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@ -15,7 +15,7 @@
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% \documentclass[blind,alpha-refs]{wiley-article}
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% Add additional packages here if required
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,longtable,mhchem,siunitx}
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,longtable,mhchem,siunitx,rotating}
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\usepackage[
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colorlinks=true,
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@ -135,14 +135,14 @@ In the same vein, we have also produced chemically-accurate theoretical 0-0 ener
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We refer the interested reader to Ref.~\cite{Loos_2019b} where we review the generic benchmark studies devoted to adiabatic and 0-0 energies performed in the past two decades.
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%%% FIGURE 1 %%%
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\begin{figure}[ht]
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\begin{figure}
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\centering
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\includegraphics[width=0.5\linewidth]{fig1/fig1}
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\caption{Composition of each of the five subsets making up the present QUEST dataset of highly-accurate vertical excitation energies.}
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\label{fig:scheme}
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\end{figure}
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The QUEST dataset has the particularity to be based in a large proportion on selected configuration interaction (SCI) reference excitation energies as well as high-order equation-of-motion (EOM) CC methods such as EOM-CCSDT \cite{Hirata_2000} and EOM-CCSDTQ \cite{Oliphant_1991,Kucharski_1992}.
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The QUEST dataset has the particularity to be based in a large proportion on selected configuration interaction (SCI) reference excitation energies as well as high-order equation-of-motion (EOM) CC methods such as EOM-CCSDT and EOM-CCSDTQ \cite{Hirata_2000}.
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Recently, SCI methods have been a force to reckon with for the computation of highly-accurate energies in small- and medium-sized molecules as they yield near full configuration interaction (FCI) quality energies for only a fraction of the computational cost of a genuine FCI calculation \cite{Booth_2009,Booth_2010,Cleland_2010,Booth_2011,Daday_2012,Blunt_2015,Ghanem_2019,Deustua_2017,Deustua_2018,Holmes_2017,Chien_2018,Li_2018,Yao_2020,Li_2020,Eriksen_2017,Eriksen_2018,Eriksen_2019a,Eriksen_2019b,Xu_2018,Xu_2020,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c,Loos_2020a,Loos_2020e}.
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Due to the fairly natural idea underlying these methods, the SCI family is composed by numerous members \cite{Bender_1969,Whitten_1969,Huron_1973,Abrams_2005,Bunge_2006,Bytautas_2009,Giner_2013,Caffarel_2014,Giner_2015,Garniron_2017b,Caffarel_2016a,Caffarel_2016b,Holmes_2016,Sharma_2017,Holmes_2017,Chien_2018,Scemama_2018,Scemama_2018b,Garniron_2018,Evangelista_2014,Schriber_2016,Schriber_2017,Liu_2016,Per_2017,Ohtsuka_2017,Zimmerman_2017,Li_2018,Ohtsuka_2017,Coe_2018,Loos_2019}.
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Their fundamental philosophy consists, roughly speaking, in retaining only the most energetically relevant determinants of the FCI space following a given criterion to slow down the exponential increase of the size of the CI expansion.
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@ -317,50 +317,56 @@ If all the values of $P(\mathcal{G})$ are below $0.8$, $M$ is chosen such that $
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A Python code associated with this procedure is provided in the {\SupInf}.
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The singlet and triplet excitation energies obtained at the FCI/6-31+G(d) level are reported in Table \ref{tab:cycles} alongside the CC3 and CCSDT values in the same basis from Ref.~\cite{Loos_2020b}.
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The singlet and triplet excitation energies obtained at the FCI/6-31+G(d) level are reported in Table \ref{tab:cycles} alongside the computed error bar estimated with the method presented above and the CC3 and CCSDT values from Ref.~\cite{Loos_2020b} computed in the same basis.
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For the sake of comparison, we also report the estimated value of the excitation energies obtained via a three-point linear extrapolation considering the three largest SCI wave functions.
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In such a case, the error bar is estimated via the difference in excitation energies obtained with the three-point linear extrapolation and the largest variational wave function.
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This strategy has been considered in some of our previous works \cite{Loos_2020b,Loos_2020c}.
