The water-assisted reaction (shown in Fig. ) is qualitatively reproducing the tendency of MP2 results, namely, a less exothermic reaction with respect to the intramolecular transfer with a more stable keto form. Note that, in the figure, the reactant and the product are set to 0 and 1, taken from the MP2/spAug-cc-pVDZ optimized structures in the gas phase (see supporting information). The stability of the keto form predicted by DFTB methods is underestimated by 9-10 kcal•mol -1 with respect to the MP2 results. However, the DFTB methods predict a large decrease in the activation barrier with respect to the intramolecular transfer. In this case, all DFTB methods tend to underestimate the barrier height by 4-6 kcal•mol -1 . The three DFTB methods predict the maximum of the free energy at different one-dimensional projected collective variables (ζ = 0.13 for DFTB3-3OB, ζ = 0.32 for DFTB2-OB2 and ζ = 0.46 for DFTB2-MIO). This deserves a further analysis on the free energy barrier by each method. To further explore the water assisted mechanism, two dimensional free energy surface (FES) using three DFTB methods with the ODP reaction coordinate (ζ) and the perpendicular vector ( X ⊥ ) are generated and shown in Fig. . None of the DFTB/MM method predict a simultaneous pterin-water proton transfer. DFTB2-MIO shows a minimum for the enol and keto forms at (ζ, X ⊥ ) = (-0.1, 0.4) and (ζ, X ⊥ ) = (1.0, 0.0) respectively. The transition state corresponding to the simultaneous proton transfer appears in the (ζ, X ⊥ ) = (0.2, 0.0) region, making the FES antisymmetric. However, a lower energetic transition state (ζ, X ⊥ ) = (0.2, 1.0) is found. In Fig. (a), the histograms of sampled regions are projected on the collective variables defined by