The histograms thus indicate that DFTB2-MIO/MM favors a single proton transfer from water to pterin, generating thus an OH -intermediate followed by a proton transfer from pterin, in contrast with the simultaneous proton transfer predicted by ab initio simulations. DFTB2-OB2 and DFTB3-3OB exhibit a nearly symmetric FES, where the minima of enol and keto forms appear at (ζ, X ⊥ ) = (0.0, 0.0) and (ζ, X ⊥ ) = (1.0, 0.0) respectively. The transition state corresponding to a simultaneous proton transfer appears in the (ζ, X ⊥ ) = (0.5, 0.0) region. DFTB3-3OB predicts a large barrier for that region, which is not properly sampled despite the applied bias. In the case of DFTB2-OB2, the lowest energy transition state is found at the region (ζ, X ⊥ ) = (0.5, 0.7). In the case of DFTB3-3OB, due to the large area of transition state, transition state is passed through the minimum energy path in the (ζ, X ⊥ ) = (0.5, 1.0) region. In Fig. (b) for DFTB2-OB2/MM and (c) for DFTB3-3OB/MM, the histograms projected on the collective variables defined in Eqs. 17 and 18, indicate that both methods favors a sequential proton transfer. At variance with DFTB2-MIO/MM, in this case, DFTB2-OB2/MM and DFTB3-3OB/MM tend to favor a hydronium (H 3 O + ) intermediate followed by a proton transfer from hydronium to pterin.