The memory kernel is crucial for simulating the dynamics of the electronic degrees of freedom. However, calculating K ( τ τ ) presents difficulties due to its time-dependent nature. Additionally, the time dependency of K ( τ τ ) is complex because it is governed by the projection-dependent propagator, e − − i Q L τ τ / ℏ ℏ . Therefore, the exact memory kernel is difficult to calculate except for several analytically solvable models proposed by Shi-Geva to remove the projection operator Q .