with Ψ i and Ψ j representing the electronic wave functions of states i and j and their respective potential energies E i and E j , whereas E j > E i . Fitting these couplings presents significant challenges arising from the intrinsic properties of NACs, characterized by their lack of smoothness and arbitrary sign variations. Specifically, complications arise at conical intersections, critical points in NAMD simulations where the energy levels of electronic states i and j coincide. However, as electronic states become degenerate, NACs tend toward infinity (cf. equation 1), giving rise to singularities in their values. To address this issue, SpaiNN incorporates a smoothing process into its pipeline. This smoothing procedure involves scaling the original NACs by the energy difference between the two states involved in the coupling, denoted as E j -E i (j > i), expressed as: