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.