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\begin { document}
% addresses
\newcommand { \LCPQ } { Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\' e de Toulouse, CNRS, UPS, France}
\newcommand { \CEISAM } { Universit\' e de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France}
\title { Benchmarking CASPT3 vertical excitation energies}
\author { Martial \surname { Boggio-Pasqua} }
\email { martial.boggio@irsamc.ups-tlse.fr}
\affiliation { \LCPQ }
\author { Denis \surname { Jacquemin} }
\affiliation { \CEISAM }
\author { Pierre-Fran\c { c} ois \surname { Loos} }
\email { loos@irsamc.ups-tlse.fr}
\affiliation { \LCPQ }
% Abstract
\begin { abstract}
%\bigskip
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% Title
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section { Introduction}
\label { sec:intro}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Perturbation theory is a relatively inexpensive and size-extensive route towards the exact solution of the Schr\" odinger equation.
However, it rarely works this way in practice as the perturbative series may exhibit quite a large spectrum of behaviors. \cite { Olsen_ 1996,Christiansen_ 1996,Cremer_ 1996,Olsen_ 2000,Olsen_ 2019,Stillinger_ 2000,Goodson_ 2000a,Goodson_ 2000b,Goodson_ 2004,Sergeev_ 2005,Sergeev_ 2006,Goodson_ 2011}
For example, in single-reference M{ \o } ller-Plesset (MP) perturbation theory, \cite { Moller_ 1934} erratic, slowly convergent, and divergent behaviors have been observed. \cite { Laidig_ 1985,Knowles_ 1985,Handy_ 1985,Gill_ 1986,Laidig_ 1987,Nobes_ 1987,Gill_ 1988,Gill_ 1988a,Lepetit_ 1988,Leininger_ 2000,Malrieu_ 2003,Damour_ 2021}
Systematic improvement is thus difficult to contemplate and it is extremely challenging to predict, \textit { a priori} , the behavior of the series. \cite { Marie_ 2021a}
This has led to the development, in certain specific contexts, of empirical strategy like MP2.5 where one simply averages the second-order (MP2) and third-order (MP3) total energies. \cite { Pitonak_ 2009}
Extension of single-reference perturbation theory to electronic excited states is far from being trivial, and the algebraic diagrammatic
construction (ADC) approximation of the polarization propagator is probably the most natural. \cite { Schirmer_ 1982,Schirmer_ 1991,Barth_ 1995,Schirmer_ 2004,Schirmer_ 2018,Trofimov_ 1997,Trofimov_ 1997b,Trofimov_ 2002,Trofimov_ 2005,Trofimov_ 2006,Harbach_ 2014,Dreuw_ 2015}
However, the ADC series naturally inherits from the drawbacks of its MP parent and it has been shown to be not particularly rapidly convergent in the context of vertical excitation energies. \cite { Veril_ 2021}
This has led some of the authors to recently propose the ADC(2.5) composite approach, where, in the same spirit as MP2.5, one averages the second-order [ADC(2)] and third-order [ADC(3)] vertical transition energies. \cite { Loos_ 2020d}
Multi-reference perturbation theory is somewhat easier to generalise to excited states as one selects the states of interest to include in the reference space via the so-called complete-active-space self-consistent field (CASSCF) formalism, hence catching efficiently static correlation in the zeroth-order wave function.
The missing dynamical correlation can then be caught via low-order multi-reference perturbation theory, as performed in the complete-active-space second-order perturbation theory (CASPT2) of Roos and
coworkers, \cite { Andersson_ 1990,Andersson_ 1992,Roos_ 1995a} Hirao's multireference second-order M{ \o } llet-Plesset (MRMP2) approach, \cite { Hirao_ 1992} or the $ N $ -electron valence state second-order perturbation theory (NEVPT2) developed by Angeli, Malrieu, and coworkers. \cite { Angeli_ 2001a,Angeli_ 2001b,Angeli_ 2002}
However, the equations are much more involved than their single-reference counterparts and many schemes have been developed.
From the three methods mentioned above, CASPT2 is the most popular approach although it has well-document weaknesses.
In the context of excited states, the most severe one is certainly the intruder state problem which describes a situation where one or several determinants of the outer space, known as perturbers, has an energy close to the zeroth-order CASSCF wave function, hence producing divergences in the denominators of the second-order perturbative energy.
One can then introduce a shift in the denominators to avoid such common situations, and correcting the second-order energt for the use of this shift.
The use of real-valued level shift \cite { Roos_ 1995b} or an imaginary level shift \cite { Forsberg_ 1997} in the case of ``weak'' intruder states have been successfully tested \cite { Roos_ 1996} and is now routine in excited-state calculations. \cite { Schapiro_ 2013,Zobel_ 2017,Sarka_ 2022}
\titou { The third bottleneck was found in evaluating a large number of chemical problems for which systematic errors were noticed \cite { Andersson_ 1993,Andersson_ 1995} and ascribed to the unbalanced description of the zeroth-order Hamiltonian
for the open- and closed-shell electronic configurations. This systematic error can be attenuated by introducing an additional parameter, the so-called ionization-potential-electron-affinity (IPEA) shift, in the zeroth-order
Hamiltonian. \cite { Ghigo_ 2004} }
Recently, based on the highly-accurate vertical excitation energies of the QUEST dababase, we have reported an exhaustive benchmark of CASPT2 and NEVPT2 for 284 exited states of diverse nature computed in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. \cite { Sarka_ 2022}
Our main take-home message was that both CASPT2 with IPEA shift and partially-contracted version of NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of \SI { 0.11} { } and \SI { 0.13} { \eV } , respectively.
These values are found to be rather uniform for the various subgroups of transitions.
Here, going one step further in the perturbative expansion, we propose to assess the performances of complete-active-space third-order perturbation theory (CASPT3).
Third-order perturbation theory has a bad reputation especially within MP scheme because of its possible oscillatory behavior.
Because it catches both static (via CASSCF) and dynamic (via PT2) correlation, CASPT2 has been used a lot to compute vertical excitation energies in realistic systems.
Same for NEVPT2 which is an improvement of CASPT2 that does not suffer from the intruder state problem which causes singularities when one or more reference states become (nearly) degenerate with a state in the complementary configuration space.
Example of rhodopsin?
Third-order version have been developed but rarely used and accuracy still need to be assessed. \cite { Grabarek_ 2016}
Pioneering work along these lines is due to Werner which develops a CASPT3 code in MOLPRO \cite { Werner_ 2020} based on a hack of the MRCI module. \cite { Werner_ 1996}
There is also the NEVPT3 method of Angeli and coworkers. \cite { Angeli_ 2006}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section { Computational details}
\label { sec:compdet}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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All the CASPT2 and CASPT3 calculations have been carried out with MOLPRO within the RS2 and RS3 schemes. \cite { Werner_ 2020}
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Both methods have been tested with and without IPEA (labeled as NOIPEA).
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of acetaldehyde.}
\label { tab:acetaldehyde}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a',a'' ) $ & $ ( A',A'' ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A'' ( n, \pis ) $ & (3,2) & (1,1) & 4.62$ ^ a $ & 4.35$ ^ a $ & 4.13$ ^ a $ & 4.44$ ^ a $ & 4.41$ ^ a $ & 4.31\\
$ ^ 3 A'' ( n, \pis ) $ & (3,2) & (1,1) & 4.28$ ^ a $ & 3.94$ ^ a $ & 3.71$ ^ a $ & 4.06$ ^ a $ & 4.03$ ^ a $ & 3.97\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Reference (6e,5o) active space including valence $ \nO $ , $ \piCO $ , $ \sigCO $ , $ \pisCO $ and $ \sigsCO $ orbitals.
\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of acetone.}
\label { tab:acetone}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A _ 2 ( n, \pis ) $ & (2,3,1,0) & (1,0,0,2) & 4.77$ ^ a $ & 4.44$ ^ a $ & 4.19$ ^ a $ & 4.57$ ^ a $ & 4.55$ ^ a $ & 4.47\\
$ ^ 1 B _ 2 ( n, 3 s ) $ & (4,2,1,0) & (1,0,2,0) & 5.50$ ^ b $ & 6.46$ ^ b $ & 6.35$ ^ b $ & 6.64$ ^ b $ & 6.67$ ^ b $ & 6.46\\
$ ^ 1 A _ 2 ( n, 3 p _ x ) $ & (2,3,1,0) & (1,0,0,2) & 7.46$ ^ a $ & 7.80$ ^ a $ & 7.55$ ^ a $ & 7.76$ ^ a $ & 7.68$ ^ a $ & 7.47\\
$ ^ 1 A _ 1 ( n, 3 p _ y ) $ & (2,2,2,0) & (2,0,0,0) & 7.03$ ^ c $ & 7.67$ ^ c $ & 7.46$ ^ c $ & 7.76$ ^ c $ & 7.75$ ^ c $ & 7.51\\
$ ^ 1 B _ 2 ( n, 3 p _ z ) $ & (4,2,1,0) & (1,0,2,0) & 6.44$ ^ b $ & 7.56$ ^ b $ & 7.47$ ^ b $ & 7.73$ ^ b $ & 7.76$ ^ b $ & 7.62\\
$ ^ 3 A _ 2 ( n, \pis ) $ & (2,2,1,0) & (1,0,0,1) & 4.47$ ^ d $ & 4.13$ ^ d $ & 3.89$ ^ d $ & 4.27$ ^ d $ & 4.24$ ^ d $ & 4.13\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (2,2,0,0) & (2,0,0,0) & 6.22$ ^ e $ & 6.24$ ^ e $ & 6.07$ ^ e $ & 6.26$ ^ e $ & 6.22$ ^ e $ & 6.25\\
\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ Using reference (6e,6o) active space including valence $ \pi $ , $ \nO $ , $ \sigCO $ , $ \sigsCO $ and $ 3 p _ x $ orbitals.
$ ^ b $ Using reference (6e,7o) active space including valence $ \pi $ , $ \nO $ , $ \sigCO $ , $ \sigsCO $ , $ 3 s $ and $ 3 p _ z $ orbitals.
$ ^ c $ Using reference (6e,6o) active space including valence $ \pi $ , $ \nO $ , $ \sigCO $ , $ \sigsCO $ and $ 3 p _ y $ orbitals.
$ ^ d $ Using reference (6e,5o) active space including valence $ \pi $ , $ \nO $ , $ \sigCO $ and $ \sigsCO $ orbitals.
$ ^ e $ Using reference (4e,4o) active space including valence $ \pi $ , $ \sigCO $ , $ \sigsCO $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of acrolein.}
\label { tab:acrolein}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a',a'' ) $ & $ ( A',A'' ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A'' ( n, \pis ) $ & (1,5) & (1,3) & 3.48$ ^ c $ & 3.58$ ^ c $ & 3.46$ ^ c $ & 3.66$ ^ c $ & 3.66$ ^ c $ & 3.78\\
$ ^ 1 A' ( \pi , \pis ) $ & (2,4) & (4,0) & 8.84$ ^ d $ & 6.93$ ^ d $ & 6.28$ ^ d $ & 7.18$ ^ d $ & 7.05$ ^ d $ & 6.69\\
$ ^ 1 A'' ( n, \pis ) $ & (1,5) & (1,3) & 6.76$ ^ { c,e } $ & 6.79$ ^ { a,e } $ & 6.34$ ^ { a,e } $ & 6.88$ ^ { a,e } $ & 6.80$ ^ { a,e } $ & 6.72\\
$ ^ 1 A' ( n, 3 s ) $ & (2,4) & (4,0) & 7.20$ ^ d $ & 7.21$ ^ d $ & 6.98$ ^ d $ & 7.20$ ^ d $ & 7.16$ ^ d $ & 7.08\\
$ ^ 1 A' ( \pi ^ 2 , \pis ^ 2 ) $ & (2,4) & (4,0) & 7.91$ ^ d $ & 8.10$ ^ d $ & 7.75$ ^ d $ & 8.02$ ^ d $ & 7.95$ ^ d $ & 7.87\\
$ ^ 3 A'' ( n, \pis ) $ & (1,5) & (1,3) & 3.25$ ^ c $ & 3.28$ ^ c $ & 3.15$ ^ c $ & 3.39$ ^ c $ & 3.40$ ^ c $ & 3.51\\
$ ^ 3 A' ( \pi , \pis ) $ & (2,4) & (4,0) & 3.89$ ^ d $ & 4.01$ ^ d $ & 3.78$ ^ d $ & 3.96$ ^ d $ & 3.91$ ^ d $ & 3.94\\
$ ^ 3 A' ( \pi , \pis ) $ & (2,4) & (4,0) & 5.89$ ^ d $ & 6.20$ ^ d $ & 5.93$ ^ d $ & 6.10$ ^ d $ & 6.02$ ^ d $ & 6.18\\
$ ^ 3 A'' ( n, \pis ) $ & (1,5) & (1,3) & 6.67$ ^ { c,e } $ & 6.65$ ^ { c,e } $ & 6.21$ ^ { c,e } $ & 6.74$ ^ { c,e } $ & 6.66$ ^ { c,e } $ & 6.54\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (12e,12o) active space including valence $ \pi $ , $ \sigCC $ , $ \sigsCO $ , $ \sigsCC $ , $ \sigsCO $ , $ \nO $ and $ 3 s $ orbitals.
