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On the convergence of SCF algorithms for the Hartree-Fock equations

Published online by Cambridge University Press:  15 April 2002

Eric Cancès
CERMICS, École Nationale des Ponts et Chaussées, 6 et 8 avenue Pascal, Cité Descartes, 77455 Champs-sur-Marne Cedex 2, France. (
Claude Le Bris
CERMICS, École Nationale des Ponts et Chaussées, 6 et 8 avenue Pascal, Cité Descartes, 77455 Champs-sur-Marne Cedex 2, France. (
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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.

Research Article
© EDP Sciences, SMAI, 2000

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