where t ∈ (0, ∆t). The mapping variables are propagated using a velocity-Verlet scheme (by splitting the real and complex components of Z) which solves the first equation in Eq. 18 for spin-LSC for spin-PLDM, noting the only difference is that the spin-PLDM contains two sets of mapping variables {Z, Z } that are propagated independently from one another. Finally, the mapping variables are rotated to the time ∆t basis via the time-overlap matrix S(0, ∆t) as S T (0, ∆t) × Z(∆t) → Z(∆t).