$ ^ b $ Level shift det to \SI { 0.4} { \hartree } .
$ ^ c $ Using reference (6e,6o) active space including valence $ \pi $ , $ \nO $ and $ 3 p _ z $ orbitals.
$ ^ d $ Using reference (6e,6o) active space including valence $ \pi $ , $ \nO $ and $ 3 s $ orbitals.
$ ^ e $ Substantial Rydberg and doubly-excited character.
$ ^ f $ Substantial doubly-excited character.
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\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of benzene.}
\label { tab:benzene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ g,b _ { 3 u } ,b _ { 2 u } ,b _ { 1 g } ,b _ { 1 u } ,b _ { 2 g } ,b _ { 3 g } ,a _ u ) $ & $ ( A _ g,B _ { 3 u } ,B _ { 2 u } ,B _ { 1 g } ,B _ { 1 u } ,B _ { 2 g } ,B _ { 3 g } ,A _ u ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 B _ { 2 u } ( \pi , \pis ) $ & (0,0,0,0,2,1,2,1) & (1,1,0,0,0,0,0,0) & 4.98$ ^ a $ & 5.14$ ^ a $ & 4.66$ ^ a $ & 5.09$ ^ a $ & 5.01$ ^ a $ & 5.06\\
$ ^ 1 B _ { 1 u } ( \pi , \pis ) $ & (0,0,0,0,4,1,2,2) & (1,1,2,0,0,0,0,0) & 7.27$ ^ b $ & 6.65$ ^ b $ & 6.23$ ^ b $ & 6.67$ ^ b $ & 6.58$ ^ b $ & 6.45\\
$ ^ 1 E _ { 1 g } ( \pi , 3 s ) $ & (1,0,0,0,2,1,2,1) & (1,0,0,0,0,1,1,0) & 5.90$ ^ c $ & 6.70$ ^ c $ & 6.57$ ^ c $ & 6.56$ ^ c $ & 6.51$ ^ c $ & 6.52\\
$ ^ 1 A _ { 2 u } ( \pi , 3 p _ { x,y } ) $ & (0,1,1,0,2,1,2,1) & (1,0,0,0,2,0,0,1) & 6.14$ ^ d $ & 7.21$ ^ d $ & 7.07$ ^ d $ & 7.07$ ^ d $ & 7.02$ ^ d $ & 7.08\\
$ ^ 1 E _ { 2 u } ( \pi , 3 p _ { x,y } ) $ & (0,1,1,0,2,1,2,1) & (1,0,0,0,2,0,0,1) & 6.21$ ^ d $ & 7.26$ ^ d $ & 7.12$ ^ d $ & 7.13$ ^ d $ & 7.08$ ^ d $ & 7.15\\
$ ^ 1 E _ { 2 g } ( \pi ^ 2 , \pis ^ 2 ) $ & (0,0,0,0,2,1,2,1) & (2,0,0,1,0,0,0,0) & 8.10$ ^ a $ & 8.31$ ^ a $ & 7.82$ ^ { a,e } $ & 8.26$ ^ a $ & 8.16$ ^ { a,e } $ & 8.28\\
$ ^ 3 B _ { 1 u } ( \pi , \pis ) $ & (0,0,0,0,4,1,2,2) & (1,0,1,0,0,0,0,0) & 3.85$ ^ b $ & 4.22$ ^ b $ & 3.92$ ^ b $ & 4.14$ ^ b $ & 4.08$ ^ b $ & 4.16\\
$ ^ 3 E _ { 1 u } ( \pi , \pis ) $ & (0,0,0,0,4,1,2,2) & (1,1,1,0,0,0,0,0) & 4.85$ ^ b $ & 4.89$ ^ b $ & 4.51$ ^ b $ & 4.87$ ^ b $ & 4.80$ ^ b $ & 4.85\\
$ ^ 3 B _ { 2 u } ( \pi , \pis ) $ & (0,0,0,0,4,1,2,2) & (1,1,0,0,0,0,0,0) & 6.75$ ^ b $ & 5.85$ ^ b $ & 5.40$ ^ b $ & 5.90$ ^ b $ & 5.81$ ^ b $ & 5.81\\
\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ Using reference (6e,6o) active space including valence $ \pi $ orbitals.
$ ^ b $ Using reference (6e,9o) active space including valence $ \pi $ and three $ 3 p _ z $ orbitals.
$ ^ c $ Using reference (6e,7o) active space including valence $ \pi $ and $ 3 s $ orbitals.
$ ^ d $ Using reference (6e,8o) active space including valence $ \pi $ , $ 3 p _ x $ and $ 3 p _ y $ orbitals.
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$ ^ e $ Level shift set to \SI { 0.4} { \hartree } .
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of butadiene.}
\label { tab:butadiene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ g,a _ u,b _ u,b _ g ) $ & $ ( A _ g,A _ u,B _ u,B _ g ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 B _ u ( \pi , \pis ) $ & (0,4,0,4) & (1,0,2,0) & 6.65$ ^ a $ & 6.76$ ^ a $ & 6.52$ ^ a $ & 6.72$ ^ a $ & 6.65$ ^ a $ & 6.22\\
$ ^ 1 B _ g ( \pi , 3 s ) $ & (4,2,3,2) & (1,0,0,1) & 5.94$ ^ b $ & 6.49$ ^ b $ & 6.32$ ^ b $ & 6.43$ ^ b $ & 6.38$ ^ b $ & 6.33\\
$ ^ 1 A _ g ( \pi ^ 2 , \pis ^ 2 ) $ & (3,2,3,2) & (2,0,0,0) & 6.99$ ^ c $ & 6.74$ ^ c $ & 6.30$ ^ { c,d } $ & 6.73$ ^ c $ & 6.66$ ^ { c,d } $ & 6.50\\
$ ^ 1 A _ u ( \pi , 3 p _ x ) $ & (3,2,5,2) & (1,2,0,0) & 5.95$ ^ e $ & 6.74$ ^ e $ & 6.64$ ^ e $ & 6.70$ ^ e $ & 6.67$ ^ e $ & 6.64\\
$ ^ 1 A _ u ( \pi , 3 p _ y ) $ & (3,2,5,2) & (1,2,0,0) & 6.12$ ^ e $ & 6.95$ ^ e $ & 6.84$ ^ e $ & 6.90$ ^ e $ & 6.86$ ^ e $ & 6.80\\
$ ^ 1 B _ u ( \pi , 3 p _ z ) $ & (0,4,0,4) & (1,0,2,0) & 7.93$ ^ a $ & 7.60$ ^ a $ & 7.30$ ^ a $ & 7.62$ ^ a $ & 7.54$ ^ a $ & 7.68\\
$ ^ 3 B _ u ( \pi , \pis ) $ & (3,2,3,2) & (1,0,1,0) & 3.55$ ^ c $ & 3.40$ ^ c $ & 3.19$ ^ c $ & 3.40$ ^ c $ & 3.35$ ^ c $ & 3.36\\
$ ^ 3 A _ g ( \pi , \pis ) $ & (3,2,3,2) & (2,0,0,0) & 5.52$ ^ c $ & 5.32$ ^ c $ & 4.93$ ^ c $ & 5.29$ ^ c $ & 5.19$ ^ c $ & 5.20\\
$ ^ 3 B _ g ( \pi , 3 s ) $ & (4,2,3,2) & (1,0,0,1) & 5.89$ ^ b $ & 6.44$ ^ b $ & 6.27$ ^ b $ & 6.38$ ^ b $ & 6.33$ ^ b $ & 6.29\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ Using reference (4e,8o) active space including valence $ \pi $ and four $ 3 p _ z $ .
$ ^ b $ Using reference (10e,11o) active space including valence $ \pi $ , $ \sigCC $ , $ \sigsCC $ and $ 3 s $ orbitals.
$ ^ c $ Using reference (10e,10o) active space including valence $ \pi $ , $ \sigCC $ and $ \sigsCC $ orbitals.
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$ ^ d $ Level shift set to \SI { 0.4} { \hartree } .
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$ ^ e $ Using reference (10e,12o) active space including valence $ \pi $ , $ \sigCC $ , $ \sigsCC $ , $ 3 p _ x $ and $ 3 p _ y $ orbitals.
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\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of carbon trimer.}
\label { tab:carbon_ trimer}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ g,b _ { 3 u } ,b _ { 2 u } ,b _ { 1 g } ,b _ { 1 u } ,b _ { 2 g } ,b _ { 3 g } ,a _ u ) $ & $ ( A _ g,B _ { 3 u } ,B _ { 2 u } ,B _ { 1 g } ,B _ { 1 u } ,B _ { 2 g } ,B _ { 3 g } ,A _ u ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ 1 \Delta _ g ( n ^ 2 , \pis ^ 2 ) $ & (3,2,2,0,3,1,1,0) & (2,0,0,1,0,0,0,0) & 4.98$ ^ a $ & 5.08$ ^ a $ & 4.85$ ^ { a,b } $ & 5.20$ ^ a $ & 5.19$ ^ { a,c } $ & 5.22\\
$ 1 \Sigma _ g ^ + ( n ^ 2 , \pis ^ 2 ) $ & (3,2,2,0,3,1,1,0) & (2,0,0,0,0,0,0,0) & 5.84$ ^ a $ & 5.82$ ^ a $ & 5.58$ ^ { a,c } $ & 5.92$ ^ a $ & 5.89$ ^ { a,b } $ & 5.91\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ All calculations using a full valence (12e,12o) active space.
$ ^ b $ Level shift set to \SI { 0.4} { \hartree } .
$ ^ c $ Level shift set to \SI { 0.5} { \hartree } .
\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyanoacetylene.$ ^ a $ }
\label { tab:cyanoacetylene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 \Sigma ^ - ( \pi , \pis ) $ & (0,4,4,0) & (1,0,0,1) & 6.54 & 5.85 & 5.47 & 5.89 & 5.81 & 5.80\\
$ ^ 1 \Delta ( \pi , \pis ) $ & (0,4,4,0) & (2,0,0,1) & 6.80 & 6.13 & 5.78 & 6.17 & 6.09 & 6.07\\
$ ^ 3 \Sigma ^ + ( \pi , \pis ) $ & (0,4,4,0) & (2,0,0,0) & 4.86 & 4.45 & 4.04 & 4.52 & 4.45 & 4.44\\
$ ^ 3 \Delta ( \pi , \pis ) $ & (0,4,4,0) & (2,0,0,1) & 5.64 & 5.21 & 4.86 & 5.26 & 5.19 & 5.21\\
$ ^ 1 A'' [ F ] ( \pi , \pis ) $ & ($ a' $ :4,$ a'' $ :4) & ($ A' $ :1,$ A'' $ :1) & 4.30 & 3.67 & 3.47 & 3.64 & 3.58 & 3.54\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ All calculations using a full valence $ \pi $ active space of (8e,8o).
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\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyanoformaldehyde.}
\label { tab:cyanoformaldehyde}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a',a'' ) $ & $ ( A',A'' ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 A'' ( n, \pis ) $ & (3,4) & (1,2) & 4.02$ ^ a $ & 3.98$ ^ a $ & 3.67$ ^ a $ & 3.94$ ^ a $ & 3.89$ ^ a $ & 3.81\\
$ ^ 1 A'' ( \pi , \pis ) $ & (3,4) & (1,2) & 7.61$ ^ a $ & 6.79$ ^ a $ & 6.43$ ^ a $ & 6.77$ ^ a $ & 6.67$ ^ a $ & 6.46\\
$ ^ 3 A'' ( n, \pis ) $ & (3,4) & (1,1) & 3.52$ ^ a $ & 3.46$ ^ a $ & 3.25$ ^ a $ & 3.51$ ^ a $ & 3.50$ ^ a $ & 3.44\\
$ ^ 3 A' ( \pi , \pis ) $ & (2,4) & (2,0) & 4.98$ ^ b $ & 5.25$ ^ b $ & 5.03$ ^ b $ & 5.16$ ^ b $ & 5.12$ ^ b $ & 5.01\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ Using reference (8e,7o) active space including valence $ \pi $ and $ \nO $ orbitals.
$ ^ b $ Using reference (6e,6o) active space including valence $ \pi $ orbitals.