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\alert{Here comes the discussion of the results.}
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%%% TABLE I %%%
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\begin{table}
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\centering
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\caption{Singlet and triplet excitation energies obtained at the CC3, CCSDT, and FCI levels of theory with the 6-31+G* basis set for various five- and six-membered rings.}
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\label{tab:cycles}
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\begin{threeparttable}
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\begin{tabular}{lccrr}
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\begin{tabular}{lccrrr}
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\headrow
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\thead{Molecule} & \thead{Transition} & \thead{CC3} & \thead{CCSDT} & \thead{FCI}\\
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\mc{5}{c}{Five-membered rings} \\
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Cyclopentadiene & $^1 B_2 (\pi \ra \pis)$ & 5.79 & 5.80 & 5.80(2) \\
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& $^3 B_2 (\pi \ra \pis)$ & 3.33 & 3.33 & 3.32(4) \\
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Furan & $^1A_2(\pi \ra 3s)$ & 6.26 & 6.28 & 6.31(5) \\
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& $^3B_2(\pi \ra \pis)$ & 4.28 & 4.28 & 4.26(4) \\
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Imidazole & $^1A''(\pi \ra 3s)$ & 5.77 & 5.77 & 5.78(5) \\
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& $^3A'(\pi \ra \pis)$ & 4.83 & 4.81 & 4.82(7) \\
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Pyrrole & $^1A_2(\pi \ra 3s)$ & 5.25 & 5.25 & 5.23(7) \\
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& $^3B_2(\pi \ra \pis)$ & 4.59 & 4.58 & 4.54(7) \\
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Thiophene & $^1A_1(\pi \ra \pis)$ & 5.79 & 5.77 & 5.75(8) \\
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& $^3B_2(\pi \ra \pis)$ & 3.95 & 3.94 & 3.98(1) \\
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\mc{5}{c}{Six-membered rings} \\
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Benzene & $^1B_{2u}(\pi \ra \pis)$ & 5.13 & 5.10 & 5.06(9) \\
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& $^3B_{1u}(\pi \ra \pis)$ & 4.18 & 4.16 & 4.28(6) \\
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Cyclopentadienone & $^1A_2(n \ra \pis)$ & 3.03 & 3.03 & 3.08(2) \\
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& $^3B_2(\pi \ra \pis)$ & 2.30 & 2.32 & 2.37(5) \\
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Pyrazine & $^1B_{3u}(n \ra \pis)$ & 4.28 & 4.28 & 4.26(9) \\
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& $^3B_{3u}(n \ra \pis)$ & 3.68 & 3.68 & 3.70(3) \\
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Tetrazine & $^1B_{3u}(n \ra \pis)$ & 2.53 & 2.54 & 2.56(5) \\
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& $^3B_{3u}(n \ra \pis)$ & 1.87 & 1.88 & 1.91(3) \\
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Pyridazine & $^1B_1(n \ra \pis)$ & 3.95 & 3.95 & 3.97(10) \\
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& $^3B_1(n \ra \pis)$ & 3.27 & 3.26 & 3.27(15) \\
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Pyridine & $^1B_1(n \ra \pis)$ & 5.12 & 5.10 & 5.15(12) \\
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& $^3A_1(\pi \ra \pis)$ & 4.33 & 4.31 & 4.42(85) \\
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Pyrimidine & $^1B_1(n \ra \pis)$ & 4.58 & 4.57 & 4.64(11) \\
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& $^3B_1(n \ra \pis)$ & 4.20 & 4.20 & 4.55(37) \\
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Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.77(13) \\
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& $^3A_2''(n \ra \pis)$ & 4.40 & 4.40 & 4.45(39) \\
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\thead{Molecule} & \thead{Transition} & \thead{CC3} & \thead{CCSDT} & \thead{FCI$^a$} & \thead{FCI$^b$}\\
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\mc{6}{c}{Five-membered rings} \\
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Cyclopentadiene & $^1 B_2 (\pi \ra \pis)$ & 5.79 & 5.80 & 5.80(2) & 5.79(2) \\%& 5.79(7)
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& $^3 B_2 (\pi \ra \pis)$ & 3.33 & 3.33 & 3.32(4) & 3.29(7) \\%& 3.29(1)
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Furan & $^1A_2(\pi \ra 3s)$ & 6.26 & 6.28 & 6.31(5) & 6.37(1) \\%& 6.37(8)
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& $^3B_2(\pi \ra \pis)$ & 4.28 & 4.28 & 4.26(4) & 4.22(7) \\%& 4.22(14)
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Imidazole & $^1A''(\pi \ra 3s)$ & 5.77 & 5.77 & 5.78(5) & 5.96(14) \\%& 5.96(31)
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& $^3A'(\pi \ra \pis)$ & 4.83 & 4.81 & 4.82(7) & 4.65(22) \\%& 4.65(35)
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Pyrrole & $^1A_2(\pi \ra 3s)$ & 5.25 & 5.25 & 5.23(7) & 5.31(1) \\%& 5.31(26)
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& $^3B_2(\pi \ra \pis)$ & 4.59 & 4.58 & 4.54(7) & 4.37(23) \\%& 4.37(35)
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Thiophene & $^1A_1(\pi \ra \pis)$ & 5.79 & 5.77 & 5.75(8) & 5.73(9) \\%& 5.73(7)
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& $^3B_2(\pi \ra \pis)$ & 3.95 & 3.94 & 3.98(1) & 3.99(2) \\%& 3.99(8)
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\mc{6}{c}{Six-membered rings} \\
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Benzene & $^1B_{2u}(\pi \ra \pis)$ & 5.13 & 5.10 & 5.06(9) & 5.21(7) \\%& 5.21(36)
