DFT Calculations, Atomic Ionization Potentials -- Which Exchange-Correlation Functional to Use, to Preserve Koopmans Theorem? I have a program which can perform density-functional calculations for atoms, given a density functional. 

Of course the simplest form of exchange potential to use is one relevant for a uniform electron gas (i.e. the original Kohn-Sham exchange, proportional to $n_e^{1/3}$). A good correlation functional is also available. However when I performed calculations for some atoms the energy of the highest occupied orbital differs greatly from the ionization potential (off by a few eVs!). 

That the energy of the highest occupied orbital equals the ionisation potential of the neutral atom is known as Koopmans' Theorem. I get a feeling from the literature that DFT can be quite accurate. So what's wrong?

Interestingly when I use the Slater exchange functional, coupled with a correction suggested by Skillman (i.e. replacing the potential by $1/r$ when the overall potential drops below that value), the results improve significantly. (See the book "Atomic Structure Calculations" by Herman Skillman). Well, maybe I should follow this recipe, but it seems the procedure is quite ad-hoc.

My question is, are there any functionals which will give reasonable values for the atomic ionisation potentials? I do not want to implement methods like the optimised effective potential method since the latter is not readily generalised to a finite-temperature scenario. Thanks.
I think the most widely-used approach at the moment comes from Roi Baer and Leeor Kronik and others, e.g.


Phys. Rev. Lett. (2010) 105, art. 266802
Phys. Rev. B (2011) 84, art. 075144


Basically the idea is to tune the range-separation parameter $\gamma$ between short-range and long-range electrostatic effects in a range-separated hybrid functional. You find a match such that Koopmans' theorem holds.

The result is an "optimally-tuned" range-separated hybrid DFT functional (OT-RSH).

It's not perfect, for example, it violates size consistency: J. Chem. Phys. (2013) 138, 204115