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Manuscript/Cover_Letter/CoverLetter.tex
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\begin{document} \begin{document}
\begin{letter}% \begin{letter}%
{To the Editors of the Journal of Chemical Theory and Computation,} {To the Editors of the Journal of Chemical Physics,}
\opening{Dear Editors,} \opening{Dear Editors,}
\justifying \justifying
Please find enclosed our manuscript entitled \textit{``Accurate full configuration interaction correlation energy estimates for five- and six-membered ring molecules''}, Please find enclosed our manuscript entitled \textit{``Accurate full configuration interaction correlation energy estimates for five- and six-membered ring molecules''},
which we would like you to consider as a Regular Article in the \textit{Journal of Chemical Theory and Computation}. which we would like you to consider as a Regular Article in the \textit{Journal of Chemical Physics}.
Thanks to the selected configuration interaction (SCI) algorithm named \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI), in the present manuscript, we have been able to produce FCI-quality frozen-core correlation energies for twelve cyclic molecules in the correlation-consistent double-$\zeta$ Dunning basis set (cc-pVDZ). Thanks to the selected configuration interaction (SCI) algorithm named \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI), in the present manuscript, we have been able to produce FCI-quality frozen-core correlation energies for twelve cyclic molecules in the correlation-consistent double-$\zeta$ Dunning basis set (cc-pVDZ).
These estimates, which are likely accurate to a few tenths of a millihartree, have been obtained by extrapolating \textit{orbital-optimized} CIPSI energies to the FCI limit. These estimates, which are likely accurate to a few tenths of a millihartree, have been obtained by extrapolating \textit{orbital-optimized} CIPSI energies to the FCI limit.

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Manuscript/Ec.bib
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%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/ %% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2021-07-31 20:50:49 +0200 %% Created for Pierre-Francois Loos at 2021-07-31 22:13:58 +0200
%% Saved with string encoding Unicode (UTF-8) %% Saved with string encoding Unicode (UTF-8)
@ -2626,16 +2626,12 @@
@article{gamess, @article{gamess,
author = {Barca, Giuseppe M. J. and Bertoni, Colleen and Carrington, Laura and Datta, Dipayan and De Silva, Nuwan and Deustua, J. Emiliano and Fedorov, Dmitri G. and Gour, Jeffrey R. and Gunina, Anastasia O. and Guidez, Emilie and Harville, Taylor and Irle, Stephan and Ivanic, Joe and Kowalski, Karol and Leang, Sarom S. and Li, Hui and Li, Wei and Lutz, Jesse J. and Magoulas, Ilias and Mato, Joani and Mironov, Vladimir and Nakata, Hiroya and Pham, Buu Q. and Piecuch, Piotr and Poole, David and Pruitt, Spencer R. and Rendell, Alistair P. and Roskop, Luke B. and Ruedenberg, Klaus and Sattasathuchana, Tosaporn and Schmidt, Michael W. and Shen, Jun and Slipchenko, Lyudmila and Sosonkina, Masha and Sundriyal, Vaibhav and Tiwari, Ananta and Galvez Vallejo, Jorge L. and Westheimer, Bryce and Wloch, Marta and Xu, Peng and Zahariev, Federico and Gordon, Mark S.}, author = {Barca, Giuseppe M. J. and Bertoni, Colleen and Carrington, Laura and Datta, Dipayan and De Silva, Nuwan and Deustua, J. Emiliano and Fedorov, Dmitri G. and Gour, Jeffrey R. and Gunina, Anastasia O. and Guidez, Emilie and Harville, Taylor and Irle, Stephan and Ivanic, Joe and Kowalski, Karol and Leang, Sarom S. and Li, Hui and Li, Wei and Lutz, Jesse J. and Magoulas, Ilias and Mato, Joani and Mironov, Vladimir and Nakata, Hiroya and Pham, Buu Q. and Piecuch, Piotr and Poole, David and Pruitt, Spencer R. and Rendell, Alistair P. and Roskop, Luke B. and Ruedenberg, Klaus and Sattasathuchana, Tosaporn and Schmidt, Michael W. and Shen, Jun and Slipchenko, Lyudmila and Sosonkina, Masha and Sundriyal, Vaibhav and Tiwari, Ananta and Galvez Vallejo, Jorge L. and Westheimer, Bryce and Wloch, Marta and Xu, Peng and Zahariev, Federico and Gordon, Mark S.},
