Unrestricted Hartree-Fock theorems,

Unfortunately, differences in the spatial orbitals for different spins may be impractical if Cl calculations are performed afterward to improve the Hartree-Fock calculation. Therefore, the variation is restricted, to keep the same spatial function for spin up and spin down. This method is called restricted Hartree-Fock (RHF). The original method with unlimited variation of the orbital functions is called unrestricted Hartree-Fock (UHF). Only the latter satisfies the BriUouin theorem. 

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