From the data, it is clear that the resulting energies and couplings are smooth: the diabatization is robust. Next, in Fig. , we plot the diabatic couplings between the diabat 0 and the diabat 1 averaging, one does not properly the ground state and the excited state (and the gap is often too large). Third, by comparing (a) with (b) or (c) with (d), we find that the results do not change a lot after adding electron-electron repulsion (U = 0.1); it would seem that, within this model, the main impact of electron-electron repulsion is on the barriers present in the ground state. For instance, for the U = 0 case in Fig. (a), the symmetric barrier is 0.013;