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\documentclass[10pt]{letter}
\usepackage{UPS_letterhead,xcolor,mhchem,mathpazo,ragged2e,hyperref}
\newcommand{\alert}[1]{\textcolor{red}{#1}}
\definecolor{darkgreen}{HTML}{009900}
\begin{document}
\begin{letter}%
{To the Editors of the Journal of Chemical Physics}
\opening{Dear Editors,}
\justifying
Please find attached a revised version of the note entitled
\begin{quote}
\textit{``The performance of CIPSI on the ground state electronic energy of benzene''}.
\end{quote}
We thank the reviewers for their constructive comments.
Our detailed responses to their comments can be found below.
For convenience, changes are highlighted in red in the revised version of the manuscript.
We look forward to hearing from you.
\closing{Sincerely, the authors.}
%%% REVIEWER 1 %%%
\noindent \textbf{\large Authors' answer to Reviewer \#2}
\begin{itemize}
\item
{As a follow-up note to the recent benchmarking work of Eriksen et al., the authors present the correlation energy of ground state benzene calculated using CIPSI, another flavor in the Selected Configuration Interaction plus Perturbation family. In this endeavor, four combinations regarding the choice of orbitals and perturbation corrections are tested. The best result is obtained from constructing a set of localized orbitals from natural orbitals using a Boys-Foster localization procedure as well as employing a renormalized version of the PT2 correction in the perturbative stage. The final energy agrees with the theoretical estimate of the blind test and is also very close to the best post blind test estimate in the SCI+PT category.
Benchmarking is indeed an important and essential component in the development of electronic structure theories. It is good that the authors complement the benchmark dataset. Overall, the work is well-motivated and generally explained in a clear and organized manner. However, there are also a few issues to be addressed or clarified. }
\\
\alert{}
\item
{In the manuscript, the authors reason that rPT2 should be employed because its correction behaves more linearly than its PT2 counterpart.
Do authors know of a formal reason to believe that?
I believe that the authors have performed numerical tests to confirm this finding in a previous paper and I think should give a citation in the sentence. }
\\
\alert{The rPT2 correction corresponds to a partial resummation of some of the higher-order diagrams from many-body perturbation theory.
As correctly pointed out by the reviewer, this correction has been thoroughly tested in Ref.~, and we have then added this reference to the sentence as requested.}
\item
{It is not very clear how the extrapolation is actually done.
The authors mention twice that the result is obtained from a "four-point linear extrapolation".
However, according to the right panel of FIG. 1 along with TABLE II, many more than four calculations must be done, which is of course a good thing for extrapolation.
Then are the four points randomly selected from a bunch of them?
Whatever it is, the authors might want to clarify the confusion.}
\\
\alert{Sorry for the confusion. We have taken the four last points which correspond to the four largest variational wave functions.
This is now clearly stated in the revised manuscript.}
\item
{Although a general description of the method is given by the authors, more technical details might be needed to better improve reproducibility, such as values of the thresholds to select the most energetically relevant determinants etc.. I realize that this ia a note and the authors want to keep it short. In light of this the authors might want to include an input file in their appendix. Because their quantum package is publicly available, it might make it easy for someone to reproduce their findings. }
\\
\alert{}
\end{itemize}
%%% REVIEWER 2 %%%
\noindent \textbf{\large Authors' answer to Reviewer \#2}
\begin{itemize}
\item
{In the present Note, the authors Loos, Damour, and Scemama report on the performance of their modern, determinant-driven version of the CIPSI method for the case of the benzene molecule in a standard Dunning correlation-consistent DZ basis set.
In particular, the authors compare their results against a recent blind challenge by Eriksen et al., initially deposited on the arXiv preprint server, and now published in JPCL (DOI: 10.1021/acs.jpclett.0c02621).
While the final findings of the present work are obviously not blinded, it is the belief of this reviewer that these additional results are still valuable as a community resource.
