  We show that a novel, general phase space mapping Hamiltonian for
nonadiabatic systems, which is reminiscent of the renowned Meyer-Miller mapping
Hamiltonian, involves a commutator variable matrix rather than the conventional
zero-point-energy parameter. In the exact mapping formulation on constraint
space for phase space approaches for nonadiabatic dynamics, the general mapping
Hamiltonian with commutator variables can be employed to generate approximate
trajectory-based dynamics. Various benchmark model tests, which range from gas
phase to condensed phase systems, suggest that the overall performance of the
general mapping Hamiltonian is better than that of the conventional
Meyer-Miller Hamiltonian.
