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/content/aip/journal/jcp/142/14/10.1063/1.4917303
2015-04-08
2016-12-02

Abstract

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(N4) 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(N2) integrals. Here, it is shown that the storage can be further reduced to O( 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.

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