\,463 & 9.67 & -114.218\,915 & -113.839\,985 & 10.31 \\
|
|
& & AVTZ & -114.317\,029 & -113.965\,465 & 9.57 & -114.317\,029 & -113.941\,143 & 10.23 \\
|
|
& & AVQZ & -114.349\,335 & -113.998\,350 & 9.55 & -114.349\,335 & -113.973\,756 & 10.22 \\
|
|
& PC-NEVPT2(4,3) & 6-31+G* & -114.173\,095 & -113.831\,834 & 9.29 & -114.173\,095 & -113.774\,873 & 10.84 \\
|
|
& & AVDZ & -114.219\,119 & -113.885\,309 & 9.08 & -114.219\,119 & -113.837\,756 & 10.38 \\
|
|
& & AVTZ & -114.316\,536 & -113.987\,365 & 8.96 & -114.316\,536 & -113.938\,195 & 10.30 \\
|
|
& & AVQZ & -114.348\,498 & -114.020\,453 & 8.93 & -114.348\,498 & -113.970\,486 & 10.29 \\
|
|
& SC-NEVPT2(4,3) & 6-31+G* & -114.172\,451 & -113.819\,698 & 9.60 & -114.172\,451 & -113.773\,374 & 10.86 \\
|
|
& & AVDZ & -114.218\,408 & -113.872\,839 & 9.40 & -114.218\,408 & -113.835\,975 & 10.41 \\
|
|
& & AVTZ & -114.315\,807 & -113.974\,856 & 9.28 & -114.315\,807 & -113.936\,333 & 10.33 \\
|
|
& & AVQZ & -114.347\,768 & -114.007\,835 & 9.25 & -114.347\,768 & -113.968\,621 & 10.32 \\
|
|
& SA-CASSCF(6,5) & 6-31+G* & -113.923\,326 & -113.516\,669 & 11.07 & -113.923\,326 & -113.463\,675 & 12.51 \\
|
|
& & AVDZ & -113.936\,789 & -113.535\,947 & 10.91 & -113.936\,789 & -113.487\,565 & 12.22 \\
|
|
& & AVTZ & -113.965\,022 & -113.565\,649 & 10.87 & -113.965\,022 & -113.515\,771 & 12.22 \\
|
|
& & AVQZ & -113.972\,475 & -113.573\,112 & 10.87 & -113.972\,475 & -113.523\,326 & 12.22 \\
|
|
& CASPT2(6,5) & 6-31+G* & -114.168\,576 & -113.797\,541 & 10.10 & -114.168\,576 & -113.771\,544 & 10.80 \\
|
|
& & AVDZ & -114.214\,497 & -113.850\,396 & 9.91 & -114.214\,497 & -113.833\,160 & 10.38 \\
|
|
& & AVTZ & -114.312\,046 & -113.952\,410 & 9.79 & -114.312\,046 & -113.934\,618 & 10.27 \\
|
|
& & AVQZ & -114.344\,054 & -113.985\,267 & 9.76 & -114.344\,054 & -113.967\,170 & 10.26 \\
|
|
& MS-CASPT2(6,5) & 6-31+G* & -114.169\,130 & -113.798\,631 & 10.08 & -114.169\,130 & -113.769\,900 & 10.86 \\
|
|
& & AVDZ & -114.215\,151 & -113.851\,965 & 9.88 & -114.215\,151 & -113.830\,937 & 10.45 \\
|
|
& & AVTZ & -114.312\,919 & -113.953\,623 & 9.78 & -114.312\,919 & -113.932\,532 & 10.35 \\
|
|
& & AVQZ & -114.345\,057 & -113.986\,272 & 9.76 & -114.345\,057 & -113.965\,161 & 10.34 \\
|
|
& XMS-CASPT2(6,5) & 6-31+G* & -114.168\,274 & -113.799\,663 & 10.03 & -114.168\,274 & -113.768\,890 & 10.87 \\
|
|
& & AVDZ & -114.214\,224 & -113.853\,375 & 9.82 & -114.214\,224 & -113.829\,632 & 10.47 \\
|
|
& & AVTZ & -114.311\,859 & -113.955\,167 & 9.71 & -114.311\,859 & -113.931\,240 & 10.36 \\
|
|
& & AVQZ & -114.343\,925 & -113.987\,863 & 9.69 & -114.343\,925 & -113.963\,884 & 10.34 \\
|
|
& PC-NEVPT2(6,5) & 6-31+G* & -114.164\,041 & -113.797\,582 & 9.97 & -114.164\,041 & -113.765\,688 & 10.84 \\
|
|
& & AVDZ & -114.208\,870 & -113.849\,954 & 9.77 & -114.208\,870 & -113.827\,797 & 10.37 \\
|
|
& & AVTZ & -114.305\,480 & -113.951\,302 & 9.64 & -114.305\,480 & -113.928\,261 & 10.26 \\
|
|
& & AVQZ & -114.337\,071 & -113.983\,857 & 9.61 & -114.337\,071 & -113.960\,344 & 10.25 \\
|
|
& SC-NEVPT2(6,5) & 6-31+G* & -114.160\,723 & -113.782\,789 & 10.28 & -114.160\,723 & -113.761\,439 & 10.87 \\
|
|
& & AVDZ & -114.205\,182 & -113.833\,995 & 10.10 & -114.205\,182 & -113.823\,061 & 10.40 \\
|
|
& & AVTZ & -114.301\,651 & -113.935\,028 & 9.98 & -114.301\,651 & -113.923\,273 & 10.30 \\
|
|
& & AVQZ & -114.333\,299 & -113.967\,528 & 9.95 & -114.333\,299 & -113.955\,272 & 10.29 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
|
|
%------------------------------
|
|
\subsection{Glyoxal}
|
|
%------------------------------
|
|
|
|
%%% GLYOXAL %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:glyoxal_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of glyoxal for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
|
|
The $(8,6)$ active space contains the $\piCC$, $\piCO$, $\pisCC$ and $\pisCO$ orbitals as well as the two lone pairs $\nO$ on the oxygen atoms.
