The fourth term in Eq. 8, known as the Hartree potential, corresponds to the classical electron-electron interaction energy contribution from the Coulomb operator, whereas v XC is the unknown exchange-correlation (XC) potential defined as the functional derivative of the XC energy with respect to the one-electron density. The XC potential formally depends on the initial state of the interacting system, Ψ 0 , and the Kohn-Sham initial state, Φ 0 , as well as the intermediate TDKS densities n t ′ <t .. When using the real-time TDKS (RT-TDKS) method, the initial state and intermediate TDKS densities are often not taken into consideration, an assumption leading to what is known as the "adiabatic approximation", where only the instantaneous electron density n t is input into the XC potential just as is done with the groundstate density functional theory. The adiabatic approximation appears to work well in some instances, such as ionization, where the electron removal may keep the system closer to the neutral reference state compared to electron excitation. There are several proposed XC functionals and time-dependent formulations that incorporate memory effects, at least partially. However, in none of these cases the resonance condition, an important consideration when modeling coherent electron dynamics, is satisfied. Time-dependent Hartree-Fock (TDHF) theory has developed independently 80 of Kohn-Sham TDDFT, but can be thought of as a special case of the generalized Kohn-Sham formalism. The XC potential in Eq. 8 is then the exchange operator from HF theory. This substitution results in a Liouville-von Neumann equation involving the time-dependent Fock operator: