ON THE ANALYSIS OF THE DISCRETIZED KOHN-SHAM DENSITY FUNCTIONAL THEORY

doi:10.1137/140957962

	ON THE ANALYSIS OF THE DISCRETIZED KOHN-SHAM DENSITY FUNCTIONAL THEORY
	Liu, Xin1 ; Wen, Zaiwen 2; Wang, Xiao 3; Ulbrich, Michael 4; Yuan, Yaxiang1
	2015
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	53 期号:4 页码:1758-1785
摘要	In this paper, we study a few theoretical issues in the discretized Kohn-Sham (KS) density functional theory. The equivalence between either a local or global minimizer of the KS total energy minimization problem and the solution to the KS equation is established under certain assumptions. The nonzero charge densities of a strong local minimizer are shown to be bounded from below by a positive constant uniformly. We analyze the self-consistent field (SCF) iteration by formulating the KS equation as a fixed point map with respect to the potential. The Jacobian of these fixed point maps is derived explicitly. Both global and local convergence of the simple mixing scheme can be established if the gap between the occupied states and unoccupied states is sufficiently large. This assumption can be relaxed in certain cases. Numerical experiments based on the MATLAB toolbox KSSOLV show that it holds on a few simple examples. Although our assumption on the gap is very stringent, our analysis is still valuable for a better understanding of the KS minimization problem, the KS equation, and the SCF iteration.
关键词	Kohn-Sham total energy minimization Kohn-Sham equation self-consistent field iteration nonlinear eigenvalue problem
DOI	10.1137/140957962
语种	英语
资助项目	NSFC[11101409] ; NSFC[11331012] ; NSFC[11322109] ; NSFC[91330202] ; NSFC[11301505] ; National Center for Mathematics and Interdisciplinary Sciences, CAS ; National Basic Research Project[2015CB856000] ; UCAS president grant[Y35101AY00] ; [119103S175]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000360692100006
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20744
专题	计算数学与科学工程计算研究所
通讯作者	Liu, Xin
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing 100864, Peoples R China 2.Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China 4.Tech Univ Munich, Dept Math, Chair Math Optimizat, D-85747 Garching, Germany
推荐引用方式 GB/T 7714	Liu, Xin,Wen, Zaiwen,Wang, Xiao,et al. ON THE ANALYSIS OF THE DISCRETIZED KOHN-SHAM DENSITY FUNCTIONAL THEORY[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2015,53(4):1758-1785.
APA	Liu, Xin,Wen, Zaiwen,Wang, Xiao,Ulbrich, Michael,&Yuan, Yaxiang.(2015).ON THE ANALYSIS OF THE DISCRETIZED KOHN-SHAM DENSITY FUNCTIONAL THEORY.SIAM JOURNAL ON NUMERICAL ANALYSIS,53(4),1758-1785.
MLA	Liu, Xin,et al."ON THE ANALYSIS OF THE DISCRETIZED KOHN-SHAM DENSITY FUNCTIONAL THEORY".SIAM JOURNAL ON NUMERICAL ANALYSIS 53.4(2015):1758-1785.