We further explored the nature of the spin-PLDM correlation function by examining the various components (initially focused contributions λ and λ ) individually. Here we noted that when calculating an initial population element |σ σ|, the off-diagonal initially focused conditions σλ (where λ = σ) contribute nearly the same magnitude and sign to the overall correlation function as λσ. Thus, calculating one and doubling its weight provides the same contribution to the total correlation function. Further, the other diagonal contributions λλ (with λ = σ) have minimal magnitude in their contribution to the overall correlation function and can be ignored. In this sense, an approximate scheme can be constructed, at least in these few example systems explored in this work. In this case, one only needs to calculate a single column of initially focused density matrix elements, σλ, which reduces the computational cost from N 2 to N converged simulations, still amounting to more computations than the spin-LSC approach which only ever requires one converged initial condition given an initial excitation to |σ σ|.