to the minima of this lower contour) and the transition states, or free energy saddle points (corresponding to the maxima of the lower contour). On the ( θ, φ ) plane, $^{4}$C$_{1}$ (0,-), $^{1}$C$_{4}$ ( π ,-), and 3 , $^{O}$B ( π/ 2,0) conformers are clearly recognizable as minima basins. Notice that, due to the periodic nature of φ , the 3 , $^{O}$B conformer appears in this representation to be split in two across the φ = 0 line. Another local minimum basin, more shallow than the previous ones is located around the $^{1}$S$_{3}$ ( π/ 2,7 π/ 6) conformer and seems to include also some other near boat-like conformer. This kind of occurrence can be a natural feature for gluco-pyranoses, because of the high flexibility of the ring conformers along the pseudo-rotational path (lo- cated at θ = π/ 2). A more detailed description of this local minimum is anyway beyond the interest of this work, because of its very high free energy. In addition to the free energy profile, in Fig. 4 we show an analogous plot, presented both on the ( θ, φ ) plane (upper panel), and projected onto the φ = 0 plane (lower panel), of the correction to the free energy profile coming from the umbrella sampling phase, − k b T ln ρ$_{bias}$ ( s ). Performing a screening of this contribution is quite important, because it allows to check if residual meta-stabilities (recognizable as basins) are left after the meta- dynamics phase, and whether an ergodic sample of the interesting region in the ( θ, φ ) plane has been performed or not: poorly sampled regions will appear wither as peaks. In Fig. 4 it is possible to see that the metadynamics run performed reasonably well. Indeed, the paths connecting the original metastable states do not show residual metastabilities, being the more pronounced minimum, located close to (0 , π/ 3), only ≃ 2 kJ/mol deep. It is seen that the complete space of puckering angles has been sampled properly. Corrections to the free energy difference between $^{4}$C$_{1}$ and $^{1}$C$_{4}$ are ≃ 2 kJ/mol. In case of the next most populated state, 3 , $^{O}$B, the correction increases to ≃ 4 kJ/mol, while for other states the correction can reach, but never exceeds, ≃ 6 kJ/mol with respect to the free energy of $^{4}$C$_{1}$ . The umbrella phase thus contributes in a significant way to the estimate of free energy differences, and — as expected — appears to be more important for less populated states and for transition states. Both the $^{1}$C$_{4}$ and 3 , $^{O}$B puckering free energies (local minima at about 10 and 17 kJ/mol, respectively) appear to be lower than what one would expect. In particular, the free energy of the inverted chair is about 15 kJ/mol lower than both our reference values $^{62,63}$. This free energy difference leads to a inverted chair population of about 1%, which can be observed during regular molecular dynamics runs at equilibrium. While not strictly incompatible with 13