conclusion done

Manuscript/FCI2.tex

@@ -121,17 +121,17 @@ We use this series of theoretical best estimates to benchmark a series of popula
 
 Accurately describing transition energies between the electronic ground state (GS) and excited states (ES) remains an important challenge in quantum chemistry. When dealing with large compounds in complex environments,
 one is typically limited to the use of time-dependent density-functional theory (TD-DFT), \cite{Cas95,Ulr12b,Ada13a} a successful yet far from flawless approach. In particular, to perform TD-DFT calculations, one must 
-choose an ``appropriate'' exchange-correlation functional, which is difficult yet primordial as the impact of the exchange-correlation functional is exacerbated in TD-DFT as compared to DFT. \cite{Lau13} Such selection can, of course, rely 
-on the intrinsic features of each exchange-correlation functional, \eg, it is well-known that range-separated hybrids provide a more physically-sound description of long-range charge-transfer transitions than semi-local exchange-correlation functionals. \cite{Dre04,Pea08}
-However, to obtain a quantitative assessment of the accuracy that can be expected from TD-DFT calculations, benchmarks are needed.  This is why many assessment of TD-DFT performances for various properties are
-available. \cite{Lau13} While several of these benchmarks use experimental data as reference, typically band shapes \cite{Die04,Die04b,Avi13,Cha13,Lat15b,Mun15,Vaz15,San16b} or 0-0 energies, 
-\cite{Die04b,Goe10a,Jac12d,Chi13b,Win13,Fan14b,Jac14a,Jac15b,Loo19b} using theoretical best estimates (TBE) obtained with more refined levels of theory as references,  \cite{Sch08,Sau09,Sil10b,Sil10c,Sch17,Loo18a} 
-is advantageous as it allows comparisons on a perfectly equal footing (same geometry, vertical transitions, no environmental effects...).  For such works, the challenge is in fact to obtain accurate TBE, as high-level theories 
-generally come with a dreadful scaling with system size and, in addition, typically require large atomic basis sets to deliver transition energies close to the basis set limit.
+choose an ``appropriate'' exchange-correlation functional, which is difficult yet primordial as the impact of the exchange-correlation functional is exacerbated within TD-DFT as compared to DFT. \cite{Lau13} Such selection can, of course, rely 
+on the intrinsic features of the various exchange-correlation functional families, \eg, it is well-known that range-separated hybrids provide a more physically-sound description of long-range charge-transfer transitions than semi-local exchange-correlation functionals. \cite{Dre04,Pea08}
+However, to obtain a quantitative assessment of the accuracy that can be expected from TD-DFT calculations, benchmarks cannot be avoided.  This is why so many assessments of TD-DFT performances for various properties are
+available. \cite{Lau13} While several of these benchmarks rely on experimental data as reference (typically band shapes \cite{Die04,Die04b,Avi13,Cha13,Lat15b,Mun15,Vaz15,San16b} or 0-0 energies 
+\cite{Die04b,Goe10a,Jac12d,Chi13b,Win13,Fan14b,Jac14a,Jac15b,Loo19b}), reference from theoretical best estimates (TBE) based on state-of-the-art computational methods \cite{Sch08,Sau09,Sil10b,Sil10c,Sch17,Loo18a} 
+is advantageous as it allows comparisons on a perfectly equal footing (same geometry, vertical transitions, no environmental effects, etc).  In such a case, the challenge is in fact to obtain accurate TBE, as these top-notch theoretical models
+generally come with a dreadful scaling with system size and, in addition, typically require large atomic basis sets to deliver transition energies close to the complete basis set (CBS) limit.
 
-More than 20 years ago, Serrano-Andr\`es, Roos, and their coworkers proposed an impressive series of reference transition energies for several typical conjugated organic molecules (butadiene, furan, pyrrole, tetrazine...).
-\cite{Ful92,Ser93,Ser93b,Ser93c,Lor95b,Mer96,Mer96b,Roo96,Ser96b} To this end, they relied on the Complete Active Space Second-Order Perturbation Theory  ({\CASPT}) approach with the largest active spaces and basis sets
-they could offer at that time, typically using experimental GS geometries.  Beyond comparisons with experiments, which are always challenging when computing vertical transition energies, \cite{San16b} there was no approach 
+More than 20 years ago, Serrano-Andr\`es, Roos, and coworkers compiled an impressive series of reference transition energies for several typical conjugated organic molecules (butadiene, furan, pyrrole, tetrazine, \ldots).
+\cite{Ful92,Ser93,Ser93b,Ser93c,Lor95b,Mer96,Mer96b,Roo96,Ser96b} To this end, they relied on experimental GS geometries and the complete-active-space second-order perturbation theory ({\CASPT}) approach with the largest active spaces and basis sets
+one could dream of at the time.  Beyond comparisons with experiments, which are always challenging when computing vertical transition energies, \cite{San16b} there was no approach 
 available at that time to ascertain the accuracy of the obtained transition energies. These {\CASPT} values were latter used to assess the performances of TD-DFT combined with various exchange-correlation functionals, \cite{Toz99b,Bur02} and remained for a long
 time the best references available. A decade ago, Thiel and coworkers defined TBE for 104 singlet and 63 triplet valence ES in 28 small and medium conjugated CNOH organic molecules. \cite{Sch08,Sil10b,Sil10c}  These TBE 
 were computed on MP2/6-31G(d) structures with several levels of theories, notably {\CASPT} and various Coupled-Cluster levels ({\CCD}, {\CCSD}, and {\CCT}). Interestingly, while the default reference approach used by Thiel to define his
@@ -1473,20 +1473,19 @@ CCSDT-3		&0.05	&		&0.06	&0.03	&0.08	&0.04\\
 
