Structured Eigenvalue Problems in Electronic Structure Methods from a Unified Perspective

作     者：Zhendong Li 李振东

作者机构：Key Laboratory of Theoretical and Computational PhotochemistryMinistry of EducationCollege of ChemistryBeijing Normal UniversityBeijing 100875China 

基　　金：supported by the National Natural Science Foundation of China (No.21973003) the Beijing Normal University Startup Package 

出 版 物：《Chinese Journal of Chemical Physics》 (化学物理学报（英文）)

年 卷 期：2021年第34卷第5期

页      码：525-531,I0002页

摘      要：In(relativistic)electronic structure methods,the quaternion matrix eigenvalue problem and the linear response(Bethe-Salpeter)eigenvalue problem for excitation energies are two frequently encoun-tered structured eigenvalue *** the former problem was thoroughly studied,the later problem in its most general form,namely,the complex case without assuming the positive definiteness of the electronic Hessian,was not fully *** view of their very similar mathematical structures,we examined these two problems from a unified point of *** showed that the identification of Lie group structures for their eigenvectors provides a framework to design diagonalization algorithms as well as numerical optimizations techniques on the corresponding *** using the same reduction algorithm for the quaternion matrix eigenvalue problem,we provided a necessary and sufficient condition to characterize the different scenarios,where the eigenvalues of the original linear response eigenvalue problem are real,purely imaginary,or *** result can be viewed as a natural generalization of the well-known condition for the real matrix case.

主 题 词：Structured eigenvalue problem Electronic structure Bethe-Salpeter equation 

学科分类：07[理学] 070201[070201] 0702[理学-物理学类] 

核心收录：

D　O　I：10.1063/1674-0068/cjcp2107119

馆 藏 号：203105833...