  Unrestricted DFT methods are typically expected to describe the homolytic
dissociation of nonpolar single bonds in neutral species with qualitative
accuracy, due to the lack of significant delocalization error. We however find
that many widely used density functional approximations fail to describe
features along the dissociation curve of the simple H$_2$ molecule. This is not
an universal failure of DFT in the sense that many classic functionals like PBE
and B3LYP give very reasonable results, as do some more modern methods like
MS2. However, some other widely used functionals like B97-D (empirically
fitted) and TPSS (non-empirically constrained) predict qualitatively wrong
static polarizabilities, force constants and some even introduce an artificial
barrier against association of independent H atoms to form H$_2$. The
polarizability and force constant prediction failures appear to stem from
incomplete spin localization into individual H atoms beyond the Coulson-Fisher
point, resulting in `fractionally bonded' species where the ionic contributions
to the Slater determinant are not completely eliminated, unlike the case of
unrestricted Hartree-Fock. These errors therefore appear to be a consequence of
poor self-consistent density prediction by the problematic functional. The same
reasons could potentially lead to spurious barriers towards H atom association,
indirectly also leading to incorrect forces. These unphysicalities suggest that
the use of problematic functionals is probably unwise in \textit{ab initio}
dynamics calculations, especially if strong electrostatic interactions are
possible.