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\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyanogen.$ ^ a $ }
\label { tab:cyanogen}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ g,b _ { 3 u } ,b _ { 2 u } ,b _ { 1 g } ,b _ { 1 u } ,b _ { 2 g } ,b _ { 3 g } ,a _ u ) $ & $ ( A _ g,B _ { 3 u } ,B _ { 2 u } ,B _ { 1 g } ,B _ { 1 u } ,B _ { 2 g } ,B _ { 3 g } ,A _ u ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 \Sigma _ u ^ - ( \pi , \pis ) $ & (0,2,2,0,0,2,2,0) & (1,0,0,0,0,0,0,1) & 7.14 & 6.40 & 6.03 & 6.46 & 6.39 & 6.39\\
$ ^ 1 \Delta _ u ( \pi , \pis ) $ & (0,2,2,0,0,2,2,0) & (1,0,0,0,1,0,0,1) & 7.46 & 6.70 & 6.35 & 6.75 & 6.68 & 6.66\\
$ ^ 3 \Sigma _ u ^ + ( \pi , \pis ) $ & (0,2,2,0,0,2,2,0) & (1,0,0,0,1,0,0,0) & 5.28 & 4.85 & 4.46 & 4.95 & 4.89 & 4.91\\
$ ^ 1 \Sigma _ u ^ - [ F ] ( \pi , \pis ) $ & (0,2,2,0,0,2,2,0) & (1,0,0,0,0,0,0,1) & 5.68 & 5.07 & 4.75 & 5.11 & 5.04 & 5.05\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ All calculations using a full valence $ \pi $ active space of (8e,8o).
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\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyclopentadiene.}
\label { tab:cyclopentadiene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 B _ 2 ( \pi , \pis ) $ & (0,4,0,2) & (1,0,2,0) & 6.71$ ^ a $ & 5.96$ ^ a $ & 5.62$ ^ a $ & 6.06$ ^ a $ & 5.99$ ^ a $ & 5.56\\
$ ^ 1 A _ 2 ( \pi , 3 s ) $ & (2,2,0,2) & (1,0,0,2) & 5.21$ ^ b $ & 5.88$ ^ b $ & 5.78$ ^ b $ & 5.81$ ^ b $ & 5.77$ ^ b $ & 5.78\\
$ ^ 1 B _ 1 ( \pi , 3 p _ y ) $ & (0,2,1,2) & (1,1,0,0) & 6.08$ ^ c $ & 6.59$ ^ c $ & 6.44$ ^ c $ & 6.47$ ^ c $ & 6.41$ ^ c $ & 6.41\\
$ ^ 1 A _ 2 ( \pi , 3 p _ z ) $ & (2,2,0,2) & (1,0,0,2) & 5.78$ ^ b $ & 6.55$ ^ b $ & 6.46$ ^ b $ & 6.45$ ^ b $ & 6.41$ ^ b $ & 6.46\\
$ ^ 1 B _ 2 ( \pi , 3 p _ x ) $ & (0,4,0,2) & (1,0,2,0) & 6.16$ ^ a $ & 6.72$ ^ a $ & 6.56$ ^ a $ & 6.61$ ^ a $ & 6.54$ ^ a $ & 6.56\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,2,0,2) & (3,0,0,0) & 6.49$ ^ { d,e } $ & 6.63$ ^ { d,e } $ & 6.13$ ^ { d,e } $ & 6.59$ ^ { d,e } $ & 6.50$ ^ { d,e } $ & 6.52\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (0,2,0,2) & (1,0,1,0) & 3.26$ ^ d $ & 3.34$ ^ d $ & 3.09$ ^ d $ & 3.31$ ^ d $ & 3.26$ ^ d $ & 3.31\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,2,0,2) & (3,0,0,0) & 4.92$ ^ d $ & 5.14$ ^ d $ & 4.78$ ^ d $ & 5.10$ ^ d $ & 5.03$ ^ d $ & 5.11\\
$ ^ 3 A _ 2 ( \pi , 3 s ) $ & (1,2,0,2) & (1,0,0,1) & 5.53$ ^ f $ & 5.91$ ^ f $ & 5.74$ ^ f $ & 5.81$ ^ f $ & 5.75$ ^ f $ & 5.73\\
$ ^ 3 B _ 1 ( \pi , 3 p _ y ) $ & (0,2,1,2) & (1,1,0,0) & 6.05$ ^ c $ & 6.56$ ^ c $ & 6.40$ ^ c $ & 6.43$ ^ c $ & 6.37$ ^ c $ & 6.36\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ Using reference (4e,6o) active space including valence $ \pi $ and two $ 3 p _ x $ orbitals.
$ ^ b $ Using reference (4e,6o) active space including valence $ \pi $ , $ 3 s $ and $ 3 p _ z $ orbitals.
$ ^ c $ Using reference (4e,5o) active space including valence $ \pi $ and $ 3 p _ y $ orbitals.
$ ^ d $ Using reference (4e,4o) active space including valence $ \pi $ orbitals.
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$ ^ e $ Strong double-excitation character.
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$ ^ f $ Using reference (4e,5o) active space including valence $ \pi $ and $ 3 s $ orbitals.
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\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyclopropene.}
\label { tab:cyclopropene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 B _ 1 ( \sig , \pis ) $ & (3,1,3,1) & (1,1,0,0) & 7.48$ ^ a $ & 6.86$ ^ a $ & 6.58$ ^ a $ & 6.85$ ^ a $ & 6.77$ ^ a $ & 6.68\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (3,1,3,1) & (1,0,1,0) & 7.47$ ^ a $ & 6.89$ ^ a $ & 6.47$ ^ a $ & 6.96$ ^ a $ & 6.87$ ^ a $ & 6.79\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (3,1,3,1) & (1,0,1,0) & 4.60$ ^ a $ & 4.47$ ^ a $ & 4.27$ ^ a $ & 4.46$ ^ a $ & 4.40$ ^ a $ & 4.38\\
$ ^ 3 B _ 1 ( \sig , \pis ) $ & (3,1,3,1) & (1,1,0,0) & 7.08$ ^ a $ & 6.56$ ^ a $ & 6.32$ ^ a $ & 6.55$ ^ a $ & 6.47$ ^ a $ & 6.45\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Reference (8e,8o) active space including valence $ \piCC $ , $ \sigCC $ and $ \pisCC $ , $ \sigsCC $ orbitals.
\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyclopropenethione.}
\label { tab:cyclopropenethione}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 A _ 2 ( n, \pis ) $ & (0,3,1,1) & (1,0,0,1) & 3.44$ ^ a $ & 3.43$ ^ a $ & 3.14$ ^ a $ & 3.46$ ^ a $ & 3.40$ ^ a $ & 3.41\\
$ ^ 1 B _ 1 ( n, \pis ) $ & (0,3,1,1) & (1,1,0,0) & 3.57$ ^ a $ & 3.45$ ^ a $ & 3.17$ ^ a $ & 3.52$ ^ a $ & 3.46$ ^ a $ & 3.45\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (2,3,1,1) & (1,0,3,0) & 4.51$ ^ b $ & 4.64$ ^ b $ & 4.35$ ^ b $ & 4.66$ ^ b $ & 4.61$ ^ b $ & 4.60\\
$ ^ 1 B _ 2 ( n, 3 s ) $ & (2,3,1,1) & (1,0,3,0) & 4.59$ ^ b $ & 5.25$ ^ b $ & 5.15$ ^ b $ & 5.25$ ^ b $ & 5.22$ ^ b $ & 5.34\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,3,0,1) & (2,0,0,0) & 6.46$ ^ c $ & 5.84$ ^ c $ & 5.32$ ^ c $ & 5.88$ ^ c $ & 5.75$ ^ c $ & 5.46\\
$ ^ 1 B _ 2 ( n, 3 p _ z ) $ & (2,3,1,1) & (1,0,3,0) & 5.27$ ^ b $ & 5.93$ ^ b $ & 5.86$ ^ b $ & 5.92$ ^ b $ & 5.90$ ^ b $ & 5.92\\
$ ^ 3 A _ 2 ( n, \pis ) $ & (0,3,1,1) & (1,0,0,1) & 3.26$ ^ a $ & 3.28$ ^ a $ & 3.00$ ^ a $ & 3.33$ ^ a $ & 3.28$ ^ a $ & 3.28\\
$ ^ 3 B _ 1 ( n, \pis ) $ & (0,3,1,1) & (1,1,0,0) & 3.51$ ^ a $ & 3.35$ ^ a $ & 3.07$ ^ a $ & 3.42$ ^ a $ & 3.36$ ^ a $ & 3.32\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (2,3,1,1) & (1,0,3,0) & 3.80$ ^ b $ & 3.97$ ^ b $ & 3.75$ ^ b $ & 3.99$ ^ b $ & 3.95$ ^ b $ & 4.01\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,3,0,1) & (2,0,0,0) & 3.83$ ^ c $ & 4.01$ ^ c $ & 3.77$ ^ c $ & 4.00$ ^ c $ & 3.95$ ^ c $ & 4.01\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ Using reference (6e,5o) active space including valence $ \pi $ and $ \nS $ .
$ ^ b $ Using reference (6e,7o) active space including valence $ \pi $ , $ \nS $ , $ 3 s $ and $ 3 p _ z $ .
$ ^ c $ Using reference (4e,4o) active space including valence $ \pi $ .
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\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyclopropenone.}
\label { tab:cyclopropenone}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 B _ 1 ( n, \pis ) $ & (2,3,1,1) & (1,3,0,0) & 4.92$ ^ a $ & 4.12$ ^ a $ & 3.75$ ^ a $ & 4.40$ ^ a $ & 4.38$ ^ a $ & 4.26\\
$ ^ 1 A _ 2 ( n, \pis ) $ & (0,4,2,1) & (1,0,0,3) & 5.64$ ^ b $ & 5.62$ ^ b $ & 5.31$ ^ b $ & 5.67$ ^ b $ & 5.64$ ^ b $ & 5.55\\
$ ^ 1 B _ 2 ( n, 3 s ) $ & (2,3,1,1) & (1,0,3,0) & 5.68$ ^ a $ & 6.28$ ^ a $ & 6.21$ ^ a $ & 6.41$ ^ a $ & 6.44$ ^ a $ & 6.34\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (2,3,1,1) & (1,0,3,0) & 6.40$ ^ a $ & 6.54$ ^ a $ & 6.20$ ^ a $ & 6.63$ ^ a $ & 6.62$ ^ a $ & 6.54\\
$ ^ 1 B _ 2 ( n, 3 p _ z ) $ & (2,3,1,1) & (1,0,3,0) & 6.35$ ^ a $ & 6.84$ ^ a $ & 6.70$ ^ a $ & 6.99$ ^ a $ & 7.01$ ^ a $ & 6.98\\
$ ^ 1 A _ 1 ( n, 3 p _ y ) $ & (0,4,2,1) & (4,0,0,0) & 6.84$ ^ b $ & 7.27$ ^ b $ & 7.03$ ^ b $ & 7.26$ ^ b $ & 7.24$ ^ b $ & 7.02\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,4,2,1) & (4,0,0,0) & 10.42$ ^ b $ & 8.96$ ^ b $ & 8.11$ ^ b $ & 9.21$ ^ b $ & 9.07$ ^ b $ & 8.28\\
$ ^ 3 B _ 1 ( n, \pis ) $ & (2,3,1,1) & (1,3,0,0) & 4.72$ ^ a $ & 3.65$ ^ a $ & 3.28$ ^ a $ & 4.00$ ^ a $ & 3.98$ ^ a $ & 3.93\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (2,3,1,1) & (1,0,3,0) & 4.39$ ^ a $ & 4.76$ ^ a $ & 4.60$ ^ a $ & 4.76$ ^ a $ & 4.74$ ^ a $ & 4.88\\
$ ^ 3 A _ 2 ( n, \pis ) $ & (0,4,2,1) & (1,0,0,3) & 5.40$ ^ b $ & 5.36$ ^ b $ & 5.06$ ^ b $ & 5.44$ ^ b $ & 5.42$ ^ b $ & 5.35\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,4,2,1) & (4,0,0,0) & 6.59$ ^ b $ & 6.93$ ^ b $ & 6.61$ ^ b $ & 6.86$ ^ b $ & 6.82$ ^ b $ & 6.79\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ Using reference (6e,7o) active space including valence $ \pi $ , $ \nO $ , $ 3 s $ and $ 3 p _ z $ .
$ ^ b $ Using reference (6e,7o) active space including valence $ \pi $ , $ \nO $ , $ 3 p _ x $ and $ 3 p _ y $ .