|
|
The $(14,12)$ active space adds up the $\siCC$, $\siCO$, $\sisCC$ and $\sisCO$ orbitals.
|
|
The state-averaged (SA) CASSCF calculation is performed with $2$ states.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Glyoxal & SA-CASSCF(8,6) & 6-31+G* & -226.657\,931 & -226.442\,282 & 5.87 \\
|
|
& & AVDZ & -226.685\,161 & -226.471\,894 & 5.80 \\
|
|
& & AVTZ & -226.737\,720 & -226.525\,322 & 5.78 \\
|
|
& & AVQZ & -226.752\,190 & -226.540\,026 & 5.77 \\
|
|
& CASPT2(8,6) & 6-31+G* & -227.186\,625 & -226.978\,713 & 5.66 \\
|
|
& & AVDZ & -227.263\,032 & -227.059\,166 & 5.55 \\
|
|
& & AVTZ & -227.451\,133 & -227.248\,454 & 5.52 \\
|
|
& & AVQZ & -227.513\,827 & -227.310\,931 & 5.52 \\
|
|
& PC-NEVPT2(8,6) & 6-31+G* & -227.187\,115 & -226.975\,789 & 5.75 \\
|
|
& & AVDZ & -227.262\,427 & -227.055\,140 & 5.64 \\
|
|
& & AVTZ & -227.449\,337 & -227.242\,966 & 5.62 \\
|
|
& & AVQZ & -227.511\,566 & -227.304\,962 & 5.62 \\
|
|
& SC-NEVPT2(8,6) & 6-31+G* & -227.184\,722 & -226.973\,382 & 5.75 \\
|
|
& & AVDZ & -227.259\,926 & -227.052\,509 & 5.64 \\
|
|
& & AVTZ & -227.446\,780 & -227.240\,281 & 5.62 \\
|
|
& & AVQZ & -227.508\,996 & -227.302\,250 & 5.63 \\
|
|
& SA-CASSCF(14,12) & 6-31+G* & -226.766\,881 & -226.545\,762 & 6.02 \\
|
|
& & AVDZ & -226.794\,485 & -226.576\,274 & 5.94 \\
|
|
& & AVTZ & -226.847\,573 & -226.629\,865 & 5.92 \\
|
|
& & AVQZ & -226.862\,224 & -226.644\,714 & 5.92 \\
|
|
& CASPT2(14,12) & 6-31+G* & -227.188\,569 & -226.983\,415 & 5.58 \\
|
|
& & AVDZ & -227.264\,637 & -227.063\,793 & 5.47 \\
|
|
& & AVTZ & -227.451\,181 & -227.251\,897 & 5.42 \\
|
|
& & AVQZ & -227.513\,332 & -227.313\,900 & 5.43 \\
|
|
& PC-NEVPT2(14,12) & 6-31+G* & -227.172\,385 & -226.964\,396 & 5.66 \\
|
|
& & AVDZ & -227.245\,339 & -227.041\,117 & 5.56 \\
|
|
& & AVTZ & -227.428\,412 & -227.225\,630 & 5.52 \\
|
|
& & AVQZ & -227.489\,355 & -227.286\,451 & 5.52 \\
|
|
& SC-NEVPT2(14,12) & 6-31+G* & -227.163\,921 & -226.955\,257 & 5.68 \\
|
|
& & AVDZ & -227.236\,400 & -227.031\,296 & 5.58 \\
|
|
& & AVTZ & -227.419\,144 & -227.215\,337 & 5.55 \\
|
|
& & AVQZ & -227.479\,947 & -227.276\,034 & 5.55 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
|
|
|
|
|
|
%------------------------------
|
|
\subsection{Hexatriene}
|
|
%------------------------------
|
|
|
|
%%% HEXATRIENE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:hexatriene_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of hexatriene for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
|
|
The $(6,6)$ active space contains the $\piCC$ and $\pisCC$ orbitals.
