Self-interaction correction scheme for approximate Kohn-Sham potentials

Recently [Phys. Rev. Lett. 108, 253005 (2012)], we observed that approximate Hartree-exchange-correlation potentials constructed from electron densities depleted at the highest-occupied molecular orbital ( HOMO) level mimic the exact potential at intermediate distances from the nuclei; we then used this fact to obtain accurate Rydberg excitation energies of atoms and molecules within time-dependent density-functional linear-response theory employing standard semilocal approximations. Here we reinterpret this method as a form of self-interaction correction for Kohn-Sham potentials. We show that the greatest improvement in HOMO eigenvalues occurs when the charge removed from the HOMO level is about 1/2 electron, which explains why the Slater transition-state method works well for predicting ionization energies. The greatest improvement in Kohn-Sham orbital gaps, however, is achieved when about 1/4 electron is removed, which is why smaller HOMO depopulations are required for obtaining accurate excitation energies. The relationship between our self-interaction correction scheme, Slater's transition-state technique, and the X alpha method is also clarified.