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45
Manuscript/CBD.bib
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@ -1,13 +1,54 @@
%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
%% https://bibdesk.sourceforge.io/ %% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2022-03-23 22:21:51 +0100 %% Created for Pierre-Francois Loos at 2022-03-24 14:53:30 +0100
%% Saved with string encoding Unicode (UTF-8) %% Saved with string encoding Unicode (UTF-8)
@article{Hirata_1999,
abstract = {A computationally simple method for molecular excited states, namely, the Tamm--Dancoff approximation to time-dependent density functional theory, is proposed and implemented. This method yields excitation energies for several closed- and open-shell molecules that are essentially of the same quality as those obtained from time-dependent density functional theory itself, when the same exchange-correlation functional is used.},
author = {So Hirata and Martin Head-Gordon},
date-added = {2022-03-24 14:53:06 +0100},
date-modified = {2022-03-24 14:53:21 +0100},
doi = {https://doi.org/10.1016/S0009-2614(99)01149-5},
journal = {Chem. Phys. Lett.},
number = {3},
pages = {291-299},
title = {Time-dependent density functional theory within the Tamm--Dancoff approximation},
volume = {314},
year = {1999},
bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0009261499011495},
bdsk-url-2 = {https://doi.org/10.1016/S0009-2614(99)01149-5}}
@article{qchem,
author = {Epifanovsky,Evgeny and Gilbert,Andrew T. B. and Feng,Xintian and Lee,Joonho and Mao,Yuezhi and Mardirossian,Narbe and Pokhilko,Pavel and White,Alec F. and Coons,Marc P. and Dempwolff,Adrian L. and Gan,Zhengting and Hait,Diptarka and Horn,Paul R. and Jacobson,Leif D. and Kaliman,Ilya and Kussmann,J{\"o}rg and Lange,Adrian W. and Lao,Ka Un and Levine,Daniel S. and Liu,Jie and McKenzie,Simon C. and Morrison,Adrian F. and Nanda,Kaushik D. and Plasser,Felix and Rehn,Dirk R. and Vidal,Marta L. and You,Zhi-Qiang and Zhu,Ying and Alam,Bushra and Albrecht,Benjamin J. and Aldossary,Abdulrahman and Alguire,Ethan and Andersen,Josefine H. and Athavale,Vishikh and Barton,Dennis and Begam,Khadiza and Behn,Andrew and Bellonzi,Nicole and Bernard,Yves A. and Berquist,Eric J. and Burton,Hugh G. A. and Carreras,Abel and Carter-Fenk,Kevin and Chakraborty,Romit and Chien,Alan D. and Closser,Kristina D. and Cofer-Shabica,Vale and Dasgupta,Saswata and de Wergifosse,Marc and Deng,Jia and Diedenhofen,Michael and Do,Hainam and Ehlert,Sebastian and Fang,Po-Tung and Fatehi,Shervin and Feng,Qingguo and Friedhoff,Triet and Gayvert,James and Ge,Qinghui and Gidofalvi,Gergely and Goldey,Matthew and Gomes,Joe and Gonz{\'a}lez-Espinoza,Cristina E. and Gulania,Sahil and Gunina,Anastasia O. and Hanson-Heine,Magnus W. D. and Harbach,Phillip H. P. and Hauser,Andreas and Herbst,Michael F. and Hern{\'a}ndez Vera,Mario and Hodecker,Manuel and Holden,Zachary C. and Houck,Shannon and Huang,Xunkun and Hui,Kerwin and Huynh,Bang C. and Ivanov,Maxim and J{\'a}sz,{\'A}d{\'a}m and Ji,Hyunjun and Jiang,Hanjie and Kaduk,Benjamin and K{\"a}hler,Sven and Khistyaev,Kirill and Kim,Jaehoon and Kis,Gergely and Klunzinger,Phil and Koczor-Benda,Zsuzsanna and Koh,Joong Hoon and Kosenkov,Dimitri and Koulias,Laura and Kowalczyk,Tim and Krauter,Caroline M. and Kue,Karl and Kunitsa,Alexander and Kus,Thomas and Ladj{\'a}nszki,Istv{\'a}n and Landau,Arie and Lawler,Keith V. and Lefrancois,Daniel and Lehtola,Susi and Li,Run R. and Li,Yi-Pei and Liang,Jiashu and Liebenthal,Marcus and Lin,Hung-Hsuan and Lin,You-Sheng and Liu,Fenglai and Liu,Kuan-Yu and Loipersberger,Matthias and Luenser,Arne and Manjanath,Aaditya and Manohar,Prashant and Mansoor,Erum and Manzer,Sam F. and Mao,Shan-Ping and Marenich,Aleksandr V. and Markovich,Thomas and Mason,Stephen and Maurer,Simon A. and McLaughlin,Peter F. and Menger,Maximilian F. S. J. and Mewes,Jan-Michael and Mewes,Stefanie A. and Morgante,Pierpaolo and Mullinax,J. Wayne and Oosterbaan,Katherine J. and Paran,Garrette and Paul,Alexander C. and Paul,Suranjan K. and Pavo{\v s}evi{\'c},Fabijan and Pei,Zheng and Prager,Stefan and Proynov,Emil I. and R{\'a}k,{\'A}d{\'a}m and Ramos-Cordoba,Eloy and Rana,Bhaskar and Rask,Alan E. and Rettig,Adam and Richard,Ryan M. and Rob,Fazle and Rossomme,Elliot and Scheele,Tarek and Scheurer,Maximilian and Schneider,Matthias and Sergueev,Nickolai and Sharada,Shaama M. and Skomorowski,Wojciech and Small,David W. and Stein,Christopher J. and Su,Yu-Chuan and Sundstrom,Eric J. and Tao,Zhen and Thirman,Jonathan and Tornai,G{\'a}bor J. and Tsuchimochi,Takashi and Tubman,Norm M. and Veccham,Srimukh Prasad and Vydrov,Oleg and Wenzel,Jan and Witte,Jon and Yamada,Atsushi and Yao,Kun and Yeganeh,Sina and Yost,Shane R. and Zech,Alexander and Zhang,Igor Ying and Zhang,Xing and Zhang,Yu and Zuev,Dmitry and Aspuru-Guzik,Al{\'a}n and Bell,Alexis T. and Besley,Nicholas A. and Bravaya,Ksenia B. and Brooks,Bernard R. and Casanova,David and Chai,Jeng-Da and Coriani,Sonia and Cramer,Christopher J. and Cserey,Gy{\"o}rgy and DePrince,A. Eugene and DiStasio,Robert A. and Dreuw,Andreas and Dunietz,Barry D. and Furlani,Thomas R. and Goddard,William A. and Hammes-Schiffer,Sharon and Head-Gordon,Teresa and Hehre,Warren J. and Hsu,Chao-Ping and Jagau,Thomas-C. and Jung,Yousung and Klamt,Andreas and Kong,Jing and Lambrecht,Daniel S. and Liang,WanZhen and Mayhall,Nicholas J. and McCurdy,C. William and Neaton,Jeffrey B. and Ochsenfeld,Christian and Parkhill,John A. and Peverati,Roberto and Rassolov,Vitaly A. and Shao,Yihan and Slipchenko,Lyudmila V. and Stauch,Tim and Steele,Ryan P. and Subotnik,Joseph E. and Thom,Alex J. W. and Tkatchenko,Alexandre and Truhlar,Donald G. and Van Voorhis,Troy and Wesolowski,Tomasz A. and Whaley,K. Birgitta and Woodcock,H. Lee and Zimmerman,Paul M. and Faraji,Shirin and Gill,Peter M. W. and Head-Gordon,Martin and Herbert,John M. and Krylov,Anna I.},
date-added = {2022-03-24 14:04:49 +0100},
date-modified = {2022-03-24 14:05:03 +0100},
doi = {10.1063/5.0055522},
journal = {J. Chem. Phys.},
number = {8},
pages = {084801},
title = {Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package},
volume = {155},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1063/5.0055522}}
@article{Loos_2021b,
author = {Loos, Pierre-Fran{\c c}ois and Jacquemin, Denis},
date-added = {2022-03-24 13:24:14 +0100},
date-modified = {2022-03-24 13:24:14 +0100},
doi = {10.1021/acs.jpca.1c08524},
journal = {J. Phys. Chem. A},
number = {47},
pages = {10174-10188},
title = {A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Bicyclic Systems},
volume = {125},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1021/acs.jpca.1c08524}}
@article{Werner_2020, @article{Werner_2020,
author = {Werner,Hans-Joachim and Knowles,Peter J. and Manby,Frederick R. and Black,Joshua A. and Doll,Klaus and He{\ss}elmann,Andreas and Kats,Daniel and K{\"o}hn,Andreas and Korona,Tatiana and Kreplin,David A. and Ma,Qianli and Miller,Thomas F. and Mitrushchenkov,Alexander and Peterson,Kirk A. and Polyak,Iakov and Rauhut,Guntram and Sibaev,Marat}, author = {Werner,Hans-Joachim and Knowles,Peter J. and Manby,Frederick R. and Black,Joshua A. and Doll,Klaus and He{\ss}elmann,Andreas and Kats,Daniel and K{\"o}hn,Andreas and Korona,Tatiana and Kreplin,David A. and Ma,Qianli and Miller,Thomas F. and Mitrushchenkov,Alexander and Peterson,Kirk A. and Polyak,Iakov and Rauhut,Guntram and Sibaev,Marat},
date-added = {2022-03-23 22:21:43 +0100}, date-added = {2022-03-23 22:21:43 +0100},

60
Manuscript/CBD.tex
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@ -315,32 +315,37 @@ First, we consider the autoisomerization barrier (Subsection \ref{sec:auto}) and
For the SCI calculations, we rely on the CIPSI algorithm which is implemented in QUANTUM PACKAGE. \cite{Garniron_2019} For the SCI calculations, we rely on the CIPSI algorithm which is implemented in QUANTUM PACKAGE. \cite{Garniron_2019}