The manuscript is reasonably well written (bar the occasional grammatical error/typo, which the authors are sure to locate upon revising the manuscript), and I surely deem it suitable for future publication in JCP.
However, I'd like to encourage the authors to take the following concerns and comments into account before submitting a revised version of the manuscript.}
\\
\alert{}
\item
{The authors have opted for providing the reader with raw data in tabulated form, which is a real asset.
Now, if I were to extrapolate correlated energies myself (for instance, using the polyfit() function of the NumPy library), by means of a weighted fit of the total results to either a linear or a quadratic polynomial in the perturbative correction (using the inverse square of said correction as the weight function), I generally find quite a significant spread in the final results?
It would be valuable to the work if the authors were to indicate the variance with respect to the number of points used in the extrapolations; in the linear extrapolations, one could use, say, between 3-5 points, whereas between 4-6 points could be used in the quadratic fits?
In any case, the authors should comment (in more detail) on their choice of fitting function and number of data points.}
\\
\alert{}
\item
{As an aside, it would seem like the fifth last point differs ever so slightly from the general trend (regardless of the choice of (r)MP2)? Can the authors explain why?
Surely, inclusion of this point in the fitting procedure would bring about changes to the final extrapolated result?}
\\
\alert{}
\item
{It would be interesting if the authors could comment (even speculatively) on why results in the localized FB basis are significantly lower (and hence, in the authors' own words, more trustworthy) than the corresponding results in the NO basis.}
\\
\alert{}
\item
{Why are the rMP2-based corrections considered superior to the corresponding corrections based on MP2?
Because of the improved linear proportionality in Fig.~1?
If so, the authors might want to discuss exactly why a linear relationship is to be expected.}
\\
\alert{}
\item
{Some of the method acronyms have not been properly introduced in the text, and some have been slightly misrepresented, e.g., MBE-FCI (many-body expanded FCI) and FCCR, which is not a selected CC model. Also, some references appear to be missing, e.g., for iCI and DMRG.}
\\
\alert{}
\item
{Why are FB orbitals preferred over, e.g., PM orbitals or IBOs?}
\\
\alert{Boys-Foster is the only localization criterion implemented in QUANTUM PACKAGE.}
\item
{The benzene geometry was not optimized as part of the work behind Ref.~17.
However, an adequate reference may be found in Ref.~17.}
\\
\alert{We have added the corresponding reference to the work of Schreiber et al.}
\end{itemize}
\end{letter}
\end{document}

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%ANU etterhead Yves
%version 1.0 12/06/08
%need to be improved
\RequirePackage{graphicx}
%%%%%%%%%%%%%%%%%%%%% DEFINE USER-SPECIFIC MACROS BELOW %%%%%%%%%%%%%%%%%%%%%
\def\Who {Pierre-Fran\c{c}ois Loos}
\def\What {Dr}
\def\Where {Universit\'e Paul Sabatier}
\def\Address {Laboratoire de Chimie et Physique Quantiques}
\def\CityZip {Toulouse, France}
\def\Email {loos@irsamc.ups-tlse.fr}
\def\TEL {+33 5 61 55 73 39}
\def\URL {} % NOTE: use $\sim$ for tilde
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MARGINS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\textwidth 6in
\textheight 9.25in
\oddsidemargin 0.25in
\evensidemargin 0.25in
\topmargin -1.50in
\longindentation 0.50\textwidth
\parindent 5ex
%%%%%%%%%%%%%%%%%%%%%%%%%%% ADDRESS MACRO BELOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\address{
\includegraphics[height=0.7in]{CNRS_logo.pdf} \hspace*{\fill}\includegraphics[height=0.7in]{UPS_logo.pdf}
\\
\hrulefill
\\
{\small \What~\Who\hspace*{\fill} Telephone:\ \TEL
