强关联多电子体系的优化模型与算法  

OPTIMIZATION MODELS AND APPROACHES FOR STRONGLY CORRELATED ELECTRONS SYSTEMS

作　　者：刘歆 Liu Xin(LSEC,ICMSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院数学与系统科学研究院,计算数学与科学工程计算研究所,科学与工程计算国家重点实验室,北京100190 [2]中国科学院大学,北京100049

出　　处：《计算数学》2023年第2期141-159,共19页Mathematica Numerica Sinica

基　　金：国家重点研发计划(2020YFA0711900,2020YFA0711904);国家杰出青年基金(12125108);国家自然科学基金(11971466,11991021,11991020,12021001,12288201)资助。

摘　　要：在电子结构计算领域,Kohn-Sham方程是最为广泛使用的数学模型之一.然而,由于现有的交换关联能近似仍存在缺陷,Kohn-Sham方程无法较好地描述强关联多电子体系.近年来,有学者从密度泛函理论的强相关极限出发,提出了严格关联电子能量的优化模型.该模型有望弥补Kohn-Sham方程的缺陷,从而拓宽密度泛函理论的应用面.由于在该模型中存在维数灾难,近年来,它的一些低维转化模型陆续被提出.在本文中,我们将介绍严格关联电子能量的优化模型、它的研究重点以及现有的一些低维转化模型.我们也将介绍这些转化模型的数值求解方法,并探讨未来的研究方向.In electronic structure calculations,Kohn-Sham equations rank among the most widely adopted mathematical models.However,due to the deficiency of available approximations for exchange-correlation energy,Kohn-Sham equations cannot well describe strongly correlated electrons systems at present.In recent decades,some researchers have studied the optimization models of strictly-correlated-electrons energy,starting from the strong-interaction limit of density functional theory.These models are hopeful to amend the very deficiency of Kohn-Sham equations and therefore broaden the applicability of the density functional theory.Since the curse of dimensionality resides in these models,some low-dimensional reformulations have been proposed.In this paper,we introduce the optimization models of strictly-correlated-electrons energy,highlight the research focus,and describe some lowdimensional reformulations.We also present the numerical approaches for these reformulations and shed light on the directions of future research.

关 键 词：强关联多电子体系 电子结构计算 维数灾难 低维转化 可扩展性 

分 类 号：O411[理学—理论物理]