To treat electronic states on equal footing, we use a state-averaged formalism where the ground and excited states are expanded with the same set of determinants but with different CI coefficients. To treat electronic states on equal footing, we use a state-averaged formalism where the ground and excited states are expanded with the same set of determinants but with different CI coefficients.
Note that the determinant selection for these states are performed simultaneously via the protocol described in Refs.~\onlinecite{Scemama_2019,Garniron_2019}. Note that the determinant selection for these states are performed simultaneously via the protocol described in Refs.~\onlinecite{Scemama_2019,Garniron_2019}.
\titou{For a given size of the variational wave function, the CIPSI energy is the sum of two terms: the variational energy obtained by diagonalization of the CI matrix in the reference space and a second-order perturbative correction which estimates the contribution of the determinants not included in the variational space (estimate error in the truncation).
It is possible to estimate the FCI limit for the total energies and compute the corresponding transition energies by extrapolating this second-order correction to zero. For a given size of the variational wave function, the CIPSI energy is the sum of two terms: the variational energy obtained by diagonalization of the CI matrix in the reference space $E_\text{var}$ and a second-order perturbative correction $E_\text{PT2}$ which estimates the contribution of the external determinants that are not included in the variational space at a given iteration.
Extrapolation brings error and we can estimate this one by energy difference between excitation energies obtained with the largest SCI wave function and the FCI extrapolated value. The sum of these two energies is, for large enough wave functions, an estimate of the FCI energy, \ie, $E_\text{FCI} \approx E_\text{var} + E_\text{PT2}$.
These errors provide a rough idea of the quality of the FCI extrapolation and cannot be seen as true bar error, they are reported in the following tables.} It is possible to estimate more precisely the FCI energy via an extrapolation procedure, where the variational energy is extrapolated to $E_\text{PT2} = 0$. \cite{Holmes_2017}
Excitation energies are then computed as differences of extrapolated total energies. \cite{Chien_2018,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c}
Additionally, an error bar can be provided via a recent method based on Gaussian random variables as described in Ref.~\onlinecite{Veril_2021}.
This type of extrapolation procedures is now routine in SCI methods as well as other state-of-the-art techniques. \cite{Eriksen_2020,Loos_2020e,Eriksen_2021}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Coupled-cluster calculations} \subsection{Coupled-cluster calculations}
\label{sec:CC} \label{sec:CC}
Coupled-cluster theory provides a hierarchy of methods that yield increasingly accurate energies via the increase of the maximum excitation degree of the cluster operator: CC with singles and doubles (CCSD), CC with singles, doubles, and triples (CCSDT) as well as CC with singles, doubles, triples, and quadruples (CCSDTQ). \alert{Coupled-cluster theory provides a hierarchy of methods that yields increasingly accurate energies by ramping up the maximum excitation degree of the cluster operator: CC with singles and doubles (CCSD), CC with singles, doubles, and triples (CCSDT), CC with singles, doubles, triples, and quadruples (CCSDTQ), etc.
%Without any truncation of the cluster operator, one has the full CC (FCC) that is equivalent to the full configuration interaction (FCI) giving the exact energy and wave function of the system for a fixed atomic basis set. %Without any truncation of the cluster operator, one has the full CC (FCC) that is equivalent to the full configuration interaction (FCI) giving the exact energy and wave function of the system for a fixed atomic basis set.