\\
\Where\hspace*{\fill} Email:\ \Email
\\
\Address\hspace*{\fill}
\\
\CityZip\hspace*{\fill} \URL}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%% OTHER MACROS BELOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\signature{\What~\Who}
\def\opening#1{\ifx\@empty\fromaddress
\thispagestyle{firstpage}
\hspace*{\longindendation}\today\par
\else \thispagestyle{empty}
{\centering\fromaddress \vspace{5\parskip} \\
\today\hspace*{\fill}\par}
\fi
\vspace{3\parskip}
{\raggedright \toname \\ \toaddress \par}\vspace{3\parskip}
\noindent #1\par\raggedright\parindent 5ex\par
}
%I do not know what does the macro below
%\long\def\closing#1{\par\nobreak\vspace{\parskip}
%\stopbreaks
%\noindent
%\ifx\@empty\fromaddress\else
%\hspace*{\longindentation}\fi
%\parbox{\indentedwidth}{\raggedright
%\ignorespaces #1\vskip .65in
%\ifx\@empty\fromsig
%\else \fromsig \fi\strut}
%\vspace*{\fill}
% \par}

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benzene.bib
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%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2020-08-25 18:15:28 +0200
%% Created for Pierre-Francois Loos at 2020-10-09 09:41:12 +0200
%% Saved with string encoding Unicode (UTF-8)
@ -17,7 +17,8 @@
Pages = {7910--7915},
Title = {Generalized Many-Body Expanded Full Configuration Interaction Theory},
Volume = {27},
Year = {2019}}
Year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.9b02968}}
@article{Eriksen_2017,
Author = {J. J. Eriksen and F. Lipparini and J. Gauss},
@ -291,12 +292,14 @@
Year = {2016},
Bdsk-Url-1 = {https://doi.org/10.1063/1.4955109}}
@misc{Lee_2020,
Archiveprefix = {arXiv},
@article{Lee_2020,
Author = {Joonho Lee and Fionn D. Malone and David R. Reichman},
Eprint = {2008.04736},
Primaryclass = {physics.chem-ph},
Title = {Note: The performance of phaseless auxiliary-field quantum Monte Carlo on the ground state electronic energy of benzene},
Date-Modified = {2020-10-09 09:41:09 +0200},
Doi = {10.1063/5.0024835},
Journal = {J. Chem. Phys.},
Pages = {126101},
Title = {The performance of phaseless auxiliary-field quantum Monte Carlo on the ground state electronic energy of benzene},
Volume = {153},
Year = {2020}}
@article{Williams_2020,
@ -476,12 +479,14 @@
Year = {2018},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00680}}
@misc{Eriksen_2020,
Archiveprefix = {arXiv},
@article{Eriksen_2020,
Author = {Janus J. Eriksen and Tyler A. Anderson and J. Emiliano Deustua and Khaldoon Ghanem and Diptarka Hait and Mark R. Hoffmann and Seunghoon Lee and Daniel S. Levine and Ilias Magoulas and Jun Shen and Norman M. Tubman and K. Birgitta Whaley and Enhua Xu and Yuan Yao and Ning Zhang and Ali Alavi and Garnet Kin-Lic Chan and Martin Head-Gordon and Wenjian Liu and Piotr Piecuch and Sandeep Sharma and Seiichiro L. Ten-no and C. J. Umrigar and J{\"u}rgen Gauss},
Eprint = {2008.02678},
Primaryclass = {physics.chem-ph},
Date-Modified = {2020-10-09 09:34:57 +0200},
Doi = {10.1021/acs.jpclett.0c02621},
Journal = {J. Phys. Chem. Lett.},
Pages = {8922--8929},
Title = {The Ground State Electronic Energy of Benzene},
Volume = {11},
Year = {2020}}
@article{Evangelista_2014,

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benzene.tex
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% Abstract
\begin{abstract}
Following the recent work of Eriksen \textit{et al.}~[\href{https://arxiv.org/abs/2008.02678}{arXiv:2008.02678 [physics.chem-ph]}], we report the performance of the \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) method on the non-relativistic frozen-core correlation energy of the benzene molecule in the cc-pVDZ basis. Following our usual protocol, we obtain a correlation energy of $-863.4$ m$E_h$ which agrees with the theoretical estimate of $-863$ m$E_h$ proposed by Eriksen \textit{et al.}~using an extensive array of highly-accurate new electronic structure methods.
