minor typos
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@ -361,7 +361,6 @@ For a given $\tn{2}{}(\br{})$, some of the authors proposed the following functi
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As illustrated in the context of RS-DFT, \cite{FerGinTou-JCP-19} such a functional form is able to treat both weakly and strongly correlated systems thanks to the explicit inclusion of $\e{\text{c}}{\PBE}$ and $\tn{2}{}$, respectively.
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Therefore, in the present context, we introduce the general form of the $\PBE$-based complementary functional within a given basis set $\Bas$
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\begin{multline}
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\label{eq:def_pbe_tot}
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\bE{\PBE}{\Bas}[\n{}{},\tn{2}{},\rsmu{}{\Bas}] =
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\int \n{}{}(\br{})
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\\
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@ -371,7 +370,6 @@ which has an explicit dependency on both the range-separation function $\rsmu{}{
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In Ref.~\onlinecite{LooPraSceTouGin-JPCL-19}, some of the authors introduced a version of the $\PBE$-based functional, here-referred as $\PBEUEG$
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\begin{equation}
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\label{eq:def_pbe_tot}
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\bE{\PBEUEG}{\Bas}
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\equiv
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\bE{\PBE}{\Bas}[\n{}{},\n{2}{\UEG},\rsmu{}{\Bas}],
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@ -395,7 +393,6 @@ Therefore, as in Ref.~\onlinecite{FerGinTou-JCP-19}, we define a better approxim
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which directly follows from the large-$\mu$ extrapolation of the exact on-top pair density proposed by Gori-Giorgi and Savin \cite{GorSav-PRA-06} in the context of RS-DFT.
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Using this new ingredient, we propose here the ``$\PBE$-ontop'' (\PBEot) functional
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\begin{equation}
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\label{eq:def_pbe_tot}
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\bE{\PBEot}{\Bas}
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\equiv
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\bE{\PBE}{\Bas}[\n{}{},\ttn{2}{\Bas},\rsmu{}{\Bas}].
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@ -157,7 +157,7 @@
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\title{Supporting Information for ``Chemically Accurate Excitation Energies With Small Basis Sets''}
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\author{Emmanuel Giner}
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\email[Corresponding author: \jt{JTcomment: I propose to also put EG as a corresponding author}]{emmanuel.giner@lct.jussieu.fr}
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\email[Corresponding author: ]{emmanuel.giner@lct.jussieu.fr}
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\affiliation{\LCT}
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\author{Anthony Scemama}
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\affiliation{\LCPQ}
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@ -336,7 +336,7 @@ Here, we report the absolute energetic corrections for each state of each molecu
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& -39.04124(1)
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& -39.00044(1) \\
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\\
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exFCI+$\PBE$ & AVDZ & -39.07282(1)
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exFCI+$\PBEUEG$ & AVDZ & -39.07282(1)
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& -39.06150(1)
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& -39.02181(1)
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& -38.97873(1) \\
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@ -361,24 +361,8 @@ Here, we report the absolute energetic corrections for each state of each molecu
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& -39.07959(2)
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& -39.04267(1)
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& -39.00135(1) \\
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\\
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SHCI\fnm[1] & AVQZ & -39.08849(1)
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& -39.07404(1)
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& -39.03711(1)
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& -38.99603(1) \\
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CR-EOMCC (2,3)D\fnm[2]& AVQZ& -39.08817
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& -39.07303
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& -39.03450
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& -38.99457 \\
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FCI\fnm[3] & TZ2P & -39.066738
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& -39.048984
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& -39.010059
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& -38.968471 \\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Semistochastic heat-bath CI (SHCI) calculations from Ref.~\onlinecite{ChiHolAdaOttUmrShaZim-JPCA-18}.}
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\fnt[2]{Completely-renormalized equation-of-motion coupled cluster (CR-EOMCC) calculations from Refs.~\onlinecite{SheLeiVanSch-JCP-98, JenBun-JCP-88}.}
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\fnt[3]{Reference \onlinecite{SheLeiVanSch-JCP-98}.}
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\end{table*}
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\end{squeezetable}
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%%% %%% %%% %%%
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@ -388,14 +372,14 @@ Here, we report the absolute energetic corrections for each state of each molecu
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\begin{squeezetable}
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\begin{table*}[h]
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\caption{
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Basis set energetic corrections (in hartree) on absorption energies for excited states of ammonia, carbon dimer, water, and ethylene for various methods and basis sets.}
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Basis set energetic corrections (in hartree) on absorption energies for excited states of water, ammonia, carbon dimer and ethylene for various methods and basis sets.}
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\begin{ruledtabular}{}
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\begin{tabular}{llddddddddd}
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& & \mc{9}{c}{Deviation with respect to TBE}
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\\
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\cline{3-11}
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& & \mc{3}{c}{exFCI+$\PBEot$}
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& \mc{3}{c}{exFCI+$\PBE$}
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& \mc{3}{c}{exFCI+$\PBEUEG$}
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& \mc{3}{c}{exFCI+$\LDA$}
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\\
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\cline{3-5} \cline{6-8} \cline{9-11}
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@ -405,6 +389,42 @@ Here, we report the absolute energetic corrections for each state of each molecu