%However, due to the computational exponential scaling with system size we have to use truncated CC methods. %However, due to the computational exponential scaling with system size we have to use truncated CC methods.
Here, we performed different types of CC calculations using different codes. Here, we performed different types of CC calculations using different codes.
CCSD, CCSDT, and CCSDTQ calculations are achieved with \textcolor{red}{CFOUR}. CCSD, CCSDT, and CCSDTQ calculations are achieved with \textcolor{red}{CFOUR}.
The calculations in the context of CC response theory or ``approximate'' series (CC3 and CC4) are performed with \textcolor{red}{DALTON}.\cite{Aidas_2014} The calculations in the context of CC response theory or ``approximate'' series (CC3 and CC4) are performed with \textcolor{red}{DALTON}.\cite{Aidas_2014}
The CC with singles, doubles, triples and quadruples (CCSDTQ) are done with the \titou{CFOUR} code. The CC with singles, doubles, triples and quadruples (CCSDTQ) are done with the \titou{CFOUR} code.
The CC2, \cite{Christiansen_1995,Hattig_2000} CC3 \cite{Christiansen_1995,Koch_1995} and CC4 \cite{Kallay_2005,Matthews_2020} methods can be seen as cheaper approximations of CCSD, \cite{Purvis_1982} CCSDT \cite{Noga_1987a} and CCSDTQ \cite{Kucharski_1991a} by skipping the most expensive terms and avoiding the storage of higher-excitations amplitudes. The CC2, \cite{Christiansen_1995,Hattig_2000} CC3 \cite{Christiansen_1995,Koch_1995} and CC4 \cite{Kallay_2005,Matthews_2020} methods can be seen as cheaper approximations of CCSD, \cite{Purvis_1982} CCSDT \cite{Noga_1987a} and CCSDTQ \cite{Kucharski_1991a} by skipping the most expensive terms and avoiding the storage of higher-excitations amplitudes.}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Multi-configurational calculations} \subsection{Multi-configurational calculations}
\label{sec:Multi} \label{sec:Multi}
State-averaged CASSCF (SA-CASSCF) calculations are performed with MOLPRO. \cite{Werner_2020} State-averaged CASSCF (SA-CASSCF) calculations are performed with MOLPRO. \cite{Werner_2020}
\titou{state-average procedure?} For each excited state, a set of state-averaged orbitals is computed by taking into account the the excited state of interest as well as the ground state (even if it has a different symmetry).
On top of these, CASPT2 calculations are performed within the RS2 contraction scheme, while the NEVPT2 energies are computed within both partially contracted (PC) and strongly contracted (SC) scheme. \cite{Angeli_2001,Angeli_2001a,Angeli_2002} On top of these, CASPT2 calculations are performed within the RS2 contraction scheme, while the NEVPT2 energies are computed within both partially contracted (PC) and strongly contracted (SC) scheme. \cite{Angeli_2001,Angeli_2001a,Angeli_2002}
PC-NEVPT2 is theoretically more accurate than SC-NEVPT2 due to the larger number of external configurations and greater flexibility. PC-NEVPT2 is theoretically more accurate than SC-NEVPT2 due to the larger number of external configurations and greater flexibility.
For the sake of comparison, in some cases, we have also performed multi-reference CI (MRCI) calculations.
All these calculations are also carried out with MOLPRO. \cite{Werner_2020}
%and extended multistate (XMS) CASPT2 calculations are also performed in the cas of strong mixing between states with same spin and spatial symmetries. %and extended multistate (XMS) CASPT2 calculations are also performed in the cas of strong mixing between states with same spin and spatial symmetries.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -348,24 +353,27 @@ PC-NEVPT2 is theoretically more accurate than SC-NEVPT2 due to the larger number
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Spin-flip calculations} \subsection{Spin-flip calculations}
\label{sec:sf} \label{sec:sf}
In both arrangements, CBD has a singlet ground state, for the spin-flip calculations we consider the lowest triplet state as reference. Within the spin-flip formalism, one considers the lowest triplet state as reference instead of the singlet ground state.
Spin-flip techniques are broadly accessible and here, among them, we explore algebraic-diagrammatic construction \cite{Schirmer_1982} (ADC) using standard ADC(2)-s \cite{Trofimov_1997,Dreuw_2015} and extended ADC(2)-x \cite{Dreuw_2015} schemes as well as the ADC(3) \cite{Dreuw_2015,Trofimov_2002,Harbach_2014} scheme. Nowadays, spin-flip techniques are broadly accessible thanks to intensive developments in the electronic structure community (see Ref.~\onlinecite{Casanova_2020} and references therein).
