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Martial+Denis corrections

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6
Manuscript/CBD.tex
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@ -403,7 +403,7 @@ We note that SF-ADC(2)-x [which scales as $\order*{N^6}$] is probably not worth
This behavior was previously reported by Dreuw's group. \cite{Wormit_2014,Harbach_2014,Dreuw_2015} This behavior was previously reported by Dreuw's group. \cite{Wormit_2014,Harbach_2014,Dreuw_2015}
Overall, even with the best exchange-correlation functional, SF-TD-DFT is clearly outperformed by the more expensive SF-ADC models. Overall, even with the best exchange-correlation functional, SF-TD-DFT is clearly outperformed by the more expensive SF-ADC models.
\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, a observation in agreement with previous results by Manohar and Krylov. \cite{Manohar_2008} \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}). 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. 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, contrary to a previous statement, \cite{Manohar_2008} the (fT) correction performs better than the (dT) correction for the energy barrier.
@ -612,8 +612,8 @@ 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. \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} 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, this was also pointed out in the study of Manohar and Krylov. \cite{Manohar_2008}
Again, our SF-EOM-CCSD results are very similar than the ones obtained in previous studies \cite{Manohar_2008,Lefrancois_2015}. 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}). 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.} Note that the (dT) correction slightly outperforms the (fT) correction as previously observed \cite{Manohar_2008} and theoretically expected.}

15
Response_Letter/Response_Letter.tex
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@ -66,21 +66,21 @@ Some illuminating comments on this issue would be welcome.}
\alert{We thank the reviewer for this interesting comment. \alert{We thank the reviewer for this interesting comment.
Indeed, at the $D_{4h}$ $T_1$ optimized geometry, we have used the conventional standard orientation where two $C_2$ axes run through the carbon atoms. Indeed, at the $D_{4h}$ $T_1$ optimized geometry, we have used the conventional standard orientation where two $C_2$ axes run through the carbon atoms.
In this conventional orientation, the singlet ground state $1 ^1B_{1g}$ remains $1 ^1B_{1g}$ in the $D_{2h}$ point group and the singlet excited state $1 ^1A_{1g}$ becomes $1 ^1A_g$ in the $D_{2h}$ point group. In this conventional orientation, the singlet ground state $1 ^1B_{1g}$ remains $1 ^1B_{1g}$ in the $D_{2h}$ point group and the singlet excited state $1 ^1A_{1g}$ becomes $1 ^1A_g$ in the $D_{2h}$ point group.
As pointed out by the reviewer, upon rotating the molecular framework by 45 degrees in the ($xy$) plane, the two $C_2$ axes then bisect the carbon-carbon bonds. As pointed out by the reviewer, upon rotation of the molecular framework by 45 degrees in the ($xy$) plane, the two $C_2$ axes bisect the carbon-carbon bonds.
This induces a different orbital picture. The correlation between the orbitals and states in the new molecular framework are illustrated in the figure below at the CASSCF(4,4) level. This induces a different orbital picture. The correlation between the orbitals and states in the new molecular framework are illustrated in the figure below at the CASSCF(4,4) level.
In this new orientation, the two singlet states $1 ^1B_{1g}$ and $1 ^1A_{1g}$ become both $1 ^1A_{g}$ in the $D_{2h}$ point group. In this new orientation, the two singlet states $1 ^1B_{1g}$ and $1 ^1A_{1g}$ become both $1 ^1A_{g}$ in the $D_{2h}$ point group.
Because of the different orbital picture (the frontier orbitals are localized on two carbon atoms in the standard orientation and on four carbon atoms in the other orientation), the new CI coefficients resulting from this rotation bring also a different wave function representation. Because of the different orbital picture (the frontier orbitals are localized on two carbon atoms in the standard orientation and on four carbon atoms in the other orientation), the new CI coefficients resulting from this rotation also bring a different wave function representation.
Whereas the $1 ^1B_{1g}$ ground state is described in a one-electron-excitation picture in the standard orientation (the $1 ^1A_{1g}$ excited state involves a double excitation), the corresponding $1 ^1B_{1g}$ ground state in the new orientation involves a two-electron-excitation picture (the $1 ^1A_{1g}$ excited state also involves a double excitation). Whereas the $1 ^1B_{1g}$ ground state is described in a one-electron-excitation picture in the standard orientation (the $1 ^1A_{1g}$ excited state involves a double excitation), the corresponding $1 ^1B_{1g}$ ground state in the new orientation involves a two-electron-excitation picture (the $1 ^1A_{1g}$ excited state also involves a double excitation).
