Describing long-range charge-separation processes with subsystem density-functional theory.

Long-range charge-transfer processes in extended systems are difficult to describe with quantum chemical methods. In particular, cost-effective (non-hybrid) approximations within time-dependent density functional theory (DFT) are not applicable unless special precautions are taken. Here, we show that the efficient subsystem DFT can be employed as a constrained DFT variant to describe the energetics of long-range charge-separation processes. A formal analysis of the energy components in subsystem DFT for such excitation energies is presented, which demonstrates that both the distance dependence and the long-range limit are correctly described. In addition, electronic couplings for these processes as needed for rate constants in Marcus theory can be obtained from this method. It is shown that the electronic structure of charge-separated states constructed by a positively charged subsystem interacting with a negatively charged one is difficult to converge - charge leaking from the negative subsystem to the positive one can occur. This problem is related to the delocalization error in DFT and can be overcome with asymptotically correct exchange-correlation (XC) potentials or XC potentials including a sufficiently large amount of exact exchange. We also outline an approximate way to obtain charge-transfer couplings between locally excited and charge-separated states.