Neglecting the other diagonal initial conditions is corroborated by the results of the main text, where the P 00 never contributed any appreciable amount of population. The other off-diagonal initial conditions P λλ where λ = i and λ = 1 require an examination of a system with more than two electronic states. Fig. in the Supporting Information presents the population dynamics for the FMO 7-state model system which has been previously studied with spin-PLDM and achieves superior accuracy compared to FSSH, SQC, and spin-LSC, matching the benchmark hierarchical equations of motion (HEOM) result. Fig. presents the partial contributions to the ground state S 0 population as well as the single-column approximation which yields the same accuracy as the full spin-PLDM correlation function result with 7 converged simulations instead of 49, a reduction of 86% in computational cost. The other diagonal and off-diagonal initial conditions are shown in Figs. and show less than 0.3% contribution at all times.