|
|
The state-averaged (SA) CASSCF calculation is performed with $2$ states.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Hexatriene & SA-CASSCF(6,6) & 6-31+G* & -231.892\,206 & -231.685\,636 & 5.62 \\
|
|
& & AVDZ & -231.912\,669 & -231.705\,976 & 5.62 \\
|
|
& & AVTZ & -231.968\,514 & -231.762\,041 & 5.62 \\
|
|
& & AVQZ & -231.981\,952 & -231.775\,526 & 5.62 \\
|
|
& CASPT2(6,6) & 6-31+G* & -232.569\,064 & -232.362\,351 & 5.62 \\
|
|
& & AVDZ & -232.658\,877 & -232.452\,721 & 5.61 \\
|
|
& & AVTZ & -232.870\,299 & -232.665\,237 & 5.58 \\
|
|
& & AVQZ & -232.935\,889 & -232.730\,678 & 5.58 \\
|
|
& PC-NEVPT2(6,6) & 6-31+G* & -232.581\,395 & -232.372\,911 & 5.67 \\
|
|
& & AVDZ & -232.670\,452 & -232.462\,312 & 5.66 \\
|
|
& & AVTZ & -232.881\,425 & -232.674\,317 & 5.64 \\
|
|
& & AVQZ & -232.946\,879 & -232.739\,625 & 5.64 \\
|
|
& SC-NEVPT2(6,6) & 6-31+G* & -232.580\,549 & -232.371\,009 & 5.70 \\
|
|
& & AVDZ & -232.669\,518 & -232.460\,234 & 5.69 \\
|
|
& & AVTZ & -232.880\,451 & -232.672\,201 & 5.67 \\
|
|
& & AVQZ & -232.945\,903 & -232.737\,479 & 5.67 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Nitrosomethane}
|
|
%------------------------------
|
|
|
|
%%% NITROSOMETHANE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:nitrosomethane_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of nitrosomethane for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
|
|
The $(12,9)$ active space contains all the valence orbitals of the \ce{NO} fragment and the $\si_{\ce{CN}}$ and $\sis_{\ce{CN}}$ orbitals.
|
|
The state-averaged (SA) CASSCF calculation is performed with $2$ states.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{llcddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{}{'}} & \mcc{2\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Nitrosomethane & SA-CASSCF(12,9) & 6-31+G* & -168.951\,279 & -168.766\,809 & 5.02 \\
|
|
& & AVDZ & -168.974\,372 & -168.790\,139 & 5.01 \\
|
|
& & AVTZ & -169.012\,519 & -168.830\,006 & 4.97 \\
|
|
& & AVQZ & -169.023\,256 & -168.840\,918 & 4.96 \\
|
|
& CASPT2(12,9) & 6-31+G* & -169.303\,499 & -169.122\,262 & 4.93 \\
|
|
& & AVDZ & -169.370\,350 & -169.190\,998 & 4.88 \\
|
|
& & AVTZ & -169.513\,053 & -169.336\,897 & 4.79 \\
|
|
& & AVQZ & -169.559\,726 & -169.384\,048 & 4.78 \\
|
|
& PC-NEVPT2(12,9) & 6-31+G* & -169.289\,373 & -169.108\,467 & 4.92 \\
|
|
& & AVDZ & -169.354\,372 & -169.174\,985 & 4.88 \\
|
|
& & AVTZ & -169.492\,645 & -169.316\,471 & 4.79 \\
|
|
& & AVQZ & -169.537\,983 & -169.362\,288 & 4.78 \\
|
|
& SC-NEVPT2(12,9) & 6-31+G* & -169.282\,438 & -169.100\,953 & 4.94 \\
|
|
& & AVDZ & -169.346\,856 & -169.166\,729 & 4.90 \\
|
|
& & AVTZ & -169.484\,718 & -169.307\,777 & 4.81 \\
|
|
& & AVQZ & -169.529\,935 & -169.353\,475 & 4.80 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Nitroxyl}
|
|
%------------------------------
|
|
|
|
%%% NITRSOXYL %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:nitroxyl_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of nitroxyl for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
|
|
The $(12,9)$ active space contains all the valence orbitals (including the $\si_{\ce{CH}}$ and $\sis_{\ce{CH}}$ orbitals).
