Two avenues to self-interaction correction within Kohn-Sham theory:: unitary invariance is the shortcut

The most widely used density functionals for the exchange-correlation energy are inexact for one-electron systems. Their self-interaction errors can be severe in some applications. The problem is not only to correct the self-interaction error, but to do so in a way that will not violate size-consistency and will not go outside the standard Kohn-Sham density functional theory. The solution via the optimized effective potential (OEP) method will be discussed, first for the Perdew-Zunger self-interaction correction (whose performance for molecules is briefly summarized) and then for the more modern self-interaction corrections based upon unitarily invariant indicators of iso-orbital regions. For the latter approaches, the OEP construction is greatly simplified. The kinetic-energy-based iso-orbital indicator tau(sigma)(W)(r)/tau(sigma)(r) will be discussed and plotted, along with an alternative exchange-based indicator.