contribute significantly to the chemistry and physics of monosaccharides. For pyranoses, only the $^{4}$C$_{1}$ and $^{1}$C$_{4}$ conformations happen to be eligible to be the most stable conformations, that is, global minima which are well separated in energy from neighbouring local ones. Other conformers such as boats and skew-boats can in principle appear as local, scarcely populated minima, while half-chairs and envelopes usually correspond to maxima or saddle points and are typical transition states between boats and chairs. 

The concept of puckering in rings (specifically, in six-membered rings) dates back to the studies of Sachse 55,56 on cyclohexane in the late nineteenth century, and has been later ap- plied also to saccharidic rings $^{57}$. Although it was clear that the most stable conformers could have been only either of the two chairs, lack of quantitative information on their relative abundance stimulated many theoretical approaches (for an historical review the reader can look at Ref. 58). Semiempirical approaches accounting for the Hassel-Ottar effect (insta- bility of 1,3-diaxial hydroxymethyl – hydroxyl conformation) and other instability factors introduced by Reeves and Kelly 59–61 allowed to understand that for most pyranoses the $^{1}$C$_{4}$ conformation, rather that the $^{4}$C$_{1}$ , is the most stable one, while in few cases an equilibrium between the two is possible. A quantitative estimate of the free energy difference between puckered conformers in aqueous solution (and not, as it is sometimes erroneously reported, in vacuum) came first with the analysis performed by Angyal who assigned, employing again an empirical scheme, specific free energy contributions to the different destabilizing interac- tions. The various terms were derived from measured equilibria in solution of cyclitols with their borate complexes $^{62}$. Later, employing a molecular-mechanical approach, Vijayalakshmi and Rao 63 obtained other estimates, which were anyway compatible with the inverted chair free energies predicted by Angyal. 

Semiempirical methods have been in general a quite successful approach for determining the stereochemical properties of numerous cyclic compounds $^{64}$. Unfortunately, experimental estimates of the ring conformational free energy are not feasible for many pyranoses, mostly because the populations of the less stable conformers are are usually too tiny to be detected with probes such as NMR $^{65,66}$. For some pyranoses, however, the destabilizing effects in the $^{4}$C$_{1}$ and $^{1}$C$_{4}$ conformations are similar and, as in the case of idose, the relative population of these two conformers becomes an experimentally accessible quantity. Indeed, in Refs. 62,63 the free energy differences estimated for α -d- Ido and β -d- Ido were proven to be compatible with the experimental findings obtained by Snyder and Serianni years later 67 (see Tab. II). 

