103 lines
5.6 KiB
TeX
103 lines
5.6 KiB
TeX
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\documentclass[aps,prb,reprint,noshowkeys,superscriptaddress]{revtex4-1}
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,wrapfig}
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\newcommand{\QP}{\textsc{quantum package}}
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]{hyperref}
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\begin{document}
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\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
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\title{Note: The performance of CIPSI on the ground state electronic energy of benzene}
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\author{Pierre-Fran\c{c}ois Loos}
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\email{loos@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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\author{Anthony Scemama}
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\email{scemama@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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\maketitle
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% The context
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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 belonging to the \textit{Simons Collaboration on the Many-Electron Problem} to contribute to this endeavour.
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A large panel of highly-accurate methods were considered:
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(i) coupled cluster theory with singles, doubles, triples, and quadruples (CCSDTQ),
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(ii) the many-body expansion approach (MBE-FCI),
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(iii) three selected configuration interaction (SCI) methods including a second-order perturbative correction (ASCI, iCI, and SHCI),
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(iv) a selected coupled-cluster theory method including a second-order perturbative correction (FCCR),
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(v) the density-matrix renornalization group approach (DMRG), and
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(vi) two flavors of full configuration interaction quantum Monte Carlo (AS-FCIQMC and CAD-FCIQMC).
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We refer the interested reader to Ref.~\onlinecite{Eriksen_2020} and its supporting information for additional details on each method and their corresponding references.
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Soon after, Lee \textit{et al.} reported phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) correlation energies for the very same problem. \cite{Lee_2020}
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% The system
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The target application is the non-relativistic frozen-core correlation energy of the benzene molecule in the cc-pVDZ basis.
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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.
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%Needless to say that this size of Hilbert space cannot be tackled with conventional, deterministic FCI algorithm with current architecture.
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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}.
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%%% TABLE 1 %%%
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\begin{table}
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\caption{
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The frozen-core correlation energy (in m$E_h$) of benzene in the cc-pVDZ basis set using various methods.
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\label{tab:energy}
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}
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\begin{ruledtabular}
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\begin{tabular}{ccc}
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Method & $E_c$ & Ref. \\
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\hline
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ASCI & $-860.0(2)$ & \onlinecite{Eriksen_2020} \\
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iCIPT2 & $-861.1(5)$ & \onlinecite{Eriksen_2020} \\
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CCSDTQ & $-862.4$ & \onlinecite{Eriksen_2020} \\
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DMRG & $-862.8(7)$ & \onlinecite{Eriksen_2020} \\
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FCCR(2) & $-863.0$ & \onlinecite{Eriksen_2020} \\
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CAD-FCIQMC & $-863.4$ & \onlinecite{Eriksen_2020} \\
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AS-FCIQMC & $-863.7(3)$ & \onlinecite{Eriksen_2020} \\
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SHCI & $-864.2(2)$ & \onlinecite{Eriksen_2020} \\
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\hline
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ph-AFQMC & $-864.3(4)$ & \onlinecite{Lee_2020} \\
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\hline
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CIPSI & XXX & This work\\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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% CIPSI
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In this Note, we report the frozen-core correlation energy obtained with a fourth flavor of SCI known as \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI), which also includes a second-order perturbative (PT2) correction.
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In short, the CIPSI algorithm belongs to the family of SCI+PT2 methods.
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From an historical point of view, CIPSI is probably the oldest SCI algorithm developed in 1973 by Huron, Rancurel, and Malrieu. \cite{Huron_1973}
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Recently, the determinant-driven CIPSI algorithm has been efficiently implemented in the open-source programming environment {\QP} by one of us (AS) enabling to perform massively parallel computations. \cite{}
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In particular, we were able to compute highly-accurate calculations of ground- and excited-state energies of small- and medium-sized molecules. \cite{}
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The particularity of the current implementation is that the selection step and the PT2 correction are computed \textit{simultaneously} via a hybrid semistochastic algorithm. \cite{}
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Moreover, a renormalized version of the PT2 correction dubbed rPT2 has been recently implemented for a more efficient extrapolation to the FCI limit. \cite{}
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We refer the interested reader to Ref.~\onlinecite{} where one can find all the details regarding the implementation of the CIPSI algorithm.
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The present calculations have been performed on the AMD partition of GENCI's Irene supercomputer.
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Each Irene's AMD node is a dual-socket \titou{Intel(R) Xeon(R) Platinum 8168 CPU@2.70 GHz with 192GiB of RAM}, with a total of 128 physical CPU cores.
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This work was performed using HPC resources from GENCI-TGCC (Grand Challenge 2019-gch0418) and from CALMIP (Toulouse) under allocation 2019-0510.
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\bibliography{benzene}
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\end{document}
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