The novel approach to nonadiabatic quantum dynamics greatly increases the accuracy of the most popular semiclassical technique while maintaining its simplicity and efficiency. Unlike the standard Tully surface hopping in Hilbert space, which deals with population flow, the new strategy in Liouville space puts population and coherence on equal footing. Dual avoided crossing and energy transfer models show that the accuracy is improved in both diabatic and adiabatic representations and that Liouville space simulation converges faster with the number of trajectories than Hilbert space simulation. The constructed master equation accurately captures superexchange, tunneling, and quantum interference. These effects are essential for charge, phonon and energy transport and scattering, exciton fission and fusion, quantum optics and computing, and many other areas of physics and chemistry.
Keywords: Liouville space; quantum coherence and interference; superexchange; surface hopping; tunneling.