We also use spin-flip within the TD-DFT \cite{Casida_1995} framework. Here, we explore the spin-flip version \cite{Lefrancois_2015} of the algebraic-diagrammatic construction \cite{Schirmer_1982} (ADC) using the standard and extended second-order ADC schemes, SF-ADC(2)-s \cite{Trofimov_1997,Dreuw_2015} and SF-ADC(2)-x, \cite{Dreuw_2015} as well as its third-order version, SF-ADC(3). \cite{Dreuw_2015,Trofimov_2002,Harbach_2014}
The standard and extended spin-flip ADC(2) (SF-ADC(2)-s and SF-ADC(2)-x respectively) and SF-ADC(3) are performed using Q-CHEM 5.2.1. \cite{Shao_2015} These calculations are performed using Q-CHEM 5.2.1. \cite{qchem}
Spin-flip TD-DFT calculations are also performed using Q-CHEM 5.2.1.
The B3LYP,\cite{Becke_1988b,Lee_1988a,Becke_1993b} PBE0 \cite{Adamo_1999a,Ernzerhof_1999} and BH\&HLYP hybrid GGA functionals are considered, they contain 20\%, 25\%, 50\% of exact exchange and are labeled, respectively, as SF-BLYP, SF-B3LYP, SF-PBE0, SF-BH\&HLYP. We have also carried out spin-flip calculations within the TD-DFT framework (SF-TD-DFT), \cite{Shao_2015} and these are also performed with Q-CHEM 5.2.1. \cite{qchem}
We also have done spin-flip TD-DFT calculations using range-separated hybrid (RSH) functionals as: CAM-B3LYP,\cite{Yanai_2004a} LC-$\omega$PBE08 \cite{Weintraub_2009a} and $\omega$B97X-V. \cite{Mardirossian_2014} The B3LYP, \cite{Becke_1988b,Lee_1988a,Becke_1993b} PBE0 \cite{Adamo_1999a,Ernzerhof_1999} and BH\&HLYP hybrid functionals are considered, which contain 20\%, 25\%, 50\% of exact exchange, respectively.
The main difference here between these RSH functionals is the amount of exact-exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V. These calculations are labeled as SF-TD-BLYP, SF-TD-B3LYP, SF-TD-PBE0, and SF-TD-BH\&HLYP in the following.
To complete the use of spin-flip TD-DFT we also considered the hybrid meta-GGA functional M06-2X \cite{Zhao_2008} and the RSH meta-GGA functional M11.\cite{Peverati_2011} Additionally, we have also computed SF-TD-DFT excitation energies using range-separated hybrid functionals: CAM-B3LYP,\cite{Yanai_2004a} LC-$\omega$PBE08, \cite{Weintraub_2009a} and $\omega$B97X-V. \cite{Mardirossian_2014}
Note that all SF-TD-DFT calculations are done within the TDA approximation. The main difference between these range-separated functionals is their amount of exact exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V.
Finally, the hybrid meta-GGA functional M06-2X \cite{Zhao_2008} and the range-separated hybrid meta-GGA functional M11 \cite{Peverati_2011} are also employed.
Note that all SF-TD-DFT calculations are done within the Tamm-Dancoff approximation. \cite{Hirata_1999}
%EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1. %EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Theoretical best estimates} \subsection{Theoretical best estimates}
All the calculations are performed using four basis set, the 6-31+G(d) basis and the aug-cc-pVXZ with X $=$ D, T, Q.\cite{dunning_1989} When technically possible, each level of theory is tested with four Gaussian basis sets, namely, the 6-31+G(d) basis and the aug-cc-pVXZ with X $=$ D, T, Q. \cite{Dunning_1989}
For each studied quantity, i.e., the autoisomerisation barrier and the vertical excitations, we provide a theoretical best estimate (TBE). For each studied quantity, i.e., the autoisomerisation barrier and the vertical excitations, we provide a theoretical best estimate (TBE).
These TBEs are provided using extrapolated CCSDTQ/aug-cc-pVTZ values when possible and using NEVPT2(12,12) otherwise. These TBEs are provided using extrapolated CCSDTQ/aug-cc-pVTZ values when possible and using NEVPT2(12,12) otherwise.
\alert{CIPSI calculations are a safety net to check the convergence of CCSDTQ.}
The extrapolation of the CCSDTQ/aug-cc-pVTZ values is done using two schemes. The extrapolation of the CCSDTQ/aug-cc-pVTZ values is done using two schemes.