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& $^3B_{1u}(\pi \ra \pis)$ & 4.18 & 4.16 & 4.28(6) & 4.17(7) \\%& 4.17(67)
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Cyclopentadienone & $^1A_2(n \ra \pis)$ & 3.03 & 3.03 & 3.08(2) & 3.13(3) \\%& 3.13(8)
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& $^3B_2(\pi \ra \pis)$ & 2.30 & 2.32 & 2.37(5) & 2.10(25) \\%& 2.10(45)
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Pyrazine & $^1B_{3u}(n \ra \pis)$ & 4.28 & 4.28 & 4.26(9) & 4.10(25) \\%& 4.10(8)
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& $^3B_{3u}(n \ra \pis)$ & 3.68 & 3.68 & 3.70(3) & 3.70(1) \\%& 3.70(37)
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Tetrazine & $^1B_{3u}(n \ra \pis)$ & 2.53 & 2.54 & 2.56(5) & 5.07(16) \\%& 5.07(77)
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& $^3B_{3u}(n \ra \pis)$ & 1.87 & 1.88 & 1.91(3) & 4.04(49) \\%& 4.04(40)
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Pyridazine & $^1B_1(n \ra \pis)$ & 3.95 & 3.95 & 3.97(10)& 3.60(43) \\%& 3.60(26)
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& $^3B_1(n \ra \pis)$ & 3.27 & 3.26 & 3.27(15)& 3.46(14) \\%& 3.46(1.61)
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Pyridine & $^1B_1(n \ra \pis)$ & 5.12 & 5.10 & 5.15(12)& 4.90(24) \\%& 4.90(1.34)
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& $^3A_1(\pi \ra \pis)$ & 4.33 & 4.31 & 4.42(85)& 3.68(1.05) \\%& 3.68(0.65)
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Pyrimidine & $^1B_1(n \ra \pis)$ & 4.58 & 4.57 & 4.64(11)& 2.54(5) \\%& 2.54(13)
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& $^3B_1(n \ra \pis)$ & 4.20 & 4.20 & 4.55(37)& 2.18(27) \\%& 2.18(29)
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Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.77(13)& 5.12(51) \\%& 5.12(13)
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& $^3A_2''(n \ra \pis)$ & 4.40 & 4.40 & 4.45(39)& 4.73(6) \\%& 4.73(1.07)
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%\hiderowcolors
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\hline % Please only put a hline at the end of the table
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\end{tabular}
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%\begin{tablenotes}
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%\item JKL, just keep laughing; MN, merry noise.
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%\end{tablenotes}
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\begin{tablenotes}
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\item $^a$ Error bar estimated thanks to the present method (see Sec.~\ref{sec:error}).
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\item $^b$ Error bar estimated as the difference in excitation energies obtained with the three-point linear extrapolation and the largest variational wave function.
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\end{tablenotes}
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\end{threeparttable}
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\end{table}
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@ -377,7 +383,7 @@ Each of the five subsets making up the QUEST dataset is detailed below.
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Throughout the present article, we report several statistical indicators: the mean signed error (MSE), mean absolute error (MAE), root-mean square error (RMSE), and standard deviation of the errors (SDE).
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%%% FIGURE 2 %%%
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\begin{figure}[ht]
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\begin{figure}
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\centering
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\includegraphics[width=0.8\linewidth]{fig2}
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\caption{Molecules each of the five subsets making up the present QUEST dataset of highly-accurate vertical excitation energies:
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@ -436,159 +442,194 @@ Likewise, the excitation energies obtained with CCSD are much less satisfying fo
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%=======================
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The QUEST\#5 subset is composed by additional accurate excitation energies that we have produced for the present article.
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This new set gathers small molecules as well as larger molecules (aza-naphthalene, benzoquinone, cyclopentadienone, cyclopentadienethione, hexatriene, maleimide, naphthalene, nitroxyl, streptocyanine-C3, streptocyanine-C5, and thioacrolein).
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Each of these molecules are discussed below and comparisons are made with literature data.
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QUEST\#5 does also provide additional FCI/6-31+G* estimates of the lowest singlet and triplet transitions for the five- and six-membered rings considered in QUEST\#3.
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The extrapolation errors for these quite challenging calculations are computed with the scheme presented in Sec.~\ref{sec:error}.
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This new set gathers 13 new systems composed by small molecules as well as larger molecules (aza-naphthalene, benzoquinone, cyclopentadienone, cyclopentadienethione, diazirine, hexatriene, maleimide, naphthalene, nitroxyl, octatetraene, streptocyanine-C3, streptocyanine-C5, and thioacrolein).
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The interested reader will find in the {\SupInf} a detailed discussion for each of these molecules in which comparisons are made with literature data.
