The bonded hydrogen molecule

For bond distances shorter than 2.30flo. the optimized RHF and UHF wave functions are identical and there is no conflict between the spin-symmehy requirements and energy minimization. In addition, the Hartree-Fock wave function dominates the exact wave function, contributing a weight of 0.98 to the FCI wave function at the equilibrium geometry see Table 5.4. 

The Hartree-Fock equilibrium bond distance of the hydrogen molecule is 1.387oo. just. % shorter than the FCI value of 1.402ao- In Section 15.3, we shall see that this excellent behaviour with respect to bond distances is often observed for the Hartree-Fock approximation and that Hartree-Fock bond lengths are typically 2-3 pm too short. 

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