Explicitly using this formulation, means that the y quantity must be evaluated for two different potentials and this could increase the computational cost for the equations of motion in a specific time-domain significantly. However, in the case where the two PESs are fitted to the same fit basis, and no non-linear optimization of fit functions are required, the update of the potential is obtained at essentially no cost by a continuous update of the sum-over-products coefficients in Eq. 13