1211.5950 (Eli Kraisler et al.)

The piecewise-linearity of approximate density functionals revisited:
implications for frontier orbital energies    [PDF]

Eli Kraisler, Leeor Kronik

In the exact Kohn-Sham density-functional theory (DFT), the total energy versus the number of electrons is a series of linear segments between integer points. However, commonly used approximate density functionals produce total energies that do not exhibit this piecewise-linear behavior. As a result, the ionization potential theorem, equating the highest occupied eigenvalue with the ionization potential, is grossly disobeyed. Here, we show that, contrary to conventional wisdom, most of the required piecewise-linearity of an arbitrary approximate density functional can be restored by careful consideration of the ensemble generalization of DFT. Furthermore, the resulting formulation introduces the desired derivative discontinuity to the exchange-correlation potential. All this is achieved while neither introducing empiricism nor changing the underlying functional form. The power of the approach is demonstrated on benchmark systems using the local density approximation as an illustrative example.

View original: http://arxiv.org/abs/1211.5950