|
|
The state-averaged (SA) CASSCF calculation is performed with $2$ states.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{4-6}
|
|
& & & \mcc{1\,\ex{1}{A}{}{'}} & \mcc{2\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Nitroxyl& SA-CASSCF(12,9) & 6-31+G* & -129.911\,884 & -129.735\,534 & 4.80 \\
|
|
& & AVDZ & -129.932\,723 & -129.760\,088 & 4.70 \\
|
|
& & AVTZ & -129.960\,749 & -129.789\,113 & 4.67 \\
|
|
& & AVQZ & -129.969\,310 & -129.797\,750 & 4.67 \\
|
|
& CASPT2(12,9) & 6-31+G* & -130.133\,397 & -129.966\,066 & 4.55 \\
|
|
& & AVDZ & -130.182\,652 & -130.018\,908 & 4.46 \\
|
|
& & AVTZ & -130.286\,304 & -130.125\,988 & 4.36 \\
|
|
& & AVQZ & -130.321\,398 & -130.161\,843 & 4.34 \\
|
|
& PC-NEVPT2(12,9) & 6-31+G* & -130.119\,401 & -129.951\,698 & 4.56 \\
|
|
& & AVDZ & -130.166\,359 & -130.002\,551 & 4.46 \\
|
|
& & AVTZ & -130.265\,882 & -130.105\,240 & 4.37 \\
|
|
& & AVQZ & -130.299\,672 & -130.139\,724 & 4.35 \\
|
|
& SC-NEVPT2(12,9) & 6-31+G* & -130.113\,407 & -129.944\,930 & 4.58 \\
|
|
& & AVDZ & -130.159\,685 & -129.994\,868 & 4.48 \\
|
|
& & AVTZ & -130.258\,778 & -130.097\,150 & 4.40 \\
|
|
& & AVQZ & -130.292\,532 & -130.131\,589 & 4.38 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
|
|
%------------------------------
|
|
\subsection{Pyrazine}
|
|
%------------------------------
|
|
|
|
%%% PYRAZINE %%%
|
|
\begin{squeezetable}
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:pyrazine_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of pyrazine for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
Note the inversion of the two transitions compared to coupled cluster calculations (see Table \ref{tab:pyrazine_CC}).
|
|
The $(10,8)$ active space corresponds to the valence $\pi$ space and the two lone pairs $\nN$ on the nitrogen atoms.
|
|
The state-averaged (SA) CASSCF calculation for both transitions is performed with $3$ states.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{llldddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}}
|
|
& \mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{4-6} \cline{7-9}
|
|
& & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{3\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Pyrazine & SA-CASSCF(10,8) & 6-31+G* & -262.766\,608 & -262.466\,222 & 8.17 & -262.766\,608 & -262.455\,042 & 8.48 \\
|
|
& & AVDZ & -262.792\,310 & -262.492\,573 & 8.16 & -262.792\,310 & -262.481\,386 & 8.46 \\
|
|
& & AVTZ & -262.848\,167 & -262.550\,711 & 8.09 & -262.848\,167 & -262.538\,133 & 8.44 \\
|
|
& & AVQZ & -262.863\,329 & -262.566\,129 & 8.09 & -262.863\,329 & -262.553\,469 & 8.43 \\
|
|
& CASPT2(10,8) & 6-31+G* & -263.497\,967 & -263.201\,845 & 8.06 & -263.497\,967 & -263.170\,469 & 8.91 \\
|
|
& & AVDZ & -263.570\,062 & -263.279\,499 & 7.91 & -263.570\,062 & -263.244\,814 & 8.85 \\
|
|
& & AVTZ & -263.792\,911 & -263.505\,970 & 7.81 & -263.792\,911 & -263.470\,505 & 8.77 \\
|
|
& & AVQZ & -263.865\,083 & -263.578\,276 & 7.80 & -263.865\,083 & -263.542\,729 & 8.77 \\
|
|
& MS-CASPT2(10,8) & 6-31+G* & -263.498\,163 & -263.201\,849 & 8.06 & -263.498\,163 & -263.170\,269 & 8.92 \\
|
|
& & AVDZ & -263.570\,282 & -263.279\,508 & 7.91 & -263.570\,282 & -263.244\,585 & 8.86 \\
|
|
& & AVTZ & -263.793\,167 & -263.505\,971 & 7.81 & -263.793\,167 & -263.470\,248 & 8.79 \\
|
|
& & AVQZ & -263.865\,351 & -263.578\,276 & 7.81 & -263.865\,351 & -263.542\,460 & 8.79 \\
|
|
& XMS-CASPT2(10,8) & 6-31+G* & -263.498\,193 & -263.201\,862 & 8.06 & -263.498\,193 & -263.170\,207 & 8.92 \\
|
|
& & AVDZ & -263.570\,300 & -263.279\,528 & 7.91 & -263.570\,300 & -263.244\,520 & 8.86 \\
|
|
& & AVTZ & -263.793\,179 & -263.505\,986 & 7.81 & -263.793\,179 & -263.470\,190 & 8.79 \\
|
|
& & AVQZ & -263.865\,363 & -263.578\,291 & 7.81 & -263.865\,363 & -263.542\,403 & 8.79 \\
|
|
& PC-NEVPT2(10,8) & 6-31+G* & -263.504\,412 & -263.201\,181 & 8.25 & -263.504\,412 & -263.169\,289 & 9.12 \\
|
|
& & AVDZ & -263.575\,850 & -263.277\,429 & 8.12 & -263.575\,850 & -263.242\,663 & 9.07 \\
|
|
