报告题目

Off-Diagonal Low Rank (ODLR): a secret key to new low-scaling computational chemistry methods

报告人

王子宽 研究员

报告人单位

山东大学光学高等研究中心

报告时间

2025年11月12日（星期三）10:00

报告地点

东区物质科研楼B楼B604会议室

主办单位

精准智能化学全国重点实验室

报告摘要

Quantum chemistry calculations can often be sped up by exploiting the sparsity and/or low numerical rank of certain matrices or tensors, such as density matrices, Fock matrices and electron repulsion integral (ERI) tensors, which underlies many popular low-scaling methods, such as linear scaling self-consistent field (SCF) and resolution of the identity (RI) methods. However, many chemically relevant matrices are both dense and high-rank, as exemplified by the density matrices, localized molecular orbital (LMO) coefficient matrices, Fock matrices and nuclear Hessian matrices of systems with vanishing HOMO-LUMO gaps and zero electronic temperature.

In this talk, I’ll show that the off-diagonal blocks of such matrices have low rank, despite that the blocks are dense, and despite that the whole matrix has high rank. The physical origin of this phenomenon is that these matrices can be expressed as a local-in-space but nonlocal-in-energy component, plus a nonlocal-in-space but local-in-energy component; the former is clustered near the diagonal of the matrix, while the latter has low rank. I then discuss possible ways to exploit this off-diagonal low rank (ODLR) property to accelerate calculations, exemplified by the estimation of the nuclear Hessian of a molecule using only O(1) gradients, instead of O(Natom) gradients as conventional seminumerical Hessian algorithms would require. The talk is concluded by a proposal of linear scaling SCF algorithms of gapless systems at zero electronic temperature, which have up to now been elusive due to the breakdown of Kohn’s conjecture.

报告人简介

王子宽，2018年于北京大学获博士学位，随后先后于北京大学、山东大学、马克斯-普朗克煤炭研究所从事博后/访问学者研究，现为山东大学光学高等研究中心研究员。主要研究兴趣为面向大体系光化学反应的电子结构方法开发与应用。迄今发表SCI论文45篇，其中在Acc. Chem. Res., Nat. Commun., J. Am. Chem. Soc., J. Chem. Theory Comput., J. Chem. Phys.等期刊上发表一作/共同一作/通讯作者文章17篇，为国际知名量化软件ORCA、BDF贡献代码数万行。