Fast periodic Gaussian density fitting by range separation

TL;DR

This paper introduces a range-separated Gaussian density fitting method for periodic systems that significantly accelerates calculations with minimal accuracy loss, enabling more efficient electronic structure computations.

Contribution

The paper develops a novel range-separated Gaussian density fitting approach that improves computational efficiency for periodic systems by dividing integrals into real and reciprocal space parts.

Findings

Achieves about 10-fold speedup over previous methods

Scales sublinearly to linearly with the number of k-points

Maintains high accuracy with controllable error levels

Abstract

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 $10$-fold speedups over the previously developed GDF with little precision loss. The error introduced by RSGDF is about $10^{-5}~E_{\textrm{h}}$ 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. [The article has been accepted by The Journal of Chemical Physics.]