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%--------------------------------------
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\subsubsection{Toward larger molecules}
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%--------------------------------------
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\alert{Here comes Denis' discussion of each new molecule.}
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\begin{table}[bt]
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\centering
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\caption{Singlet and triplet excitation energies of various molecules obtained at the CC3, CCSDT, NEVPT2, and FCI levels of theory.}
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\begin{threeparttable}
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\begin{tabular}{lccrrr}
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\headrow
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& & \mc{4}{c}{6-31+G*} \\
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\thead{Molecule} & \thead{Transition} & \thead{CC3} & \thead{CCSDT} & \thead{NEVPT2} & \thead{FCI}\\
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Aza-naphthalene
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& $^1B_{3g}(n \ra \pis)$ \\
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& $^1B_{2u}(\pi \ra \pis)$ \\
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& $^1B_{1u}(n \ra \pis)$ \\
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& $^1B_{2g}(n \ra \pis)$ \\
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& $^1B_{2g}(n \ra \pis)$ \\
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& $^1B_{1u}(n \ra \pis)$ \\
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& $^1A_u(n \ra \pis)$ \\
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& $^1B_{3u}(\pi \ra \pis)$ \\
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& $^1A_g(\pi \ra \pis)$ \\
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& $^1A_u(n \ra \pis)$ \\
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& $^1A_g(n \ra 3s)$ \\
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& $^3B_{3g}(n \ra \pis)$ \\
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& $^3B_{2u}(\pi \ra \pis)$ \\
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& $^3B_{3u}(\pi \ra \pis)$ \\
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& $^3B_{1u}(n \ra \pis)$ \\
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& $^3B_{2g}(n \ra \pis)$ \\
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& $^3B_{2g}(n \ra \pis)$ \\
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& $^3B_{3u}(\pi \ra \pis)$ \\
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& $^3A_u(n \ra \pis)$ \\
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Benzoquinone
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& $^1 B_{1g}(n \ra \pis)$ & & & & \\
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& $^1 A_{u}(n \ra \pis)$ & & & & \\
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& $^1 A_{g}(\double)$ & & & & \\
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& $^1 B_{3g}(\pi \ra \pis)$ & & & & \\
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& $^1 B_{3u}(n \ra \pis)$ & & & & \\
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& $^1 B_{2g}(n \ra \pis)$ & & & & \\
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& $^1 A_{u}(n \ra \pis)$ & & & & \\
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& $^1 B_{1g}(n \ra \pis)$ & & & & \\
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& $^1 B_{2g}(n \ra \pis)$ & & & & \\
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& $^3 B_{1g}(n \ra \pis)$ & & & & \\
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& $^3 A_{u}(n \ra \pis)$ & & & & \\
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& $^3 B_{1u}(\pi \ra \pis)$ & & & & \\
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& $^3 B_{3g}(\pi \ra \pis)$ & & & & \\
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Cyclopentadienone
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& $^1A_2(n \ra \pis)$ \\
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& $^1B_2(\pi \ra \pis)$ \\
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& $^1B_1(\double)$ \\
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& $^1A_1(\double)$ \\
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& $^1A_1(\pi \ra \pis)$ \\
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& $^3B_2(\pi \ra \pis)$ \\
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& $^3A_2( \ra \pis)$ \\
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& $^3A_1(\pi \ra \pis)$ \\
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& $^3B_1(\double)$ \\
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Cyclopentadienethione
