Most notably, the partial linearized density matrix (PLDM), state-dependent ring polymer molecular dynamics , quantum-classical path integral (QCPI) approach , the quantum classical Lioua) Electronic mail: bweight@ur.rochester.edu b) Electronic mail: mandal@tamu.edu c) Electronic mail: pengfei.huo@rochester.edu ville equation (QCLE) dynamics, and the symmetric quasi-classical (SQC) approach with trajectoryspecific zero-point energy. Even more recently, the spinmapping formalism has been shown to provide a substantial increase in accuracy in non-adiabatic benchmark systems, such as the Fenna-Matthew-Olson (FMO) complex, the spin-boson models, as well as others. Another related approach is the generalized discrete truncated Wigner approximation (GDTWA). A recent connection between the popular FSSH and mapping approaches has recently been developed and tested in both model and ab initio settings is the mapping approach to surface hopping (MASH). The spin-mapping approaches build upon the idea of mapping the electronic Hilbert space to one of different types. For example, the Meyer-Miller-Stock-Thoss (MMST) mapping relations, employed, for example, in the development of the SQC and PLDM approaches, rely on mapping the N electronic states to that of a set of N quantum harmonic oscillators, each of which are projected to include only their ground and excited states. One of the main drawbacks of this mapping is that the Hilbert space of the quantum harmonic oscillator is larger than that of the original electronic system and so requires projection or the normalization of the population to restrict the dynamics to these DOFs. However, the spinmapping formalism instead is able to map the electronic dynamics onto the surface of a set of spin-1/2 systems (i.e., Bloch spheres) where, by construction, the normalization of the total population is guaranteed since the radius of the Bloch sphere is fixed.