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Nonadiabatic dynamical processes are one of the most important quantummechanical phenomena in chemical, materials, biological, and environmentalmolecular systems, where the coupling between different electronic states iseither inherent in the molecular structure or induced by the (intense) externalfield. The curse of dimensionality indicates the intractable exponentialscaling of calculation effort with system size and restricts the implementationof numerically exact approaches for realistic large systems. The phase spaceformulation of quantum mechanics offers an important theoretical framework forconstructing practical approximate trajectory-based methods for quantumdynamics. This Account reviews our recent progress in phase space mappingtheory: a unified framework for constructing the mapping Hamiltonian on phasespace for coupled F-state systems where the renowned Meyer-Miller Hamiltonianmodel is a special case, a general phase space formulation of quantum mechanicsfor nonadiabatic systems where the electronic degrees of freedom are mappedonto constraint space and the nuclear degrees of freedom are mapped ontoinfinite space, and an isomorphism between the mapping phase space approach fornonadiabatic systems and that for nonequilibrium electron transport processes.

Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics