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General properties of the hartree-fock problem demonstrated on the frontier orbital model

II. Analysis of the customary iterative procedure

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Abstract

The commutator relation between the Hartree-Fock matrix and the one-electron density matrix in Fukui's frontier molecular orbital model has been used to investigate the various kinds of ending of the customary iterative SCF procedure. Step by step description of the iterative SCF procedure has been given in an illustrative graphical way. There is a close connection among the symmetry nonadapted RHF solution for symmetrical molecules, the UHF solution for the closed shell molecules, the complex HF solution and the occurrence of oscillation for the iterative procedure. It has been explicitly shown that the nonconvergence of the usual iterative procedure occurs when the Coulombic interaction between not fully coupled spins of the molecular systems with a certain amount of diradical character is sufficiently weak. The results of the analysis concerning the properties of the Hartree-Fock approach are generalized for the asymmetrical molecules.

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On leave of absence from Institute “Rudjer Bošković”, Zagéb, Yugoslavia.

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Bonačić-Koutecký, V., Koutecký, J. General properties of the hartree-fock problem demonstrated on the frontier orbital model. Theoret. Chim. Acta 36, 163–180 (1975). https://doi.org/10.1007/BF00572557

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Key words

  • Hartree-Fock problem
  • Frontier molecular orbital model