revision manuscript

Manuscript/CBD.tex

@@ -70,7 +70,7 @@
 
 \title{Reference Energies for Cyclobutadiene: Automerization and Excited States}
 
-\author{Enzo \surname{Monino}}
+\author{Enzo \surname{Monino}*}
 	\email{emonino@irsamc.ups-tlse.fr}
 	\affiliation{\LCPQ}	 
 \author{Martial \surname{Boggio-Pasqua}}
@@ -79,12 +79,12 @@
 	\affiliation{\LCPQ}
 \author{Denis \surname{Jacquemin}}
 	\affiliation{\CEISAM}
-\author{Pierre-Fran\c{c}ois \surname{Loos}}
+\author{Pierre-Fran\c{c}ois \surname{Loos}*}
 	\email{loos@irsamc.ups-tlse.fr}
 	\affiliation{\LCPQ}
 
 \begin{abstract}
-\section*{Abstract}	
+\paragraph*{Abstract:}	
 Cyclobutadiene is a well-known playground for theoretical chemists and is particularly suitable to test ground- and excited-state methods.
 Indeed, due to its high spatial symmetry, especially at the $D_{4h}$ square geometry but also in the $D_{2h}$ rectangular arrangement, the ground and excited states of cyclobutadiene exhibit multi-configurational characters and single-reference methods, such as \alert{standard} adiabatic time-dependent density-functional theory (TD-DFT) or \alert{standard} equation-of-motion coupled cluster (EOM-CC), are notoriously known to struggle in such situations.
 In this work, using a large panel of methods and basis sets, we provide an extensive computational study of the automerization barrier (defined as the difference between the square and rectangular ground-state energies) and the vertical excitation energies at $D_{2h}$ and $D_{4h}$ equilibrium structures. 
@@ -406,7 +406,7 @@ Overall, even with the best exchange-correlation functional, SF-TD-DFT is clearl
 \alert{We observe that SF-EOM-CCSD/aug-cc-pVTZ tends to underestimate by about \SI{1.5}{\kcalmol} the energy barrier compared to the TBE, an observation in agreement with previous results by Manohar and Krylov. \cite{Manohar_2008}
 This can be alleviated by including the triples correction with SF-EOM-CCSD(fT) and SF-EOM-CCSD(dT) (see {\SupInf} where we have reported the data from Ref.~\onlinecite{Manohar_2008}). 
 We also note that the SF-EOM-CCSD values for the energy barrier are close to the ones obtained with the more expensive (standard) CC3 method, yet less accurate than values computed with the cheaper SF-ADC(2)-s formalism. 
-Note that, contrary to a previous statement, \cite{Manohar_2008} the (fT) correction performs better than the (dT) correction for the energy barrier. 
+Note that, in contrast to a previous statement, \cite{Manohar_2008} the (fT) correction performs better than the (dT) correction for the energy barrier. 
 However, for the excited states, the situation is reversed (see below).}
 
 Concerning the multi-reference approaches with the minimal (4e,4o) active space, the TBEs are bracketed by the CASPT2 and NEVPT2 values that differ by approximately \SI{1.5}{\kcalmol} for all bases.
@@ -612,7 +612,7 @@ Also, as reported previously, \cite{Loos_2020d} SF-ADC(2)-s and SF-ADC(3) have m
 
