Volume 34, Number 4, July/August 2000
|Page(s)||749 - 774|
|Published online||15 April 2002|
On the convergence of SCF algorithms for the Hartree-Fock equations
CERMICS, École Nationale des Ponts et Chaussées,
6 et 8 avenue Pascal, Cité Descartes, 77455 Champs-sur-Marne
Cedex 2, France. (email@example.com)
2 CERMICS, École Nationale des Ponts et Chaussées, 6 et 8 avenue Pascal, Cité Descartes, 77455 Champs-sur-Marne Cedex 2, France. (firstname.lastname@example.org)
Revised: 3 March 2000
The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists.
Mathematics Subject Classification: 35P30 / 65C20 / 65K10 / 81-08 / 81Q05 / 81Q10
Key words: Nonlinear eigenvalue problem / Hartree-Fock equations / self-consistent field / convergence analysis.
© EDP Sciences, SMAI, 2000
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