where 2γ b is viewed as a parameter which specifies the zero-point energy (ZPE) of the mapping oscillators. In principle, 2γ b is state-specific and trajectory-specific. The MMST mapping Hamiltonian has been historically justified by Stock and Thoss using the raising and lowering operators of a harmonic oscillator as the mapping operator. Recently, a more natural mapping has been derived using the SU (N ) Lie group theory or so-called generalized spin mapping approach, which is connected to the MMST mapping approach. Classical trajectories are generated based on Hamilton's equations of motion (EOM) for