The first one uses CC4 values for the extrapolation and proceed as follows The first one uses CC4 values for the extrapolation and proceed as follows
\begin{equation} \begin{equation}
@ -606,7 +614,7 @@ CC4 &6-31+G(d)& & $3.343$ & $4.067$ \\
CCSDTQ &6-31+G(d)& & $3.340$ & $4.073$ \\ CCSDTQ &6-31+G(d)& & $3.340$ & $4.073$ \\
& aug-cc-pVDZ & & $\left[3.161\right]$\fnm[2]& $\left[4.047\right]$\fnm[2] \\ & aug-cc-pVDZ & & $\left[3.161\right]$\fnm[2]& $\left[4.047\right]$\fnm[2] \\
& aug-cc-pVTZ & & $\left[3.125\right]$\fnm[3]& $\left[4.149\right]$\fnm[3]\\[0.1cm] & aug-cc-pVTZ & & $\left[3.125\right]$\fnm[3]& $\left[4.149\right]$\fnm[3]\\[0.1cm]
SA2-CASSCF(4,4) &6-31+G(d)& $1.662$ & $4.657$ & $4.439$ \\ SA-CASSCF(4,4) &6-31+G(d)& $1.662$ & $4.657$ & $4.439$ \\
& aug-cc-pVDZ & $1.672$ & $4.563$ & $4.448$ \\ & aug-cc-pVDZ & $1.672$ & $4.563$ & $4.448$ \\
& aug-cc-pVTZ & $1.670$ & $4.546$ & $4.441$ \\ & aug-cc-pVTZ & $1.670$ & $4.546$ & $4.441$ \\
& aug-cc-pVQZ & $1.671$ & $4.549$ & $4.440$ \\[0.1cm] & aug-cc-pVQZ & $1.671$ & $4.549$ & $4.440$ \\[0.1cm]
@ -630,7 +638,7 @@ MRCI(4,4) &6-31+G(d)& $1.564$ & $3.802$ & $4.265$ \\
& aug-cc-pVDZ & $1.558$ & $3.670$ & $4.254$ \\ & aug-cc-pVDZ & $1.558$ & $3.670$ & $4.254$ \\
& aug-cc-pVTZ & $1.568$ & $3.678$ & $4.270$ \\ & aug-cc-pVTZ & $1.568$ & $3.678$ & $4.270$ \\
& aug-cc-pVQZ & $1.574$ & $3.681$ & $4.280$ \\[0.1cm] & aug-cc-pVQZ & $1.574$ & $3.681$ & $4.280$ \\[0.1cm]
SA2-CASSCF(12,12) &6-31+G(d)& $1.675$ & $3.924$ & $4.220$ \\ SA-CASSCF(12,12) &6-31+G(d)& $1.675$ & $3.924$ & $4.220$ \\
& aug-cc-pVDZ & $1.685$ & $3.856$ & $4.221$ \\ & aug-cc-pVDZ & $1.685$ & $3.856$ & $4.221$ \\
& aug-cc-pVTZ & $1.686$ & $3.844$ & $4.217$ \\ & aug-cc-pVTZ & $1.686$ & $3.844$ & $4.217$ \\
& aug-cc-pVQZ & $1.687$ & $3.846$ & $4.216$ \\[0.1cm] & aug-cc-pVQZ & $1.687$ & $3.846$ & $4.216$ \\[0.1cm]
@ -776,7 +784,7 @@ CC4 & 6-31+G(d) & & $1.604$ & $2.121$ \\
CCSDTQ & 6-31+G(d) & $0.205$ & $1.593$ & $2.134$ \\ CCSDTQ & 6-31+G(d) & $0.205$ & $1.593$ & $2.134$ \\
& aug-cc-pVDZ & $\left[0.160\right]$\fnm[2] & $\left[1.528 \right]$\fnm[4]&$\left[1.947\right]$\fnm[4] \\ & aug-cc-pVDZ & $\left[0.160\right]$\fnm[2] & $\left[1.528 \right]$\fnm[4]&$\left[1.947\right]$\fnm[4] \\
& aug-cc-pVTZ & $\left[0.144\right]$\fnm[3] & $\left[1.500 \right]$\fnm[5]&$\left[2.034\right]$\fnm[5] \\ [0.1cm] & aug-cc-pVTZ & $\left[0.144\right]$\fnm[3] & $\left[1.500 \right]$\fnm[5]&$\left[2.034\right]$\fnm[5] \\ [0.1cm]
SA2-CASSCF(4,4) & 6-31+G(d) & $0.447$ & $2.257$ & $3.549$ \\ SA-CASSCF(4,4) & 6-31+G(d) & $0.447$ & $2.257$ & $3.549$ \\
