Fast periodic Gaussian density fitting by range separation

We present an efficient implementation of periodic Gaussian density fitting (GDF) using the Coulomb metric. The three-center integrals are divided into two parts by range-separating the Coulomb kernel, with the short-range part evaluated in real space and the long-range part in reciprocal space. With a few algorithmic optimizations, we show that this new method-which we call range-separated GDF (RSGDF)-scales sublinearly to linearly with the number of k-points for small to medium-sized k-point meshes that are commonly used in periodic calculations with electron correlation. Numerical results on a few three-dimensional solids show about ten-fold speedups over the previously developed GDF with little precision loss. The error introduced by RSGDF is about 10(-5)E(h) in the converged Hartree-Fock energy with default auxiliary basis sets and can be systematically reduced by increasing the size of the auxiliary basis with little extra work.

Automated summary

This paper presents an efficient implementation of periodic Gaussian density fitting using the Coulomb metric. The method, called range-separated GDF (RSGDF), scales sublinearly to linearly with the number of k-points for small to medium-sized k-point meshes commonly used in periodic calculations with electron correlation. Numerical results show significant speedups with little precision loss compared to previously developed GDF.