& & AVTZ & -263.797\,309 & -263.501\,963 & 8.04 & -263.797\,309 & -263.466\,615 & 9.00 \\
|
|
& & AVQZ & -263.869\,053 & -263.573\,733 & 8.04 & -263.869\,053 & -263.538\,356 & 9.00 \\
|
|
& SC-NEVPT2(10,8) & 6-31+G* & -263.502\,262 & -263.198\,175 & 8.27 & -263.502\,262 & -263.165\,513 & 9.16 \\
|
|
& & AVDZ & -263.573\,569 & -263.274\,044 & 8.15 & -263.573\,569 & -263.238\,492 & 9.12 \\
|
|
& & AVTZ & -263.794\,986 & -263.498\,517 & 8.07 & -263.794\,986 & -263.462\,364 & 9.05 \\
|
|
& & AVQZ & -263.866\,723 & -263.570\,259 & 8.07 & -263.866\,723 & -263.534\,098 & 9.05 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
\end{squeezetable}
|
|
|
|
|
|
|
|
%------------------------------
|
|
\subsection{Tetrazine}
|
|
%------------------------------
|
|
|
|
%%% TETRAZINE %%%
|
|
\begin{squeezetable}
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:tetrazine_CAS}
|
|
Energies (in hartree) and transition energies $\Delta E$ (in eV) of tetrazine for various methods and basis sets.
|
|
The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
|
|
The $(14,10)$ active space corresponds to the valence $\pi$ space and the four lone pairs $\nN$ on the nitrogen atoms.
|
|
The state-averaged (SA) CASSCF calculations for the 1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{}, 1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{B}{3g}{} and 1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{3}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2} transitions are performed separately with $2$ states.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllddddddddd}
|
|
Molecule & Method & Basis & \mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{}: \tr{n,n}{\pis,\pis}}
|
|
& \mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2}}
|
|
& \mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{3}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2}} \\
|
|
\cline{4-6} \cline{7-9} \cline{10-12}
|
|
& & & \mcc{1\,\ex{1}{A}{1g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{A}{1g}{}} & \mcc{1\,\ex{1}{B}{3g}{}} & \mcc{$\Delta E$}
|
|
& \mcc{1\,\ex{1}{A}{1g}{}} & \mcc{1\,\ex{3}{B}{3g}{}} & \mcc{$\Delta E$} \\
|
|
\hline
|
|
Tetrazine & SA-CASSCF(14,10) & 6-31+G* & -294.690\,221 & -294.490\,365 & 5.44 & -294.690\,155 & -294.448\,416 & 6.58 & -294.690\,183 & -294.449\,273 & 6.56\\
|
|
& & AVDZ & -294.727\,767 & -294.526\,292 & 5.48 & -294.727\,650 & -294.483\,506 & 6.64 & -294.727\,698 & -294.484\,773 & 6.61\\
|
|
& & AVTZ & -294.786\,064 & -294.586\,910 & 5.42 & -294.785\,943 & -294.543\,776 & 6.59 & -294.786\,000 & -294.544\,836 & 6.56\\
|
|
& & AVQZ & -294.803\,516 & -294.604\,540 & 5.41 & -294.803\,391 & -294.561\,405 & 6.58 & -294.803\,451 & -294.562\,445 & 6.56\\
|
|
& CASPT2(14,10) & 6-31+G* & -295.477\,304 & -295.298\,713 & 4.86 & -295.471\,597 & -295.251\,195 & 6.00 & -295.471\,629 & -295.267\,973 & 5.54\\
|
|
& & AVDZ & -295.553\,748 & -295.377\,640 & 4.79 & -295.548\,053 & -295.329\,564 & 5.95 & -295.548\,168 & -295.347\,101 & 5.47\\
|
|
& & AVTZ & -295.792\,600 & -295.620\,128 & 4.69 & -295.786\,792 & -295.571\,688 & 5.85 & -295.786\,920 & -295.588\,928 & 5.39\\
|
|
& & AVQZ & -295.872\,580 & -295.700\,460 & 4.68 & -295.866\,703 & -295.651\,866 & 5.85 & -295.866\,836 & -295.668\,899 & 5.39\\
|
|
& PC-NEVPT2(14,10) & 6-31+G* & -295.472\,765 & -295.298\,260 & 4.75 & -295.471\,378 & -295.241\,519 & 6.25 & -295.472\,493 & -295.265\,525 & 5.63\\
|
|
& & AVDZ & -295.548\,353 & -295.375\,655 & 4.70 & -295.547\,076 & -295.318\,367 & 6.22 & -295.548\,211 & -295.343\,195 & 5.58\\
|
|
& & AVTZ & -295.784\,554 & -295.615\,226 & 4.61 & -295.783\,476 & -295.557\,518 & 6.15 & -295.784\,648 & -295.582\,320 & 5.51\\
|
|
& & AVQZ & -295.863\,782 & -295.694\,805 & 4.60 & -295.862\,719 & -295.636\,896 & 6.14 & -295.863\,910 & -295.661\,564 & 5.51\\
|
|
& SC-NEVPT2(14,10) & 6-31+G* & -295.469\,393 & -295.292\,159 & 4.82 & -295.467\,983 & -295.236\,511 & 6.30 & -295.468\,997 & -295.259\,950 & 5.69\\
|
|
