Abstract
We reexamine the open shell restricted Hartree-Fock theory and develop Fock-like operators that are quite general and easy to implement on a computer. We present a table of ‘vector coupling coefficients’ that define this operator for most of the cases that commonly arise. We compare the form of this operator with that suggested by others, and discuss the orbitals obtained by this procedure with respect to the generalised Brillouin's theorem, and the orbital energies with respect to Koopmans' approximation.
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a Not unique. Such situations should be followed by configuration interaction treatment within the active orbital manifoldbIn theD 2h subgroups of the octahedron, thed(τ) orbitals belong to different irreducible representations. Similarly in theC 2v subgroup of the tetrahedron, thed(τ) orbitals belong to different irreducible representations. Only if the orbitals are subgroup basis do the above expressions hold.N= total number of electrons;M= number of open shell orbitals;Op= number of open shell operators;n μ = occupation number for shellμ = N/M; ↑ represents anα electron; ↓ represents aβ electron; ↕ represents a doubly occupied orbital. The last eight cases representd orbitals in an octahedral field
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Dedicated to Professor J. Koutecký on the occasion of his 65th birthday
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Edwards, W.D., Zerner, M.C. A generalized restricted open-shell Fock operator. Theoret. Chim. Acta 72, 347–361 (1987). https://doi.org/10.1007/BF01192227
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DOI: https://doi.org/10.1007/BF01192227