Dear Gyorgy,

I think that the energy for radicals, radical anions and radical cations should be calculated by both RHF and UHF methods. Comparisons of the calculated values by the two methods with experimental values should be made in order to draw lines on the systems to be better predicted by RHF and those to be better predicted by UHF. 

UHF  method has one drawback. A single Slater determinant of different orbitals for different spins is not a satisfactory eigenfunction of the total spin operator - S2. The ground state is contaminated by excited states. Despite this drawback, the unrestricted Hartree–Fock method is used frequently, and in preference to the restricted open-shell Hartree–Fock (ROHF) method, because UHF is simpler to code, easier to develop post-Hartree–Fock methods with, and returns unique functions unlike ROHF where different Fock operators can give the same final wave function.

In contrast to UHF, the ROHF wave function is a satisfactory eigenfunction of the total spin operator - S2 (no Spin contamination).

Developing post-Hartree–Fock methods based on a ROHF wave function is inherently more difficult than using a UHF wave function, due to the lack of a unique set of molecular orbitals. However, different choices of reference orbitals have shown to provide similar results, and thus many different post-Hartree–Fock methods have been implemented in a variety of electronic structure packages. 

Hoping this will contribute to the discussion on this topic,

Rafik

Dear Rafik, thank you very much for the informative answer