Density-functional theory (DFT) is a widely-used theoretical framework for studying the electronic properties of matter. Present-day approximations to the exchange-correlation density-functional already make DFT 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. Among these are the deviation of the energy versus number of electrons from piecewise-linearity, inability to satisfy the ionization potential (IP) theorem (i.e. to predict the ionization energy via the HOMO energy), failure to predict the fundamental gap in semiconductors and molecular systems, and the fractional dissociation problem (where a system dissociates into fragments that are charged with a fractional number of electrons). All these challenges can be addressed using the ensemble approach in DFT. Specifically, we have recently proposed a generalization procedure [1,2], applicable to any existing exchange-correlation functional, which strongly reduces the deviation of the total energy of a system, as a function of the number of electrons, from the expected piecewise-linear behavior. As a result, prediction of the IP and of the fundamental gap from orbital energies, for finite systems like molecules and atoms, becomes much more accurate . Furthermore, the fractional dissociation problem is completely eliminated, as demonstrated for well-separated diatomic molecules .
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 E. Kraisler, T. Schmidt, S. Kümmel, L. Kronik, J. Chem. Phys. 143, 104105 (2015)
 E. Kraisler, L. Kronik, Phys. Rev. A 91, 032504 (2015)