 \alert{Interestingly, we observe that the SF-EOM-CCSD excitation energies are systematically larger than the TBEs by approximately \SI{0.2}{\eV} with a nice consistency throughout the various (singly- and doubly-) excited states. 
 Moreover, SF-EOM-CCSD excitation energies are somehow closer to their SF-ADC(2)-s analogs (with an energy difference of about \SI{0.1}{\eV}) than the other schemes as already noticed by LeFrançois and co-workers. \cite{Lefrancois_2015}
-We see that the SF-EOM-CCSD excitations energies for the triplet state are larger of about \SI{0.3}{\eV} compared to the CCSD ones, this was also pointed out in the study of Manohar and Krylov. \cite{Manohar_2008}
+We see that the SF-EOM-CCSD excitations energies for the triplet state are larger of about \SI{0.3}{\eV} compared to the CCSD ones, which was also pointed out in the study of Manohar and Krylov. \cite{Manohar_2008}
 Again, our SF-EOM-CCSD results are very similar to the ones obtained in previous studies \cite{Manohar_2008,Lefrancois_2015}. 
 We can logically expect similar trend for SF-EOM-CCSD(fT) and SF-EOM-CCSD(dT) that lower the excitation energies and tend to be in better agreement with respect to the TBE (see {\SupInf}). 
 Note that the (dT) correction slightly outperforms the (fT) correction as previously observed \cite{Manohar_2008} and theoretically expected.}
@@ -814,7 +814,7 @@ Concerning the singlet-triplet gap, each scheme predicts it to be positive.
 Although it provides a decent singlet-triplet gap value, SF-ADC(2)-x seems to particularly struggle with the singlet excited states ({\Aoneg} and {\Btwog}), especially for the doubly-excited state {\Aoneg} where it underestimates the vertical excitation energy by \SI{0.4}{\eV}. 
 Again, averaging the SF-ADC(2)-s and SF-ADC(3) transition energies is beneficial in most cases at the exception of {\Aoneg}.
 Although the basis set effects are larger than at the SF-TD-DFT level, they remain quite moderate at the SF-ADC level, and this holds for wave function methods in general.
-\alert{Concerning the SF-EOM-CCSD excitation energies at the {\Dfour} square planar equilibrium geometry, very similar conclusions to the ones stated in the previous  section dealing with the excitation energies at the {\Dtwo} rectangular equilibrium geometry can be drawn: (i) SF-EOM-CCSD systematically and consistently overestimates the TBEs by approximately \SI{0.2}{\eV} and are less accurate than SF-ADC(2)-s, (ii) the non-iterative triples corrections tend to give a better agreement with respect to the TBE (see {\SupInf}), and (iii) the (dT) correction performs better than the (fT) one.}
+\alert{Concerning the SF-EOM-CCSD excitation energies at the {\Dfour} square planar equilibrium geometry, very similar conclusions to the ones provided in the previous section dealing with the excitation energies at the {\Dtwo} rectangular equilibrium geometry can be drawn: (i) SF-EOM-CCSD systematically and consistently overestimates the TBEs by approximately \SI{0.2}{\eV} and is less accurate than SF-ADC(2)-s, (ii) the non-iterative triples corrections tend to give a better agreement with respect to the TBE (see {\SupInf}), and (iii) the (dT) correction performs better than the (fT) one.}
 
 Let us turn to the multi-reference results (Table \ref{tab:D4h}).
 For both active spaces, expectedly, CASSCF does not provide a quantitive energetic description, although it is worth mentioning that the right state ordering is preserved.
@@ -850,7 +850,7 @@ This has been shown to be clearly beneficial for the automerization barrier and
 \item At the SF-ADC level, we have found that, as expected, the extended scheme, SF-ADC(2)-x, systematically worsen the results compared to the cheaper standard version, SF-ADC(2)-s. 
 Moreover, as previously reported, SF-ADC(2)-s and SF-ADC(3) have opposite error patterns which means that SF-ADC(2.5) emerges as an excellent compromise.
 
-\item \alert{SF-EOM-CCSD shows similar performance than the cheaper SF-ADC(2)-s formalism, especially for the excitation energies. 
+\item \alert{SF-EOM-CCSD shows similar performance as the cheaper SF-ADC(2)-s formalism, especially for the excitation energies. 
 As previously reported, the two variants including non-iterative triples corrections, SF-EOM-CCSD(dT) and SF-EOM-CCSD(fT), improve the results, the (dT) correction performing slightly better for the vertical excitation energies computed at the {\Dtwo} and {\Dfour} equilibrium geometries.}
 
 \item For the {\Dfour} square planar structure, a faithful energetic description of the excited states is harder to reach at the SF-TD-DFT level because of the strong multi-configurational character.

Manuscript/sup-CBD.tex

@@ -79,9 +79,9 @@
 
 \begin{document}	
 
-\title{Supporting Information for ``Reference Energies for Cyclobutadiene: Autoisomerization and Excited States''}
+\title{Supporting Information for ``Reference Energies for Cyclobutadiene: Automerization and Excited States''}
 
-\author{Enzo \surname{Monino}}
+\author{Enzo \surname{Monino}*}
 	\email{emonino@irsamc.ups-tlse.fr}
 	\affiliation{\LCPQ}	 
 \author{Martial \surname{Boggio-Pasqua}}
@@ -90,7 +90,7 @@
 	\affiliation{\LCPQ}
 \author{Denis \surname{Jacquemin}}
 	\affiliation{\CEISAM}
-\author{Pierre-Fran\c{c}ois \surname{Loos}}
+\author{Pierre-Fran\c{c}ois \surname{Loos}*}
 	\email{loos@irsamc.ups-tlse.fr}
 	\affiliation{\LCPQ}