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Title: Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm

Abstract

Construction of the exact exchange matrix, K, is typically the rate-determining step in hybrid density functional theory, and therefore, new approaches with increased efficiency are highly desirable. We present a framework with potential for greatly improved efficiency by computing a compressed exchange matrix that yields the exact exchange energy, gradient, and direct inversion of the iterative subspace (DIIS) error vector. The compressed exchange matrix is constructed with one index in the compact molecular orbital basis and the other index in the full atomic orbital basis. To illustrate the advantages, we present a practical algorithm that uses this framework in conjunction with the resolution of the identity (RI) approximation. We demonstrate that convergence using this method, referred to hereafter as occupied orbital RI-K (occ-RI-K), in combination with the DIIS algorithm is well-behaved, that the accuracy of computed energetics is excellent (identical to conventional RI-K), and that significant speedups can be obtained over existing integral-direct and RI-K methods. For a 4400 basis function C{sub 68}H{sub 22} hydrogen-terminated graphene fragment, our algorithm yields a 14 × speedup over the conventional algorithm and a speedup of 3.3 × over RI-K.

Authors:
; ; ;  [1]
  1. Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
Publication Date:
OSTI Identifier:
22489722
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 143; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; ALGORITHMS; DENSITY FUNCTIONAL METHOD; EFFICIENCY; EVALUATION; GRAPHENE; HYDROGEN; MOLECULAR ORBITAL METHOD

Citation Formats

Manzer, Samuel, Horn, Paul R., Mardirossian, Narbe, and Head-Gordon, Martin. Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm. United States: N. p., 2015. Web. doi:10.1063/1.4923369.
Manzer, Samuel, Horn, Paul R., Mardirossian, Narbe, & Head-Gordon, Martin. Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm. United States. https://doi.org/10.1063/1.4923369
Manzer, Samuel, Horn, Paul R., Mardirossian, Narbe, and Head-Gordon, Martin. 2015. "Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm". United States. https://doi.org/10.1063/1.4923369.
@article{osti_22489722,
title = {Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm},
author = {Manzer, Samuel and Horn, Paul R. and Mardirossian, Narbe and Head-Gordon, Martin},
abstractNote = {Construction of the exact exchange matrix, K, is typically the rate-determining step in hybrid density functional theory, and therefore, new approaches with increased efficiency are highly desirable. We present a framework with potential for greatly improved efficiency by computing a compressed exchange matrix that yields the exact exchange energy, gradient, and direct inversion of the iterative subspace (DIIS) error vector. The compressed exchange matrix is constructed with one index in the compact molecular orbital basis and the other index in the full atomic orbital basis. To illustrate the advantages, we present a practical algorithm that uses this framework in conjunction with the resolution of the identity (RI) approximation. We demonstrate that convergence using this method, referred to hereafter as occupied orbital RI-K (occ-RI-K), in combination with the DIIS algorithm is well-behaved, that the accuracy of computed energetics is excellent (identical to conventional RI-K), and that significant speedups can be obtained over existing integral-direct and RI-K methods. For a 4400 basis function C{sub 68}H{sub 22} hydrogen-terminated graphene fragment, our algorithm yields a 14 × speedup over the conventional algorithm and a speedup of 3.3 × over RI-K.},
doi = {10.1063/1.4923369},
url = {https://www.osti.gov/biblio/22489722}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 2,
volume = 143,
place = {United States},
year = {Tue Jul 14 00:00:00 EDT 2015},
month = {Tue Jul 14 00:00:00 EDT 2015}
}