 \section{Conclusions and outlook}
 
-We have determined highly-accurate vertical transition energies for a set of 27 medium-sized organic molecules containing from 4 to 6 (non-hydrogen) atoms. To this end, we used several theoretical levels 
-and basis sets, but our theoretical best estimates are mainly based on  {\CCSDTQ} (4 atoms) or  {\CCSDT} (5 and 6 atoms) values determined with diffuse containing basis sets. For the vast majority of the 
-listed excited-states, this contribution is the first to disclose (sometimes basis-set extrapolated) {\CCSDT}/{\AVTZ} and  (true) {\CCT}/{\AVQZ} transition energies as well as {\CCT}/{\AVTZ} oscillator strengths
-for all dipole-allowed transitions. The set contains a total of 238 transition energies and 90 oscillator strengths, including a reasonably good balance between singlet and triplet transition energies and valence 
-and Rydberg states. Amongst these 238 transitions, we consider that 224 are ``safe'' TBE, that is, that they are chemically accurate (mean error below $0.043$ eV or $1$ kcal.mol$^{-1}$ for the considered geometry), 
-allowing to establish a reasonable error bar for lower-cost ES models daily used by computational chemists. In this framework, we benchmarked eight popular methods, CIS(D),  {\AD}, {\CCD}, {\STEOM}, {\CCSD}, 
-CCSDR(3),  CCSDT-3, and {\CCT}.  It turned out that the latter approach is extremely accurate, and, very likely should be more trusted than {\CASPT} or {\NEV} but for ES dominated by a double
-excitation character.  Other methods including corrections for the triples yield a mean absolute deviation of ca. 0.05 eV, whereas none of the second-order approach is chemically accurate, with MAE
-in the 0.12--0.23 eV range.
+We have computed highly-accurate vertical transition energies for a set of 27 medium-sized organic molecules containing from 4 to 6 (non-hydrogen) atoms. To this end, we employed several state-of-the-art theoretical models with increasingly large diffuse basis sets.
+However, most of our theoretical best estimates are based on {\CCSDTQ} (4 atoms) or {\CCSDT} (5 and 6 atoms) excitation energies. For the vast majority of the 
+listed excited states, the present contribution is the very first to disclose (sometimes basis-set extrapolated) {\CCSDT}/{\AVTZ} and (true) {\CCT}/{\AVQZ} transition energies as well as {\CCT}/{\AVTZ} oscillator strengths
+for each dipole-allowed transition. Our set contains a total of 238 transition energies and 90 oscillator strengths, with a reasonably good balance between singlet, triplet, valence, 
+and Rydberg states. Amongst these 238 transitions, we believe that 224 are ``solid'' TBE, \ie, they are chemically accurate (mean error below $0.043$ eV or $1$ kcal.mol$^{-1}$) for the considered geometry.
+It allows us to establish a reasonable error bar for several popular ES models with lower computational cost: CIS(D), {\AD}, {\CCD}, {\STEOM}, {\CCSD}, 
+CCSDR(3),  CCSDT-3, and {\CCT}. It turns out that the latter approach is extremely accurate, and, very likely should be considered as more robust and trustworthy than {\CASPT} or {\NEV}, except for ES with a predominant double
+excitation character.  Other methods including corrections for the triples yield a mean absolute deviation around $0.05$ eV, whereas none of the second-order approach has been found to be chemically accurate with MAE
+in the $0.12$--$0.23$ eV range.
 
 Paraphrasing Thiel and coworkers, \cite{Sch08} we hope that this new set of vertical transition energies, combined or not with the ones described in our previous works, \cite{Loo18a,Loo19c} will be useful for the community,
-will stimulate further developments and analyses in the field, and will provide new grounds for appraising the \emph{pros} and \emph{cons} of ES approaches already available or under development.  We can 
-crystal-ball that the emergence of new {\sCI} algorithms optimized for modern computer architectures will likely lead to the revision of some the present TBE, further allowing to climb one step on the accuracy 
-ladder.
+will stimulate further developments and analyses in the field, and will provide new grounds for appraising the \emph{pros} and \emph{cons} of ES models already available or currently under development.  We can 
+crystal-ball that the emergence of new {\sCI} algorithms optimized for modern computer architectures will likely lead to the revision of some the present TBE, allowing to climb even higher on the accuracy ladder.
 
 \begin{suppinfo}
 Geometries.