Eq. 9 can then be solved numerically, here using the modified mid-point unitary transformation (MMUT) algorithm, restarted every 100 time-steps to remedy energy drifts. The RT-TDHF method, owing to the dependence of the Fock operator on the electronic density that parallels the dependence of the Kohn-Sham Hamiltonian on the electronic density, suffers from similar issues as RT-TDDFT electron dynamics within the adiabatic approximation, namely incorrect Rabi oscillations, peak shifting, and a poor description of charge transfer. TDHF theory does not formally account for memory effects, thus there is no path forward for improving these deficiencies in TDHF theory. However, it is important to understand the limitations and applicability of TDHF theory in comparison to TDCIS, a method similar to TDHF in terms of spatial nonlocality but one that has no densitydependence in the potential.