Interpolative Separable Density Fitting for Accelerating Two-Electron Integrals: A Theoretical Perspective

Abstract

Low-rank approximations have long been considered an efficient way to accelerate electronic structure calculations associated with the evaluation of electron repulsion integrals (ERIs). As an accurate and efficient algorithm for compressing the ERI tensor, the interpolative separable density fitting (ISDF) decomposition has recently attracted great attention in this context. In this perspective, we introduce the ISDF decomposition from the theoretical aspects and technique details. The ISDF decomposition can construct a fully separable low-rank approximation (tensor hypercontraction factorization) of ERIs in real space with a cubic cost, offering great flexibility for accelerating high-scaling electronic structure calculations. We review the typical applications of ISDF in hybrid functionals, time-dependent density functional theory, and GW approximation. Finally, we discuss the promising directions for future development of ISDF.

Excited State Properties of Point Defects in Semiconductors and Insulators Investigated with Time-Dependent Density Functional Theory

“…We are exploring the possibility of extending our TDDFT calculations by incorporating additional hybrid functionals, possibly leading to an improvement in the description of screening effects in solids, especially in low-dimensional hosts such as two-dimensional hexagonal boron nitride (2D-hBN) . Work is in progress to further accelerate TDDFT calculations through the use of density fitting techniques, , which could enable the direct study of multiple point defects and their interactions in the same supercell. Other interesting future efforts include the implementation of spin-flip TDDFT with the multicollinear formalism to reduce numerical instabilities , and coupling TDDFT with analytical nuclear forces and molecular dynamics.…”

Machine Learning K-Means Clustering in Interpolative Separable Density Fitting Algorithm: Advancing Accurate and Efficient Cubic-Scaling Density Functional Perturbation Theory Calculations within Plane Waves

“…Interpolation Separable Density Fitting. The ISDF 10,11 algorithm is a grid-based low-rank approximation of electron repulsion integrals with an overall complexity of O(N e 3 ), 12 which efficiently compresses the redundant information in the transpose of the Khatri−Rao product of Kohn−Sham orbitals M r r ( ) ( )…”

“…Different from the aforementioned applications of the ISDF 12 algorithm, within the context of the DFPT calculations, the target objects of the ISDF algorithm are no longer pairs of the same type of Kohn−Sham orbitals. In case of plane-wave DFPT calculations, ψ i and g j represent the Kohn−Sham electron orbital and the gradient of the external potential with respect to atomic displacement, respectively, and their physical behavior is entirely distinct from the conventional case of ISDF in other electronic structure calculations.…”

“…As a result, the problem becomes a weighted K-means clustering problem, and the algorithm gives the specific process of the K-means clustering algorithm to calculate the interpolation points in the ISDF 12 decomposition. Here, w(r k ) is the weight function.…”

Even Faster Exact Exchange for Solids via Tensor Hypercontraction

“…The adaptively compressed exchange (ACE) algorithm, similar to the occ-RI-K algorithm developed for molecular systems, has become the most common way to speed up exact exchange evaluation in plane wave-based periodic quantum chemistry codes . More recently, the interpolative separable density fitting (ISDF) − approach to THC has been shown to offer considerable speedup for both Γ-point and k -point plane wave calculations. − …”