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SCF algorithms for HF electronic calculations. (English) Zbl 0992.81103
Defranceschi, M. (ed.) et al., Mathematical models and methods for ab initio quantum chemistry. Berlin: Springer. Lect. Notes Chem. 74, 17-43 (2000).
Summary: 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. Basic numerical simulations pointing out the principal features of the various algorithms under study are also provided.
For the entire collection see [Zbl 0979.00023].

MSC:
81V55 Molecular physics
81-08 Computational methods for problems pertaining to quantum theory
81-04 Software, source code, etc. for problems pertaining to quantum theory
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