ISDF

ISDF stands for interpolative separable density fitting, a numerical technique used in quantum chemistry to approximate electron repulsion integrals (ERIs). The method seeks a low-rank, separable representation of the four-index ERI tensor by introducing a small set of interpolation points and associated interpolation vectors. In practice, products of basis functions are approximated using information evaluated at these points, allowing the ERIs to be expressed as a sum over a modest number of auxiliary terms. This reduces both memory requirements and computational cost compared with conventional density fitting schemes, enabling more efficient HF, DFT, and post-HF calculations for larger systems or higher-accuracy treatments.

ISDF yields near-linear scaling with system size under common implementations and complements other acceleration techniques such as resolution-of-the-identity (RI) and tensor hypercontraction. Limitations include the nontrivial selection of interpolation points, potential loss of accuracy if the point set is insufficient, and added algorithmic complexity in some software pipelines. ISDF variants include randomized sampling procedures to choose interpolation points and adaptive schemes that adjust the auxiliary set in response to target accuracy.

See also: density fitting, RI, tensor hypercontraction.