date-modified = {2021-07-31 22:09:07 +0200},
doi = {10.1063/5.0005188}, doi = {10.1063/5.0005188},
issn = {0021-9606, 1089-7690}, journal = {J. Chem. Phys.},
journal = {The Journal of Chemical Physics},
language = {en},
month = apr,
number = {15}, number = {15},
pages = {154102}, pages = {154102},
title = {Recent developments in the general atomic and molecular electronic structure system}, title = {Recent developments in the general atomic and molecular electronic structure system},
url = {http://aip.scitation.org/doi/10.1063/5.0005188},
urldate = {2020-06-18},
volume = {152}, volume = {152},
year = {2020}, year = {2020},
Bdsk-Url-1 = {http://aip.scitation.org/doi/10.1063/5.0005188}, Bdsk-Url-1 = {http://aip.scitation.org/doi/10.1063/5.0005188},

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Manuscript/Ec.tex
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@ -76,8 +76,7 @@
\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} \newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
\newcommand{\CEISAM}{Universit\'e de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France} \newcommand{\CEISAM}{Universit\'e de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France}
\title{Accurate full configuration interaction correlation energy estimates for five- and six-membered rings}%DJ: il apparait pas mais ring molecules => rings \title{Accurate full configuration interaction correlation energy estimates for five- and six-membered rings}
%DJ: Quand je compile, j'ai un soucis dans les affiliations: vs etes ts ˆ Nantes sauf Yann => check ?
\author{Yann \surname{Damour}} \author{Yann \surname{Damour}}
\affiliation{\LCPQ} \affiliation{\LCPQ}
@ -88,8 +87,7 @@
\author{Michel \surname{Caffarel}} \author{Michel \surname{Caffarel}}
\affiliation{\LCPQ} \affiliation{\LCPQ}
\author{Denis \surname{Jacquemin}} \author{Denis \surname{Jacquemin}}
%DJ: En terme de calculs/efforts, j'ai je pense mŽritŽ la *. En terme d'idŽes, je ne pense pas. Je te laisse juger et je me rangerais derri<72>re ton avis sans le moindre souci. \email{Denis.Jacquemin@univ-nantes.fr}
%\email{Denis.Jacquemin@univ-nantes.fr}
\affiliation{\CEISAM} \affiliation{\CEISAM}
\author{Anthony \surname{Scemama}} \author{Anthony \surname{Scemama}}
\email{scemama@irsamc.ups-tlse.fr} \email{scemama@irsamc.ups-tlse.fr}
@ -186,7 +184,7 @@ Finally, we draw our conclusions in Sec.~\ref{sec:ccl}.
Here, we provide key details about the CIPSI method \cite{Huron_1973,Garniron_2019} as well as the orbital optimization procedure which has been shown to be highly effective in the context of SHCI by Umrigar and coworkers. \cite{Eriksen_2020,Yao_2020,Yao_2021} Here, we provide key details about the CIPSI method \cite{Huron_1973,Garniron_2019} as well as the orbital optimization procedure which has been shown to be highly effective in the context of SHCI by Umrigar and coworkers. \cite{Eriksen_2020,Yao_2020,Yao_2021}
Although we focus on the ground state, the present discussion can be easily extended to excited states. \cite{Scemama_2019,Veril_2021} Although we focus on the ground state, the present discussion can be easily extended to excited states. \cite{Scemama_2019,Veril_2021}
At the $k$th iteration, the total CIPSI energy $\ECIPSI^{(k)}$ is defined as the sum of the variational energy%DJ Change kth en k^th, idem plus bas (cherche textsuperscript si tu n'aimes pas) At the $k$th iteration, the total CIPSI energy $\ECIPSI^{(k)}$ is defined as the sum of the variational energy
\begin{equation} \begin{equation}
\Evar^{(k)} = \frac{\mel*{\Psivar^{(k)}}{\hH}{\Psivar^{(k)}}}{\braket*{\Psivar^{(k)}}{\Psivar^{(k)}}} \Evar^{(k)} = \frac{\mel*{\Psivar^{(k)}}{\hH}{\Psivar^{(k)}}}{\braket*{\Psivar^{(k)}}{\Psivar^{(k)}}}
\end{equation} \end{equation}
@ -207,7 +205,7 @@ In the selection step, the perturbers corresponding to the largest $\abs*{e_{\al
In our implementation, the size of the variational space is roughly doubled at each iteration. In our implementation, the size of the variational space is roughly doubled at each iteration.
