On the convergence of the self-consistent field iteration in Kohn-Sham density functional theory

SIAM Journal on Matrix Analysis and Applications

Volumn 35, Issue 2, 2014, Pages 546-558

  Liu, Xin ^a   Wang, Xiao ^b   Wen, Zaiwen ^c   Yuan, Yaxiang ^a  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

^c PEKING UNIVERSITY   (China)

Author keywords

Global convergence; Kohn Sham equation; Kohn Sham total energy functional; Local convergence rate; Nonlinear eigenvalue problem; Self consistent field iteration

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS;

GLOBAL CONVER-GENCE; KOHN SHAM EQUATIONS; LOCAL CONVERGENCE; NONLINEAR EIGENVALUE PROBLEM; SELF-CONSISTENT FIELD; TOTAL ENERGY FUNCTIONAL;

HAMILTONIANS;

EID: 84904008585     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/130911032     Document Type: Article

References (23)

1. C. L. Bris, Computational chemistry from the perspective of numerical analysis, Acta Numer., 14 (2005), pp. 363-444.
2. E. Cancès, SCF algorithms for Hartree-Fock electronic calculations, Lecture Notes in Chem., 74 (2000), pp. 17-43.
3. E. Cancès, Self-consistent field algorithms for Kohn-Sham models with fractional occupation numbers, J. Chem. Phys., 114 (2001), pp. 10616-10622. (Pubitemid 32611155)
4. E. Cancès and C. L. Bris, Can we outperform the DIIS approach for electronic structure calculations?, Internat. J. Quantum Chem., 79 (2000), pp. 82-90.
5. E. Cancès and C. L. Bris, On the convergence of SCF algorithms for the Hartree-Fock equations, Math. Model. Numer. Anal., 34 (2000), pp. 749-774.
6. E. Cancès, M. Defranceschi, W. Kutzelnigg, C. L. Bris, and Y. Maday, Computational quantum chemistry: A primer, in Handbook of Numerical Analysis, Volume X: Special Volume: Computational Chemistry, North-Holland, 2003, pp. 3-270.
7. E. Cancès and K. Pernal, Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations, J. Chem. Phys., 128 (2008), pp. 108-134.
8. A. Edelman, T. Arias, and S. Smith, The geometry of algorithms with orthogonality constraints, SIAM J. Matrix Anal. Appl., 20 (1998), pp. 303-353. (Pubitemid 129333771)
9. W. Gao, C. Yang, and J. Meza, Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method, Technical report, Lawrence Berkeley National Laboratory, 2009.
10. G. Golub and C. V. Loan, Matrix Computaion, The Johns Hopkins University Press, Baltimore, MD, 1996.
11. G. P. Kerker, Efficient iteration scheme for self-consistent pseudopotential calculations, Phys. Rev. B, 23 (1981), pp. 3082-3084.
12. J. Koutecký and V. Bonacic, On the convergence difficulties in the iterative Hartree-Fock procedure, J. Chem. Phys., 55 (1971), pp. 2408-2413.
13. G. Kresse and J. Furthmuller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Materials Sci., 6 (1996), pp. 15- 50. (Pubitemid 126412269)
14. K. N. Kudin, G. E. Scuseria, and E. Cancès, A black-box self-consistent field convergence algorithm: One step closer, J. Chem. Phys., 116 (2002), pp. 8255-8261. (Pubitemid 34599822)
15. A. Levitt, Convergence of gradient-based algorithms for the Hartree-Fock equations, ESAIM: Math. Model. Numer. Anal., 46 (2012), pp. 1321-1336.
16. R. M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, Cambridge, 2004.
17. R. Schneider, T. Rohwedder, A. Neelov, Johannes, and Blauert, Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure, J. Comput. Math., 27 (2009), pp. 360-393.
18. G. W. Stewart, Error bounds for approximation invariant subspace of closed linear operators, SIAM Rev., 15 (1973), pp. 27-64.
19. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: An Introduction to Advanced Electronic Structure Theory, Dover, New York, 1996.
20. Z. Wen, A. Milzarek, M. Ulbrich, and H. Zhang, Adaptive regularized self-consistent field iteration with exact Hessian for electronic structure calculation, SIAM J. Sci. Comput., 35 (2013), pp. A1299-A1324.
21. C. Yang, W. Gao, and J. Meza, On the convergence of the self-consistent field iteration for a class of nonlinear eigenvalue problems, SIAM J. Matrix Anal. Appl., 30 (2009), pp. 1773-1788.
22. C. Yang, J. C. Meza, B. Lee, and L.-W. Wang, KSSOLV - A MATLAB toolbox for solving the Kohn-Sham equations, ACM Trans. Math. Software, 36 (2009), pp. 1-35.
23. C. Yang, J. C. Meza, and L. Wang, A trust region direct constrained minimization algorithm for the Kohn-Sham equation, SIAM J. Sci. Comput., 29 (2007), pp. 1854-1875.