  There are several approximations to the exchange-correlation functional in
density-functional theory that accurately predict total energy-related
properties of many-electron systems, such as binding energies, bond lengths,
and crystal structures. Other approximations are designed to describe
potential-related processes, such as charge transfer and photoemission.
However, the development of a functional which can serve the two purposes
simultaneously is a long-standing challenge. Trying to address it, we employ in
the current work the ensemble generalization procedure proposed in Phys. Rev.
Lett. 110, 126403 (2013). Focusing on the prediction of the ionization
potential via the highest occupied Kohn-Sham eigenvalue, we examine a variety
of exchange-correlation approximations: the local spin-density approximation,
semi-local generalized gradient approximations, and global and local hybrid
functionals. Results for a test set of 26 diatomic molecules and single atoms
are presented. We find that the aforementioned ensemble generalization
systematically improves the prediction of the ionization potential, for various
systems and exchange-correlation functionals, without compromising the accuracy
of total energy-related properties. We specifically examine hybrid functionals.
These depend on a parameter controlling the ratio of semi-local to non-local
functional components. The ionization potential obtained with
ensemble-generalized functionals is found to depend only weakly on the
parameter value, contrary to common experience with non-generalized hybrids,
thus eliminating one aspect of the so-called `parameter dilemma' of hybrid
functionals.
