Non-adiabatic couplings in Liouville description of mixed quantum-classical dynamics

An alternative Liouville formulation of mixed quantum-classical dynamics is presented, placing a particular focus on the non-adiabatic couplings in the adiabatic basis. Our formulation does not contain the `momentum jumpʹ operation which has played a vital role in the previous formulation by Kapral and Ciccotti [J. Chem. Phys. 110 (1999) 8919] in its trajectory implementation but has caused instability problem around the classical turning points.