& & AVDZ & -295.544\,750 & -295.369\,146 & 4.78 & -295.543\,436 & -295.312\,892 & 6.27 & -295.544\,465 & -295.337\,135 & 5.64\\
|
|
& & AVTZ & -295.780\,889 & -295.608\,612 & 4.69 & -295.779\,775 & -295.551\,944 & 6.20 & -295.780\,838 & -295.576\,130 & 5.57\\
|
|
& & AVQZ & -295.860\,099 & -295.688\,149 & 4.68 & -295.859\,007 & -295.631\,295 & 6.20 & -295.860\,088 & -295.655\,345 & 5.57\\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
\end{squeezetable}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\section{Energetics of selected CI calculations}
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
%------------------------------
|
|
\subsection{Acrolein}
|
|
%------------------------------
|
|
|
|
%%% ACROLEIN %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:acrolein_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of acrolein for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddddddd}
|
|
Molecule& Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi}{\pis}}
|
|
& \mc{4}{c}{1\,\ex{1}{A}{g}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{5-8} \cline{9-12}
|
|
& & & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} & \mcc{Error}
|
|
& \mcc{1\,\ex{1}{A}{g}{}} & \mcc{3\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Acrolein & sCI+PT2 & 6-31+G* & $228\,482\,893$ & -191.3674 & -191.1124 & 6.94 &
|
|
& -191.3674 & -191.0708 & 8.07 \\
|
|
% & & AVDZ & $128\,777\,969$ & & & \\
|
|
& exFCI & 6-31+G* & & -191.3720 & -191.1190 & 6.89 & 0.02
|
|
& -191.3720 & -191.0782 & 8.00 & 0.03 \\
|
|
% & & AVDZ & & & & & \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Benzene}
|
|
%------------------------------
|
|
|
|
%%% BENZENE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:benzene_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of benzene for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddd}
|
|
Molecule& Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{E}{2g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{5-8}
|
|
& & & & \mcc{1\,\ex{1}{S}{}{}} & \mcc{1\,\ex{1}{D}{}{'}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Benzene & sCI+PT2 & 6-31+G* & $128\,138\,453$ & -231.5185 & -231.2089 & 8.43 \\
|
|
& & AVDZ & $$ & & & \\
|
|
& exFCI & 6-31+G* & & -231.5384 & -231.2299 & 8.40 & 0.03 \\
|
|
& & AVDZ & & & & & \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Beryllium}
|
|
%------------------------------
|
|
|
|
%%% BERYLLIUM %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:Be_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of beryllium for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddd}
|
|
Molecule& Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{S}{}{} $\ra$ 1\,\ex{1}{D}{}{}: \tr{2s^2}{2p^2}} \\
|
|
\cline{5-8}
|
|
& & & & \mcc{1\,\ex{1}{S}{}{}} & \mcc{1\,\ex{1}{D}{}{'}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Beryllium & sCI+PT2 & 6-31+G* & $6\,061$ & -14.6156 & -14.3202 & 8.04 \\
|
|
& & AVDZ & $4\,515$ & -14.6175 & -14.3520 & 7.22 \\
|
|
& & AVTZ & $259\,196$ & -14.6244 & -14.3616 & 7.15 \\
|
|
& & AVQZ & $1\,266\,592$ & -14.6403 & -14.3790 & 7.11 \\
|
|
& exFCI & 6-31+G* & & -14.6156 & -14.3202 & 8.04 & 0.00 \\
|
|
& & AVDZ & & -14.6175 & -14.3520 & 7.22 & 0.00 \\
|
|
& & AVTZ & & -14.6244 & -14.3616 & 7.15 & 0.00 \\
|
|
& & AVQZ & & -14.6403 & -14.3790 & 7.11 & 0.00 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Butadiene}
|
|
%------------------------------
|
|
|
|
%%% BUTADIENE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:butadiene_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of butadiene for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddd}
|
|
Molecule& Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{5-8}
|
|
& & & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Butadiene & sCI+PT2 & 6-31+G* & $92\,506\,300$ & -155.4884 & -155.2463 & 6.59 \\
|
|
& & AVDZ & $59\,594\,588$ & -155.5559 & -155.3142 & 6.58 \\
|
|
& exFCI & 6-31+G* & & -155.4942 & -155.2537 & 6.55 & 0.03 \\
|
|
& & AVDZ & & -155.5652 & -155.3259 & 6.51 & 0.12 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Carbon dimer}