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& $^1A_2(n \ra \pis)$ \\
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& $^1B_2(\pi \ra \pis)$ \\
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& $^1B_1(\double)$ \\
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& $^1A_1(\pi \ra \pis)$ \\
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& $^1A_1(\double)$ \\
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& $^3A_2(n \ra \pis)$ \\
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& $^3B_2(\pi \ra \pis)$ \\
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& $^3A_1(\pi \ra \pis)$ \\
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& $^3B_1(\double)$ \\
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Hexatriene
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& $^1B_u(\pi \ra \pis)$ \\
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& $^1A_g(\pi \ra \pis)$ \\
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& $^1A_u(\pi \ra 3s)$ \\
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& $^1B_g(\pi \ra 3p)$ \\
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& $^3B_u(\pi \ra \pis)$ \\
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& $^3A_g(\pi \ra \pis)$ \\
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Maleimide
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& $^1B_1(n \ra \pis)$ \\
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& $^1A_2(n \ra \pis)$ \\
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& $^1B_2 (\pi \ra \pis)$ \\
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& $^1B_2(\pi \ra \pis)$ \\
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& $^1B_2(n \ra 3s)$ \\
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& $^3B_1(n \ra \pis)$ \\
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& $^3B_2(\pi \ra \pis)$ \\
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& $^3B_2(\pi \ra \pis)$ \\
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& $^3A_2(n \ra \pis)$ \\
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Naphthalene
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& $^1B_{3u}(\pi \ra \pis)$ \\
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& $^1B_{2u}(\pi \ra \pis)$ \\
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& $^1A_u(\pi \ra 3s)$ \\
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& $^1B_{1g}(\pi \ra \pis)$ \\
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& $^1A_g(\pi \ra \pis)$ \\
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& $^1B_{3g}(\pi \ra 3p)$ \\
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& $^1B_{2g}(\pi \ra 3p)$ \\
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& $^1B_{3u}(\pi \ra \pis)$ \\
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& $^1B_{1u}(\pi \ra 3s)$ \\
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& $^1B_{2u}(\pi \ra \pis)$ \\
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& $^1B_{1g}(\pi \ra \pis)$ \\
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& $^1A_g(\pi \ra \pis)$ \\
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& $^3B_{2u}(\pi \ra \pis)$ \\
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& $^3B_{3u}(\pi \ra \pis)$ \\
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& $^3B_{1g}(\pi \ra \pis)$ \\
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& $^3B_{2u}(\pi \ra \pis)$ \\
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& $^3B_{3u}(\pi \ra \pis)$ \\
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& $^3A_g(\pi \ra \pis)$ \\
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& $^3B_{1g}(\pi \ra \pis)$ \\
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& $^3A_g(\pi \ra \pis)$ \\
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Nitroxyl
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& $^1A''(n \ra \pis)$ \\
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& $^1A'(\double)$ \\
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& $^1A'$ \\
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& $^3A''(n \ra \pis)$ \\
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& $^3A'(\pi \ra \pis)$ \\
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Streptocyanine-C3
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& $^1B_2(\pi \ra \pis)$ \\
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& $^3B_2(\pi \ra \pis)$ \\
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Streptocyanine-C5
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& $^1B_2(\pi \ra \pis)$ \\
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& $^3B_2(\pi \ra \pis)$ \\
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Thioacrolein
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& $^1A''(n \ra \pis)$ \\