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\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of diacetylene.$ ^ a $ }
\label { tab:diacetylene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ g,b _ { 3 u } ,b _ { 2 u } ,b _ { 1 g } ,b _ { 1 u } ,b _ { 2 g } ,b _ { 3 g } ,a _ u ) $ & $ ( A _ g,B _ { 3 u } ,B _ { 2 u } ,B _ { 1 g } ,B _ { 1 u } ,B _ { 2 g } ,B _ { 3 g } ,A _ u ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 \Sigma _ u ^ - ( \pi , \pis ) $ & (0,2,2,0,0,2,2,0) & (1,0,0,0,0,0,0,1) & 6.13 & 5.42 & 5.01 & 5.45 & 5.36 & 5.33\\
$ ^ 1 \Delta _ u ( \pi , \pis ) $ & (0,2,2,0,0,2,2,0) & (1,0,0,0,1,0,0,1) & 6.39 & 5.68 & 5.30 & 5.72 & 5.63 & 5.61\\
$ ^ 3 \Sigma _ u ^ + ( \pi , \pis ) $ & (0,2,2,0,0,2,2,0) & (1,0,0,0,1,0,0,0) & 4.54 & 4.11 & 3.67 & 4.17 & 4.09 & 4.10\\
$ ^ 3 \Delta _ u ( \pi , \pis ) $ & (0,2,2,0,0,2,2,0) & (1,0,0,0,1,0,0,1) & 5.28 & 4.82 & 4.45 & 4.86 & 4.78 & 4.78\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ All calculations using a full valence $ \pi $ active space of (8e,8o).
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\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of diazomethane.}
\label { tab:diazomethane}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A _ 2 ( \pi , \pis ) $ & (4,3,2,0) & (1,0,0,1) & 3.27$ ^ a $ & 3.13$ ^ a $ & 2.92$ ^ a $ & 3.09$ ^ a $ & 3.04$ ^ a $ & 3.14\\
$ ^ 1 B _ 1 ( \pi , 3 s ) $ & (5,3,2,0) & (1,1,0,0) & 4.59$ ^ b $ & 5.50$ ^ b $ & 5.30$ ^ b $ & 5.48$ ^ b $ & 5.45$ ^ b $ & 5.54\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (4,4,2,0) & (3,0,0,0) & 5.65$ ^ c $ & 6.21$ ^ c $ & 5.92$ ^ c $ & 6.18$ ^ c $ & 6.13$ ^ c $ & 5.90\\
$ ^ 3 A _ 2 ( \pi , \pis ) $ & (4,3,2,0) & (1,0,0,1) & 3.02$ ^ a $ & 2.87$ ^ a $ & 2.67$ ^ a $ & 2.84$ ^ a $ & 2.79$ ^ a $ & 2.79\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (4,3,2,0) & (2,0,0,0) & 4.27$ ^ a $ & 4.10$ ^ a $ & 3.88$ ^ a $ & 4.06$ ^ a $ & 4.01$ ^ a $ & 4.05\\
$ ^ 3 B _ 1 ( \pi , 3 s ) $ & (5,3,2,0) & (1,1,0,0) & 4.45$ ^ b $ & 5.34$ ^ b $ & 5.15$ ^ b $ & 5.33$ ^ b $ & 5.30$ ^ b $ & 5.35\\
$ ^ 3 A _ 1 ( \pi , 3 p ) $ & (4,4,2,0) & (3,0,0,0) & 6.34$ ^ c $ & 7.00$ ^ c $ & 6.76$ ^ c $ & 6.96$ ^ c $ & 6.91$ ^ c $ & 6.82\\
$ ^ 1 A'' [ F ] ( \pi , \pis ) $ & ($ a' $ :6,$ a'' $ :3) & ($ A' $ :1,$ A'' $ :1) & 0.72$ ^ a $ & 0.69$ ^ a $ & 0.52$ ^ a $ & 0.66$ ^ a $ & 0.62$ ^ a $ & 0.71\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Reference (10e,9o) active space including valence $ \pi $ , $ \sigCN $ , $ \sigNN $ and $ \sigsCN $ , $ \sigsNN $ orbitals.
$ ^ b $ Reference (10e,10o) active space including valence $ \pi $ , $ \sigCN $ , $ \sigNN $ and $ \sigsCN $ , $ \sigsNN $ , Rydberg $ 3 s $ orbitals.
$ ^ c $ Reference (10e,10o) active space including valence $ \pi $ , $ \sigCN $ , $ \sigNN $ and $ \sigsCN $ , $ \sigsNN $ , Rydberg $ 3 p $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of formamide.}
\label { tab:formamide}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a',a'' ) $ & $ ( A',A'' ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A'' ( n, \pis ) $ & (5,3) & (1,1) & 5.95$ ^ a $ & 5.66$ ^ a $ & 5.45$ ^ a $ & 5.71$ ^ a $ & 5.67$ ^ a $ & 5.65\\
$ ^ 1 A' ( n, 3 s ) $ & (7,3) & (4,0) & 6.17$ ^ b $ & 6.80$ ^ b $ & 6.64$ ^ b $ & 6.82$ ^ b $ & 6.81$ ^ b $ & 6.77\\
$ ^ 1 A' ( n, 3 p ) $ & (7,3) & (4,0) & 6.74$ ^ b $ & 7.45$ ^ b $ & 7.32$ ^ b $ & 7.46$ ^ b $ & 7.46$ ^ b $ & 7.38\\
$ ^ 1 A' ( \pi , \pis ) $ & (7,3) & (4,0) & 8.80$ ^ b $ & 7.88$ ^ b $ & 7.13$ ^ b $ & 7.95$ ^ b $ & 7.78$ ^ b $ & 7.63\\
$ ^ 3 A'' ( n, \pis ) $ & (5,3) & (1,1) & 5.89$ ^ a $ & 5.36$ ^ a $ & 5.16$ ^ a $ & 5.41$ ^ a $ & 5.37$ ^ a $ & 5.38\\
$ ^ 3 A' ( \pi , \pis ) $ & (4,3) & (2,0) & 6.10$ ^ c $ & 5.88$ ^ c $ & 5.62$ ^ c $ & 5.91$ ^ c $ & 5.87$ ^ c $ & 5.81\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Reference (10e,8o) active space including valence $ \pi $ , $ \nO $ , $ \sigCN $ , $ \sigCO $ and $ \sigsCN $ , $ \sigsCO $ orbitals.
$ ^ b $ Reference (10e,10o) active space including valence $ \pi $ , $ \nO $ , $ \sigCN $ , $ \sigCO $ and $ \sigsCN $ , $ \sigsCO $ , Rydberg $ 3 s $ and $ 3 p $ orbitals.
$ ^ c $ Reference (8e,7o) active space including valence $ \pi $ , $ \sigCN $ , $ \sigCO $ and $ \sigsCN $ , $ \sigsCO $ orbitals.
\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of furan.}
\label { tab:furan}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 A _ 2 ( \pi , 3 s ) $ & (2,3,0,2) & (1,0,0,2) & 5.26$ ^ a $ & 6.16$ ^ a $ & 6.04$ ^ a $ & 6.06$ ^ a $ & 6.02$ ^ a $ & 6.09\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (0,4,0,2) & (1,0,2,0) & 7.78$ ^ b $ & 6.59$ ^ b $ & 6.02$ ^ b $ & 6.80$ ^ b $ & 6.71$ ^ b $ & 6.37\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,3,0,2) & (3,0,0,0) & 6.73$ ^ { c,d } $ & 6.66$ ^ { c,d } $ & 6.10$ ^ { c,d } $ & 6.69$ ^ { c,d } $ & 6.62$ ^ { c,d } $ & 6.56\\
$ ^ 1 B _ 1 ( \pi , 3 p _ y ) $ & (0,3,1,2) & (1,1,0,0) & 6.07$ ^ e $ & 6.79$ ^ e $ & 6.63$ ^ e $ & 6.65$ ^ e $ & 6.60$ ^ e $ & 6.64\\
$ ^ 1 A _ 2 ( \pi , 3 p _ z ) $ & (2,3,0,2) & (1,0,0,2) & 5.87$ ^ a $ & 6.87$ ^ a $ & 6.77$ ^ a $ & 6.76$ ^ a $ & 6.72$ ^ a $ & 6.81\\
$ ^ 1 B _ 2 ( \pi , 3 p _ x ) $ & (0,4,0,2) & (1,0,2,0) & 6.54$ ^ b $ & 7.11$ ^ b $ & 6.84$ ^ b $ & 6.96$ ^ b $ & 6.88$ ^ b $ & 7.24\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (0,3,0,2) & (1,0,1,0) & 3.94$ ^ c $ & 4.26$ ^ c $ & 4.01$ ^ c $ & 4.17$ ^ c $ & 4.12$ ^ c $ & 4.20\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,3,0,2) & (3,0,0,0) & 5.41$ ^ c $ & 5.50$ ^ c $ & 5.09$ ^ c $ & 5.47$ ^ c $ & 5.40$ ^ c $ & 5.46\\
$ ^ 3 A _ 2 ( \pi , 3 s ) $ & (1,3,0,2) & (1,0,0,1) & 5.57$ ^ f $ & 6.16$ ^ f $ & 5.99$ ^ f $ & 6.05$ ^ f $ & 5.99$ ^ f $ & 6.02\\
$ ^ 3 B _ 1 ( \pi , 3 p _ y ) $ & (0,3,1,2) & (1,1,0,0) & 6.04$ ^ e $ & 6.76$ ^ e $ & 6.60$ ^ e $ & 6.62$ ^ e $ & 6.56$ ^ e $ & 6.59\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ Using reference (6e,7o) active space including valence $ \pi $ , $ 3 s $ and $ 3 p _ z $ orbitals.
$ ^ b $ Using reference (6e,6o) active space including valence $ \pi $ and $ 3 p _ x $ orbitals.
$ ^ c $ Using reference (6e,5o) active space including valence $ \pi $ orbitals.
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$ ^ d $ Strong double-excitation character.
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$ ^ e $ Using reference (6e,6o) active space including valence $ \pi $ and $ 3 p _ y $ orbitals.
$ ^ f $ Using reference (6e,6o) active space including valence $ \pi $ and $ 3 s $ orbitals.
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\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of imidazole.}
\label { tab:imidazole}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a',a'' ) $ & $ ( A',A'' ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 A'' ( \pi , 3 s ) $ & (2,5) & (1,3) & 5.04$ ^ a $ & 5.88$ ^ a $ & 5.66$ ^ a $ & 5.74$ ^ a $ & 5.68$ ^ a $ & 5.70\\
$ ^ 1 A' ( \pi , 3 p ) $ & (0,9) & (3,0) & 6.18$ ^ b $ & 6.69$ ^ b $ & 6.45$ ^ b $ & 6.61$ ^ b $ & 6.56$ ^ b $ & 6.41\\
$ ^ 1 A'' ( \pi , 3 p ) $ & (4,6) & (1,7) & 5.43$ ^ c $ & 6.57$ ^ c $ & 6.47$ ^ c $ & 6.47$ ^ c $ & 6.44$ ^ c $ & 6.50\\
$ ^ 1 A'' ( n, \pis ) $ & (2,5) & (1,3) & 7.13$ ^ a $ & 6.94$ ^ a $ & 6.57$ ^ a $ & 6.92$ ^ a $ & 6.85$ ^ a $ & 6.73\\
$ ^ 1 A'' ( \pi , 3 p ) $ & (4,6) & (1,7) & 5.74$ ^ c $ & 6.87$ ^ c $ & 6.67$ ^ c $ & 6.79$ ^ c $ & 6.77$ ^ c $ & ---\\
$ ^ 1 A'' ( \pi , 3 s ) $ & (4,6) & (1,7) & 5.68$ ^ c $ & 6.89$ ^ c $ & 6.70$ ^ c $ & 6.82$ ^ c $ & 6.79$ ^ c $ & ---\\
$ ^ 1 A' ( \pi , \pis ) $ & (0,9) & (3,0) & 6.73$ ^ b $ & 6.88$ ^ b $ & 6.46$ ^ b $ & 6.89$ ^ b $ & 6.83$ ^ b $ & 6.87\\
$ ^ 1 A' ( n, 3 s ) $ & (2,5) & (2,0) & 6.36$ ^ a $ & 7.10$ ^ a $ & 6.91$ ^ a $ & 7.09$ ^ a $ & 7.07$ ^ a $ & 7.02\\
$ ^ 3 A' ( \pi , \pis ) $ & (0,9) & (3,0) & 4.55$ ^ b $ & 4.78$ ^ b $ & 4.53$ ^ b $ & 4.73$ ^ b $ & 4.68$ ^ b $ & 4.73\\
$ ^ 3 A'' ( \pi , 3 s ) $ & (2,5) & (1,3) & 5.03$ ^ a $ & 5.86$ ^ a $ & 5.63$ ^ a $ & 5.72$ ^ a $ & 5.66$ ^ a $ & 5.66\\
$ ^ 3 A' ( \pi , \pis ) $ & (0,9) & (3,0) & 5.69$ ^ b $ & 5.85$ ^ b $ & 5.48$ ^ b $ & 5.80$ ^ b $ & 5.72$ ^ b $ & 5.74\\
$ ^ 3 A'' ( n, \pis ) $ & (2,5) & (1,3) & 6.58$ ^ a $ & 6.44$ ^ a $ & 6.10$ ^ a $ & 6.43$ ^ a $ & 6.37$ ^ a $ & 6.31\\
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\end { tabular}
\end { ruledtabular}
\flushleft
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$ ^ a $ Using reference $ ( 8 e, 7 o ) $ active space including valence $ \pi $ , $ \nN $ and $ 3 s $ orbitals.
