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Spin‐Projected EHF equations
Author(s) -
Pavlides P.,
Sales K. D.
Publication year - 1987
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560320609
Subject(s) - orthogonality , brillouin zone , open shell , linear combination of atomic orbitals , infinitesimal , euler equations , diagonal , atomic orbital , mathematical physics , mathematics , mathematical analysis , quantum mechanics , physics , geometry , electron
Extended Hartree‐Fock ( EHF ) equations are developed for the general open‐shell case using a modified pair‐orthogonality‐constrained variation ( POCV ) method. The EHF energy is expressed in terms of corresponding orbitals that are required to remain orthogonal and paired for all arbitrary infinitesimal variations. The Euler equations for each set of orbitals are reduced to unique pseudosecular equations, the LCAO form of which may easily be derived. The Euler equations and the expressions obtained for the off‐diagonal elements of the ϵ γδ (γ, δ = a or b ) matrices for the closed‐shell case are identical to those obtained by Mayer, who used the generalized Brillouin theorem method. However, the present method yields equations for both closed‐ and open‐shell cases and for any spin state.