Abstract
This paper presents some mathematical results on SCF algorithms for solving the Hartree-Fock problem. In the first part of the article the focus is on two classical SCF procedures, namely the Roothaan algorithm and the level-shifting algorithm. It is demonstrated that the Roothaan algorithm either converges towards a solution to the Hartree-Fock equations or oscillates between two states which are not solution to the Hartree-Fock equations, any other behavior (oscillations between more than two states, “chaotic” behavior, ... ) being excluded. The level-shifting algorithm is then proved to converge for large enough shift parameter, whatever the initial guess. The second part of the article details the convergence properties of a new algorithm recently introduced by Le Bris and the author, the so-called Optimal Damping Algorithm (ODA). Basic numerical simulations pointing out the principal features of the various algorithms under study are also provided.
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© 2000 Springer-Verlag Berlin Heidelberg
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Cancès, E. (2000). SCF algorithms for HF electronic calculations. In: Mathematical Models and Methods for Ab Initio Quantum Chemistry. Lecture Notes in Chemistry, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57237-1_2
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DOI: https://doi.org/10.1007/978-3-642-57237-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67631-7
Online ISBN: 978-3-642-57237-1
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