Variations of the CTMQC algorithm have been explored, for example, using the electronic equation Eq.( ) within a surface-hopping (SH) or Ehrenfest (Eh) scheme for the nuclear evolution , resulting in a family of trajectory-based methods. A central feature of these methods is the coupling of trajectories through the nuclear quantum momentum Eq. (20) appearing in the EF terms. This term can be computed in two different ways. The original definition (Q 0 ) implies using Eq. (20) where the nuclear density is reconstructed as a sum of gaussians centered at the position of the classical trajectories or by placing the gaussian functions on auxiliary trajectories 41 created on non-active BO PES to approximate this coupling locally. This definition potentially leads to unphysical spurious net electronic population transfer in regions of zero NAC . To circumvent this problem, the quantum momentum is redefined (Q m ) by imposing, per degree of freedom, zero net population transfer between each pair of electronic states coming from the CT term Ntr α