Theoretical description of charge migration with a single Slater-determinant and beyond

Triggered by the interest to study charge migration in large molecular systems, a simple methodology has recently been proposed based on straightforward density functional theory calculations. This approach describes the time evolution of the initially created hole density in terms of the time evolution of the ionized highest occupied molecular orbital (HOMO). Here we demonstrate that this time-dependent analog of Koopmans' theorem is not valid, and instead of the time evolution of the HOMO, the time evolution of the orbitals that remain occupied in the cation determines the evolution of the initially created hole in the framework of time-dependent single-determinant theories. Numerical examples underline that for a proper description of charge migration processes, an explicit treatment of the electron correlation is indispensable. Moreover, they also demonstrate that the attempts to describe charge migration based on Kohn-Sham density functional theory using conventional exchange-correlation functionals are doomed to fail due to the well-known self-interaction error.