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On the convergence of SCF algorithmsfor the Hartree-Fock equations

Published online by Cambridge University Press:  15 April 2002

Eric Cancès and
Claude Le Bris
Eric Cancès
Affiliation:
CERMICS, École Nationale des Ponts et Chaussées, 6 et 8 avenue Pascal, Cité Descartes, 77455 Champs-sur-Marne Cedex 2, France. (cances@cermics.enpc.fr)
Claude Le Bris
Affiliation:
CERMICS, École Nationale des Ponts et Chaussées, 6 et 8 avenue Pascal, Cité Descartes, 77455 Champs-sur-Marne Cedex 2, France. (lebris@cermics.enpc.fr)
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Abstract

The present work is a mathematical analysis of two algorithms, namelythe Roothaan and the level-shifting algorithms, commonly used inpractice to solve the Hartree-Fock equations. The level-shiftingalgorithm is proved to be well-posed and to converge provided the shiftparameter is large enough. On the contrary, cases when the Roothaanalgorithm is not well defined or fails in converging areexhibited. These mathematical results are confronted to numericalexperiments performed by chemists.

Keywords

Nonlinear eigenvalue problemHartree-Fock equationsself-consistent fieldconvergence analysis.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 4 , July 2000, pp. 749 - 774
Copyright
© EDP Sciences, SMAI, 2000

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