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](http://en.wikipedia.org/wiki/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](http://dx.doi.org/10.1103/PhysRevLett.105.266802)
* [*Phys. Rev. B* (2011) 84, art. 075144](http://dx.doi.org/10.1103/PhysRevB.84.075144)


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](http://dx.doi.org/10.1063/1.4807325)


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