& aug-cc-pVDZ & $0.438$ & $2.240$ & $3.443$ \\ & aug-cc-pVDZ & $0.438$ & $2.240$ & $3.443$ \\
& aug-cc-pVTZ & $0.434$ & $2.234$ & $3.424$ \\ & aug-cc-pVTZ & $0.434$ & $2.234$ & $3.424$ \\
& aug-cc-pVQZ & $0.435$ & $2.235$ & $3.427$ \\[0.1cm] & aug-cc-pVQZ & $0.435$ & $2.235$ & $3.427$ \\[0.1cm]
@ -796,7 +804,7 @@ MRCI(4,4) & 6-31+G(d) & $0.297$ & $1.861$ & $2.571$ \\
& aug-cc-pVDZ & $0.273$ & $1.823$ & $2.419$ \\ & aug-cc-pVDZ & $0.273$ & $1.823$ & $2.419$ \\
& aug-cc-pVTZ & $0.271$ & $1.824$ & $2.415$ \\ & aug-cc-pVTZ & $0.271$ & $1.824$ & $2.415$ \\
& aug-cc-pVQZ & $0.273$ & $1.825$ & $2.413$ \\[0.1cm] & aug-cc-pVQZ & $0.273$ & $1.825$ & $2.413$ \\[0.1cm]
SA2-CASSCF(12,12) & 6-31+G(d) & $0.386$ & $1.974$ & $2.736$ \\ SA-CASSCF(12,12) & 6-31+G(d) & $0.386$ & $1.974$ & $2.736$ \\
& aug-cc-pVDZ & $0.374$ & $1.947$ & $2.649$ \\ & aug-cc-pVDZ & $0.374$ & $1.947$ & $2.649$ \\
& aug-cc-pVTZ & $0.370$ & $1.943$ & $2.634$ \\ & aug-cc-pVTZ & $0.370$ & $1.943$ & $2.634$ \\
& aug-cc-pVQZ & $0.371$ & $1.945$ & $2.637$ \\[0.1cm] & aug-cc-pVQZ & $0.371$ & $1.945$ & $2.637$ \\[0.1cm]
@ -885,13 +893,13 @@ Finally we look at the vertical energy errors for the \Dfour structure. First, w
%CCSDT & $-0.25$ & $-0.051$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\ %CCSDT & $-0.25$ & $-0.051$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\
%CC4 & $-0.11$ & & $0.003$ & $-0.006$ & & $0.011$ & $-0.013$ \\ %CC4 & $-0.11$ & & $0.003$ & $-0.006$ & & $0.011$ & $-0.013$ \\
%CCSDTQ & $0.00$ & & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\[0.1cm] %CCSDTQ & $0.00$ & & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\[0.1cm]
%SA2-CASSCF(4,4) & & $0.208$ & $1.421$ & $0.292$ & $0.290$ & $0.734$ & $1.390$ \\ %SA-CASSCF(4,4) & & $0.208$ & $1.421$ & $0.292$ & $0.290$ & $0.734$ & $1.390$ \\
%CASPT2(4,4) & & $-0.050$ & $-0.202$ & $-0.077$ & $-0.016$ & $0.006$ & $-0.399$ \\ %CASPT2(4,4) & & $-0.050$ & $-0.202$ & $-0.077$ & $-0.016$ & $0.006$ & $-0.399$ \\
%XMS-CASPT2(4,4) & & & & $-0.035$ & & & \\ %XMS-CASPT2(4,4) & & & & $-0.035$ & & & \\
%SC-NEVPT2(4,4) & & $-0.083$ & $-0.703$ & $-0.041$ & $-0.120$ & $-0.072$ & $-0.979$ \\ %SC-NEVPT2(4,4) & & $-0.083$ & $-0.703$ & $-0.041$ & $-0.120$ & $-0.072$ & $-0.979$ \\
%PC-NEVPT2(4,4) & & $-0.080$ & $-0.757$ & $-0.066$ & $-0.118$ & $-0.097$ & $-1.031$ \\ %PC-NEVPT2(4,4) & & $-0.080$ & $-0.757$ & $-0.066$ & $-0.118$ & $-0.097$ & $-1.031$ \\
%MRCI(4,4) & & $0.106$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\[0.1cm] %MRCI(4,4) & & $0.106$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\[0.1cm]
