Best practices for hybrid semiclassical simulations of nonadiabatic dynamics

Hybrid semiclassical (SC) approaches offer an efficient route to simulations of nonadiabatic dynamics by selectively quantizing key degrees of freedom, retaining much of the accuracy of quantum-limit SC methods at a reduced computational cost. In this work, we establish practical guidelines for selecting an appropriate hybrid SC approach based on system characteristics and the observable of interest. We compare several hybrid SC methods for nonadiabatic dynamics, including the mixed quantum-classical initial value representation (MQC-IVR and its variants), the partial linearized density matrix (PLDM) method, and the recently introduced nonadiabatic hybrid wigner dynamics (NHWD). Using a 1D scattering model and spin-boson models spanning weak and strong system-bath coupling regimes, we benchmark these SC methods against numerically exact quantum dynamics and the classical-limit linearized semiclassical (LSC) approximation. We show that the optimal choice of hybrid method and the degrees of freedom to quantize depend on the observable of interest: electronic observables, such as state population, are accurately captured by quantizing only the electronic state variables, whereas nuclear observables require explicit quantization of relevant nuclear modes. We further find that NHWD is particularly effective for systems with strong electronic-nuclear coupling, where quantization of electronic and nuclear degrees of freedom is required. Finally, we demonstrate that using the symmetrized form of the Meyer-Miller-Stock-Thoss mapping Hamiltonian consistently improves the accuracy of hybrid SC simulations.