2000 | OriginalPaper | Buchkapitel
SCF algorithms for HF electronic calculations
verfasst von : Eric Cancès
Erschienen in: Mathematical Models and Methods for Ab Initio Quantum Chemistry
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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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.