On the exact treatment of Time Dependent Self-Interaction Correction
  We present a new formulation of the time-dependent self-interaction correction (TDSIC). It is derived variationally obeying explicitly the constraints on orthonormality of the occupied single-particle orbitals. The thus emerging rather involved symmetry condition amongst the orbitals is dealt with using two separate sets of (occupied) single-particle wavefunctions, related by a unitary transformation. The double-set TDSIC scheme is well suited for numerical implementation. We present results for laser-excited dynamics in a 1D model for a molecule and in fully fledged 3D calculations. 
J. Messud, P. M. Dinh, P.-G. Reinhard, E. Suraud