I've tried UHF method with N2 and, using Multiwfn, it gave identical results to those of RHF method. So I assumed there was no problem with UHF per se. I tried UHF method again with O2 but with multiplicity = 1 rather than 3, and it gave identical results to those of RHF method (with multiplicity = 1, of course).

I concluded that it was all about multiplicity not about the nature of the Hartree-Fock method. So I think the results mentioned in the original post, indeed, seem to be correct and that the O2 case is different than N2 and F2 due to its different multiplicity.

I have checked O2-UHF.wfn, the result seems to be correct. ESP is indeed positive everywhere on the vdW surface. This is never necessarily wrong.

Well. At least this means there is nothing wrong with my input file.

I'am working on a series of diatomic molecules. N2 and F2 molecules exhibit areas with positive and negative values. Additionally, O2 with RHF-based wavefunction is consistent with that trend.  I cannot think of an intuitive reason that makes oxygen different.

N2.wfn

F2.wfn

Yes it can, due to the concentration of all the positive charge in one point while the counterpart negative charge is distributed over a relatively large space.  But my intuition, along with some calculations of course, tells me that for diatomic molecules, whether homonuclear or heteronuclear, we should obtain both positive and negative areas on VdW surface. I will reinvestigate the O2 case anyway.

Thanks and regards,

When I perform a molecular surface analysis of oxygen (O2), using GAMESS-US .wfn file (extracted from the .dat file) as input, the obtained results depend on whether the Hartree-Fock wavefunction is restricted or unrestricted.

The problem is that with the unrestricted wavefunction the results are not chemically sound. For example, all the molecular surface has a positive ESP:

,,
Minimal value:      0.10957 kcal/mol   Maximal value:      3.56581 kcal/mol
Overall surface area:         179.61505 Bohr^2  (  50.29734 Angstrom^2)
Positive surface area:        179.61505 Bohr^2  (  50.29734 Angstrom^2)
Negative surface area:          0.00000 Bohr^2  (   0.00000 Angstrom^2)
,,

The restricted HF method gives sound results in Multiwfn analysis, but it, simply, is not the best practice. Should I use the restricted HF instead of UHF in Multiwfn analysis?

O2-UHF.wfn

O2-RHF.wfn