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Title: Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory

Abstract

We present a systematically improvable tensor hypercontraction (THC) factorization based on interpolative separable density fitting (ISDF). We illustrate algorithmic details to achieve this within the framework of Becke's atom-centered quadrature grid. A single ISDF parameter cISDF controls the trade-off between accuracy and cost. In particular, cISDF sets the number of interpolation points used in THC, NIP = cISDF × NX with NX being the number of auxiliary basis functions. In conjunction with the resolution-of-the-identity (RI) technique, we develop and investigate the THC-RI algorithms for cubic-scaling exact exchange for Hartree-Fock and range-separated hybrids (e.g., ωB97X-V) and quartic-scaling second- and third-order Møller-Plesset theory (MP2 and MP3). These algorithms were evaluated over the W4-11 thermochemistry (atomization energy) set and A24 noncovalent interaction benchmark set with standard Dunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ). We demonstrate the convergence of THC-RI algorithms to numerically exact RI results using ISDF points. Based on these, we make recommendations on cISDF for each basis set and method. We also demonstrate the utility of THC-RI exact exchange and MP2 for larger systems such as water clusters and C20. We stress that more challenges await in obtaining accurate and numerically stable THC factorization for wave function amplitudes as wellmore » as for the space spanned by virtual orbitals in large basis sets and implementing sparsity-aware THC-RI algorithms.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]
+ Show Author Affiliations
  1. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Div.
  2. Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
OSTI Identifier:
1779232
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 16; Journal Issue: 1; 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

Lee, Joonho, Lin, Lin, and Head-Gordon, Martin. Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory. United States: N. p., 2019. Web. doi:10.1021/acs.jctc.9b00820.
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Lee, Joonho, Lin, Lin, & Head-Gordon, Martin. Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory. United States. https://doi.org/10.1021/acs.jctc.9b00820
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Lee, Joonho, Lin, Lin, and Head-Gordon, Martin. Tue . "Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory". United States. https://doi.org/10.1021/acs.jctc.9b00820. https://www.osti.gov/servlets/purl/1779232.
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@article{osti_1779232,
title = {Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory},
author = {Lee, Joonho and Lin, Lin and Head-Gordon, Martin},
abstractNote = {We present a systematically improvable tensor hypercontraction (THC) factorization based on interpolative separable density fitting (ISDF). We illustrate algorithmic details to achieve this within the framework of Becke's atom-centered quadrature grid. A single ISDF parameter cISDF controls the trade-off between accuracy and cost. In particular, cISDF sets the number of interpolation points used in THC, NIP = cISDF × NX with NX being the number of auxiliary basis functions. In conjunction with the resolution-of-the-identity (RI) technique, we develop and investigate the THC-RI algorithms for cubic-scaling exact exchange for Hartree-Fock and range-separated hybrids (e.g., ωB97X-V) and quartic-scaling second- and third-order Møller-Plesset theory (MP2 and MP3). These algorithms were evaluated over the W4-11 thermochemistry (atomization energy) set and A24 noncovalent interaction benchmark set with standard Dunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ). We demonstrate the convergence of THC-RI algorithms to numerically exact RI results using ISDF points. Based on these, we make recommendations on cISDF for each basis set and method. We also demonstrate the utility of THC-RI exact exchange and MP2 for larger systems such as water clusters and C20. We stress that more challenges await in obtaining accurate and numerically stable THC factorization for wave function amplitudes as well as for the space spanned by virtual orbitals in large basis sets and implementing sparsity-aware THC-RI algorithms.},
doi = {10.1021/acs.jctc.9b00820},
journal = {Journal of Chemical Theory and Computation},
number = 1,
volume = 16,
place = {United States},
year = {Tue Dec 03 00:00:00 EST 2019},
month = {Tue Dec 03 00:00:00 EST 2019}
}
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journal, October 1993

Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity
journal, May 2016

  • Song, Chenchen; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 144, Issue 17
  • DOI: 10.1063/1.4948438

Interpolative Separable Density Fitting through Centroidal Voronoi Tessellation with Applications to Hybrid Functional Electronic Structure Calculations
journal, January 2018

  • Dong, Kun; Hu, Wei; Lin, Lin
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 3
  • DOI: 10.1021/acs.jctc.7b01113

Tensor Hypercontraction Equation-of-Motion Second-Order Approximate Coupled Cluster: Electronic Excitation Energies in O(N4) Time
journal, July 2013

  • Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M.
  • The Journal of Physical Chemistry B, Vol. 117, Issue 42
  • DOI: 10.1021/jp4021905

Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction
journal, May 2014

  • Parrish, Robert M.; Sherrill, C. David; Hohenstein, Edward G.
  • The Journal of Chemical Physics, Vol. 140, Issue 18
  • DOI: 10.1063/1.4876016

Tensor-Structured Coupled Cluster Theory
text, January 2017

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