|
|
%------------------------------
|
|
|
|
%%% CARBON DIMER %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:C2_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of the carbon dimer for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllldddddddd}
|
|
Molecule & Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}}
|
|
& \mc{4}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}} \\
|
|
\cline{5-8} \cline{9-12}
|
|
& & & & \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{2\,\ex{1}{\Sigma}{g}{+}} & \mcc{$\Delta E$} & \mcc{Error}
|
|
& \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{1\,\ex{1}{\Delta}{g}{}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Carbon dimer& sCI+PT2 & 6-31+G* & $4\,859\,181$ & -75.7276 & -75.6434 & 2.29 & & -75.7276 & -75.6354 & 2.51 & \\
|
|
& & AVDZ & $9\,012\,864$ & -75.7360 & -75.6546 & 2.21 & & -75.7360 & -75.6440 & 2.50 & \\
|
|
& & AVTZ & $7\,403\,397$ & -75.7885 & -75.7117 & 2.09 & & -75.7885 & -75.6995 & 2.42 & \\
|
|
& & AVQZ & $4\,996\,718$ & -75.8040 & -75.7283 & 2.06 & & -75.8040 & -75.7144 & 2.39 & \\
|
|
& exFCI & 6-31+G* & & -75.7276 & -75.6434 & 2.29 & 0.00 & -75.7276 & -75.6354 & 2.51 & 0.00 \\
|
|
& & AVDZ & & -75.7360 & -75.6546 & 2.21 & 0.00 & -75.7360 & -75.6440 & 2.51 & 0.00 \\
|
|
& & AVTZ & & -75.7884 & -75.7116 & 2.09 & 0.00 & -75.7884 & -75.6995 & 2.42 & 0.00 \\
|
|
& & AVQZ & & -75.8038 & -75.7281 & 2.06 & 0.00 & -75.8038 & -75.7158 & 2.40 & 0.01 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Carbon trimer}
|
|
%------------------------------
|
|
|
|
%%% CARBON TRIMER %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:C3_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of the carbon trimer for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddddddd}
|
|
Molecule & Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}}
|
|
& \mc{4}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}} \\
|
|
\cline{5-8} \cline{9-12}
|
|
& & & & \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{2\,\ex{1}{\Sigma}{g}{+}} & \mcc{$\Delta E$} & \mcc{Error}
|
|
& \mcc{1\,\ex{1}{\Sigma}{g}{+}} & \mcc{1\,\ex{1}{\Delta}{g}{}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Carbon trimer& sCI+PT2 & 6-31+G* & $11\,618\,295$ & -113.7435 & -113.5500 & 5.26 & & -113.7435 & -113.5256 & 5.93 & \\
|
|
& & AVDZ & $12\,016\,205$ & -113.7570 & -113.5655 & 5.21 & & -113.7570 & -113.5408 & 5.88 & \\
|
|
& & AVTZ & $21\,185\,136$ & -113.8422 & -113.6501 & 5.23 & & -113.8422 & -113.6253 & 5.90 & \\
|
|
& & AVQZ & $1\,819\,523$ & -113.8687 & -113.6753 & 5.26 & & -113.8687 & -113.6509 & 5.92 & \\
|
|
& exFCI & 6-31+G* & & -113.7438 & -113.5502 & 5.27 & 0.01& -113.7438 & -113.5258 & 5.93 & 0.01\\
|
|
& & AVDZ & & -113.7573 & -113.5660 & 5.21 & 0.00& -113.7573 & -113.5413 & 5.88 & 0.00\\
|
|
& & AVTZ & & -113.8427 & -113.6510 & 5.22 & 0.04& -113.8427 & -113.6256 & 5.91 & 0.02\\
|
|
& & AVQZ & & -113.8636 & -113.6714 & 5.23 & 0.05& -113.8636 & -113.6483 & 5.86 & 0.01\\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Ethylene}
|
|
%------------------------------
|
|
|
|
%%% ETHYLENE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:ethylene_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of ethylene for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddd}
|
|
Molecule& Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}} \\
|
|
\cline{5-8}
|
|
& & & & \mcc{1\,\ex{1}{A}{g}{}} & \mcc{2\,\ex{1}{A}{g}{}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Ethylene & sCI+PT2 & 6-31+G* & $6\,533\,117$ & -78.3261 & -77.8338 & 13.39 \\
|
|
& & AVDZ & $8\,143\,431$ & -78.3701 & -77.8893 & 13.08 \\
|
|
& & AVTZ & $6\,116\,916$ & -78.4460 & -77.9709 & 12.93 \\
|
|
& exFCI & 6-31+G* & & -78.3260 & -77.8341 & 13.38 & 0.06 \\
|
|
& & AVDZ & & -78.3700 & -77.8896 & 13.07 & 0.01 \\
|
|
& & AVTZ & & -78.4460 & -77.9712 & 12.92 & 0.06 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Formaldehyde}
|
|
%------------------------------
|
|
|
