The accuracy of the NE-FGR and E-FGR dynamics is assessed by comparing them to the numerically exact hierarchical equations of motion (HEOM) method. Here, we only compute the exact population dynamics for N = 5 with HEOM. Fig. shows that E-FGR accurately captures the HEOM dynamics. This is expected since reorganization energy λ = 14 meV is chosen to be less than k B T ≈ 26 meV and √ N g c = 50 meV, such that under this the weak system-bath coupling condition, the perturbative approximation in FGR is valid. Further, both NE-FGR and E-FGR are expected to be more accurate in the experimentally relevant collective regime, because the off-diagonal system-bath coupling scales with 1/N , making the perturbative approximation valid under the large N limit.