Linear-scaling implementation of exact exchange using the density matrix: method and accuracy

Details Linear-scaling implementation of exact exchange using the density matrix: method and accuracy Linear-scaling implementation of exact exchange using the density matrix: method and accuracy

2011-12-27

arxiv.org/abs/1112.5989v1

Physics

Chemical Physics

Scientific paper

In this work we consider the enhancement of the computational efficiency in exact exchange calculation using the density matrix and local support functions. We introduce a numerical method which avoids the explicit calculation the four-center electron repulsion integrals (ERIs) and reduces the prefactor scaling by a factor M, where M is the number atoms within the range of the exact exchange Hamiltonian. This approach, which uses three-center reduction integrals, takes advantage of a discrete grid which enables a direct summation over the support functions in a localized space. Using the sparsity property of the density matrix, the scaling of the prefactor can be further reduced to reach asymptotically O(M). Influence of the fast Fourier transform and real space Poisson solver upon the ERI accuracy is discussed. Finally, various factors influencing the performance of the algorithm are investigated in terms of execution time and memory usage.

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