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& \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
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\\
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\hline
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Water & $1\,^{1}A_1$
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& -0.058\,765 & -0.024\,014 & -0.011\,990
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& -0.066\,603 & -0.027\,236 & -0.013\,127
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& -0.059\,660 & -0.027\,777 & -0.014\,274
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\\
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& $1\,^{1}B_1$
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& -0.052\,137 & -0.021\,369 & -0.010\,611
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& -0.061\,033 & -0.025\,180 & -0.012\,076
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& -0.054\,803 & -0.025\,596 & -0.013\,154
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\\
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& $1\,^{1}A_2$
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& -0.052\,102 & -0.021\,325 & -0.010\,591
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& -0.061\,406 & -0.025\,263 & -0.012\,114
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& -0.055\,215 & -0.025\,776 & -0.013\,270
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\\
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& $2\,^{1}A_1$
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& -0.052\,995 & -0.021\,690 & -0.010\,852
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& -0.061\,959 & -0.025\,457 & -0.012\,258
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& -0.055\,301 & -0.025\,786 & -0.013\,304
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\\
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& $1\,^{3}B_1$
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& -0.051\,161 & -0.020\,974 & -0.010\,117
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& -0.057\,882 & -0.023\,791 & -0.011\,280
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& -0.052\,744 & -0.024\,500 & -0.012\,358
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\\
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& $1\,^{3}A_2$
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& -0.051\,244 & -0.020\,982 & -0.010\,115
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& -0.058\,090 & -0.023\,847 & -0.011\,302
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& -0.052\,729 & -0.024\,611 & -0.012\,398
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\\
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& $1\,^{3}A_1$
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& -0.052\,193 & -0.021\,398 & -0.010\,401
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& -0.059\,073 & -0.024\,272 & -0.011\,595
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& -0.053\,409 & -0.024\,840 & -0.012\,699
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\\
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\\
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Ammonia & $1\,^{1}A_{1}$
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& -0.044\,635 & -0.016\,982 & -0.008\,134
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& -0.051\,254 & -0.019\,468 & -0.008\,997
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@ -452,53 +472,6 @@ Here, we report the absolute energetic corrections for each state of each molecu
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& -0.049\,208 & -0.021\,292 & -0.01\,0257
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\\
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\\
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% Carbon monoxyde & $1\,^{1}\Sigma^+$
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% & -0.074\,328 & -0.031\,117 & -0.015\,510
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% & -0.084\,655 & -0.035\,318 & -0.017\,142
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% & -0.076\,668 & -0.077\,437 & -0.018\,768
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% \\
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% & $1\,^{1}\Pi$
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% & -0.075\,790 & -0.031\,456 & -0.016\,083
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% & -0.085\,494 & -0.035\,255 & -0.017\,182
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% & -0.036\,301 & -0.036\,359 & -0.018\,855
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% \\
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% \\
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Water & $1\,^{1}A_1$
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& -0.058\,765 & -0.024\,014 & -0.011\,990
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& -0.066\,603 & -0.027\,236 & -0.013\,127
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& -0.059\,660 & -0.027\,777 & -0.014\,274
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\\
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& $1\,^{1}B_1$
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& -0.052\,137 & -0.021\,369 & -0.010\,611
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& -0.061\,033 & -0.025\,180 & -0.012\,076
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& -0.054\,803 & -0.025\,596 & -0.013\,154
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\\
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& $1\,^{1}A_2$
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& -0.052\,102 & -0.021\,325 & -0.010\,591
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& -0.061\,406 & -0.025\,263 & -0.012\,114
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& -0.055\,215 & -0.025\,776 & -0.013\,270
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\\
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& $2\,^{1}A_1$
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& -0.052\,995 & -0.021\,690 & -0.010\,852
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& -0.061\,959 & -0.025\,457 & -0.012\,258
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& -0.055\,301 & -0.025\,786 & -0.013\,304
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\\
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& $1\,^{3}B_1$
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& -0.051\,161 & -0.020\,974 & -0.010\,117
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& -0.057\,882 & -0.023\,791 & -0.011\,280
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& -0.052\,744 & -0.024\,500 & -0.012\,358
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\\
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& $1\,^{3}A_2$
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& -0.051\,244 & -0.020\,982 & -0.010\,115
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& -0.058\,090 & -0.023\,847 & -0.011\,302
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& -0.052\,729 & -0.024\,611 & -0.012\,398
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\\
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& $1\,^{3}A_1$
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& -0.052\,193 & -0.021\,398 & -0.010\,401
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& -0.059\,073 & -0.024\,272 & -0.011\,595
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& -0.053\,409 & -0.024\,840 & -0.012\,699
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\\
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\\
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Ethylene & $1\,^{1}A_{1g}$
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& -0.057\,559 & -0.022\,007 &
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& -0.066\,251 & -0.024\,599 &
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