The factor (N C ) 1/2 is introduced in order to reduce the dependence of the G αβ /G αα ratios on the number of coordinates, so making the method approximately size-consistent. In the first method, the value of σ i,ν is computed only at the beginning and kept constant throughout the dynamics, meaning that the Gaussians are frozen. In the second method, the value of σ i,ν is updated at time t if the RHS of Eq. 18 for the distribution of trajectories at time t exceeds the current value of σ i,ν by a factor of (at least) 1.5 (a userdefined parameter). It is important to note that σ i,ν is never reduced. While using frozen Gaussians makes it easier to understand the impact of the variances on the quantum momentum and on the nonadiabatic dynamics, we also investigated the possibility of allowing σ i,ν to change. This second choice was motivated by the observation that, with frozen Gaussians, many trajectories became lonely.