  Many approximations within density-functional theory spuriously predict that
a many-electron system can dissociate into fractionally charged fragments.
Here, we revisit the case of dissociated diatomic molecules, known to exhibit
this problem when studied within standard approaches, including the local
spin-density approximation (LSDA). By employing our recently proposed [E.
Kraisler and L. Kronik, Phys. Rev. Lett. 110, 126403 (2013)]
ensemble-generalization we find that asymptotic fractional dissociation is
eliminated in all systems examined, even if the underlying exchange-correlation
(xc) is still the LSDA. Furthermore, as a result of the ensemble generalization
procedure, the Kohn-Sham potential develops a spatial step between the
dissociated atoms, reflecting the emergence of the derivative discontinuity in
the xc energy functional. This step, predicted in the past for the exact
Kohn-Sham potential and observed in some of its more advanced approximate
forms, is a desired feature that prevents any fractional charge transfer
between the system's fragments. It is usually believed that simple xc
approximations such as the LSDA cannot develop this step. Our findings show,
however, that ensemble generalization to fractional electron densities
automatically introduces the desired step even to the most simple approximate
xc functionals and correctly predicts asymptotic integer dissociation.