|
%%% FORMALDEHYDE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:formaldehyde_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of formaldehyde for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddd}
|
|
Molecule& Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{A}{}{} $\ra$ 3\,\ex{1}{A}{}{}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{5-8}
|
|
& & & & \mcc{1\,\ex{1}{A}{}{}} & \mcc{3\,\ex{1}{A}{}{}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Formaldehyde& sCI+PT2 & 6-31+G* & $7\,388\,887$ & -114.1970 & -113.7979 & 10.86 \\
|
|
& & AVDZ & $3\,645\,058$ & -114.2466 & -113.8621 & 10.46 \\
|
|
& & AVTZ & $4\,858\,133$ & -114.3463 & -113.9643 & 10.40 \\
|
|
& exFCI & 6-31+G* & & -114.1968 & -113.7976 & 10.86 & 0.01 \\
|
|
& & AVDZ & & -114.2458 & -113.8616 & 10.45 & 0.01 \\
|
|
& & AVTZ & & -114.3438 & -113.9636 & 10.35 & 0.03 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Glyoxal}
|
|
%------------------------------
|
|
|
|
%%% GLYOXAL %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:glyoxal_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of glyoxal for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddd}
|
|
Molecule& Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{A}{}{} $\ra$ 2\,\ex{1}{A}{}{}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{5-8}
|
|
& & & & \mcc{1\,\ex{1}{A}{}{}} & \mcc{2\,\ex{1}{A}{}{}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Glyoxal & sCI+PT2 & 6-31+G* & $118\,275\,835$ & -227.2342 & -227.0252 & 5.69 \\
|
|
& & AVDZ & $35\,354\,892$ & -227.3121 & -227.1065 & 5.59 \\
|
|
& exFCI & 6-31+G* & & -227.2376 & -227.0319 & 5.60 & 0.01 \\
|
|
& & AVDZ & & -227.3173 & -227.1161 & 5.48 & 0.00 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Nitrosomethane}
|
|
%------------------------------
|
|
|
|
%%% NITRSOMETHANE %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:nitromethane_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of nitrosomethane for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddd}
|
|
Molecule& Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{5-8}
|
|
& & & & \mcc{1\,\ex{1}{A}{}{'}} & \mcc{2\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Nitrosomethane & sCI+PT2 & 6-31+G* & $17\,390\,237$ & -169.3418 & -169.1629 & 4.87 \\
|
|
& & AVDZ & $3\,256\,229$ & -169.4117 & -169.2333 & 4.85 \\
|
|
& & AVTZ & $17\,833\,307$ & -169.5599 & -169.3834 & 4.80 \\
|
|
& exFCI & 6-31+G* & & -169.3438 & -169.1650 & 4.86 & 0.01 \\
|
|
& & AVDZ & & -169.4144 & -169.2380 & 4.80 & 0.02 \\
|
|
& & AVTZ & & -169.5647 & -169.3897 & 4.76 & 0.04 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
%------------------------------
|
|
\subsection{Nitroxyl}
|
|
%------------------------------
|
|
|
|
%%% NITROXYL %%%
|
|
\begin{table}[H]
|
|
\caption{
|
|
\label{tab:nitroxyl_sCI}
|
|
sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of nitroxyl for various methods and basis sets.
|
|
The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
|
|
}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lllrdddd}
|
|
Molecule& Method & Basis & \mcc{$\Ndet$} & \mc{4}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}} \\
|
|
\cline{5-8}
|
|
& & & & \mcc{1\,\ex{1}{A}{}{'}} & \mcc{2\,\ex{1}{A}{}{'}} & \mcc{$\Delta E$} & \mcc{Error}\\
|
|
\hline
|
|
Nitroxyl& sCI+PT2 & 6-31+G* & $19\,924\,902$ & -130.1534 & -129.9876 & 4.51 \\
|
|
& & AVDZ & $3\,502\,014$ & -130.2056 & -130.0440 & 4.40 \\
|
|
& & AVTZ & $8\,185\,333$ & -130.3125 & -130.1529 & 4.34 \\
|
|
& & AVQZ & $3\,723\,478$ & -130.3479 & -130.1888 & 4.33 \\
|
|
& exFCI & 6-31+G* & & -130.1534 & -129.9876 & 4.51 & 0.00 \\
|
|
& & AVDZ & & -130.2056 & -130.0440 & 4.40 & 0.01 \\
|
|
& & AVTZ & & -130.3113 & -130.1522 & 4.33 & 0.00 \\
|
|
& & AVQZ & & -130.3450 & -130.1864 & 4.32 & 0.00 \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table}
|
|
|
|
|
|
\bibliography{../QUEST2}
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\end{document}
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