In this work, we use the quasi-diabatic propagation scheme to directly interface the diabatic linearized (spin-LSC) and partially linearized (spin-PLDM) spinmapping approaches and the CASSCF on-the-fly electronic structure calculations to propagate ab initio non-adiabatic dynamics. We have performed on-the-fly simulations for four recently suggested molecules, ethylene, fulvene, methyliminium cation (CH 2 NH + 2 ), and 1,2-dithiane. These molecular models provide examples of common non-adiabatic phenomena found ubiquitously in realistic systems, namely conical interactions and avoided crossings and are closely related to the wellknown simple curve crossing models of Tully. We have shown that the spin-LSC method provides very accurate non-adiabatic population dynamics when comparing to ab initio multiple spawning (AIMS), exhibiting a similar level of accuracy to the recently developed symmetric quasi-classical (SQC) approach of Miller and coworkers with a trajectory-adjusted zeropoint energy parameter and that of trajectory surface hopping (TSH) with energy-based decoherence corrections. See our previous report on SQC dynamics in Ref. 62 using similar molecular models. However, the more involved spin-PLDM dynamics exhibit an equivalent or decrease in accuracy in the population dynamics for all models studied, with the Fulvene model (Fig. ) showcasing the least accurate results.