SCF algorithms for HF electronic calculations

  • Eric Cancès
Part of the Lecture Notes in Chemistry book series (LNC, volume 74)


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.


Initial Guess Shift Parameter Simple Chemical System Unfilled Shell Direct Energy Minimization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Eric Cancès
    • 1
  1. 1.CERMICSEcole Nationale des Ponts et ChausséesMarne-La-Vallée CedexFrance

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