stop coz of problem of state labels

Manuscript/CBD.tex

@@ -245,12 +245,26 @@ A theoretical best estimate is defined for the autoisomerization barrier and for
 \label{sec:intro}
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-Despite the fact that excited states are involved in ubiquitous processes such as photochemistry, catalysis or in solar cell technology, none of the many methods existing is the reference in providing accurate excitation energies. Indeed, each method has its own flaws and there are so many chemical scenario that can occur, so it is still one of the biggest challenge in theoretical chemistry. Speaking of difficult task, cyclobutadiene (CBD) molecule has been a real challenge for experimental and theoretical chemists for many decades. \cite{bally_1980} Due to his antiaromaticity \cite{minkin_1994} and his large angular strain \cite{baeyer_1885} the CBD molecule presents a high reactivity which made the synthesis of this molecule a particularly difficult exercise. H\"uckel molecular orbital theory gives a triplet state with square ({\Dfour}) geometry for the ground state of the CBD, with the two singly occupied frontier orbitals that are degenerated by symmetry. This degeneracy is lifted by the Jahn-Teller effect, meaning by distortion of the molecule (lowering symmetry), and gives a singlet state with rectangular ({\Dtwo}) geometry for the ground state. 
+Despite the fact that excited states are involved in ubiquitous processes such as photochemistry, \cite{Bernardi_1990,Bernardi_1996,Boggio-Pasqua_2007,Klessinger_1995,Olivucci_2010,Robb_2007,VanderLugt_1969} catalysis or in solar cell technology, \cite{Delgado_2010} none of the currently existing methods has been shown to provide accurate excitation energies in all scenarios due to the complexity of the process, the size of the systems, environment effects and many other possible factors.
-Indeed, synthetic work from Pettis and co-workers \cite{reeves_1969} gives a rectangular geometry to the singlet ground state of CBD and then was confirmed by experimental works. \cite{irngartinger_1983,ermer_1983,kreile_1986}
+Indeed, each computational model has its own theoretical and/or technical issues and the number of possible chemical scenario is so vast that the design of new excited-state methodologies is still a very active field of theoretical quantum chemistry.\cite{Roos_1996,Piecuch_2002,Dreuw_2005,Krylov_2006,Sneskov_2012,Gonzales_2012,Laurent_2013,Adamo_2013,Dreuw_2015,Ghosh_2018,Blase_2020,Loos_2020a,Hait_2021,Zobel_2021}
 
-At the ground state structrure ({\Dtwo}), the{ \Ag} state has a weak multi-configurational character because of the well separated frontier orbitals and can be described by single-reference methods. But at the square (\Dfour) geometry, the singlet state \sBoneg has two singly occupied frontier orbitals that are degenerated so has a two-configurational character and single-reference methods are unreliable to describe it. The singlet (\Dfour) is a transition state in the automerization reaction between the two rectangular structures (see Fig.\ref{fig:CBD}). The autoisomerization barrier (AB) for the CBD molecule is defined as the energy difference between the singlet ground state of the square (\Dfour) structure and the singlet ground state of the rectangular (\Dtwo) geometry. The energy of this barrier was predicted, experimentally, in the range of 1.6-10 \kcalmol \cite{whitman_1982} and multi-reference calculations gave an energy barrier in the range of 6-7 \kcalmol. \cite{eckert-maksic_2006}All the specificities of the CBD molecule make it a real playground for excited-states methods. 
+Speaking of difficult task, the cyclobutadiene (CBD) molecule has been a real challenge for experimental and theoretical chemistry for many decades. \cite{bally_1980} Due to its antiaromaticity \cite{minkin_1994} and large angular strain, \cite{baeyer_1885} CBD presents a high reactivity which made its synthesis a particularly difficult exercise. 
+The simple H\"uckel molecular orbital theory (wrongly) predicts a triplet ground state at the {\Dfour} square geometry, with two singly-occupied frontier orbitals that are degenerate by symmetry (Hund's rule). 
+This degeneracy is lifted by the so-called Jahn-Teller effect, \ie, by a descent in symmetry (from {\Dfour} to {\Dtwo} point group) via a geometrical distortion of the molecule.
+In such as case, H\"uckel molecular orbital theory  (correctly) predicts a closed-shell singlet ground state at the {\Dtwo} rectangular geometry. 
+\titou{Indeed, synthetic work from Pettis and co-workers \cite{reeves_1969} gives a rectangular geometry to the singlet ground state of CBD and then was confirmed by experimental works. \cite{irngartinger_1983,ermer_1983,kreile_1986}}
 
