Hydrogen molecule Hartree-Fock energy

As a final comment, it is interesting to note that this FS(K) study of the hydrogen molecule offers a new and simple illustration of the behavior of sophisticated Hartree-Fock schemes like UHF, PHF and EHF. Furthermore, it provides a very efficient numerical example of instabilities in the standard Hartree-Fock method. It is important to see that the UHF, PHF and EHF schemes all correct the wrong RHF behavior and lead to the correct dissociation limit. However, the UHF and PHF schemes only correct the wave function for large enough interatomic distances and the effect of projection in the PHF scheme even results in a spurious minimum. The EHF scheme is thus the only one which shows a lowering of the energy with respect to RHF for all interatomic distances. 

Suhai128 investigated water dimer and an infinite chain of hydrogen-bonded water molecules by means of the DFT and post-Hartree-Fock calculations. For the infinite system, the DFT(BLYP), MP2, and MP4 binding energies were within 0.2 kcal/mol, whereas the corresponding interatomic distances were within 0.04 A. A similar agreement was reported for water dimer. 

Fig. 3.6 Binding energy curves for the hydrogen molecule (lower panel). HF and HL are the Hartree-Fock and Heitler-London predictions, whereas LDA and LSDA are those for local density and local spin density approximations respectively. The upper panel gives the local magnetic moment within the LSDA self-consistent calculations. (After Gunnarsson and Lundquist (1976).)...

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