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Title: Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction

Abstract

Here, we present the rank-reduced full configuration interaction (RR-FCI) method, a variational approach for the calculation of extremely large full configuration interaction (FCI) wave functions. In this report, we show that RR-FCI can provide ground state singlet and triplet energies within kcal/mol accuracy of full CI (FCI) with computational effort scaling as the square root of the number of determinants in the CI space (compared to conventional FCI methods which scale linearly with the number of determinants). Fast graphical processing unit (GPU) accelerated projected σ = Hc matrix–vector product formation enables calculations with configuration spaces as large as 30 electrons in 30 orbitals, corresponding to an FCI calculation with over 2.4 × 1016 configurations. We apply this method in the context of complete active space configuration interaction calculations to acenes with 2–5 aromatic rings, comparing absolute energies against FCI when possible and singlet/triplet excitation energies against both density matrix renormalization group (DMRG) and experimental results. The dissociation of molecular nitrogen was also examined using both FCI and RR-FCI. In each case, we found that RR-FCI provides a low cost alternative to FCI, with particular advantages when relative energies are desired.

Authors:
 [1]; ORCiD logo [1];  [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [1]
+ Show Author Affiliations
  1. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. Michigan State Univ., East Lansing, MI (United States)
  3. Norwegian Univ. of Science and Technology, Trondheim (Norway)
Publication Date:
Research Org.:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1476143
Grant/Contract Number:  
AC02-76SF00515; CHE-1565634; 263110/F20
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 14; Journal Issue: 8; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Fales, B. Scott, Seritan, Stefan, Settje, Nick F., Levine, Benjamin G., Koch, Henrik, and Martínez, Todd J. Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction. United States: N. p., 2018. Web. doi:10.1021/acs.jctc.8b00382.
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Fales, B. Scott, Seritan, Stefan, Settje, Nick F., Levine, Benjamin G., Koch, Henrik, & Martínez, Todd J. Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction. United States. https://doi.org/10.1021/acs.jctc.8b00382
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Fales, B. Scott, Seritan, Stefan, Settje, Nick F., Levine, Benjamin G., Koch, Henrik, and Martínez, Todd J. Mon . "Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction". United States. https://doi.org/10.1021/acs.jctc.8b00382. https://www.osti.gov/servlets/purl/1476143.
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@article{osti_1476143,
title = {Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction},
author = {Fales, B. Scott and Seritan, Stefan and Settje, Nick F. and Levine, Benjamin G. and Koch, Henrik and Martínez, Todd J.},
abstractNote = {Here, we present the rank-reduced full configuration interaction (RR-FCI) method, a variational approach for the calculation of extremely large full configuration interaction (FCI) wave functions. In this report, we show that RR-FCI can provide ground state singlet and triplet energies within kcal/mol accuracy of full CI (FCI) with computational effort scaling as the square root of the number of determinants in the CI space (compared to conventional FCI methods which scale linearly with the number of determinants). Fast graphical processing unit (GPU) accelerated projected σ = Hc matrix–vector product formation enables calculations with configuration spaces as large as 30 electrons in 30 orbitals, corresponding to an FCI calculation with over 2.4 × 1016 configurations. We apply this method in the context of complete active space configuration interaction calculations to acenes with 2–5 aromatic rings, comparing absolute energies against FCI when possible and singlet/triplet excitation energies against both density matrix renormalization group (DMRG) and experimental results. The dissociation of molecular nitrogen was also examined using both FCI and RR-FCI. In each case, we found that RR-FCI provides a low cost alternative to FCI, with particular advantages when relative energies are desired.},
doi = {10.1021/acs.jctc.8b00382},
journal = {Journal of Chemical Theory and Computation},
number = 8,
volume = 14,
place = {United States},
year = {Mon Jun 11 00:00:00 EDT 2018},
month = {Mon Jun 11 00:00:00 EDT 2018}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1021/acs.jctc.8b00382
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Cited by: 21 works
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Figures / Tables:

Algorithm 1 Algorithm 1: Vectorized formation of coupling coefficients $γ$, orbital labels 1, and configuration labels IJ. $N$e is the number of $α$ electrons and bin_rep is a precomputed integer array defining the orbital occupations using binary representation. stradr() is a function that determines the string address using lexical ordering asmore » defined by Knowles and Handy (Equations 11,12) and get_parity() is a function that determines the number of particle swaps required to bring the configurations $I$ and $J$ into maximum coincidence. occ and vac are lists of occupied and vacant orbitals for a given string.« less
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    Generalized Many-Body Expanded Full Configuration Interaction Theory
    text, January 2019

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