Cancès, Eric; Le Bris, Claude
On the convergence of SCF algorithms for the Hartree-Fock equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) no. 4 , p. 749-774
Zbl 1090.65548 | MR 1784484 | 4 citations dans Numdam
URL stable : http://www.numdam.org/item?id=M2AN_2000__34_4_749_0

Bibliographie

[1] G. Auchmuty and Wenyao Jia, Convergent iterative methods for the Hartree eigenproblem. RAIRO Modél. Math. Anal. Numér. 28 (1994) 575-610. Numdam | MR 1295588 | Zbl 0821.65047

[2] V. Bach, E.H. Lieb, M. Loss and J.P. Solovej, There are no unfilled shells in unrestricted Hartree-Fock theory. Phys. Rev. Lett. 72 (1994) 2981-2983.

[3] V. Bonačić-Koutecký and J. Koutecký, General properties of the Hartree-Fock problem demonstrated on the frontier orbital model. II. Analysis of the customary iterative procedure. Theoret. Chim. Acta 36 (1975) 163-180.

[4] J.C. Facelli and R.H. Contreras, A general relation between the intrinsic convergence properties of SCF Hartree-Fock calculations and the stability conditions of their solutions. J. Chem. Phys. 79 (1983) 3421-3423.

[5] R. Fletcher, Optimization of SCF LCAO wave functions. Mol. Phys. 19 (1970) 55-63.

[6] D.R. Hartree, The calculation of atomic structures. Wiley (1957). MR 90408 | Zbl 0079.21401

[7] W.J. Hehre, L. Radom, P.V.R. Schleyer and J.A. Pople, Ab initio molecular orbital theory. Wiley (1986).

[8] A. Igawa and H. Fukutome, A new direct minimization algorithm for Hartree-Fock calculations. Progr. Theoret. Phys. 54 (1975) 1266-1281.

[9] J. Koutecký and V. Bonačić, On convergence difficulties in the iterative Hartree-Fock procedure. J. Chem. Phys. 55 (1971) 2408-2413.

[10] E.H. Lieb, Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation. Stud. Appl. Math. 57 (1977) 93-105. MR 471785 | Zbl 0369.35022

[11] E.H. Lieb, Bound on the maximum negative ionization of atoms and molecules. Phys. Rev. A 29 (1984) 3018-3028.

[12] E.H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb Systems. Comm. Math. Phys. 53 (1977) 185-194. MR 452286

[13] P.L. Lions, Solutions of Hartree-Fock equations for Coulomb systems. Comm. Math. Phys. 109 (1987) 33-97. MR 879032 | Zbl 0618.35111

[14] R. Mcweeny, The density matrix in self-consistent field theory. I. Iterative construction of the density matrix. Proc. Roy. Soc. London Ser. A 235 (1956) 496-509. MR 81755 | Zbl 0071.42302

[15] R. Mcweeny, Methods of molecular Quantum Mechanics. Academic Press (1992).

[16] J. Paldus, Hartree-Fock stability and symmetry breaking, in Self Consistent Field Theory and Application. Elsevier (1990) 1-45.

[17] P. Pulay, Improved SCF convergence acceleration. J. Comput. Chem. 3 (1982) 556-560.

[18] M. Reed and B. Simon, Methods of modern mathematical physics. I. Functional analysis. Academic Press (1980). MR 751959 | Zbl 0459.46001

[19] M. Reed and B. Simon, Methods of modern mathematical physics. IV. Analysis of operators. Academic Press (1978). MR 493421 | Zbl 0401.47001

[20] C.C.J. Roothaan, New developments in molecular orbital theory. Rev. Modern Phys. 23 (1951) 69-89. Zbl 0045.28502

[21] V.R. Saunders and I.H. Hillier, A "level-shifting" method for converging closed shell Hartree-Fock wave functions. Int. J. Quantum Chem. 7 (1973) 699-705.

[22] H.B. Schlegel and J.J.W. Mcdouall, Do you have SCF stability and convergence problems?, in Computational Advances in Organic Chemistry, Kluwer Academic (1991) 167-185.

[23] R. Seeger R. and J.A. Pople, Self-consistent molecular orbital methods. XVI. Numerically stable direct energy minimization procedures for solution of Hartree-Fock equations. J. Chem. Phys. 65 (1976) 265-271.

[24] R.E. Stanton, The existence and cure of intrinsic divergence in closed shell SCF calculations. J. Chem. Phys. 75 (1981) 3426-3432.

[25] R.E. Stanton, Intrinsic convergence in closed-shell SCF calculations. A general criterion. J. Chem. Phys. 75 (1981) 5416-5422.

[26] M.C. Zerner and M. Hehenberger, A dynamical damping scheme for converging molecular SCF calculations. Chem. Phys. Lett. 62 (1979) 550-554.