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& $^3A''(n \ra \pis)$ \\
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%\begin{table}[bt]
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%\centering
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%\caption{Singlet and triplet excitation energies of various molecules obtained at the CC3, CCSDT, NEVPT2, and FCI levels of theory.}
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%\begin{threeparttable}
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%\begin{tabular}{lccrrr}
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%\headrow
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% & & \mc{4}{c}{6-31+G*} \\
|
||||
%\thead{Molecule} & \thead{Transition} & \thead{CC3} & \thead{CCSDT} & \thead{NEVPT2} & \thead{FCI}\\
|
||||
%Aza-naphthalene
|
||||
% & $^1B_{3g}(n \ra \pis)$ \\
|
||||
% & $^1B_{2u}(\pi \ra \pis)$ \\
|
||||
% & $^1B_{1u}(n \ra \pis)$ \\
|
||||
% & $^1B_{2g}(n \ra \pis)$ \\
|
||||
% & $^1B_{2g}(n \ra \pis)$ \\
|
||||
% & $^1B_{1u}(n \ra \pis)$ \\
|
||||
% & $^1A_u(n \ra \pis)$ \\
|
||||
% & $^1B_{3u}(\pi \ra \pis)$ \\
|
||||
% & $^1A_g(\pi \ra \pis)$ \\
|
||||
% & $^1A_u(n \ra \pis)$ \\
|
||||
% & $^1A_g(n \ra 3s)$ \\
|
||||
% & $^3B_{3g}(n \ra \pis)$ \\
|
||||
% & $^3B_{2u}(\pi \ra \pis)$ \\
|
||||
% & $^3B_{3u}(\pi \ra \pis)$ \\
|
||||
% & $^3B_{1u}(n \ra \pis)$ \\
|
||||
% & $^3B_{2g}(n \ra \pis)$ \\
|
||||
% & $^3B_{2g}(n \ra \pis)$ \\
|
||||
% & $^3B_{3u}(\pi \ra \pis)$ \\
|
||||
% & $^3A_u(n \ra \pis)$ \\
|
||||
%Benzoquinone
|
||||
% & $^1 B_{1g}(n \ra \pis)$ & & & & \\
|
||||
% & $^1 A_{u}(n \ra \pis)$ & & & & \\
|
||||
% & $^1 A_{g}(\double)$ & & & & \\
|
||||
% & $^1 B_{3g}(\pi \ra \pis)$ & & & & \\
|
||||
% & $^1 B_{3u}(n \ra \pis)$ & & & & \\
|
||||
% & $^1 B_{2g}(n \ra \pis)$ & & & & \\
|
||||
% & $^1 A_{u}(n \ra \pis)$ & & & & \\
|
||||
% & $^1 B_{1g}(n \ra \pis)$ & & & & \\
|
||||
% & $^1 B_{2g}(n \ra \pis)$ & & & & \\
|
||||
% & $^3 B_{1g}(n \ra \pis)$ & & & & \\
|
||||
% & $^3 A_{u}(n \ra \pis)$ & & & & \\
|
||||
% & $^3 B_{1u}(\pi \ra \pis)$ & & & & \\
|
||||
% & $^3 B_{3g}(\pi \ra \pis)$ & & & & \\
|
||||
%Cyclopentadienone
|
||||
% & $^1A_2(n \ra \pis)$ \\
|
||||
% & $^1B_2(\pi \ra \pis)$ \\
|
||||
% & $^1B_1(\double)$ \\
|
||||
% & $^1A_1(\double)$ \\
|
||||
% & $^1A_1(\pi \ra \pis)$ \\
|
||||
% & $^3B_2(\pi \ra \pis)$ \\
|
||||
% & $^3A_2( \ra \pis)$ \\
|
||||
% & $^3A_1(\pi \ra \pis)$ \\
|
||||
% & $^3B_1(\double)$ \\
|
||||
%Cyclopentadienethione
|
||||
% & $^1A_2(n \ra \pis)$ \\
|
||||
% & $^1B_2(\pi \ra \pis)$ \\
|
||||
% & $^1B_1(\double)$ \\
|
||||
% & $^1A_1(\pi \ra \pis)$ \\
|
||||
% & $^1A_1(\double)$ \\
|
||||
% & $^3A_2(n \ra \pis)$ \\
|
||||
% & $^3B_2(\pi \ra \pis)$ \\
|
||||
% & $^3A_1(\pi \ra \pis)$ \\
|
||||
% & $^3B_1(\double)$ \\
|
||||
%Hexatriene
|
||||
% & $^1B_u(\pi \ra \pis)$ \\
|
||||
% & $^1A_g(\pi \ra \pis)$ \\
|
||||
% & $^1A_u(\pi \ra 3s)$ \\
|
||||
% & $^1B_g(\pi \ra 3p)$ \\
|
||||
% & $^3B_u(\pi \ra \pis)$ \\
|
||||
% & $^3A_g(\pi \ra \pis)$ \\
|
||||
%Maleimide
|
||||
% & $^1B_1(n \ra \pis)$ \\
|
||||
% & $^1A_2(n \ra \pis)$ \\
|
||||
% & $^1B_2 (\pi \ra \pis)$ \\
|
||||
% & $^1B_2(\pi \ra \pis)$ \\
|
||||
% & $^1B_2(n \ra 3s)$ \\
|
||||
% & $^3B_1(n \ra \pis)$ \\
|
||||
% & $^3B_2(\pi \ra \pis)$ \\
|
||||
% & $^3B_2(\pi \ra \pis)$ \\
|
||||
% & $^3A_2(n \ra \pis)$ \\
|
||||
%Naphthalene
|
||||
% & $^1B_{3u}(\pi \ra \pis)$ \\
|
||||
% & $^1B_{2u}(\pi \ra \pis)$ \\
|
||||
% & $^1A_u(\pi \ra 3s)$ \\
|
||||
% & $^1B_{1g}(\pi \ra \pis)$ \\
|
||||
% & $^1A_g(\pi \ra \pis)$ \\
|
||||
% & $^1B_{3g}(\pi \ra 3p)$ \\
|
||||
% & $^1B_{2g}(\pi \ra 3p)$ \\
|
||||
% & $^1B_{3u}(\pi \ra \pis)$ \\
|
||||
% & $^1B_{1u}(\pi \ra 3s)$ \\
|
||||
% & $^1B_{2u}(\pi \ra \pis)$ \\
|
||||
% & $^1B_{1g}(\pi \ra \pis)$ \\
|
||||
% & $^1A_g(\pi \ra \pis)$ \\
|
||||
% & $^3B_{2u}(\pi \ra \pis)$ \\
|
||||
% & $^3B_{3u}(\pi \ra \pis)$ \\
|
||||
% & $^3B_{1g}(\pi \ra \pis)$ \\
|
||||
% & $^3B_{2u}(\pi \ra \pis)$ \\
|
||||
% & $^3B_{3u}(\pi \ra \pis)$ \\
|
||||
% & $^3A_g(\pi \ra \pis)$ \\
|
||||
% & $^3B_{1g}(\pi \ra \pis)$ \\
|
||||
% & $^3A_g(\pi \ra \pis)$ \\
|
||||
%Nitroxyl
|
||||
% & $^1A''(n \ra \pis)$ \\
|
||||
% & $^1A'(\double)$ \\
|
||||
% & $^1A'$ \\
|
||||
% & $^3A''(n \ra \pis)$ \\
|
||||
% & $^3A'(\pi \ra \pis)$ \\
|
||||
%Streptocyanine-C3
|
||||
% & $^1B_2(\pi \ra \pis)$ \\
|
||||
% & $^3B_2(\pi \ra \pis)$ \\
|
||||
%Streptocyanine-C5
|
||||
% & $^1B_2(\pi \ra \pis)$ \\
|
||||
% & $^3B_2(\pi \ra \pis)$ \\
|
||||
%Thioacrolein
|
||||
% & $^1A''(n \ra \pis)$ \\
|
||||
% & $^3A''(n \ra \pis)$ \\
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
%\hline % Please only put a hline at the end of the table
|
||||
%\end{tabular}
|
||||
|
||||
%\begin{tablenotes}
|
||||
%\item JKL, just keep laughing; MN, merry noise.
