GRADIENT FLOW BASED KOHN-SHAM DENSITY FUNCTIONAL THEORY MODEL

doi:10.1137/19M1276170

	GRADIENT FLOW BASED KOHN-SHAM DENSITY FUNCTIONAL THEORY MODEL
	Dai, Xiaoying 1,2; Wang, Qiao 3; Zhou, Aihui 1,2
刊名	MULTISCALE MODELING & SIMULATION
	2020
卷号	18 期号:4 页码:1621-1663
关键词	density functional theory dynamical system gradient flow orthogonality preserving eigenvalue problem energy minimization
ISSN号	1540-3459
DOI	10.1137/19M1276170
英文摘要	In this paper, we propose and analyze a gradient flow based model for electronic structure calculations. First, based on an extended gradient flow proposed in this paper, we propose a Kohn-Sham gradient flow based model. We prove that our gradient flow based model is orthogonality preserving, the extended gradient has an exponential decay over time t, and the equilibrium point is a local minimizer of the Kohn-Sham energy functional. Then we propose a midpoint scheme to carry out the temporal discretization, which is proven to be orthogonality preserving, too. Based on the midpoint scheme, we design a practical orthogonality preserving iteration scheme which can deal with the propagation of the gradient flow based model and prove that the scheme produces approximations that converge to a local minimizer with some convergence rate under some reasonable assumptions. Finally, we report a number of numerical experiments that validate our theoretical results.
资助项目	National Key Research and Development Program of China[2019YFA0709601] ; National Natural Science Foundation of China[91730302] ; National Natural Science Foundation of China[11671389] ; Key Research Program of Frontier Sciences of the Chinese Academy of Sciences[QYZDJ-SSW-SYS010]
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000600667900009
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/57907]
专题	中国科学院数学与系统科学研究院
通讯作者	Dai, Xiaoying
作者单位	1.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Beijing Univ Civil Engn & Architecture, Sch Sci, Beijing 102616, Peoples R China
推荐引用方式 GB/T 7714	Dai, Xiaoying,Wang, Qiao,Zhou, Aihui. GRADIENT FLOW BASED KOHN-SHAM DENSITY FUNCTIONAL THEORY MODEL[J]. MULTISCALE MODELING & SIMULATION,2020,18(4):1621-1663.
APA	Dai, Xiaoying,Wang, Qiao,&Zhou, Aihui.(2020).GRADIENT FLOW BASED KOHN-SHAM DENSITY FUNCTIONAL THEORY MODEL.MULTISCALE MODELING & SIMULATION,18(4),1621-1663.
MLA	Dai, Xiaoying,et al."GRADIENT FLOW BASED KOHN-SHAM DENSITY FUNCTIONAL THEORY MODEL".MULTISCALE MODELING & SIMULATION 18.4(2020):1621-1663.