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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| Institution: | (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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