Fig. shows the popular decoherence-corrected surface hopping approach (dTSH) , which is a popular method that captures much of the decoherence that standard FSSH fails to capture. Fig. presents the γcorrected SQC approach using the triangle windowing (γ-SQC-∆). Fig. and Fig. show the two new approaches of this work: spin-LSC and spin-PLDM, respectively. At short times (less than 30 fs), all methods capture the correct population dynamics which exhibits 10 fs of plateau followed by a short decrease and another short plateau (i.e., a shoulder). Though, dTSH and spin-LSC capture the AIMS result better than γ-SQC-∆ and spin-PLDM. At medium times (more than 30 fs and less than 50 fs), only dTSH is able to capture the AIMS result, followed closely by spin-LSC. Both γ-SQC-∆ and spin-PLDM overestimate the population in the S 1 state. At longer times, none of the methods accurately capture the AIMS result; however, spin-LSC captures the over- all trends the best at all times, though underestimating the S 1 population at longer times. For the molecular systems simulated here, Spin-PLDM seems to overestimate the population at all times. Furthermore, the initial S 1 population (between 0 and 15 fs) goes above 1.0, which implies that 1000 trajectories were not sufficient to fully converge this correlation function. Recall, the cost of spin-PLDM scales poorly with the number of states N , since N 2 converged population dynamics: 1000 × 2 2 trajectories in this case, 4× more expensive than spin-LSC, γ-SQC-∆, and dTSH. However, as we will discuss later (in Fig. ), a major simplification of spin-PLDM can be made by excluding some of the N 2 initial conditions present in the full spin-PLDM correlation function. Overall, all four approaches capture the general physics of ethylene CI dynamics. Thus, a strict delineation of each method's quality is not straightforward.