%SA2-CASSCF(12,12) & $2.66$ & $0.224$ & $0.719$ & $0.068$ & $0.226$ & $0.443$ & $0.600$ \\ %SA-CASSCF(12,12) & $2.66$ & $0.224$ & $0.719$ & $0.068$ & $0.226$ & $0.443$ & $0.600$ \\
%CASPT2(12,12) & & $0.018$ & $0.058$ & $-0.106$ & $0.039$ & $0.038$ & $-0.108$ \\ %CASPT2(12,12) & & $0.018$ & $0.058$ & $-0.106$ & $0.039$ & $0.038$ & $-0.108$ \\
%XMS-CASPT2(12,12) & & & & $-0.090$ & & & \\ %XMS-CASPT2(12,12) & & & & $-0.090$ & & & \\
%SC-NEVPT2(12,12) & $-0.65$ & $0.039$ & $0.063$ & $-0.063$ & $0.021$ & $0.046$ & $-0.142$ \\ %SC-NEVPT2(12,12) & $-0.65$ & $0.039$ & $0.063$ & $-0.063$ & $0.021$ & $0.046$ & $-0.142$ \\
@ -939,13 +947,13 @@ CC3 & $-1.05$ & $-0.060$ & $-0.006$ & $0.628$ & & $0.162$ & $0.686$ \\
CCSDT & $-0.25$ & $-0.051$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\ CCSDT & $-0.25$ & $-0.051$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\
CC4 & $-0.11$ & & $0.003$ & $-0.006$ & & $0.011$ & $-0.013$ \\ CC4 & $-0.11$ & & $0.003$ & $-0.006$ & & $0.011$ & $-0.013$ \\
CCSDTQ & $0.00$ & & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\[0.1cm] CCSDTQ & $0.00$ & & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\[0.1cm]
SA2-CASSCF(4,4) & & $0.208$ & $1.421$ & $0.292$ & $0.290$ & $0.734$ & $1.390$ \\ SA-CASSCF(4,4) & & $0.208$ & $1.421$ & $0.292$ & $0.290$ & $0.734$ & $1.390$ \\
CASPT2(4,4) & & $-0.050$ & $-0.202$ & $-0.077$ & $-0.016$ & $0.006$ & $-0.399$ \\ CASPT2(4,4) & & $-0.050$ & $-0.202$ & $-0.077$ & $-0.016$ & $0.006$ & $-0.399$ \\
%XMS-CASPT2(4,4) & & & & $-0.035$ & & & \\ %XMS-CASPT2(4,4) & & & & $-0.035$ & & & \\
SC-NEVPT2(4,4) & & $-0.083$ & $-0.703$ & $-0.041$ & $-0.120$ & $-0.072$ & $-0.979$ \\ SC-NEVPT2(4,4) & & $-0.083$ & $-0.703$ & $-0.041$ & $-0.120$ & $-0.072$ & $-0.979$ \\
PC-NEVPT2(4,4) & & $-0.080$ & $-0.757$ & $-0.066$ & $-0.118$ & $-0.097$ & $-1.031$ \\ PC-NEVPT2(4,4) & & $-0.080$ & $-0.757$ & $-0.066$ & $-0.118$ & $-0.097$ & $-1.031$ \\
MRCI(4,4) & & $0.106$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\[0.1cm] MRCI(4,4) & & $0.106$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\[0.1cm]
SA2-CASSCF(12,12) & $2.66$ & $0.224$ & $0.719$ & $0.068$ & $0.226$ & $0.443$ & $0.600$ \\ SA-CASSCF(12,12) & $2.66$ & $0.224$ & $0.719$ & $0.068$ & $0.226$ & $0.443$ & $0.600$ \\
CASPT2(12,12) & & $0.018$ & $0.058$ & $-0.106$ & $0.039$ & $0.038$ & $-0.108$ \\ CASPT2(12,12) & & $0.018$ & $0.058$ & $-0.106$ & $0.039$ & $0.038$ & $-0.108$ \\
%XMS-CASPT2(12,12) & & & & $-0.090$ & & & \\ %XMS-CASPT2(12,12) & & & & $-0.090$ & & & \\
SC-NEVPT2(12,12) & $-0.65$ & $0.039$ & $0.063$ & $-0.063$ & $0.021$ & $0.046$ & $-0.142$ \\ SC-NEVPT2(12,12) & $-0.65$ & $0.039$ & $0.063$ & $-0.063$ & $0.021$ & $0.046$ & $-0.142$ \\