163 lines
9.0 KiB
TeX
163 lines
9.0 KiB
TeX
\documentclass[10pt]{letter}
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\usepackage{UPS_letterhead,xcolor,mhchem,ragged2e,hyperref}
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\newcommand{\alert}[1]{\textcolor{red}{#1}}
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\definecolor{darkgreen}{HTML}{009900}
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\begin{document}
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\begin{letter}%
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{To the Editors of the Journal of Chemical Physics,}
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\opening{Dear Editors,}
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\justifying
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Please find attached a revised version of the manuscript entitled
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\begin{quote}
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\textit{``Reference Energies for Cyclobutadiene: Automerization and Excited States''}.
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\end{quote}
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We thank the reviewers for their constructive comments and to support publication of the present manuscript.
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Our detailed responses to their comments can be found below.
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For convenience, changes are highlighted in red in the revised version of the manuscript.
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In addition, we have taken into account the non-scientific changes requested by the editorial team.
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We look forward to hearing from you.
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\closing{Sincerely, the authors.}
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\newpage
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%%% REVIEWER 1 %%%
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\noindent \textbf{\large Authors' answer to Reviewer \#1}
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{This article presents a survey of spin-flip TD-DFT, spin-flip ADC, multireference (CASSCF and MRPT), and equation-of-motion coupled cluster methods as applied to the automerization and vertical excitation energies of cyclobutadiene (CBD). As the smallest example of anti-aromaticity (and one of the smallest and most interesting exemplars of strong PJT distortion), CBD is an illuminating and challenging test case for these methods. (EOM-)CCSDTQ values, with a “pyramidal” basis set extrapolation scheme are used as the newly-proposed theoretical best estimates, and limited selected full CI (CIPSI) calculations confirm their excellent accuracy. The authors reach some interesting and useful conclusions concerning the tested methods.
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}
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\\
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\alert{
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Thank you for supporting publication of the present manuscript.
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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.}
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{This work could be published as-is in JPC, but some suggestions for ways in which the manuscript could be improved follow:}
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\\
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\alert{
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}
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\begin{enumerate}
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\item
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{The authors opt not to test SF-EOM-CC methods.
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A justification or rationalization would be helpful.
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Also, is it expected that these methods would improve on SF-ADC and/or EOM-CC?}
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\\
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\alert{The authors thanks the reviewer for this comment.
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Results for SF-EOM-CCSD, SF-EOM-CCSD(dT) and SF-EOM-CCSD(fT) have been added in the manuscript (and in the supporting information) and are discussed in the text.}
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\item
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{The issue of reference symmetry frame is very important at the D4h geometry.
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The correlated calculation (and often the reference SCF calculation) are performed in a D2h subgroup, of which there are two distinct possibilities: one with the C2’ axes running through the carbon atoms and one with the C2’ axes bisecting them.
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It seems the former has been employed.
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The latter actually could potentially provide a faster convergence to the A1g state since it exhibits strong mixing between the two major determinants via T2 even at the CCSD level.
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However, this same property leads to a distinct inability to properly access the B1g ground state via a single excitation in EOM-CC.
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Some illuminating comments on this issue would be welcome.}
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\\
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\alert{}
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\item{The authors note a significant improvement in the MRPT results as the active space is enlarged.
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However, it seems to me that the most appropriate active space (for the D4h geometry at least) is in fact (2e,2o) [i.e. $Eg^2$ at D4h].
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Within this space, the CI coefficients become fixed at D4h, leading to an “exact” SCF reference, at least in terms of static correlation.
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Perhaps the major problem with the MRPT results is not active space insufficiency, then, but intruder states?
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Can the authors perform MRCI+Q or MRAQCC calculations for comparison?}
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\\
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\alert{}
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\item
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{It seems that extrapolated CCSDTQ/aQZ values are available for the automerization barrier.
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Why are the aTZ numbers used as the TBE instead?}
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\\
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\alert{For the sake of consistency with the excitation energies and comparison, we have defined all the TBEs of the manuscript at the aug-cc-pVTZ level.
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We believe that aug-cc-pVTZ is an adequate basis in order to get accurate values for the automerization barrier and the vertical excitation energies.
