Interpolative separable density fitting on adaptive real space grids

TL;DR

This paper extends the ISDF method to adaptive real space grids, enabling efficient compression of electron repulsion integrals for highly localized basis functions, thus facilitating scalable electronic structure calculations.

Contribution

It introduces an adaptive grid-based ISDF approach using a dual-space kernel-splitting method, improving efficiency for localized basis sets in electronic structure simulations.

Findings

Comparable compression efficiency for localized and smooth basis sets

Adaptive grids resolve pair densities with minimal additional points

Enables large-scale simulations of core-level excitations

Abstract

We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle basis functions. To do so, we employ a fast adaptive algorithm, the recently-introduced dual-space multilevel kernel-splitting method, to solve the Poisson equation for the ISDF auxiliary basis functions. The adaptive grids are generated using a high-order accurate, black-box procedure that satisfies a user-specified error tolerance. Our algorithm relies on the observation, which we prove, that an adaptive grid resolving the pair densities appearing in the ERI tensor can be straightforwardly constructed from one that resolves the single-particle basis functions, with the number of required grid points differing only by a constant factor. We find that the ISDF compression efficiency for the ERI tensor with highly localized basis sets is comparable to that for smoother basis sets compatible with uniform grids. To demonstrate the performance of our procedure, we consider several molecular systems with all-electron basis sets which are intractable using uniform grid-based methods. Our work establishes a pathway for scalable many-body electronic structure simulations with arbitrary smooth basis functions, making simulations of phenomena like core-level excitations feasible on a large scale.