Functional analysis concepts and Fartree-Fock instability conditions |
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Authors: | G. Magela e Silva L. A. C. Malbouisson A. Naves de Brito J. D. M. Vianna |
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Affiliation: | (1) Departamento de Fisica, Instituto de Ciencias Exatas, Universidade de Brasilia, 70910 Brasilia, DF Brazil;(2) Instituto de Fisica, Universidade Federal da Bahia, Campus de Ondina, 40210 Salvador, BA Brazil |
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Abstract: | Concepts of functional analysis, namely, regular points, tangent subspaces, constraint surfaces, Lagrangian matrix restricted to the tangent subspace of a constraint surface, are presented in connection with the Hartree-Fock (HF) problem. The energy functional in LCAO approximation is considered to be a polynomial function of several variables subject to subsidiary conditions. General HF equations and instability conditions for the unrestricted Hartree-Fock (UHF) solutions are derived from this standpoint. |
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