Following the recent work of Eriksen \textit{et al.}~[\href{https://dx.doi.org/10.1021/acs.jpclett.0c02621}{J.~Phys.~Chem.~Lett.~\textbf{11}, 8922 (2020)}], we report the performance of the \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) method on the non-relativistic frozen-core correlation energy of the benzene molecule in the cc-pVDZ basis. Following our usual protocol, we obtain a correlation energy of $-863.4$ m$E_h$ which agrees with the theoretical estimate of $-863$ m$E_h$ proposed by Eriksen \textit{et al.}~using an extensive array of highly-accurate new electronic structure methods.
\end{abstract}
% Title
@ -60,7 +60,7 @@ Following a similar goal, we have recently proposed a large set of highly-accura
In a recent preprint, \cite{Eriksen_2020} Eriksen \textit{et al.}~have proposed a blind test for a particular electronic structure problem inviting several groups around the world to contribute to this endeavour.
In addition to coupled cluster theory with singles, doubles, triples, and quadruples (CCSDTQ), \cite{Oliphant_1991,Kucharski_1992} a large panel of highly-accurate, emerging electronic structure methods were considered:
(i) the many-body expansion FCI (MBE-FCI), \cite{Eriksen_2017,Eriksen_2018,Eriksen_2019a,Eriksen_2019b}
(ii) three SCI methods including a second-order perturbative correction (ASCI, \cite{Tubman_2016,Tubman_2018,Tubman_2020} iCI, \cite{Liu_2016} and SHCI \cite{Holmes_2016,Holmes_2017,Sharma_2017}),
(ii) three SCI methods including a second-order perturbative correction \alert{[adaptive sampling CI (ASCI), \cite{Tubman_2016,Tubman_2018,Tubman_2020} iterative CI (iCI), \cite{Liu_2016} and semistochastic heat-bath CI (SHCI) \cite{Holmes_2016,Holmes_2017,Sharma_2017}]},
(iii) a selected coupled-cluster theory method which also includes a second-order perturbative correction (FCCR), \cite{Xu_2018}
(iv) the density-matrix renornalization group approach (DMRG), \cite{White_1992} and
(v) two flavors of FCI quantum Monte Carlo (FCIQMC), \cite{Booth_2009,Cleland_2010} namely AS-FCIQMC \cite{Ghanem_2019} and CAD-FCIQMC. \cite{Deustua_2018}
@ -69,7 +69,7 @@ Soon after, Lee \textit{et al.}~reported phaseless auxiliary-field quantum Monte
% The system
The target application is the non-relativistic frozen-core correlation energy of the ground state of the benzene molecule in the cc-pVDZ basis.
The geometry of benzene has been computed at the MP2/6-31G* level and it can be found in the supporting information of Ref.~\onlinecite{Eriksen_2020} alongside its nuclear repulsion and Hartree-Fock energies.
The geometry of benzene has been computed at the MP2/6-31G* level \cite{Schreiber_2008} and it can be found in the supporting information of Ref.~\onlinecite{Eriksen_2020} alongside its nuclear repulsion and Hartree-Fock energies.
This corresponds to an active space of 30 electrons and 108 orbitals, \ie, the Hilbert space of benzene is of the order of $10^{35}$ Slater determinants.
Needless to say that this size of Hilbert space cannot be tackled by exact diagonalization with current architectures.
The correlation energies reported in Ref.~\onlinecite{Eriksen_2020} are gathered in Table \ref{tab:energy} alongside the best ph-AFQMC estimate from Ref.~\onlinecite{Lee_2020} based on a CAS(6,6) trial wave function.