Panels show the predicted Mulliken charges for the hydronium sub-units from a dynamical simulation of the reaction from eigenvector continuation with N = 40 (orange) and N = 84 (blue) training points from density matrix renormalization group. The system uses a 6-31G basis, with snapshots depicting the evolution of the molecular geometry at four evenly spaced times. Reference charges from simulations with density functional theory with a B3LYP exchange correlation (DFT, light blue, dash-dotted) and HartreeFock (HF, brown, dotted) are included for comparison. Source data are provided as a Source Data file.