|
||||
%\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
|
||||
%-----------------------------------------------------------------------
|
||||
\subsubsection{FCI excitation energies for five- and six-membered rings}
|
||||
%-----------------------------------------------------------------------
|
||||
|
||||
%\end{threeparttable}
|
||||
%\end{table}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Theoretical best estimates}
|
||||
\label{sec:TBE}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
We discuss in this section the generation of the TBEs obtained with the aug-cc-pVTZ basis as well as oscillator strengths for most transitions.
|
||||
An exhaustive list of TBEs can be found in {\SupInf}.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Benchmarks}
|
||||
\label{sec:bench}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
In this section, we report a comprehensive benchmark of various lower-order methods on the entire QUEST set which is composed by more than \alert{470} excitations.
|
||||
Statistical quantities are reported in Table \ref{tab:stat}.
|
||||
Additionally, we also provide a specific analysis for each type of excited states.
|
||||
Hence, the statistical values are reported for various types of excited states and molecular sizes for the MSE and MAE.
|
||||
|
||||
\begin{sidewaystable}
|
||||
\scriptsize
|
||||
\centering
|
||||
\caption{Mean signed error (MSE), mean absolute error (MAE), root-mean-square error (RMSE), standard deviation of the errors (SDE), as well as the maximum positive [Max(+)] and negative [Max($-$)] errors with respect to the TBE/aug-cc-pVTZ.
|
||||
For the MSE and MAE, the statistical values are reported for various types of excited states and molecular sizes.
|
||||
All quantities are given in eV. ``Count'' refers to the number of transitions considered for each method.}
|
||||
\label{tab:stat}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llccccccccccccccc}
|
||||
\headrow
|
||||
& & \thead{CIS(D)} & \thead{CC2} & \thead{CCSD(2)} & \thead{STEOM-CCSD} & \thead{CCSD} & \thead{CCSDR(3)} & \thead{CCCSDT-3} & \thead{CC3}
|
||||
& \thead{SOS-ADC(2)[TM]} & \thead{SOS-CC2[TM]} & \thead{SCS-CC2[TM]} & \thead{SOS-ADC(2) [QC]} & \thead{ADC(2)} & \thead{ADC(3)} & \thead{ADC(2.5)} \\
|
||||
Count & & 429 & 431 & 427 & 360 & 431 & 259 & 251 & 431 & 430 & 430 & 430 & 430 & 426 & 423 & 423 \\
|
||||
Max(+) & & 1.06 & 0.63 & 0.80 & 0.59 & 0.80 & 0.43 & 0.26 & 0.19 & 0.87 & 0.84 & 0.76 & 0.73 & 0.64 & 0.60 & 0.24 \\
|
||||
Min($-$) & & -0.69 & -0.71 & -0.38 & -0.56 & -0.25 & -0.07 & -0.07 & -0.09 & -0.29 & -0.24 & -0.92 & -0.46 & -0.76 & -0.79 & -0.34 \\
|
||||
MSE & & 0.13 & 0.02 & 0.18 & -0.01 & 0.10 & 0.04 & 0.04 & 0.00 & 0.18 & 0.21 & 0.15 & 0.02 & -0.01 & -0.12 & -0.06 \\
|
||||
& singlet & 0.10 & -0.02 & 0.22 & 0.03 & 0.14 & 0.04 & 0.04 & 0.00 & 0.18 & 0.20 & 0.13 & 0.00 & -0.04 & -0.08 & -0.06 \\
|
||||
& triplet & 0.19 & 0.08 & 0.14 & -0.07 & 0.03 & & & 0.00 & 0.19 & 0.22 & 0.17 & 0.04 & 0.04 & -0.18 & -0.07 \\
|
||||
