A CONJUGATE GRADIENT METHOD FOR ELECTRONIC STRUCTURE CALCULATIONS

被引：13

作者：

Dai, Xiaoying ^{[1
,2
]}

Liu, Zhuang ^{[1
,2
]}

Zhang, Liwei ^{[1
,2
]}

Zhou, Aihui ^{[1
,2
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2017年 / 39卷 / 06期

基金：

美国国家科学基金会;

关键词：

conjugate gradient method; density functional theory; electronic structure; optimization; DENSITY-FUNCTIONAL THEORY; CONSISTENT-FIELD ITERATION; ORTHOGONALITY CONSTRAINTS; OPTIMIZATION; MINIMIZATION; CONVERGENCE; GEOMETRY; EQUATION; SYSTEMS;

D O I：

10.1137/16M1072929

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a conjugate gradient method for electronic structure calculations. We propose a Hessian based step size strategy, which together with three orthogonality approaches yields three algorithms for computing the ground state energy of atomic and molecular systems. Under some mild assumptions, we prove that our algorithms converge locally. It is shown by our numerical experiments that the conjugate gradient method is efficient.

引用

页码：A2702 / A2740

页数：39

共 42 条

[11]

Fletcher R, 2005, APPL OPTIM, V96, P235

[12] Positivity of the spherically averaged atomic one-electron density [J].

Fournais, S. ;

Hoffmann-Ostenhof, M. ;

Hoffmann-Ostenhof, T. ;

Sorensen, T. Ostergaard .

MATHEMATISCHE ZEITSCHRIFT, 2008, 259 (01) :123-130

[13] Globally convergent trust-region methods for self-consistent field electronic structure calculations [J].

Francisco, JB ;

Martínez, JM ;

Martínez, L .

JOURNAL OF CHEMICAL PHYSICS, 2004, 121 (22) :10863-10878

[14]

Gao B., 2016, NEW 1 ORDER FRAMEWOR

[15]

Hager W. W., 2006, SURVEY NONLINEAR CON

[16] INHOMOGENEOUS ELECTRON-GAS [J].

RAJAGOPAL, AK ;

CALLAWAY, J .

PHYSICAL REVIEW B, 1973, 7 (05) :1912-1919

[17] A framework of constraint preserving update schemes for optimization on Stiefel manifold [J].

Jiang, Bo ;

Dai, Yu-Hong .

MATHEMATICAL PROGRAMMING, 2015, 153 (02) :535-575

[18]

Kohn W., 1965, PHYS REV A, V140, P4743

[19] ON THE ANALYSIS OF THE DISCRETIZED KOHN-SHAM DENSITY FUNCTIONAL THEORY [J].

Liu, Xin ;

Wen, Zaiwen ;

Wang, Xiao ;

Ulbrich, Michael ;

Yuan, Yaxiang .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (04) :1758-1785

[20] ON THE CONVERGENCE OF THE SELF-CONSISTENT FIELD ITERATION IN KOHN-SHAM DENSITY FUNCTIONAL THEORY [J].

Liu, Xin ;

Wang, Xiao ;

Wen, Zaiwen ;

Yuan, Yaxiang .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2014, 35 (02) :546-558

← 1 2 3 4 5 →