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$ ^ b $ Using reference $ ( 6 e, 9 o ) $ active space including valence $ \pi $ and four $ 3 p _ z $ orbitals.
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$ ^ c $ Using reference $ ( 8 e, 10 o ) $ active space including valence $ \pi $ , $ \nN $ , $ 3 s $ and three $ 3 p $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of isobutene.}
\label { tab:isobutene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
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$ ^ 1 B _ 1 ( \pi , 3 s ) $ & (3,2,0,0) & (1,1,0,0) & 6.21$ ^ a $ & 6.74$ ^ a $ & 6.59$ ^ a $ & 6.64$ ^ a $ & 6.57$ ^ a $ & 6.46\\
$ ^ 1 A _ 1 ( \pi , 3 p _ x ) $ & (2,3,0,0) & (2,0,0,0) & 6.90$ ^ b $ & 7.32$ ^ b $ & 7.14$ ^ b $ & 7.24$ ^ b $ & 7.18$ ^ b $ & 7.01\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (2,2,0,0) & (2,0,0,0) & 4.66$ ^ c $ & 4.59$ ^ c $ & 4.41$ ^ c $ & 4.58$ ^ c $ & 4.53$ ^ c $ & 4.53\\
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\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (4e,5o) active space including valence $ \pi $ , $ \sigCC $ , $ \sigsCC $ and $ 3 s $ orbitals.
$ ^ b $ Using reference (4e,5o) active space including valence $ \pi $ , $ \sigCC $ , $ \sigsCC $ and $ 3 p _ x $ orbitals.
$ ^ c $ Using reference (4e,4o) active space including valence $ \pi $ , $ \sigCC $ and $ \sigsCC $ orbitals.
\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of ketene.}
\label { tab:ketene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A 2 ( \pi , \pis ) $ & (4,3,2,0) & (1,0,0,1) & 3.98$ ^ a $ & 3.92$ ^ a $ & 3.70$ ^ a $ & 3.90$ ^ a $ & 3.85$ ^ a $ & 3.86\\
$ ^ 1 B 1 ( \pi , 3 s ) $ & (5,3,2,0) & (1,1,0,0) & 5.22$ ^ b $ & 5.99$ ^ b $ & 5.79$ ^ b $ & 6.00$ ^ b $ & 5.97$ ^ b $ & 6.01\\
$ ^ 1 A 2 ( \pi , 3 p ) $ & (4,3,3,0) & (1,0,0,2) & 6.38$ ^ c $ & 7.25$ ^ c $ & 7.05$ ^ c $ & 7.19$ ^ c $ & 7.15$ ^ c $ & 7.18\\
$ ^ 3 A 2 ( \pi , \pis ) $ & (4,3,2,0) & (1,0,0,1) & 3.92$ ^ a $ & 3.81$ ^ a $ & 3.59$ ^ a $ & 3.79$ ^ a $ & 3.74$ ^ a $ & 3.77\\
$ ^ 3 A 1 ( \pi , \pis ) $ & (4,3,2,0) & (2,0,0,0) & 5.79$ ^ a $ & 5.65$ ^ a $ & 5.43$ ^ a $ & 5.63$ ^ a $ & 5.59$ ^ a $ & 5.61\\
$ ^ 3 B 1 ( \pi , 3 s ) $ & (5,3,2,0) & (1,1,0,0) & 5.05$ ^ b $ & 5.79$ ^ b $ & 5.60$ ^ b $ & 5.80$ ^ b $ & 5.77$ ^ b $ & 5.79\\
$ ^ 3 A 2 ( \pi , 3 p ) $ & (4,3,3,0) & (1,0,0,2) & 6.35$ ^ c $ & 7.22$ ^ c $ & 7.01$ ^ c $ & 7.15$ ^ c $ & 7.11$ ^ c $ & 7.12\\
$ ^ 1 A'' [ F ] ( \pi , \pis ) $ & ($ a' $ :6,$ a'' $ :3) & ($ A' $ :1,$ A'' $ :1) & 0.95$ ^ a $ & 1.05$ ^ a $ & 0.88$ ^ a $ & 1.00$ ^ a $ & 0.95$ ^ a $ & 1.00\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Reference (10e,9o) active space including valence $ \pi $ , $ \sigCC $ , $ \sigCO $ and $ \sigsCC $ , $ \sigsCO $ orbitals.
$ ^ b $ Reference (10e,10o) active space including valence $ \pi $ , $ \sigCC $ , $ \sigCO $ and $ \sigsCC $ , $ \sigsCO $ , Rydberg $ 3 s $ orbitals.
$ ^ c $ Reference (10e,10o) active space including valence $ \pi $ , $ \sigCC $ , $ \sigCO $ and $ \sigsCC $ , $ \sigsCO $ , Rydberg $ 3 p $ orbitals.
\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of methylenecyclopropene.}
\label { tab:methylenecyclopropene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (0,3,0,1) & (1,0,1,0) & 4.47$ ^ a $ & 4.40$ ^ a $ & 4.12$ ^ a $ & 4.39$ ^ a $ & 4.33$ ^ a $ & 4.28\\
$ ^ 1 B _ 1 ( \pi , 3 s ) $ & (1,3,0,1) & (1,1,0,0) & 4.92$ ^ b $ & 5.57$ ^ b $ & 5.44$ ^ b $ & 5.46$ ^ b $ & 5.41$ ^ b $ & 5.44\\
$ ^ 1 A _ 2 ( \pi , 3 p _ y ) $ & (0,3,1,1) & (1,0,0,1) & 5.37$ ^ b $ & 6.09$ ^ b $ & 5.97$ ^ b $ & 5.97$ ^ b $ & 5.92$ ^ b $ & 5.96\\
$ ^ 1 A _ 1 ( \pi , 3 p _ x ) $ & (0,6,0,1) & (5,0,0,0) & 5.37$ ^ c $ & 6.26$ ^ c $ & 6.16$ ^ c $ & 6.17$ ^ c $ & 6.13$ ^ c $ & 6.12\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (0,3,0,1) & (1,0,1,0) & 3.44$ ^ a $ & 3.57$ ^ a $ & 3.34$ ^ a $ & 3.55$ ^ a $ & 3.49$ ^ a $ & 3.49\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,5,0,1) & (4,0,0,0) & 4.60$ ^ d $ & 4.82$ ^ d $ & 4.58$ ^ d $ & 4.77$ ^ d $ & 4.72$ ^ d $ & 4.74\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (4e,4o) active space including valence $ \pi $ .
$ ^ b $ Using reference (4e,5o) active space including valence $ \pi $ and $ 3 s $ .
$ ^ c $ Using reference (4e,5o) active space including valence $ \pi $ and $ 3 p _ y $ .
$ ^ d $ Using reference (4e,7o) active space including valence $ \pi $ , two $ 3 p _ x $ and one $ 3 d _ { xz } $ .
$ ^ e $ Using reference (4e,6o) active space including valence $ \pi $ , one $ 3 p _ x $ and one $ 3 d _ { xz } $ .
\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of nitrosomethane.}
\label { tab:nitrosomethane}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a',a'' ) $ & $ ( A',A'' ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A'' ( n, \pis ) $ & (4,2) & (1,1) & 2.12$ ^ a $ & 1.84$ ^ a $ & 1.60$ ^ a $ & 1.94$ ^ a $ & 1.91$ ^ a $ & 1.96\\
$ ^ 1 A' ( n ^ 2 , \pis ^ 2 ) $ & (4,2) & (2,0) & 4.74$ ^ a $ & 4.69$ ^ a $ & 4.67$ ^ a $ & 4.71$ ^ a $ & 4.71$ ^ a $ & 4.76\\
$ ^ 1 A' ( n, 3 s ) $ & (5,2) & (3,0) & 5.87$ ^ b $ & 6.32$ ^ b $ & 6.07$ ^ b $ & 6.34$ ^ b $ & 6.31$ ^ b $ & 6.29\\
$ ^ 3 A'' ( n, \pis ) $ & (4,2) & (1,1) & 1.31$ ^ a $ & 1.00$ ^ a $ & 0.75$ ^ a $ & 1.12$ ^ a $ & 1.09$ ^ a $ & 1.16\\
$ ^ 3 A' ( \pi , \pis ) $ & (2,2) & (2,0) & 5.52$ ^ c $ & 5.52$ ^ c $ & 5.37$ ^ c $ & 5.54$ ^ c $ & 5.50$ ^ c $ & 5.60\\
$ ^ 1 A'' [ F ] ( n, \pis ) $ & (4,2) & (1,1) & 1.83$ ^ a $ & 1.55$ ^ a $ & 1.32$ ^ a $ & 1.66$ ^ a $ & 1.62$ ^ a $ & 1.67\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Reference (8e,6o) active space including valence $ \nO $ , $ \nN $ , $ \piNO $ , $ \sigNO $ and $ \sigsNO $ , $ \pisNO $ orbitals.
$ ^ b $ Reference (8e,7o) active space including valence $ \nO $ , $ \nN $ , $ \piNO $ , $ \sigNO $ and $ \sigsNO $ , $ \pisNO $ , Rydberg 3s orbitals.
$ ^ c $ Reference (4e,4o) active space including valence $ \piNO $ , $ \sigNO $ and $ \sigsNO $ , $ \pisNO $ orbitals.
\end { table*}
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\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of propynal.}
\label { tab:propynal}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a',a'' ) $ & $ ( A',A'' ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A'' ( n, \pis ) $ & (3,4) & (1,2) & 4.00$ ^ a $ & 3.92$ ^ a $ & 3.64$ ^ a $ & 3.90$ ^ a $ & 3.86$ ^ a $ & 3.80\\
$ ^ 1 A'' ( \pi , \pis ) $ & (3,4) & (1,2) & 6.62$ ^ a $ & 5.82$ ^ a $ & 5.49$ ^ a $ & 5.81$ ^ a $ & 5.72$ ^ a $ & 5.54\\
$ ^ 3 A'' ( n, \pis ) $ & (3,4) & (1,1) & 3.52$ ^ a $ & 3.48$ ^ a $ & 3.26$ ^ a $ & 3.52$ ^ a $ & 3.50$ ^ a $ & 3.47\\
$ ^ 3 A' ( \pi , \pis ) $ & (2,4) & (2,0) & 4.69$ ^ b $ & 4.59$ ^ b $ & 4.30$ ^ b $ & 4.59$ ^ b $ & 4.54$ ^ b $ & 4.47\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (8e,7o) active space including valence $ \pi $ and $ \nO $ orbitals.
