In our recent works, we have developed and implemented the quasi-diabatic (QD) propagation scheme to seamlessly combine adiabatic electronic structure methods with diabatic quantum dynamics methods. The QD scheme relies on a short-time reference nuclear geometry (whose electronic states are often called "crude adiabatic" states), which acts as a set of locally diabatic states during a single nuclear time-step. After this shorttime propagation, the QD states are updated to the new reference geometry. In this propagation scheme, one does not construct a global diabatic representation but uses a sequence of local diabatic representations for each shorttime segment to propagate quantum dynamics. Note that the quasi-diabatic propagation scheme should not be confused with the approximate diabatic representation which is also often referred to as the "QD" representation in the literature. In this work, we use the QD propagation scheme to seamlessly combine the recently formulated spinmapping quantum dynamics methods with the adiabatic output of the state-averaged complete active space complete active space self-consistent field (SA-CAS-SCF) electronic structure method. Here we perform direct on-the-fly non-adiabatic dynamics to simulate the population dynamics of various photo-excited species, ethylene, fulvene, methyliminium cation (CH 2 NH + 2 ), and 1,2dithiane, all of which have been previously published using the higher-level, wave-packet-based ab initio multiple spawning (AIMS) approach. The AIMS results are interpreted as a benchmark for the MQC results in this work. These systems provide a set of benchmarks that explore various phenomena found in non-adiabatic dynamics, such as electronic avoided crossings and conical intersections, in a simplified way and offer a direct connection between the commonly used model systems of Tully and realistic, ab initio molecules. Our numerical results demonstrate that the linearized spin-mapping approach outperforms the partially linearized spin-mapping (spin-PLDM) approach for all ab initio systems explored in this work and offers an accuracy near the same level as the SQC or FSSH approaches but with fewer ad hoc parameters. We further explored the nature of the spin-PLDM correlation function by examining the various components individually. Here we found that an approximate scheme can be constructed to give results of similar accuracy to the full spin-PLDM correlation function, where one only needs to calculate the upper triangle of the N 2 initial conditions including the diagonal cases. This reduces the computational expense from N 2 trajectory-converged simulations to N (N -1) 2 + 1 simulations, still amounting to more computations than the spin-LSC approach which only ever requires, at most, N calculations. These simulations provide useful tests of the numerical performance of various non-adiabatic approaches beyond model systems, which have been used as the main workhorse for benchmarking new methods in the field of quantum dynamics. However, it is our hope that these benchmark studies using realistic, ab initio systems will help to foster the development of new quantum dynamics approaches.