Recently, Merlot et al. applied the pair atomic resolution of the identity (PARI) approximation for two-electron integrals to the construction of the Coulomb (PARI-J) and exchange matrices (PARI-K) (Merlot et al., J. Comp. Chem. 2013, 34, 1486). The PARI approximation can potentially yield dramatic increases in performance because of its immense locality; products of Gaussians are expanded using only the auxiliary basis functions on their respective atoms. The authors demonstrated impressive speedups compared to conventional integral calculations, but expressed reservations about the possibility of convergence difficulties due to the loss of a positive semidefinite two-electron integral tensor. Several authors have proposed corrections to this problem; however, we demonstrate that PARI-K can be applied to a wide range of chemical systems with negligible error and no convergence difficulties provided that an appropriate guess is used. Our MO-based implementation of PARI-K provides large speedups over conventional SCF and RI-K for systems of up to 4400 basis functions. Our methods are implemented using a new C++ sparse tensor library that allows for efficient on-the-fly computation of intermediate tensors in batches. Our library performs sparse tensor contractions using block-major storage and combining the sparsity of all tensors involved in a given expression to minimize the overall operation count. We illustrate how such libraries can be employed to rapidly develop local electronic structure codes.

Advances in local RI methods for SCF calculations

249th National Meeting (2015)

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