ON THE ANALYSIS OF THE DISCRETIZED KOHN-SHAM DENSITY FUNCTIONAL THEORY
文献类型：期刊论文
| 作者 | Liu, Xin1 ; Wen, Zaiwen2; Wang, Xiao3; Ulbrich, Michael4; Yuan, Yaxiang1
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| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2015 |
| 卷号 | 53期号:4页码:1758-1785 |
| 关键词 | Kohn-Sham total energy minimization Kohn-Sham equation self-consistent field iteration nonlinear eigenvalue problem |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/140957962 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000360692100006 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/20743]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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