$ ^ b $ Using reference (6e,6o) active space including valence $ \pi $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyrazine.}
\label { tab:pyrazine}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ g,b _ { 3 u } ,b _ { 2 u } ,b _ { 1 g } ,b _ { 1 u } ,b _ { 2 g } ,b _ { 3 g } ,a _ u ) $ & $ ( A _ g,B _ { 3 u } ,B _ { 2 u } ,B _ { 1 g } ,B _ { 1 u } ,B _ { 2 g } ,B _ { 3 g } ,A _ u ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 B _ { 3 u } ( n, \pis ) $ & (1,2,0,1,1,2,0,1) & (1,1,0,0,0,0,0,0) & 4.76a & 4.09a & 3.66a & 4.31a & 4.30a & 4.15\\
$ ^ 1 A _ { u } ( n, \pis ) $ & (1,2,0,1,1,2,0,1) & (1,0,0,0,0,0,0,1) & 5.90a & 4.76a & 4.26a & 5.10a & 5.10a & 4.98\\
$ ^ 1 B _ { 2 u } ( \pi , \pis ) $ & (0,2,0,1,0,2,0,1) & (1,0,1,0,0,0,0,0) & 4.97b & 5.13b & 4.65b & 5.09b & 5.03b & 5.02\\
$ ^ 1 B _ { 2 g } ( n, \pis ) $ & (1,2,0,1,1,2,0,1) & (1,0,0,0,0,1,0,0) & 5.80a & 5.68a & 5.27a & 5.73a & 5.70a & 5.71\\
$ ^ 1 A _ { g } ( n, 3 s ) $ & (2,2,0,1,1,2,0,1) & (2,0,0,0,0,0,0,0) & 6.69c & 6.66c & 6.27c & 6.81c & 6.80c & 6.65\\
$ ^ 1 B _ { 1 g } ( n, \pis ) $ & (1,2,0,1,1,2,0,1) & (1,0,0,1,0,0,0,0) & 7.16a & 6.61a & 6.07a & 6.78a & 6.76a & 6.74\\
$ ^ 1 B _ { 1 u } ( \pi , \pis ) $ & (0,4,0,1,0,2,0,2) & (1,0,0,0,3,0,0,0) & 8.04d & 7.14d & 6.72d & 7.20d & 7.12d & 6.88\\
$ ^ 1 B _ { 1 g } ( \pi , 3 s ) $ & (1,2,0,1,0,2,0,1) & (1,0,0,1,0,0,0,0) & 6.73e & 7.41e & 7.27e & 7.24e & 7.18e & 7.21\\
$ ^ 1 B _ { 2 u } ( n, 3 p _ y ) $ & (1,2,1,1,1,2,0,1) & (1,0,2,0,0,0,0,0) & 7.49f & 7.34f & 6.93f & 7.43f & 7.40f & 7.24\\
$ ^ 1 B _ { 1 u } ( n, 3 p _ z ) $ & (1,2,0,1,2,2,0,1) & (1,0,0,0,3,0,0,0) & 7.83g & 7.55g & 7.08g & 7.64g & 7.59g & 7.44\\
$ ^ 1 B _ { 1 u } ( \pi , \pis ) $ & (0,4,0,1,0,2,0,2) & (1,0,0,0,3,0,0,0) & 9.65d & 8.59d & 7.96d & 8.68d & 8.57d & 7.98\\
$ ^ 3 B _ { 3 u } ( n, \pis ) $ & (1,2,0,1,1,2,0,1) & (1,1,0,0,0,0,0,0) & 4.16a & 3.49a & 3.08a & 3.72a & 3.71a & 3.59\\
$ ^ 3 B _ { 1 u } ( \pi , \pis ) $ & (0,4,0,1,0,2,0,2) & (1,0,0,0,2,0,0,0) & 3.98d & 4.44d & 4.15d & 4.34d & 4.28d & 4.35\\
$ ^ 3 B _ { 2 u } ( \pi , \pis ) $ & (0,2,0,1,0,2,0,1) & (1,0,1,0,0,0,0,0) & 4.62b & 4.44b & 4.09b & 4.47b & 4.41b & 4.39\\
$ ^ 3 A _ { u } ( n, \pis ) $ & (1,2,0,1,1,2,0,1) & (1,0,0,0,0,0,0,1) & 5.85a & 4.73a & 4.21a & 5.07a & 5.07a & 4.93\\
$ ^ 3 B _ { 2 g } ( n, \pis ) $ & (1,2,0,1,1,2,0,1) & (1,0,0,0,0,1,0,0) & 5.25a & 5.04a & 4.66a & 5.14a & 5.11a & 5.08\\
$ ^ 3 B _ { 1 u } ( \pi , \pis ) $ & (0,4,0,1,0,2,0,2) & (1,0,0,0,2,0,0,0) & 5.15d & 5.29d & 4.92d & 5.25d & 5.19d & 5.28\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (10e,8o) active space including valence $ \pi $ and $ \nN $ orbitals.
$ ^ b $ Using reference (6e,6o) active space including valence $ \pi $ orbitals.
$ ^ c $ Using reference (10e,9o) active space including valence $ \pi $ , $ \nN $ and $ 3 s $ orbitals.
$ ^ d $ Using reference (6e,9o) active space including valence $ \pi $ and three $ 3 p _ x $ orbitals.
$ ^ e $ Using reference (6e,7o) active space including valence $ \pi $ and $ 3 s $ orbitals.
$ ^ f $ Using reference (10e,9o) active space including valence $ \pi $ , $ \nN $ and $ 3 p _ y $ orbitals.
$ ^ g $ Using reference (10e,9o) active space including valence $ \pi $ , $ \nN $ and $ 3 p _ z $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyridazine.}
\label { tab:pyridazine}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 B _ 1 ( n, \pis ) $ & (1,3,1,3) & (1,1,0,0) & 4.29$ ^ a $ & 3.74$ ^ a $ & 3.36$ ^ a $ & 3.94$ ^ a $ & 3.92$ ^ a $ & 3.83\\
$ ^ 1 A _ 2 ( n, \pis ) $ & (1,3,1,3) & (1,0,0,1) & 4.83$ ^ a $ & 4.29$ ^ a $ & 3.87$ ^ a $ & 4.49$ ^ a $ & 4.48$ ^ a $ & 4.37\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,3,0,3) & (2,0,0,0) & 5.12$ ^ b $ & 5.34$ ^ b $ & 4.87$ ^ b $ & 5.30$ ^ b $ & 5.25$ ^ b $ & 5.26\\
$ ^ 1 A _ 2 ( n, \pis ) $ & (1,3,1,3) & (1,0,0,2) & 6.26$ ^ a $ & 5.73$ ^ a $ & 5.19$ ^ a $ & 5.93$ ^ a $ & 5.89$ ^ a $ & 5.72\\
$ ^ 1 B _ 2 ( n, 3 s ) $ & (2,3,1,3) & (1,0,1,0) & 5.99$ ^ c $ & 6.18$ ^ c $ & 5.90$ ^ c $ & 6.28$ ^ c $ & 6.27$ ^ c $ & 6.17\\
$ ^ 1 B _ 1 ( n, \pis ) $ & (1,3,1,3) & (1,2,0,0) & 7.16$ ^ a $ & 6.50$ ^ a $ & 5.94$ ^ a $ & 6.72$ ^ a $ & 6.67$ ^ a $ & 6.37\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (0,5,0,4) & (1,0,1,0) & 7.54$ ^ d $ & 7.26$ ^ d $ & 6.82$ ^ d $ & 7.25$ ^ d $ & 7.17$ ^ d $ & 6.75\\
$ ^ 3 B _ 1 ( n, \pis ) $ & (1,3,1,3) & (1,1,0,0) & 3.60$ ^ a $ & 3.08$ ^ a $ & 2.72$ ^ a $ & 3.29$ ^ a $ & 3.28$ ^ a $ & 3.19\\
$ ^ 3 A _ 2 ( n, \pis ) $ & (1,3,1,3) & (1,0,0,1) & 4.49$ ^ a $ & 4.01$ ^ a $ & 3.59$ ^ a $ & 4.20$ ^ a $ & 4.18$ ^ a $ & 4.11\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (0,3,0,3) & (1,0,1,0) & 3.93$ ^ b $ & 4.44$ ^ b $ & 4.13$ ^ b $ & 4.30$ ^ b $ & 4.24$ ^ b $ & 4.34\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,3,0,3) & (2,0,0,0) & 4.93$ ^ b $ & 4.87$ ^ b $ & 4.48$ ^ b $ & 4.89$ ^ b $ & 4.83$ ^ b $ & 4.82\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (10e,8o) active space including valence $ \pi $ and $ \nN $ orbitals.
$ ^ b $ Using reference (6e,6o) active space including valence $ \pi $ orbitals.
$ ^ c $ Using reference (10e,9o) active space including valence $ \pi $ , $ \nN $ and $ 3 s $ orbitals.
$ ^ d $ Using reference (6e,9o) active space including valence $ \pi $ , $ \nN $ and three $ 3 p _ x $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyridine.}
\label { tab:pyridine}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 B _ 1 ( n, \pis ) $ & (1,4,1,2) & (1,2,0,0) & 5.43$ ^ a $ & 5.15$ ^ a $ & 4.81$ ^ a $ & 5.18$ ^ a $ & 5.13$ ^ a $ & 4.95\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (0,7,0,3) & (1,0,2,0) & 5.03$ ^ b $ & 5.18$ ^ b $ & 4.76$ ^ b $ & 5.15$ ^ b $ & 5.09$ ^ b $ & 5.14\\
$ ^ 1 A _ 2 ( n, \pis ) $ & (2,4,0,2) & (1,0,0,2) & 6.30$ ^ c $ & 5.46$ ^ c $ & 5.03$ ^ c $ & 5.63$ ^ c $ & 5.59$ ^ c $ & 5.40\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,4,0,2) & (2,0,0,0) & 7.90$ ^ d $ & 6.92$ ^ d $ & 6.27$ ^ d $ & 7.04$ ^ d $ & 6.93$ ^ d $ & 6.62\\
$ ^ 1 A _ 1 ( n, 3 s ) $ & (2,4,0,2) & (2,0,0,0) & 6.40$ ^ c $ & 6.90$ ^ c $ & 6.67$ ^ c $ & 6.97$ ^ c $ & 6.96$ ^ c $ & 6.76\\
$ ^ 1 A _ 2 ( \pi , 3 s ) $ & (2,4,0,2) & (1,0,0,2) & 6.60$ ^ c $ & 7.08$ ^ c $ & 6.87$ ^ c $ & 6.88$ ^ c $ & 6.80$ ^ c $ & 6.82\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (0,7,0,3) & (1,0,2,0) & 7.45$ ^ b $ & 7.92$ ^ b $ & 7.67$ ^ b $ & 7.80$ ^ b $ & 7.73$ ^ b $ & 7.40\\
$ ^ 1 B _ 1 ( \pi , 3 p _ y ) $ & (1,4,1,2) & (1,2,0,0) & 7.12$ ^ a $ & 7.70$ ^ a $ & 7.51$ ^ a $ & 7.48$ ^ a $ & 7.40$ ^ a $ & 7.38\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,4,0,2) & (4,0,0,0) & 9.49$ ^ d $ & 7.66$ ^ d $ & 6.63$ ^ d $ & 7.87$ ^ d $ & 7.70$ ^ d $ & 7.39\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,4,0,2) & (2,0,0,0) & 3.98$ ^ d $ & 4.40$ ^ d $ & 4.06$ ^ d $ & 4.29$ ^ d $ & 4.22$ ^ d $ & 4.30\\
$ ^ 3 B _ 1 ( n, \pis ) $ & (1,4,0,2) & (1,1,0,0) & 4.65$ ^ e $ & 4.48$ ^ e $ & 4.21$ ^ e $ & 4.57$ ^ e $ & 4.55$ ^ e $ & 4.46\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (0,7,0,3) & (1,0,2,0) & 4.83$ ^ b $ & 4.86$ ^ b $ & 4.53$ ^ b $ & 4.81$ ^ b $ & 4.74$ ^ b $ & 4.79\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,4,0,2) & (3,0,0,0) & 5.11$ ^ d $ & 5.09$ ^ d $ & 4.63$ ^ d $ & 5.09$ ^ d $ & 5.02$ ^ d $ & 5.04\\
$ ^ 3 A _ 2 ( n, \pis ) $ & (1,4,0,2) & (1,0,0,1) & 5.94$ ^ e $ & 5.33$ ^ e $ & 4.96$ ^ e $ & 5.53$ ^ e $ & 5.51$ ^ e $ & 5.36\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (0,7,0,3) & (1,0,2,0) & 6.93$ ^ b $ & 6.40$ ^ b $ & 5.99$ ^ b $ & 6.43$ ^ b $ & 6.35$ ^ b $ & 6.24\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (8e,8o) active space including valence $ \pi $ , $ \nN $ and $ 3 p _ y $ orbitals.
$ ^ b $ Using reference (6e,10o) active space including valence $ \pi $ and four $ 3 p _ x $ orbitals.
$ ^ c $ Using reference (8e,8o) active space including valence $ \pi $ , $ \nN $ and $ 3 s $ orbitals.
$ ^ d $ Using reference (6e,6o) active space including valence $ \pi $ orbitals.