-Excited states of the CBD molecule in both geometries are represented in Fig.\ref{fig:CBD}. Are represented {\Ag} and {\tBoneg} states for the rectangular geometry and {\sBoneg} and {\Atwog} for the square one. Due to energy scaling doubly excited state {\sBoneg} and {\Aoneg} for the {\Dtwo} and {\Dfour} structures, respectively, are not drawn. Doubly excited states are known to be challenging to represent for adiabatic time-dependent density functional theory \cite{casida_1995} (TD-DFT) and even for state-of-the-art methods like the approximate third-order coupled-cluster (CC3) \cite{christiansen_1995,koch_1997} or equation-of-motion coupled-cluster with singles, doubles and triples (EOM-CCSDT).\cite{kucharski_1991,kallay_2004,hirata_2000,hirata_2004}
+At the {\Dtwo} ground-state structure, the \titou{{\Ag}} state has a weak multi-configurational character with well-separated frontier orbitals that can be described by single-reference methods. 
+However, at the {\Dfour} square geometry, the singlet state {\sBoneg} has two singly occupied frontier orbitals that are degenerated so has a two-configurational character and single-reference methods are unreliable to describe it. 
+The singlet (\Dfour) is a transition state in the automerization reaction between the two rectangular structures (see Fig.~\ref{fig:CBD}). 
+The autoisomerization barrier (AB) for the CBD molecule is defined as the energy difference between the singlet ground state of the square (\Dfour) structure and the singlet ground state of the rectangular (\Dtwo) geometry. 
+The energy of this barrier was predicted, experimentally, in the range of 1.6-10 \kcalmol \cite{whitman_1982} and multi-reference calculations gave an energy barrier in the range of 6-7 \kcalmol. \cite{eckert-maksic_2006}
+All the specificities of CBD make it a real playground for excited-states methods. 
+
+The lowest-energy excited states of CBD in both geometries are represented in Fig.~\ref{fig:CBD}. 
+Are represented {\Ag} and {\tBoneg} states for the rectangular geometry and {\sBoneg} and {\Atwog} for the square one. 
+Due to energy scaling doubly excited state {\sBoneg} and {\Aoneg} for the {\Dtwo} and {\Dfour} structures, respectively, are not drawn. 
+Doubly excited states are known to be challenging to represent for adiabatic time-dependent density functional theory \cite{casida_1995} (TD-DFT) and even for state-of-the-art methods like the approximate third-order coupled-cluster (CC3) \cite{christiansen_1995,koch_1997} or equation-of-motion coupled-cluster with singles, doubles and triples (EOM-CCSDT). \cite{kucharski_1991,kallay_2004,hirata_2000,hirata_2004}
 
 In order to tackle the problems of multi-configurational character and double excitations several ways are explored. The most evident way that one can think about to describe multiconfigurational and double excitations are multiconfigurational methods.  Among these methods, one can find complete active space self-consistent field (CASSCF) \cite{roos_1996}, the second perturbation-corrected variant (CASPT2) \cite{andersson_1990} and the second-order $n$-electron valence state perturbation theory (NEVPT2). \cite{angeli_2001,angeli_2001a,angeli_2002}The exponential scaling of these methods with the size of the active space is the limitation to the application of these ones to big molecules.