can be integrated to determine the positions of the trajectories at all times that closely follow the evolution of the (exact) nuclear density. Here, A α ν (t) stands for the value of the exact TDVP at the position R α ν (t). In the gauge where the nuclear wavefunction is always real and non-negative, the second term on the right-hand side of Eq. ( ) identically vanishes and the TDVP equals the nuclear momentum field calculated from the molecular wavefunction. Therefore, to determine the (numerically exact) TDVP, the solution of the TDSE (2) is integrated over electronic positions to get the nuclear density, whose positive square root gives the nuclear wavefunction in this gauge. Dividing the molecular wavefunction by the nuclear wavefunction yields the electronic wavefunction, from Eq. ( ), and Eq. ( ) can be directly used to determine the TDVP.