II. THE PROBLEM OF PYRANOSES PUCKERING FREE ENERGY In this work we are focusing on a particular class of carbohydrates, namely, aldohexoses, saccharides of composition C$_{6}$H$_{12}$O$_{6}$. Aldohexoses can appear in nature in the form of six- membered, cyclic rings, conventionally known as the pyranose form. Pyranoses are charac- terized by the presence of five chiral centers located at the five ring carbon atoms. Following the convention of Fig. 1, these chiral carbons are here denoted as C1 (the anomeric carbon atom), C2, C3, C4 and C5 (the configurational carbon atom). This leads to quite a high number (2 5 = 32) of diastereoisomers, characterized by the axial or equatorial orientation of ring substitutents. Based on the chirality at C1 and C5 it is possible to classify pyranoses into α - and β -pyranoses or l - and d- pyranoses, respectively $^{53}$. For example, α -d- Glc and β -l- Glc differ from β -d- Glc only by the chirality at C1 and C5, respectively. For each of these two chiralities, 2 3 = 8 stereoisomers remain, which are conventionally named 53 glucose (Glc), galactose (Gal), mannose (Man), allose (All), altrose (Alt), talose (Tal), gulose (Gul) and idose (Ido). The position of substituents at the chiral centres are reported for convenience in Tab. I, for β -d- aldopyranoses. Each of these stereoisomers, in turn, can adopt different ring conformations. According to IUPAC recommendations $^{54}$, the conformation with two parallel ring sides (four coplanar atoms) and the other two atoms at opposite side of the ring plane is called chair . Chair conformers occur in two forms: the one with C4 and C1 respectively above and below the plane defined by the other four atoms, is identified by the symbol $^{4}$C$_{1}$ , while the conformer showing C1 above the ring plane and C4 below it is denoted by the symbol $^{1}$C$_{4}$ and often called inverted chair . Other puckered conformers with four coplanar atoms exist, such as the so-called boat and skew-boat (the latter also known as twist-boat). In the case of boats, two parallel ring sides define the ring plane and the atoms at the extrema of the ring are either above or below the ring plane (indicated for examples as 3 , $^{O}$B or B$_{3}$$_{,}$$_{O}$ ); in the case of skew-boats the ring plane is defined by three adjacent atoms and the nonadjacent one with the other ring atoms at opposite side (e.g. $^{3}$S$_{1}$ ) of the ring plane. Some ring conformations are depicted in Fig. 2. Conformers other than the one listed so far, which are of some relevance, are also given a conventional name, such as in the case of envelopes or of half chairs, and the reader can find a exhaustive list in Ref. 54. Obviously, many of the possible conformations are not likely to 4