It is customary, in the conformational analysis of sugar derivatives by the methods of molecular mechanics, to assume that pyranosidic rings are rigid and in either the 4C, or 'C, chair conformation. However, 3JH,H values obtained in 'H-n.m.r. spectroscopy suggest the existence of conformations other than chair forms and it is important to evaluate their structures and relative energies.
In a study of the conformation of methyl 4-O-methyl-ZO-sulfo-a-L-idopyranosiduronic acid, three conformers (4C, and 'C, chairs, and the skew-boat form "So) were computed to possess similar energies'. The analysis of a series of iduronate-containing compounds showed that significant proportions (up to 64O/) of the 'So conformer may occur, accounting for a wide range of 3JH,H values2. More recently, unusual 3JH,H values for the glucuronate residue in chondrosine were rationalised in terms of an equilibrium of the 4C, chair and one or more boat-like forms with comparable energies3.
To our knowledge, the method of computation involved has not been described. Several molecular mechanics packages afford a feature, the 'drive' (see, for example, Allinger and Yuh4), which allows the conformational energy to be minimised whilst constraining one or two dihedral angles to maintain, or reach, a given value. However, this method is not practical when dealing with pyranoid rings, because of the interdependence of the six angular values that define its geometry.
A sub-routine, built according to the mathematical methods described below, which makes use of suitable puckering co-ordinates, has been implemented in the molecular mechanics package REFINE', and was employed in the work cited abovele3.
Derivation of the algorithm. -The conformations of pyranoid rings are best described by a generalised set of puckering co-ordinates given by Cremer and Pople' VP).
These authors showed that the three puckering degrees of freedom for a sixmembered ring can be described by a 'spherical polar set' (Q, 8,4), easily derived from * Author for correspondence ' Package REF190 (I.C.M., Milano) is available from the authors.