Hereafter, we label these iterations over $k$ which consist in enlarging the variational space as \textit{macroiterations}. Hereafter, we label these iterations over $k$ which consist in enlarging the variational space as \textit{macroiterations}.
In practice, $\Evar^{(k)}$ is the lowest eigenvalue of the $\Ndet^{(k)} \times \Ndet^{(k)}$ CI matrix with elements $\mel{I}{\hH}{J}$ obtained via Davidson's algorithm. \cite{Davidson_1975} In practice, $\Evar^{(k)}$ is the lowest eigenvalue of the $\Ndet^{(k)} \times \Ndet^{(k)}$ CI matrix with elements $\mel{I}{\hH}{J}$ obtained via Davidson's algorithm. \cite{Davidson_1975}
The magnitude of $\EPT^{(k)}$ provides, at iteration $k$, a qualitative idea of the ``distance'' to the FCI limit. \cite{Garniron_2018}%DJ: j'aurais pas distance entre "", on comprend sans cela The magnitude of $\EPT^{(k)}$ provides, at iteration $k$, a qualitative idea of the distance to the FCI limit. \cite{Garniron_2018}
We then linearly extrapolate, using large variational wave functions, the CIPSI energy to $\EPT = 0$ (which effectively corresponds to the FCI limit). We then linearly extrapolate, using large variational wave functions, the CIPSI energy to $\EPT = 0$ (which effectively corresponds to the FCI limit).
Further details concerning the extrapolation procedure are provided below (see Sec.~\ref{sec:res}). Further details concerning the extrapolation procedure are provided below (see Sec.~\ref{sec:res}).
@ -631,7 +629,7 @@ Each Irene's AMD node is a dual-socket AMD Rome (EPYC) CPU at 2.60 GHz with 256G
These nodes are connected via Infiniband HDR100. These nodes are connected via Infiniband HDR100.
In total, the present calculations have required around 3~million core hours. In total, the present calculations have required around 3~million core hours.
All the data (geometries, energies, etc) and supplementary material associated with the present manuscript are openly available in Zenodo at \url{http://doi.org/XX.XXXX/zenodo.XXXXXXX}. All the data (geometries, energies, etc) and supplementary material associated with the present manuscript are openly available in Zenodo at \url{http://doi.org/10.5281/zenodo.5150663}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results and discussion} \section{Results and discussion}
@ -689,17 +687,17 @@ Unfortunately, CC with singles, doubles, triples, quadruples, and pentuples (CCS
As expected for the present set of weakly correlated systems, going from CCSD to CCSDTQ, one systematically and quickly improves the correlation energies with respective MAEs of $39.4$, $4.5$, \SI{1.8}{\milli\hartree} for CCSD, CCSDT, and CCSDTQ. As expected for the present set of weakly correlated systems, going from CCSD to CCSDTQ, one systematically and quickly improves the correlation energies with respective MAEs of $39.4$, $4.5$, \SI{1.8}{\milli\hartree} for CCSD, CCSDT, and CCSDTQ.
As usually observed, CCSD(T) (MAE of \SI{4.5}{\milli\hartree}) provides similar correlation energies than the more expensive CCSDT method by computing perturbatively (instead of iteratively) the triple excitations, while CCSD(T) and CR-CC(2,3) performs equally well. As usually observed, CCSD(T) (MAE of \SI{4.5}{\milli\hartree}) provides similar correlation energies than the more expensive CCSDT method by computing perturbatively (instead of iteratively) the triple excitations, while CCSD(T) and CR-CC(2,3) performs equally well.
Second, let us look into the MP series which is known, as mentioned in Sec.~\ref{sec:intro}, to potentially exhibit ``surprising'' behaviors depending on the type of correlation at play.\cite{Laidig_1985,Knowles_1985,Handy_1985,Gill_1986,Laidig_1987,Nobes_1987,Gill_1988,Gill_1988a,Lepetit_1988,Malrieu_2003} Second, we investigate the approximate CC series of methods CC2, CC3, and CC4.
