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Title: Communication: Practical and rigorous reduction of the many-electron quantum mechanical Coulomb problem to O(N{sup 2/3}) storage

It is tacitly accepted that, for practical basis sets consisting of N functions, solution of the two-electron Coulomb problem in quantum mechanics requires storage of O(N{sup 4}) integrals in the small N limit. For localized functions, in the large N limit, or for planewaves, due to closure, the storage can be reduced to O(N{sup 2}) integrals. Here, it is shown that the storage can be further reduced to O(N{sup 2/3}) for separable basis functions. A practical algorithm, that uses standard one-dimensional Gaussian-quadrature sums, is demonstrated. The resulting algorithm allows for the simultaneous storage, or fast reconstruction, of any two-electron Coulomb integral required for a many-electron calculation on processors with limited memory and disk space. For example, for calculations involving a basis of 9171 planewaves, the memory required to effectively store all Coulomb integrals decreases from 2.8 Gbytes to less than 2.4 Mbytes.
Authors:
 [1]
  1. Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218 (United States)
Publication Date:
OSTI Identifier:
22415622
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 14; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ELECTRONS; INTEGRALS; MATHEMATICAL SOLUTIONS; ONE-DIMENSIONAL CALCULATIONS; QUADRATURES; QUANTUM MECHANICS; SPACE