  We show that an asymmetric two-fermion two-site Hubbard model illustrates the
essential features of long-range charge-transfer dynamics in a real-space
molecule. We apply a resonant field that transfers one fermion from one site to
the other. Via constrained search we find the exact ground-state
exchange-correlation functional, and use it to propagate the Kohn-Sham system,
giving the first "adiabatically-exact" calculation of time-resolved
charge-transfer. This propagation fails to properly transfer charge. We analyze
why by comparing the exact and adiabatically-exact potentials and discuss the
role of the derivative discontinuity. The implication for real-space molecules
is that even the best possible adiabatic approximation, despite capturing
non-local step features relevant to dissociation and charge-transfer
excitations, cannot capture fully time-resolved charge-transfer dynamics.
