Self-interaction correction in a real-time Kohn-Sham scheme: access to difficult excitations in time-dependent density functional theory.

We present a real-time Kohn-Sham propagation scheme for the self-interaction correction (SIC). The multiplicative Kohn-Sham potential is constructed in real-time and real-space based on the generalized optimized effective potential equation. We demonstrate that this approach yields promising results for a wide range of test systems, including hydrogen terminated silicon clusters, conjugated molecular chains, and molecular charge-transfer systems. We analyze the nature of excitations by calculating transition densities from the time evolution and by evaluating the time-dependent exchange-correlation potential. A properly constructed Kohn-Sham SIC potential shows a time-dependent field-counteracting behavior. These favorable characteristics of the exchange-correlation potential may be lost in approximations such as the SIC-Slater potential.