Relationships between torsion angles and ring-puckering coordinates: Part III. Application to heterocyclic puckered five-membered rings

Abstract

The conformational analysis of five-membered rings is greatly facilitated by the concept of pseudorotation. The well-known pseudorotation equation for torsion angles (C. Altona and M. Sundaralingam J. Am. Chem. Soc., 94 (1972) 8205) yields a good correspondence between calculated and observed torsion angles for equilateral or nearly equilateral rings. In this communication the pseudorotation equation is extended by additional terms in order to yield an improved correspondence between calculated and observed torsion angles, especially for heterocyclic puckered rings (e.g. tetrahydrothiophene, 1,2-oxathiolane). The additional parameters, valid for a given class of five-membered rings, can be obtained either from a dataset of X-ray structures or from model structures optimized by ab initio or (semi)empirical calculations. Endocyclic bond angles in five-membered rings are correlated with the phase angle of pseudorotation P and with the puckering amplitude φ m. Coefficients for bond angle regressions with pseudorotation parameters are given for furanose and proline rings and for ring D in steroids. The geometry of a five-membered ring can be calculated with the computer program PSEU for any desired value of P and φ m. The nine independent coordinates are calculated from five torsion angles (obtained from a given P and φ m by means of the extended pseudorotation equation) and five bond distances by means of a least-squares procedure. Coefficients for functions relating the pseudorotation parameters to exocyclic bond angles and exocyclic torsion angles in furanose fragments are also established. Cartesian coordinates for model β- D-ribo- and β- D-deoxyribo furanoside fragments encompassing the full pseudorotation pathway are presented as supplementary material.