Density-functional theory (DFT) is a widely-used theoretical framework for studying the electronic properties of matter. 
Present-day approximations already make it widely applicable to a variety of many-electron systems in physics, chemistry, 
and materials science. However, there remain numerous challenges that common approximations fail to meet.  
A significant problem, which has both formal and practical implications, is the so-called problem of fractional dissociation. 
Many approximations spuriously predict that a many-electron system can dissociate into fractionally charged fragments. 
In our work, we revisit the case of dissociated diatomic molecules, known to exhibit this problem when studied within standard 
approximations, including the local spin-density approximation (LSDA). We apply the recently suggested ensemble-
generalization to LSDA (eLSDA) [1,2] and find that fractional dissociation is eliminated in all systems examined. The eLSDA 
Kohn-Sham potential develops a spatial step, associated with the emergence of the derivative discontinuity in the exchange-
correlation 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. Our findings show that, if appropriately generalized for fractional electron densities, even the most simple 
approximate functionals correctly predict integer dissociation [3].

[1] E. Kraisler, L. Kronik, Phys. Rev. Lett. 110, 126403 (2013)
[2] E. Kraisler, L. Kronik, J. Chem. Phys. 140, 18A540 (2014)
[3] E. Kraisler, L. Kronik, submitted.