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Fundamentals of Time-Resolved Charge-Transfer in Time-Dependent Density Functional Theory

We show that as an electron transfers between closed-shell molecular fragments at large separation, the exact correlation potential of time-dependent density functional theory gradually develops a step and peak structure in the bonding region. This structure has a density-dependence that is non-local both in space and time, and even the exact ground-state exchange-correlation functional fails to cap- ture it. In the complementary case of charge-transfer between open-shell fragments, an initial step and peak vanish as the charge-transfer state is reached. Lack of these structures in usual approxima- tions leads to inaccurate charge-transfer dynamics. This is dramatically illustrated by the complete lack of Rabi oscillations in the dipole moment under conditions of resonant charge-transfer.