$ ^ e $ Using reference (8e,7o) active space including valence $ \pi $ and $ \nN $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyrimidine.}
\label { tab:pyrimidine}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 B _ 1 ( n, \pis ) $ & (1,4,1,2) & (1,1,0,0) & 4.85$ ^ a $ & 4.44$ ^ a $ & 4.07$ ^ a $ & 4.58$ ^ a $ & 4.55$ ^ a $ & 4.44\\
$ ^ 1 A _ 2 ( n, \pis ) $ & (1,4,1,2) & (1,0,0,1) & 5.52$ ^ a $ & 4.80$ ^ a $ & 4.36$ ^ a $ & 5.02$ ^ a $ & 5.00$ ^ a $ & 4.85\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (0,6,0,3) & (1,0,1,0) & 5.28$ ^ b $ & 5.42$ ^ b $ & 4.98$ ^ b $ & 5.41$ ^ b $ & 5.36$ ^ b $ & 5.38\\
$ ^ 1 A _ 2 ( n, \pis ) $ & (1,4,1,2) & (1,0,0,2) & 6.70$ ^ a $ & 5.92$ ^ a $ & 5.32$ ^ a $ & 6.16$ ^ a $ & 6.10$ ^ a $ & 5.92\\
$ ^ 1 B _ 1 ( n, \pis ) $ & (1,4,1,2) & (1,2,0,0) & 7.20$ ^ a $ & 6.31$ ^ a $ & 5.65$ ^ a $ & 6.58$ ^ a $ & 6.53$ ^ a $ & 6.26\\
$ ^ 1 B _ 2 ( n, 3 s ) $ & (2,4,1,2) & (1,0,2,0) & 6.86$ ^ c $ & 6.85$ ^ c $ & 6.50$ ^ c $ & 6.89$ ^ c $ & 6.86$ ^ c $ & 6.70\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,6,0,3) & (2,0,0,0) & 7.69$ ^ b $ & 7.31$ ^ b $ & 6.94$ ^ b $ & 7.29$ ^ b $ & 7.22$ ^ b $ & 6.88\\
$ ^ 3 B _ 1 ( n, \pis ) $ & (1,4,1,2) & (1,1,0,0) & 4.45$ ^ a $ & 4.05$ ^ a $ & 3.67$ ^ a $ & 4.20$ ^ a $ & 4.18$ ^ a $ & 4.09\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,6,0,3) & (2,0,0,0) & 4.22$ ^ b $ & 4.57$ ^ b $ & 4.25$ ^ b $ & 4.51$ ^ b $ & 4.44$ ^ b $ & 4.51\\
$ ^ 3 A _ 2 ( n, \pis ) $ & (1,4,1,2) & (1,0,0,1) & 5.20$ ^ a $ & 4.63$ ^ a $ & 4.16$ ^ a $ & 4.81$ ^ a $ & 4.78$ ^ a $ & 4.66\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (0,4,0,2) & (1,0,1,0) & 5.10$ ^ d $ & 5.01$ ^ d $ & 4.60$ ^ d $ & 5.03$ ^ d $ & 4.97$ ^ d $ & 4.96\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (10e,8o) active space including valence $ \pi $ and $ \nN $ orbitals.
$ ^ b $ Using reference (6e,9o) active space including valence $ \pi $ and three $ 3 p _ x $ orbitals.
$ ^ c $ Using reference (10e,9o) active space including valence $ \pi $ , $ \nN $ and $ 3 s $ orbitals.
$ ^ d $ Using reference (6e,6o) active space including valence $ \pi $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyrrole.}
\label { tab:pyrrole}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A _ 2 ( \pi , 3 s ) $ & (1,3,0,2) & (1,0,0,1) & 4.49$ ^ a $ & 5.44$ ^ a $ & 5.23$ ^ a $ & 5.28$ ^ a $ & 5.23$ ^ a $ & 5.24\\
$ ^ 1 B _ 1 ( \pi , 3 p _ y ) $ & (0,3,1,2) & (1,1,0,0) & 5.22$ ^ b $ & 6.26$ ^ b $ & 6.07$ ^ b $ & 6.08$ ^ b $ & 6.02$ ^ b $ & 6.00\\
$ ^ 1 A _ 2 ( \pi , 3 p _ z ) $ & (2,3,0,2) & (1,0,0,2) & 4.89$ ^ c $ & 6.16$ ^ c $ & 6.02$ ^ c $ & 6.01$ ^ c $ & 5.97$ ^ c $ & 6.00\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (0,4,0,2) & (1,0,2,0) & 7.73$ ^ d $ & 6.62$ ^ d $ & 6.36$ ^ d $ & 6.45$ ^ d $ & 6.38$ ^ d $ & 6.26\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,3,0,2) & (3,0,0,0) & 6.47$ ^ e $ & 6.41$ ^ e $ & 5.84$ ^ e $ & 6.43$ ^ e $ & 6.34$ ^ e $ & 6.30\\
$ ^ 1 B _ 2 ( \pi , 3 p _ x ) $ & (0,4,0,2) & (1,0,2,0) & 5.82$ ^ d $ & 6.75$ ^ d $ & 6.11$ ^ d $ & 6.92$ ^ d $ & 6.82$ ^ d $ & 6.83\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (0,3,0,2) & (1,0,1,0) & 4.24$ ^ e $ & 4.57$ ^ e $ & 4.30$ ^ e $ & 4.49$ ^ e $ & 4.44$ ^ e $ & 4.51\\
$ ^ 3 A _ 2 ( \pi , 3 s ) $ & (1,3,0,2) & (1,0,0,1) & 4.47$ ^ a $ & 5.41$ ^ a $ & 5.21$ ^ a $ & 5.26$ ^ a $ & 5.20$ ^ a $ & 5.21\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,3,0,2) & (3,0,0,0) & 5.52$ ^ e $ & 5.50$ ^ e $ & 5.04$ ^ e $ & 5.49$ ^ e $ & 5.40$ ^ e $ & 5.45\\
$ ^ 3 B _ 1 ( \pi , 3 p _ y ) $ & (0,3,1,2) & (1,1,0,0) & 5.18$ ^ b $ & 6.22$ ^ b $ & 6.03$ ^ b $ & 6.04$ ^ b $ & 5.98$ ^ b $ & 5.91\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (6e,6o) active space including valence $ \pi $ and $ 3 s $ orbitals.
$ ^ b $ Using reference (6e,6o) active space including valence $ \pi $ and $ 3 p _ y $ orbitals.
$ ^ c $ Using reference (6e,7o) active space including valence $ \pi $ , $ 3 s $ and $ 3 p _ z $ orbitals.
$ ^ d $ Using reference (6e,6o) active space including valence $ \pi $ and $ 3 p _ x $ orbitals.
$ ^ e $ Using reference (6e,5o) active space including valence $ \pi $ orbitals.
\end { table*}
2022-03-16 16:58:52 +01:00
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of streptocyanine.}
\label { tab:streptocyanine}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (2,2,2,1) & (1,0,1,0) & 7.82$ ^ a $ & 7.17$ ^ a $ & 6.76$ ^ a $ & 7.28$ ^ a $ & 7.21$ ^ a $ & 7.13\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (2,2,2,1) & (1,0,1,0) & 5.86$ ^ a $ & 5.49$ ^ a $ & 5.22$ ^ a $ & 5.54$ ^ a $ & 5.49$ ^ a $ & 5.52\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Reference (8e,7o) active space including valence $ \pi $ , two $ \sigCN $ and two $ \sigsCN $ orbitals.
\end { table*}
2022-03-16 16:19:46 +01:00
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of tetrazine.}
\label { tab:tetrazine}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ g,b _ { 3 u } ,b _ { 2 u } ,b _ { 1 g } ,b _ { 1 u } ,b _ { 2 g } ,b _ { 3 g } ,a _ u ) $ & $ ( A _ g,B _ { 3 u } ,B _ { 2 u } ,B _ { 1 g } ,B _ { 1 u } ,B _ { 2 g } ,B _ { 3 g } ,A _ u ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 B _ { 3 u } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,1,0,0,0,0,0,0) & 2.99$ ^ a $ & 2.31$ ^ a $ & 1.91$ ^ a $ & 2.54$ ^ a $ & 2.53$ ^ a $ & 2.47\\
$ ^ 1 A _ { u } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,0,0,0,0,1) & 4.37$ ^ a $ & 3.49$ ^ a $ & 3.00$ ^ a $ & 3.77$ ^ a $ & 3.78$ ^ a $ & 3.69\\
$ ^ 1 A _ { g } ( \rm double ) $ & (1,2,1,1,1,2,1,1) & (2,0,0,0,0,0,0,0) & 5.42$ ^ a $ & 4.69$ ^ a $ & 4.48$ ^ a $ & 4.85$ ^ a $ & 4.87$ ^ a $ & ---\\
$ ^ 1 B _ { 1 g } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,1,0,0,0,0) & 5.41$ ^ a $ & 4.83$ ^ a $ & 4.33$ ^ a $ & 5.02$ ^ a $ & 5.00$ ^ a $ & 4.93\\
$ ^ 1 B _ { 2 u } ( \pi , \pis ) $ & (0,2,0,1,0,2,0,1) & (1,0,1,0,0,0,0,0) & 5.04$ ^ b $ & 5.31$ ^ b $ & 4.84$ ^ b $ & 5.26$ ^ b $ & 5.23$ ^ b $ & 5.21\\
$ ^ 1 B _ { 2 g } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,0,0,1,0,0) & 5.43$ ^ a $ & 5.38$ ^ a $ & 4.90$ ^ a $ & 5.42$ ^ a $ & 5.38$ ^ a $ & 5.45\\
$ ^ 1 A _ { u } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,0,0,0,0,2) & 6.37$ ^ a $ & 5.51$ ^ a $ & 4.92$ ^ a $ & 5.80$ ^ a $ & 5.80$ ^ a $ & 5.53\\
$ ^ 1 B _ { 3 g } ( \rm double ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,0,0,0,1,0) & 6.59$ ^ a $ & 5.85$ ^ a $ & 5.22$ ^ a $ & 6.20$ ^ a $ & 6.22$ ^ a $ & ---\\
$ ^ 1 B _ { 2 g } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,0,0,2,0,0) & 6.79$ ^ a $ & 5.96$ ^ a $ & 5.18$ ^ a $ & 6.27$ ^ a $ & 6.28$ ^ a $ & 6.12\\
$ ^ 1 B _ { 1 g } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,2,0,0,0,0) & 7.18$ ^ { a,c } $ & 6.59$ ^ { a,c } $ & 5.89$ ^ { a,c } $ & 6.79$ ^ { a,c } $ & 6.72$ ^ { a,c } $ & 6.91\\
$ ^ 3 B _ { 3 u } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,1,0,0,0,0,0,0) & 2.38$ ^ a $ & 1.70$ ^ a $ & 1.31$ ^ a $ & 1.94$ ^ a $ & 1.93$ ^ a $ & 1.85\\
$ ^ 3 A _ { u } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,0,0,0,0,1) & 4.06$ ^ a $ & 3.26$ ^ a $ & 2.78$ ^ a $ & 3.52$ ^ a $ & 3.52$ ^ a $ & 3.45\\
$ ^ 3 B _ { 1 g } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,1,0,0,0,0) & 4.66$ ^ a $ & 4.10$ ^ a $ & 3.62$ ^ a $ & 4.32$ ^ a $ & 4.30$ ^ a $ & 4.20\\
$ ^ 3 B _ { 1 u } ( \pi , \pis ) $ & (0,4,0,1,0,2,0,2) & (1,0,0,0,2,0,0,0) & 3.90$ ^ d $ & 4.55$ ^ d $ & 4.29$ ^ d $ & 4.39$ ^ d $ & 4.34$ ^ d $ & 4.49\\
$ ^ 3 B _ { 2 u } ( \pi , \pis ) $ & (0,2,0,1,0,2,0,1) & (1,0,1,0,0,0,0,0) & 4.68$ ^ b $ & 4.55$ ^ b $ & 4.20$ ^ b $ & 4.60$ ^ b $ & 4.55$ ^ b $ & 4.52\\
$ ^ 3 B _ { 2 g } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,0,0,1,0,0) & 5.17$ ^ a $ & 5.02$ ^ a $ & 4.53$ ^ a $ & 5.10$ ^ a $ & 5.07$ ^ a $ & 5.04\\
$ ^ 3 A _ { u } ( n, \pis ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,0,0,0,0,2) & 6.12$ ^ a $ & 5.07$ ^ a $ & 4.44$ ^ a $ & 5.41$ ^ a $ & 5.41$ ^ a $ & 5.11\\
$ ^ 3 B _ { 3 g } ( \rm double ) $ & (1,2,1,1,1,2,1,1) & (1,0,0,0,0,0,1,0) & 6.56$ ^ a $ & 5.39$ ^ a $ & 4.86$ ^ a $ & 5.83$ ^ a $ & 5.85$ ^ a $ & ---\\
$ ^ 3 B 1 u ( \pi , \pis ) $ & (0,4,0,1,0,2,0,2) & (1,0,0,0,2,0,0,0) & 5.32$ ^ d $ & 5.46$ ^ d $ & 5.08$ ^ d $ & 5.44$ ^ d $ & 5.39$ ^ d $ & 5.42\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (14e,10o) active space including valence $ \pi $ and $ \nN $ orbitals.
$ ^ b $ Using reference (6e,6o) active space including valence $ \pi $ orbitals.
$ ^ c $ Level shift set to \SI { 0.4} { \hartree } .
