Hefei National Research Center for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui230026, China.
J Chem Theory Comput. 2023 Feb 14;19(3):679-693. doi: 10.1021/acs.jctc.2c00927. Epub 2023 Jan 24.
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.
低秩逼近长期以来一直被认为是加速与电子排斥积分 (ERI) 评估相关的电子结构计算的有效方法。作为一种用于压缩 ERI 张量的精确高效算法，最近内插可分离密度拟合 (ISDF) 分解在这方面引起了极大的关注。在这个视角中，我们从理论方面和技术细节方面介绍 ISDF 分解。ISDF 分解可以在实空间中以立方成本构建 ERI 的完全可分离低秩逼近（张量超收缩因子分解），为加速大规模电子结构计算提供了极大的灵活性。我们回顾了 ISDF 在杂化泛函、含时密度泛函理论和 GW 近似中的典型应用。最后，我们讨论了 ISDF 未来发展的有前途的方向。
