As we mentioned in section II B, the quantum momentum is redefined in CTMQC to satisfy an exact condition of zero net population transfer in regions of zero NAC . In the same spirit, some of us recently proposed a modification to CTMQC, named the CTMQC-E algorithm , where an exact constraint, namely total energy conservation, is imposed by redefining the time-integrated adiabatic force f µ,l . This approach was inspired by the work of Min and coworkers which fixed energy conservation along each trajectory in the independent trajectory version of CTMQC that uses auxiliary trajectories to evaluate the quantum momentum. Instead CTMQC-E preserves the coupled-trajectory nature of CTMQC and allows the trajectories to exchange energy. It is the total energy of the ensemble rather than the energy of each trajectory, that is the conserved quantity. In the framework of the modified definition of the quantum momentum Eq. ( ), we see from Eq. ( ) that energy will be conserved in situations where the quantity in the square brackets, ν ∆f ν,lk • Ṙ(α) ν +∆ (α) lk is independent of the trajectory index. CTMQC-E enforces this by redefining the accumulated force f ν,l → f(β) ν,l in such a way that such term equals its trajectory average, namely