For systems with many electronic states, the number of trajectories required to converge all the partial contributions can become unmanageable. Thus one needs to resort to some approximation for the simulations. It is our experience that the spin-PLDM correlation function can be adequately represented by two approximations to the total correlation function by ignoring some of the partial contributions. The first approximation is to simply ignore all contributions except the initially excited state. In each of our models in this work, that amounts to keeping only the P 11 contribution. In the ab initio models explored in this work, the P 11 population represents at least 88% of the total contribution, at worst. The next best approximation is to take only the single diagonal contribution which corresponds to the initial excitation, P ii where i is the initial excited state as well as a single column (or row) of the density matrix that includes this initial excitation, P iλ , for example, with twice the weight. In other words, the approximation amounts to P Total = P ii + λ 2P iλ , where the factor 2 accounts for the equal contribution from both the P iλ and P λi terms (as shown in Fig. since P 01 ≈ P 10 ). This approximation amounts to only N converged initial conditions instead of N 2 as prescribed by the total correlation function.