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We explore an asymmetric two-fermion Hubbard dimer to test the accuracy ofthe adiabatic approximation of time-dependent density functional theory inmodelling time-resolved charge transfer. We show that the model sharesessential features of a ground state long-range molecule in real-space, and byapplying a resonant field we show that the model also reproduces essentialtraits of the CT dynamics. The simplicity of the model allows us to propagatewith an "adiabatically-exact" approximation, i.e. one that uses the exactground-state exchange-correlation functional, and compare with the exactpropagation. This allows us to study the impact of the time-dependentcharge-transfer step feature in the exact correlation potential of realmolecules on the resulting dynamics. Tuning the parameters of the dimer allowsa study both of charge-transfer between open-shell fragments and betweenclosed-shell fragments. We find that the adiabatically-exact functional isunable to properly transfer charge, even in situations where theadiabatically-exact resonance frequency is remarkably close to the exactresonance, and we analyze why.

Challenging Adiabatic Time-dependent Density Functional Theory with a Hubbard Dimer: The Case of Time-Resolved Long-Range Charge Transfer