Of course, these two representations are perfectly equivalent at the CASSCF level which describes single and double excitations on the same footing. Of course, these two representations are perfectly equivalent at the CASSCF level which describes single and double excitations on the same footing.
This is obviously not the case in linear response theory, as pointed out by the reviewer. This is obviously not the case in linear response theory, as pointed out by the reviewer.
As mentioned in our manuscript in section II.B., for the $D_{4h}$ arrangement, we have considered the lowest closed-shell singlet state $1 ^1A_{1g}$ as reference. As mentioned in our manuscript in section II.B., for the $D_{4h}$ arrangement, we have considered the lowest closed-shell singlet state $1 ^1A_{g}$ as reference.
Because this state has a substantial double-excitation character, we expect a significant error at the CCSD level. Because this state has a substantial double-excitation character, we expect a significant error at the CCSD level.
The $1 ^1B_{1g}$ ground state is obtained as a singly excited state from that reference, while the $1 ^1B_{2g}$ excited state should also be a mixture involving a double excitation. The $1 ^1B_{1g}$ ground state is obtained as a singly excited state from that reference, while the $1 ^1B_{2g}$ excited state should also be a mixture involving a double excitation.
In the other (non-standard) orientation, the lowest $^1A_g$ state correlates with the $1 ^1B_{1g}$ ground state, which in this orientation has a strong double-excitation character. In the other (non-standard) orientation, the lowest $^1A_g$ state correlates with the $1 ^1B_{1g}$ ground state, which in this orientation has a strong double-excitation character.
Then, the $1 ^1 A_{1g}$ excited state has also a strong double-excitation character, while the $1 ^1B_{2g}$ excited state is obtained by one-electron excitation. Then, the $1 ^1 A_{1g}$ excited state has also a strong double-excitation character, while the $1 ^1B_{2g}$ excited state is obtained by one-electron excitation.
Thus, whatever the orientation of the molecule, we will face the same problem for the reference state. Thus, whatever the orientation of the molecule, we will face the same problem for the reference state.
Note that in the case of the SF formalism, these three singlet states should all be described correctly if one takes the $1 ^3A_{2g}$ state as a reference high spin state, whatever the orientation. Note that in the case of the SF formalism, these three singlet states should all be described correctly if one takes the $1 ^3A_{2g}$ state as the reference high spin state, whatever the orientation.
This interesting comment about standard and non-standard orientations has been added to the supporting information alongside the corresponding figure.} This discussion about standard and non-standard orientations has been added to the supporting information alongside the corresponding figure.}
\includegraphics[width=\textwidth]{MOs} \includegraphics[width=\textwidth]{MOs}
@ -95,8 +95,8 @@ However, to calculate the automerization barrier, we need to make the energy dif
At this last geometry, the correct description of the static correlation requires including (4e,4o) in the active space (i.e., all valence $\pi$ orbitals). At this last geometry, the correct description of the static correlation requires including (4e,4o) in the active space (i.e., all valence $\pi$ orbitals).
In addition, there are states with ionic character which required including the dynamic electron correlation (in particular the $\sigma$-$\pi$ polarization). In addition, there are states with ionic character which required including the dynamic electron correlation (in particular the $\sigma$-$\pi$ polarization).
Thus, the improvement of our results by including all $\sigma_{CC}$ is rather expected. Thus, the improvement of our results by including all $\sigma_{CC}$ is rather expected.
We believe that the large differences observed between CASPT2 and NEVPT2 for the (4e,4o) active space is a consequence of the small active space. We believe that the large differences observed between CASPT2 and NEVPT2 for the (4e,4o) active space is a consequence of the too small active space.
As a matter of fact, when the active space is enlarged, all these issues disappear. When the active space is enlarged, all these issues disappear.
Note also that we have minimized the intruder state problem by using an appropriate level shift and that this potential problem is not present at the NEVPT2 level. Note also that we have minimized the intruder state problem by using an appropriate level shift and that this potential problem is not present at the NEVPT2 level.
As suggested by the reviewer, we have now added some results at the MRCI and MRCI+Q levels in the supporting information of the revised manuscript. As suggested by the reviewer, we have now added some results at the MRCI and MRCI+Q levels in the supporting information of the revised manuscript.
} }
@ -111,6 +111,7 @@ Defining the TBE at the aug-cc-pVQZ level would make comparison with other metho
\end{enumerate} \end{enumerate}
\pagebreak
%%% REVIEWER 2 %%% %%% REVIEWER 2 %%%
\noindent \textbf{\large Authors' answer to Reviewer \#2} \noindent \textbf{\large Authors' answer to Reviewer \#2}