179 lines
7.8 KiB
TeX
179 lines
7.8 KiB
TeX
\documentclass[10pt]{cnrslet}
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\usepackage{xcolor,mhchem,mathpazo,ragged2e}
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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\usepackage{txfonts}
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\usepackage{url}
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\newcommand{\alert}[1]{\textcolor{red}{#1}}
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\usepackage[UKenglish]{datetime}
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% Formal environment
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\usepackage[strict]{changepage}
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\definecolor{darkblue}{rgb}{0.0, 0.0, 0.55}
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\definecolor{formalshade}{rgb}{0.95,0.95,1}
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\usepackage{framed}
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\newcommand{\ajwt}[1]{{\color{red}{#1}}}
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\newenvironment{formal}{%
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\def\FrameCommand{%
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{\color{darkblue}\vrule width 2pt}%
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{\color{formalshade}\vrule width 4pt}%
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\colorbox{formalshade}%
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}%
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\MakeFramed{\advance\hsize-\width\FrameRestore}%
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\noindent\hspace{-4.55pt}% disable indenting first paragraph
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\begin{adjustwidth}{}{7pt}%
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\vspace{-4pt}%
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}
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{%
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\vspace{4pt}\end{adjustwidth}\endMakeFramed%
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\vspace{-8pt}
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}
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% Paper specifics
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\newcommand{\journal}{the Journal of Chemical Physics}
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\newcommand{\papertitle}{Stochastically accelerated perturbative triples correction in coupled cluster calculations}
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\begin{document}
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\newdateformat{UKvardate}{%
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\THEDAY\ \monthname[\THEMONTH], \THEYEAR}
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\UKvardate\renewcommand{\headrulewidth}{0pt}
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\fromwhom{}{Anthony Scemama}{}{Laboratoire de Chimie et Physique Quantiques (UMR5626)}{scemama@irsamc.ups-tlse.fr}{+33 5 6155 7339}{}
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\setsalutation{To}
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\renewcommand{\yoursdetails}{Yours sincerely, the authors}
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\begin{letter}%
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{the Editors of \textit{\journal}}
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%\opening{Dear Editors,}
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\vspace{-1em}
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\justifying
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Please find attached a manuscript entitled
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\vspace{-1.25em}
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\begin{center}
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\textbf{\papertitle{}}
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\end{center}
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\vspace{-1.25em}
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that we recently submitted as an \underline{Invited Article} to the \textit{\journal}.
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We thank the reviewers for their constructive comments and for supporting 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. We look forward to hearing from you.
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\end{letter}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\clearpage
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{\large \bf Response to Reviewer 1:}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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In this paper, calculation of the perturbative triples correction, usually
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abbreviated as (T), is considered. It is well-known that the cost of CCSD(T)
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calculations for large systems is frequently dominated by the (T) component.
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This is due to the $N^7$ scaling of the computational costs, higher than the $N^6$
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of the preceding CCSD iterations. Taking into account that the use of CCSD(T)
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is widespread nowadays, new approaches to evaluation of the (T) corrections are
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welcomed. The authors propose a novel method based on the stochastic sampling
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of the triplets of virtual orbitals. The samples are drawn according to a
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probability distribution (importance sampling) suggested in the manuscript
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which approximately describes the importance of each triplet for the final
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result. While the same triplet can be randomized several times during the Monte
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Carlo procedure, a memorization algorithm is introduced to avoid unnecessary
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recalculation. As a result, the stochastic algorithm has a small overhead
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compared with the conventional implementation and converges to the exact result
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in the limit of infinite number of samples.
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The paper is well-written, the numerical results are comprehensive and convincing and hence I recommend the paper to be published. However, I have a few minor suggestions which the authors may consider and revise their paper -- they are listed below.
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\begin{formal}
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We thank the reviewer for his/her support and remarks. His/her comments are addressed below.
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\end{formal}
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1. The authors focus primarily on the calculations of the total (T) correction
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rather than the energy differences. However, the latter are of main importance
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in most applications. The example of CuCl can be seen as involving energy
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differences (along the potential energy curve), but the they are quite large in
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comparison with, e.g. hydrogen bond strengths, dispersion forces, etc. It is
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clear that when errors in the total energies do not exceed, say, $\sigma$,
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relative energies must be accurate to within $2\sigma$ (in the worst-case
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scenario). However, most quantum-chemical methods benefit from significant
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error cancellation when energy differences are evaluated. Are there any
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prospects of carrying out the sampling in a way that would be, in some sense,
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systematic for, e.g. a water dimer and water molecule in the basis set of the
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dimer (the same number of basis set functions)?
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\begin{formal}
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This is indeed a very interesting suggestion! It is sure that modifying the
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algorithm to compute directly energy differences would be a major improvement
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of the presented algorithm. But it is not straightforward for the general case
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as it necessitates finding an efficient importance sampling function.
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As the reviewer suggests, computing the energy difference between two systems
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with the same number of orbitals, and where the orbitals can be identified as
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equivalent seems like a relatively simple first test to see the potential benefits
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of the method.
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\end{formal}
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2. The probability distribution in Eq. (7) is defined with a "threshold" for small energy differences. Alternatively, one can view this threshold a continuous parameter that "interpolates" between the uniform sampling ($e_{min} \rightarrow \infty$) and sampling based on the pure denominator (which may be unphysically small). This threshold is set to 0.2 au. Is there a justification of adopting this particular value? Are the results sensitive to this parameter (when changed within reasonable bounds)?
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\begin{formal}
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Along the dissociation curve of CuCl we have observed, with
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$\epsilon_\text{min}=0$, a slow convergence of the points at the largest
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distances. This was due to the quasi-degeneracies of the orbital energies that made
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$1/\Delta \epsilon$ diverge. We have empirically taken a value for
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$\epsilon_\text{min}$ that did not change the speed of convergence of the
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points with short distances, and that also enabled a similar convergence on the
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problematic ones.
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A sentence was added:
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\begin{quote}
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The algorithm is not very sensitive to the value of $\epsilon_{\min}$ as long as it is taken within reasonable bounds, in the range of the level-shift parameter in SCF calculations.
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\end{quote}
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\end{formal}
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3. Several typos/omissions:
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- the CCSD method should probably be cited along with (T);
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\begin{formal}
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Thank you.We have now added the citation for the CCSD method.
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\end{formal}
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- first paragraph on page 3: typo in "memorization";
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\begin{formal}
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This is not a typo. It is really \emph{memoization}: \url{https://en.wikipedia.org/wiki/Memoization}.
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\end{formal}
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- below Eq. (5): Coulomb (capital letter);
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\begin{formal}
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Thank you, this typo was fixed.
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\end{formal}
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%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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{\large \bf Response to Reviewer 2:}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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This is an excellent manuscript on combining explicit coupled cluster (CCSD) and stochastic perturbational triples to speed-up CC correlated wave function calculations. Very straightforward and "obvious" idea (in fact, a number of such techniques is used in purely stochastic codes). It should be effective since sampling and corresponding weights takes care of triples contribution with known error bars.
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Indeed, the results are solid, for example, an order of magnitude speed-up that is benchmarked against fully explicit calculations. The resource analysis shows for which situations this can be effective.
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I did not catch any obvious mistakes or shortcomings. The work is very well described and the narrative has the right level of important details.
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In fact, the results suggest that there might be other explicit-and-stochastic algorithms possible with further reduction in run times. This implies that there is a potential for a solid impact in future.
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I recommend publishing in JCP.
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\begin{formal}
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We thank the reviewer for his/her support!
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\end{formal}
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\end{document}
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