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Title: Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models

Abstract

Novel implementations based on dense tensor storage are presented here for the singlet-reference perfect quadruples (PQ) [J. A. Parkhill et al., J. Chem. Phys. 130, 084101 (2009)] and perfect hextuples (PH) [J. A. Parkhill and M. Head-Gordon, J. Chem. Phys. 133, 024103 (2010)] models. The methods are obtained as block decompositions of conventional coupled-cluster theory that are exact for four electrons in four orbitals (PQ) and six electrons in six orbitals (PH), but that can also be applied to much larger systems. PQ and PH have storage requirements that scale as the square, and as the cube of the number of active electrons, respectively, and exhibit quartic scaling of the computational effort for large systems. Applications of the new implementations are presented for full-valence calculations on linear polyenes (C nH n+2), which highlight the excellent computational scaling of the present implementations that can routinely handle active spaces of hundreds of electrons. The accuracy of the models is studied in the π space of the polyenes, in hydrogen chains (H 50), and in the π space of polyacene molecules. In all cases, the results compare favorably to density matrix renormalization group values. With the novel implementation of PQ, active spaces ofmore » 140 electrons in 140 orbitals can be solved in a matter of minutes on a single core workstation, and the relatively low polynomial scaling means that very large systems are also accessible using parallel computing.« less

Authors:
ORCiD logo [1]; ORCiD logo [2];  [3]
  1. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Chemical Sciences Division
  2. Univ. of Notre Dame, IN (United States). Dept. of Chemistry
  3. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Chemical Sciences Division; Univ. of California, Berkeley, CA (United States). Dept. of Chemistry
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division; Univ. of Notre Dame, IN (United States)
OSTI Identifier:
1436139
Alternate Identifier(s):
OSTI ID: 1328222
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 145; Journal Issue: 13; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 97 MATHEMATICS AND COMPUTING; basis sets; density functional theory; quasicrystals; polynomials; optimization; tensor methods; wave functions; dissociation energies; orbital dynamics

Citation Formats

Lehtola, Susi, Parkhill, John, and Head-Gordon, Martin. Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models. United States: N. p., 2016. Web. doi:10.1063/1.4964317.
Lehtola, Susi, Parkhill, John, & Head-Gordon, Martin. Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models. United States. doi:10.1063/1.4964317.
Lehtola, Susi, Parkhill, John, and Head-Gordon, Martin. Fri . "Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models". United States. doi:10.1063/1.4964317. https://www.osti.gov/servlets/purl/1436139.
@article{osti_1436139,
title = {Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models},
author = {Lehtola, Susi and Parkhill, John and Head-Gordon, Martin},
abstractNote = {Novel implementations based on dense tensor storage are presented here for the singlet-reference perfect quadruples (PQ) [J. A. Parkhill et al., J. Chem. Phys. 130, 084101 (2009)] and perfect hextuples (PH) [J. A. Parkhill and M. Head-Gordon, J. Chem. Phys. 133, 024103 (2010)] models. The methods are obtained as block decompositions of conventional coupled-cluster theory that are exact for four electrons in four orbitals (PQ) and six electrons in six orbitals (PH), but that can also be applied to much larger systems. PQ and PH have storage requirements that scale as the square, and as the cube of the number of active electrons, respectively, and exhibit quartic scaling of the computational effort for large systems. Applications of the new implementations are presented for full-valence calculations on linear polyenes (CnHn+2), which highlight the excellent computational scaling of the present implementations that can routinely handle active spaces of hundreds of electrons. The accuracy of the models is studied in the π space of the polyenes, in hydrogen chains (H50), and in the π space of polyacene molecules. In all cases, the results compare favorably to density matrix renormalization group values. With the novel implementation of PQ, active spaces of 140 electrons in 140 orbitals can be solved in a matter of minutes on a single core workstation, and the relatively low polynomial scaling means that very large systems are also accessible using parallel computing.},
doi = {10.1063/1.4964317},
journal = {Journal of Chemical Physics},
number = 13,
volume = 145,
place = {United States},
year = {2016},
month = {10}
}

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Cited by: 6 works
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Figures / Tables:

FIG. 1 FIG. 1: Division of the orbital space. The active space orbitals are numbered with the value of the pairing label. The hole indices are reversed, because the strongest coupling typically occurs between the highest occupied and lowest unoccupied orbitals.

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