$ ^ d $ Using reference (6e,9o) active space including valence $ \pi $ and three $ 3 p _ x $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of thioacetone.}
\label { tab:thioacetone}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A _ 2 ( n, \pis ) $ & (2,2,1,0) & (1,0,0,1) & 2.72$ ^ a $ & 2.58$ ^ a $ & 2.33$ ^ a $ & 2.60$ ^ a $ & 2.53$ ^ a $ & 2.53\\
$ ^ 1 B _ 2 ( n, 3 s ) $ & (4,2,1,0) & (1,0,2,0) & 4.80$ ^ b $ & 5.60$ ^ b $ & 5.48$ ^ b $ & 5.64$ ^ b $ & 5.61$ ^ b $ & 5.56\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (2,2,2,0) & (3,0,0,0) & 6.94$ ^ d $ & 6.42$ ^ d $ & 5.98$ ^ d $ & 6.40$ ^ d $ & 6.26$ ^ d $ & 5.88\\
$ ^ 1 B _ 2 ( n, 3 p _ z ) $ & (4,2,1,0) & (1,0,2,0) & 5.57$ ^ b $ & 6.51$ ^ b $ & 6.40$ ^ b $ & 6.53$ ^ b $ & 6.49$ ^ b $ & 6.51\\
$ ^ 1 A _ 1 ( n, 3 p _ y ) $ & (2,2,2,0) & (3,0,0,0) & 6.24$ ^ d $ & 6.66$ ^ d $ & 6.41$ ^ d $ & 6.59$ ^ d $ & 6.50$ ^ d $ & 6.61\\
$ ^ 3 A _ 2 ( n, \pis ) $ & (2,2,1,0) & (1,0,0,1) & 2.52$ ^ a $ & 2.34$ ^ a $ & 2.09$ ^ a $ & 2.38$ ^ a $ & 2.31$ ^ a $ & 2.33\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (2,2,0,0) & (2,0,0,0) & 3.52$ ^ c $ & 3.48$ ^ c $ & 3.29$ ^ c $ & 3.48$ ^ c $ & 3.43$ ^ c $ & 3.45\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (6e,5o) active space including valence $ \pi $ , $ \nO $ , $ \sigCO $ and $ \sigsCO $ orbitals.
$ ^ b $ Using reference (6e,7o) active space including valence $ \pi $ , $ \nO $ , $ \sigCO $ , $ \sigsCO $ , $ 3 s $ and $ 3 p _ z $ orbitals.
$ ^ c $ Using reference (4e,4o) active space including valence $ \pi $ , $ \sigCO $ and $ \sigsCO $ orbitals.
$ ^ d $ Using reference (6e,6o) active space including valence $ \pi $ , $ \nO $ , $ \sigCO $ , $ \sigsCO $ and $ 3 p _ y $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of thiophene.}
\label { tab:thiophene}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,3,0,2) & (3,0,0,0) & 6.11$ ^ a $ & 5.84$ ^ a $ & 5.21$ ^ a $ & 5.89$ ^ a $ & 5.79$ ^ a $ & 5.64\\
$ ^ 1 B _ 2 ( \pi , \pis ) $ & (0,5,0,2) & (1,0,2,0) & 6.94$ ^ b $ & 6.35$ ^ b $ & 5.89$ ^ b $ & 6.44$ ^ b $ & 6.35$ ^ b $ & 5.98\\
$ ^ 1 A _ 2 ( \pi , 3 s ) $ & (1,3,0,2) & (1,0,0,1) & 5.70$ ^ c $ & 6.28$ ^ c $ & 6.07$ ^ c $ & 6.16$ ^ c $ & 6.10$ ^ c $ & 6.14\\
$ ^ 1 B _ 1 ( \pi , 3 p _ y ) $ & (0,3,1,2) & (1,1,0,0) & 6.02$ ^ d $ & 6.21$ ^ d $ & 5.90$ ^ d $ & 6.16$ ^ d $ & 6.10$ ^ d $ & 6.14\\
$ ^ 1 A _ 2 ( \pi , 3 p _ y ) $ & (0,3,1,2) & (1,0,0,1) & 6.05$ ^ d $ & 6.32$ ^ d $ & 5.98$ ^ d $ & 6.28$ ^ d $ & 6.21$ ^ d $ & 6.21\\
$ ^ 1 B _ 1 ( \pi , 3 s ) $ & (1,3,1,2) & (1,2,0,0) & 5.78$ ^ e $ & 6.57$ ^ e $ & 6.28$ ^ e $ & 6.51$ ^ e $ & 6.44$ ^ e $ & 6.49\\
$ ^ 1 B _ 2 ( \pi , 3 p _ x ) $ & (0,5,0,2) & (1,0,2,0) & 6.80$ ^ b $ & 7.29$ ^ b $ & 7.03$ ^ b $ & 7.20$ ^ b $ & 7.13$ ^ b $ & 7.29\\
$ ^ 1 A _ 1 ( \pi , \pis ) $ & (0,3,0,2) & (3,0,0,0) & 8.29$ ^ { a,f } $ & 7.62$ ^ { a,f } $ & 6.85$ ^ { a,f } $ & 7.71$ ^ { a,f } $ & 7.56$ ^ { a,f } $ & 7.31\\
$ ^ 3 B _ 2 ( \pi , \pis ) $ & (0,3,0,2) & (1,0,1,0) & 3.68$ ^ a $ & 3.98$ ^ a $ & 3.71$ ^ a $ & 3.90$ ^ a $ & 3.84$ ^ a $ & 3.92\\
$ ^ 3 A _ 1 ( \pi , \pis ) $ & (0,3,0,2) & (3,0,0,0) & 4.97$ ^ a $ & 4.85$ ^ a $ & 4.39$ ^ a $ & 4.87$ ^ a $ & 4.79$ ^ a $ & 4.76\\
$ ^ 3 B _ 1 ( \pi , 3 p _ y ) $ & (0,3,1,2) & (1,1,0,0) & 5.86$ ^ d $ & 5.97$ ^ d $ & 5.64$ ^ d $ & 5.94$ ^ d $ & 5.88$ ^ d $ & 5.93\\
$ ^ 3 A _ 2 ( \pi , 3 s ) $ & (1,3,0,2) & (1,0,0,1) & 5.65$ ^ c $ & 6.22$ ^ c $ & 6.01$ ^ c $ & 6.11$ ^ c $ & 6.04$ ^ c $ & 6.08\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (6e,5o) active space including valence $ \pi $ orbitals.
$ ^ b $ Using reference (6e,7o) active space including valence $ \pi $ and two $ 3 p _ x $ orbitals.
$ ^ c $ Using reference (6e,6o) active space including valence $ \pi $ and $ 3 s $ orbitals.
$ ^ d $ Using reference (6e,6o) active space including valence $ \pi $ and $ 3 p _ y $ orbitals.
$ ^ e $ Using reference (6e,7o) active space including valence $ \pi $ , $ 3 s $ and $ 3 p _ y $ orbitals.
$ ^ f $ Strong double-excitation character.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of thiopropynal.}
\label { tab:thiopropynal}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a',a'' ) $ & $ ( A',A'' ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A'' ( n, \pis ) $ & (3,4) & (1,1) & 2.06$ ^ a $ & 2.05$ ^ a $ & 1.84$ ^ a $ & 2.05$ ^ a $ & 2.00$ ^ a $ & 2.03\\
$ ^ 3 A'' ( n, \pis ) $ & (3,4) & (1,1) & 1.85$ ^ a $ & 1.81$ ^ a $ & 1.60$ ^ a $ & 1.84$ ^ a $ & 1.79$ ^ a $ & 1.80\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (8e,7o) active space including valence $ \pi $ and $ \nO $ orbitals.
\end { table*}
\begin { table*}
\caption { CASPT3/aug-cc-pVTZ vertical transition energies (eV) of triazine.}
\label { tab:triazine}
\begin { ruledtabular}
\begin { tabular} { lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $ ( a _ 1 ,b _ 1 ,b _ 2 ,a _ 2 ) $ & $ ( A _ 1 ,B _ 1 ,B _ 2 ,A _ 2 ) $ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$ ^ 1 A _ 1 '' ( n, \pis ) $ & (2,4,1,2) & (1,2,0,2) & 5.88$ ^ a $ & 4.62$ ^ a $ & 3.90$ ^ a $ & 5.00$ ^ a $ & 4.99$ ^ a $ & 4.72\\
$ ^ 1 A _ 2 '' ( n, \pis ) $ & (2,4,1,2) & (1,1,0,0) & 5.14$ ^ a $ & 4.77$ ^ a $ & 4.39$ ^ a $ & 4.90$ ^ a $ & 4.87$ ^ a $ & 4.75\\
$ ^ 1 E'' ( n, \pis ) $ & (2,4,1,2) & (1,2,0,2) & 5.51$ ^ a $ & 4.76$ ^ a $ & 4.14$ ^ a $ & 5.01$ ^ a $ & 4.98$ ^ a $ & 4.78\\
$ ^ 1 A _ 2 ' ( \pi , \pis ) $ & (0,6,0,3) & (1,0,1,0) & 5.55$ ^ b $ & 5.76$ ^ b $ & 5.32$ ^ b $ & 5.75$ ^ b $ & 5.72$ ^ b $ & 5.75\\
$ ^ 1 A _ 1 ' ( \pi , \pis ) $ & (0,6,0,3) & (2,0,0,0) & 8.20$ ^ b $ & 7.43$ ^ b $ & 6.89$ ^ b $ & 7.50$ ^ b $ & 7.41$ ^ b $ & 7.24\\
$ ^ 1 E' ( n, 3 s ) $ & (3,4,1,2) & (2,0,2,0) & 7.40$ ^ c $ & 7.48$ ^ c $ & 7.15$ ^ c $ & 7.53$ ^ c $ & 7.49$ ^ c $ & 7.32\\
$ ^ 1 E'' ( n, \pis ) $ & (2,4,1,2) & (1,1,0,1) & 8.26$ ^ a $ & 7.75$ ^ a $ & 7.04$ ^ a $ & 7.92$ ^ a $ & 7.90$ ^ a $ & 7.78\\
$ ^ 1 E' ( \pi , \pis ) $ & (0,6,0,3) & (4,0,3,0) & 10.03$ ^ b $ & 8.65$ ^ b $ & 7.70$ ^ b $ & 8.83$ ^ b $ & 8.72$ ^ b $ & 7.94\\
$ ^ 3 A _ 2 '' ( n, \pis ) $ & (2,4,1,2) & (1,1,0,0) & 4.74$ ^ a $ & 4.37$ ^ a $ & 3.99$ ^ a $ & 4.51$ ^ a $ & 4.49$ ^ a $ & 4.33\\
$ ^ 3 E'' ( n, \pis ) $ & (2,4,1,2) & (1,2,0,2) & 5.14$ ^ a $ & 4.47$ ^ a $ & 3.88$ ^ a $ & 4.71$ ^ a $ & 4.68$ ^ a $ & 4.51\\
$ ^ 3 A _ 1 '' ( n, \pis ) $ & (2,4,1,2) & (1,2,0,2) & 5.88$ ^ a $ & 4.70$ ^ a $ & 3.94$ ^ a $ & 5.06$ ^ a $ & 5.04$ ^ a $ & 4.73\\
$ ^ 3 A _ 1 ' ( \pi , \pis ) $ & (0,6,0,3) & (2,0,0,0) & 4.46$ ^ b $ & 4.88$ ^ b $ & 4.55$ ^ b $ & 4.81$ ^ b $ & 4.75$ ^ b $ & 4.85\\
$ ^ 3 E' ( \pi , \pis ) $ & (0,6,0,3) & (3,0,1,0) & 5.57$ ^ b $ & 5.62$ ^ b $ & 5.20$ ^ b $ & 5.62$ ^ b $ & 5.57$ ^ b $ & 5.59\\
$ ^ 3 A _ 2 ' ( \pi , \pis ) $ & (0,6,0,3) & (1,0,1,0) & 7.70$ ^ b $ & 6.62$ ^ b $ & 6.12$ ^ b $ & 6.76$ ^ b $ & 6.68$ ^ b $ & 6.62\\
\end { tabular}
\end { ruledtabular}
\flushleft
$ ^ a $ Using reference (12e,9o) active space including valence $ \pi $ and $ \nN $ orbitals.
$ ^ b $ Using reference (6e,9o) active space including valence $ \pi $ and three $ 3 p _ x $ orbitals.
$ ^ c $ Using reference (12e,10o) active space including valence $ \pi $ , $ \nN $ and $ 3 s $ orbitals.
2022-03-16 11:55:01 +01:00
\end { table*}
2022-03-09 15:04:23 +01:00
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section { Results and discussion}
\label { sec:res}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section { Conclusion}
\label { sec:ccl}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin { acknowledgements}
This work was performed using HPC resources from CALMIP (Toulouse) under allocation 2021-18005.
PFL thanks the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No.~863481) for funding.
\end { acknowledgements}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section * { Supporting information available}
\label { sec:SI}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section*{Data availability statement}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%The data that support the findings of this study are openly available in Zenodo at \href{http://doi.org/XX.XXXX/zenodo.XXXXXXX}{http://doi.org/XX.XXXX/zenodo.XXXXXXX}.
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\bibliography { CASPT3}
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\end { document}