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Defining the TBE at the aug-cc-pVQZ level would make comparison with other methods quite expensive (and sometimes undoable for some of the most expensive methods.}
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\end{enumerate}
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%%% REVIEWER 2 %%%
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\noindent \textbf{\large Authors' answer to Reviewer \#2}
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{This is a useful addition to the literature, presenting extensive benchmarks on a popular system, cyclobutadiene or CB. I recommend it for the publication once the following issues are addressed.}
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\\
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\alert{Thank you for these positive comments and for supporting publication of our manuscript.
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Below, we address the points raised by Reviewer \#2.
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}
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\begin{enumerate}
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\item
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{The results for EOM-SF-CCSD and EOM-SF-CCSD(fT/dT) must be included in the paper and in the
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analysis/discussion of the results. Why to exclude the best-performing SF methods? Since this paper aspires to be a comprehensive benchmark on CB, I believe it is absolutely essential. Moreover, some of these results are already available (e.g., Ref. 105 has the results for excitation energies obtained in the same basis -- aug-cc-pVTZ that is used in the paper). Even if one needs to redo the calculations, they are very quick and can be done on a laptop in a few minutes.}
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\\
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\alert{As mentioned in the response to Reviewer \#1, results for SF-EOM-CCSD, SF-EOM-CCSD(dT) and SF-EOM-CCSD(fT) have been added in the manuscript (and in the supporting information) and are discussed in the text.}
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\item
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{The comparison of SF-ADC with EOM-SF-CCSD will be illuminating for the readers.
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For example, EOM-SF is more robust wrt reference spin-contamination compared to SF-ADC because of the CC ansatz.
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There could be other interesting differences to discuss.}
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\\
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\alert{See previous point.}
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\item
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{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.}
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\\
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\alert{Adding values from the literature? Outside the scope of the present paper?}
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\item
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{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). }
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\\
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\alert{T2: I have to check this paper...}
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\item
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{CAS-based methods are multi-reference (and also able to treat multi-configutional wfns).
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EOM-SF and EOM-EE are single-reference methods that are able to describe multi-configurational wfns.
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Please correct the section names and discussion appropriately.}
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\\
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\alert{We have modified the section names and discussion accordingly to the reviewer's suggestion.}
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\item
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{Abstract and introduction:
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please insert the word 'standard' before 'time-dependent density-functional theory (TD-DFT) or equation-of-motion ... are notoriously known to struggle in such situations.'
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The SF and DEA/DIP variants of these methods do not struggle.
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}
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\\
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\alert{This has been corrected.}
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\item
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{Intro: "Of course, single-reference methods are naturally unable to describe such situations."
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This is incorrect -- see above (EOM-SF/DIP/DEA are single reference methods capable of describing multi-configurational wfns).
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Adding the word 'standard' might help.
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Below: "and remain tortuous for state-of-the-art methods ..." -- again, need to correct, e.g., consider 'remains challenging for standard hierarchy of EOM-CC methods that are using ground-state Hartree-Fock reference'.}
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\\
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\alert{We have performed these two corrections.}
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\item{First page, last paragraph -- replace multi-configurational by multi-reference, as per above.}
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\\
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\alert{This has been corrected.}
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\item{Last paragraph of intro -- here you can introduce the idea of single-reference approach to multi-reference wfns and describe SF/DEA/DIP methods.
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Please do not call SF 'cheaper' -- this does not make sense (the cost depends on correlation treatment).
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SF is more robust and more effective at each correlation level.
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It is also more black-box, as it does not require active-space selection.
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Also, EOM-SF can systematically converge to the exact FCI answer once sufficiently high excitations are included.
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'Obviously, spin-flip methods have their own flaws, especially spin' -- why 'obviously'?
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I suggest to reword, e.g., 'One drawback of SF methods is ...'}
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\\
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\alert{The reviewer is right. We have followed the suggestion of the reviewer and performed the required modifications.}
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\item{Section IIC -- please rename.}
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\\
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\alert{Done.}
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\end{enumerate}
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\end{letter}
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\end{document}
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