As observed in our recent study on excitation energies, \cite{Loos_2021} CC4, which returns a MAE of \SI{1.5}{\milli\hartree}, is an outstanding approximation to its CCSDTQ parent (MAE of \SI{1.8}{\milli\hartree}) and is, in the present case, even slightly more accurate in terms of mean errors as well as maximum and minimum absolute errors.
Moreover, we observe that CC3 provides very accurate correlation energies with a MAE of \SI{2.7}{\milli\hartree}, showing that this iterative method is particularly effective for ground-state energetics and outperforms both the perturbative CCSD(T) and iterative CCSDT models.
It is important to mention that even if the two families of CC methods studied here are known to be non-variational (see Sec.~\ref{sec:intro}), for the present set of weakly-correlated molecular systems, they never produce a lower energy than the FCI estimate as illustrated by the systematic equality between MAEs and MSEs.
Third, let us look into the MP series which is known, as mentioned in Sec.~\ref{sec:intro}, to potentially exhibit ``surprising'' behaviors depending on the type of correlation at play.\cite{Laidig_1985,Knowles_1985,Handy_1985,Gill_1986,Laidig_1987,Nobes_1987,Gill_1988,Gill_1988a,Lepetit_1988,Malrieu_2003}
(See Ref.~\onlinecite{Marie_2021a} for a detailed discussion). (See Ref.~\onlinecite{Marie_2021a} for a detailed discussion).
For each system, the MP series decreases monotonically up to MP4 but raises quite significantly when one takes into account the fifth-order correction. For each system, the MP series decreases monotonically up to MP4 but raises quite significantly when one takes into account the fifth-order correction.
We note that the MP4 correlation energy is always quite accurate (MAE of \SI{2.1}{\milli\hartree}) and is only a few millihartree higher than the FCI value (except in the case of s-tetrazine where the MP4 number is very slightly below the reference value): MP5 (MAE of \SI{9.4}{\milli\hartree}) is thus systematically worse than MP4 for these weakly-correlated systems. We note that the MP4 correlation energy is always quite accurate (MAE of \SI{2.1}{\milli\hartree}) and is only a few millihartree higher than the FCI value (except in the case of s-tetrazine where the MP4 number is very slightly below the reference value): MP5 (MAE of \SI{9.4}{\milli\hartree}) is thus systematically worse than MP4 for these weakly-correlated systems.
Importantly here, one notices that MP4 [which scales as $\order*{N^7}$] is systematically on par with the much more expensive $\order*{N^{10}}$ CCSDTQ method which exhibits a slightly smaller MAE of \SI{1.8}{\milli\hartree}. Importantly here, one notices that MP4 [which scales as $\order*{N^7}$] is systematically on par with the much more expensive $\order*{N^{10}}$ CCSDTQ method which exhibits a slightly smaller MAE of \SI{1.8}{\milli\hartree}.
Third, we investigate the approximate CC series of methods CC2, CC3, and CC4.
As observed in our recent study on excitation energies, \cite{Loos_2021} CC4, which returns a MAE of \SI{1.5}{\milli\hartree}, is an outstanding approximation to its CCSDTQ parent and is, in the present case, even slightly more accurate in terms of mean errors as well as maximum and minimum absolute errors.
Moreover, we observe that CC3 provides very accurate correlation energies with a MAE of \SI{2.7}{\milli\hartree}, showing that this iterative method is particularly effective for ground-state energetics and outperforms both the perturbative CCSD(T) and iterative CCSDT models.
As a final remark, we would like to mention that even if the two families of CC methods studied here are known to be non-variational (see Sec.~\ref{sec:intro}), for the present set of weakly-correlated molecular systems, they never produce a lower energy than the FCI estimate as illustrated by the systematic equality between MAEs and MSEs.
%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusion} \section{Conclusion}
\label{sec:ccl} \label{sec:ccl}
@ -730,7 +728,7 @@ This project has received funding from the European Research Council (ERC) under
%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Data availability statement} \section*{Data availability statement}
%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%
The data that support the findings of this study are openly available in Zenodo at \url{http://doi.org/XX.XXXX/zenodo.XXXXXXX}. The data that support the findings of this study are openly available in Zenodo at \url{http://doi.org/10.5281/zenodo.5150663}.
%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%
\bibliography{Ec} \bibliography{Ec}