Abstract: 

Quantum trajectory surface hopping (QTSH) is a trajectory surface hopping method that is rigorously derived from the quantum-classical Liouville equation, developed to study non-adiabatic molecular dynamics of multistate systems. This work explores the unique features of QTSH - energy conservation on the ensemble level without the imposition of ad hoc momentum rescaling, and its rigorous derivation in both the diabatic and adiabatic representations - that distinguish it from the widely used fewest switches trajectory surface hopping method (FSSH). We show that in the limit of complete and localized population transfer in the adiabatic representation, the work done by the quantum force that characterizes QTSH is akin to the strict classical energy conserving momentum 'jumps' of FSSH. Our numerical results show that the feedback between nuclear and electronic degrees of freedom, mediated by the quantum forces that work to conserve the quantum-classical energy on average, is well-incorporated in QTSH. By transforming the QTSH results for the elements of the Wigner distribution and forces from one representation to another, we conclude that QTSH is representation invariant. By analyzing the classical and quantum forces for non-adiabatic processes in both the diabatic and adiabatic representations, we found that highly non-classical processes in the adiabatic representation are, conversely, highly classical in the diabatic representation. Since errors due to inconsistencies in surface hopping are larger when significant population transfers occur, it allows us to conclude that QTSH results for the highly non-classical processes in the adiabatic representation are less accurate than for the corresponding more classical processes in the diabatic representation. We exploit the representation invariance of QTSH to obtain more accurate results for the population dynamics in the adiabatic representation.