期刊
JOURNAL OF CHEMICAL PHYSICS
卷 137, 期 22, 页码 -出版社
AMER INST PHYSICS
DOI: 10.1063/1.4768233
关键词
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资金
- DOE [DE-FG02-97ER25308]
- National Science Foundation [CHE-1011360, CHE-1047577]
- Department of Defense
- NSF CRIF award [CHE-0946869]
- Georgia Tech.
- Direct For Mathematical & Physical Scien
- Division Of Chemistry [0946869] Funding Source: National Science Foundation
- Division Of Chemistry
- Direct For Mathematical & Physical Scien [1011360] Funding Source: National Science Foundation
- Office of Advanced Cyberinfrastructure (OAC)
- Direct For Computer & Info Scie & Enginr [1047577] Funding Source: National Science Foundation
The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [ E. G. Hohenstein, R. M. Parrish, and T. J. Martinez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlapmetric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r(12) operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N-5) effort if exact integrals are decomposed, or O(N-4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N-4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4768233]
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