revisions

Manuscript/sup-CBD.tex

@@ -158,6 +158,35 @@ H            -2.092429    0.000000    0.000000
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 \end{itemize}
 
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Comment about symmetry: standard vs non-standard orientation}
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+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. 
+Upon rotation of the molecular framework by 45 degrees in the $xy$ plane, the two $C_2$ axes then 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 Figure \ref{fig:sym} 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. 
+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. 
+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. 
+This is obviously not the case in linear response theory.
+As mentioned in our manuscript in section II.B., for the $D_{4h}$ arrangement, we have considered the lowest closed-shell singlet state $^1A_{g}$ as reference. 
+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. 
+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 $1 ^1A_{1g}$ 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. 
+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.
+
+\begin{figure}
+	\includegraphics[width=\textwidth]{MOs}
+	\caption{Standard vs non-standard orientation}
+	\label{fig:sym}
+\end{figure}
+
 %\begin{squeezetable}
 \begin{table*}
 	\caption{Energy differences between the states computed with various methods and the reference TBE values. 

Response_Letter/Response_Letter.tex

@@ -34,9 +34,8 @@ We look forward to hearing from you.
 \\
 \alert{
 Thank you for supporting publication of the present manuscript.
-As detailed below, we have taken into account the comments and suggestions of the reviewers that we believe have overall improved the quality of the present paper.}
-
-
+As detailed below, we have taken into account the comments and suggestions of the reviewers that we believe have overall improved the quality of the present paper.
+We thank the reviewer for his/her careful analysis of our manuscript.}
 
 {This work could be published as-is in JPC, but some suggestions for ways in which the manuscript could be improved follow:}
 \\
@@ -62,22 +61,24 @@ However, this same property leads to a distinct inability to properly access the
 Some illuminating comments on this issue would be welcome.}
 \\
 \alert{We thank the reviewer for this interesting comment. 
-Indeed, at the $D_{4h}$ T1 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 $1 ^1Ag$ in the $D_{2h}$ point group. 
+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. 
 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. 
-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. 
-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 wavefunction 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 bring also 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). 
 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.
-As mentioned in our manuscript in section IIb, 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 $^1A_{g}$ as reference. 
 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. 
 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. 
 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 a reference high spin state, whatever the orientation.
+The interested reader will find these comments in the supporting information of the revised manuscript.}
 
 \includegraphics[width=\textwidth]{MOs}
 
@@ -92,6 +93,8 @@ 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).
 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. 
+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.
+As a matter of fact, when the active space is enlarged, all these issues disappear.
 Note 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+Q level.
 }
@@ -131,17 +134,22 @@ There could be other interesting differences to discuss.}
 \alert{See previous point.}
 
 \item 
-{I also recommend to include EOM-DEA-CCSD results -- this is another extension of EOM-CCSD, which can treat diradicals. It does not suffer from spin-contamination. The method is available in Q-Chem. See here for theory description and examples: J. Chem. Phys. 154, 114115 (2021). EOM-DIP is another method, which can deal wit this type of electronic structure, but it has difficulties with diffuse basis sets (e.g., J. Chem. Phys. 135, 084109 (2011)) -- so I am not asking to add the DIP numbers, but mentioning it would be appropriate.}
+{I also recommend to include EOM-DEA-CCSD results -- this is another extension of EOM-CCSD, which can treat diradicals. 
+It does not suffer from spin-contamination. 
+The method is available in Q-Chem. 
+See here for theory description and examples: J. Chem. Phys. 154, 114115 (2021). EOM-DIP is another method, which can deal wit this type of electronic structure, but it has difficulties with diffuse basis sets (e.g., J. Chem. Phys. 135, 084109 (2011)) -- so I am not asking to add the DIP numbers, but mentioning it would be appropriate.}
 \\
-\alert{Adding values from the literature? Outside the scope of the present paper?}
+\alert{EOM-DEA-CCSD results have been added to the supporting information of the revised manuscript.
+EOM-DIP has also been mentioned as suggested by the reviewer.}
 
 \item 
 {The analysis would benefit greatly if the authors provide Head-Gordon's indices, which can be used to compare wave-functions computed by different methods in a meaningful way, as illustrated here:J. Chem. Theo. Comp. 14, 638 (2018). }
 \\
-\alert{T2: I have to check this paper... The authors thanks the referee for this valuable comment. Unfortunately, in order to obtain the Head-Gordon's indices for the different spin-flip methods used we would have to do all the calculations or at least for the aug-cc-pVTZ basis which will take too much time and resources. We have mentioned these indices in the text and we will definitely use them in future works.}
+\alert{The authors thank the referee for this valuable comment. 
+Unfortunately, in order to obtain Head-Gordon's indices for the different spin-flip methods we would have to do all the calculations or at least for the aug-cc-pVTZ basis which will take too much time and resources. We have mentioned these indices (alongside relevant references) in the text and we will definitely use them in future works.}
 
 \item 
-{CAS-based methods are multi-reference (and also able to treat multi-configutional wfns). 
+{CAS-based methods are multi-reference (and also able to treat multi-configurational wfns). 
 EOM-SF and EOM-EE are single-reference methods that are able to describe multi-configurational wfns. 
 Please correct the section names and discussion appropriately.}
 \\