& valence & 0.20 & 0.10 & 0.20 & -0.06 & 0.10 & 0.06 & 0.05 & 0.00 & 0.19 & 0.24 & 0.20 & 0.02 & 0.04 & -0.16 & -0.06 \\
|
||||
& Rydberg & -0.04 & -0.17 & 0.15 & 0.09 & 0.08 & 0.01 & 0.03 & -0.01 & 0.16 & 0.12 & 0.01 & 0.02 & -0.13 & -0.02 & -0.07 \\
|
||||
& $n \ra \pis$ & 0.16 & 0.02 & 0.24 & -0.03 & 0.17 & 0.07 & 0.07 & 0.00 & 0.26 & 0.32 & 0.22 & 0.05 & -0.05 & -0.01 & -0.03 \\
|
||||
& $\pi \ra \pis$& 0.25 & 0.17 & 0.20 & -0.07 & 0.06 & 0.05 & 0.04 & 0.00 & 0.15 & 0.19 & 0.19 & 0.00 & 0.12 & -0.27 & -0.07 \\
|
||||
& 1--3 non-H & 0.10 & 0.03 & 0.03 & -0.02 & 0.04 & 0.01 & 0.01 & 0.00 & 0.13 & 0.16 & 0.11 & -0.01 & -0.01 & -0.17 & -0.09 \\
|
||||
& 4 non-H & 0.13 & 0.04 & 0.12 & 0.00 & 0.09 & 0.03 & 0.04 & 0.00 & 0.19 & 0.26 & 0.19 & 0.03 & -0.04 & -0.10 & -0.07 \\
|
||||
& 5--6 non-H & 0.17 & 0.02 & 0.30 & -0.01 & 0.11 & 0.05 & 0.05 & 0.00 & 0.21 & 0.20 & 0.14 & 0.03 & 0.03 & -0.10 & -0.04 \\
|
||||
& 7--10 non-H & 0.15 & -0.03 & 0.42 & -0.05 & 0.22 & 0.10 & 0.08 & -0.01 & 0.26 & 0.29 & 0.19 & 0.05 & -0.06 & -0.02 & -0.04 \\
|
||||
MSE & & 0.13 & 0.02 & 0.18 & -0.01 & 0.10 & 0.04 & 0.04 & 0.00 & 0.18 & 0.21 & 0.15 & 0.02 & -0.01 & -0.12 & -0.06 \\
|
||||
SDE & & 0.24 & 0.20 & 0.21 & 0.13 & 0.12 & 0.05 & 0.04 & 0.02 & 0.17 & 0.16 & 0.16 & 0.15 & 0.20 & 0.22 & 0.08 \\
|
||||
RMSE & & 0.29 & 0.22 & 0.28 & 0.15 & 0.16 & 0.07 & 0.06 & 0.03 & 0.25 & 0.26 & 0.22 & 0.17 & 0.21 & 0.26 & 0.10 \\
|
||||
MAE & & 0.22 & 0.16 & 0.22 & 0.11 & 0.12 & 0.05 & 0.04 & 0.02 & 0.20 & 0.22 & 0.18 & 0.13 & 0.15 & 0.21 & 0.08 \\
|
||||
& singlet & 0.22 & 0.16 & 0.25 & 0.10 & 0.14 & 0.05 & 0.04 & 0.02 & 0.21 & 0.22 & 0.17 & 0.14 & 0.16 & 0.20 & 0.09 \\
|
||||
& triplet & 0.23 & 0.15 & 0.18 & 0.12 & 0.08 & & & 0.01 & 0.20 & 0.23 & 0.19 & 0.11 & 0.15 & 0.22 & 0.08 \\
|
||||
& valence & 0.22 & 0.14 & 0.24 & 0.12 & 0.13 & 0.06 & 0.05 & 0.02 & 0.21 & 0.25 & 0.20 & 0.12 & 0.13 & 0.22 & 0.08 \\
|
||||
& Rydberg & 0.22 & 0.21 & 0.19 & 0.10 & 0.08 & 0.03 & 0.03 & 0.02 & 0.20 & 0.15 & 0.13 & 0.14 & 0.21 & 0.18 & 0.09 \\
|
||||
& $n \ra \pis$ & 0.18 & 0.08 & 0.28 & 0.08 & 0.17 & 0.07 & 0.07 & 0.01 & 0.26 & 0.32 & 0.22 & 0.11 & 0.10 & 0.14 & 0.07 \\
|
||||
& $\pi \ra \pis$& 0.27 & 0.19 & 0.21 & 0.14 & 0.11 & 0.06 & 0.04 & 0.02 & 0.18 & 0.21 & 0.20 & 0.12 & 0.16 & 0.28 & 0.09 \\
|
||||
& 1--3 non-H & 0.23 & 0.19 & 0.13 & 0.10 & 0.07 & 0.03 & 0.03 & 0.02 & 0.18 & 0.20 & 0.19 & 0.14 & 0.19 & 0.24 & 0.10 \\
|
||||
& 4 non-H & 0.22 & 0.19 & 0.15 & 0.11 & 0.11 & 0.03 & 0.04 & 0.02 & 0.19 & 0.26 & 0.22 & 0.13 & 0.18 & 0.23 & 0.08 \\
|
||||
& 5--6 non-H & 0.21 & 0.12 & 0.30 & 0.12 & 0.13 & 0.06 & 0.05 & 0.01 & 0.22 & 0.21 & 0.15 & 0.11 & 0.11 & 0.19 & 0.07 \\
|
||||
& 7--10 non-H & 0.24 & 0.11 & 0.42 & 0.12 & 0.23 & 0.10 & 0.08 & 0.02 & 0.27 & 0.29 & 0.19 & 0.12 & 0.14 & 0.16 & 0.07 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{threeparttable}
|
||||
\end{sidewaystable}
|
||||
|
||||
|
||||
|
||||
|
||||
Binary file not shown.
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Reference in New Issue
Block a user