and the jump operator L only acts on the quantum DOFs in the subspace H Q . The above jump operator corresponds to a transition in the quantum subspace H Q with no impact on the classical (such as nuclear) subspace H C . We can represent this jump operator LS as well as the system Hamiltonian ĤS in a convenient basis |ψ a ⟩ ⊗ |χ ν ⟩, where |ψ a ⟩ is the diabatic basis for the quantum subsystem and |χ ν ⟩ is the discrete variable representation (DVR) basis for the classical subsystem.