RELATIONSHIPS BETWEEN TORSIONAL ANGLES AND RING-PUCKERING COORDINATES.5. APPLICATION TO 6-MEMBERED RINGS

The DE relationships derived for infinitesimal puckering of a six-memb ered ring which describe the variation of the AS RP coordinates (Phi(2 ), P-2, Phi(3)) with the CP ones (q(2), P'(2), q(3)) and those giving the dependence of the endocyclic torsion angles phi(j) upon both sets of RP coordinates have been applied to analyze a set of molecular mech anics geometries of rings (CH2)(5)X (X = CH2, O, S) as well as a set o f X-ray structures of derivatives. The parameters in the corresponding expressions have been estimated theoretically from the bond angles an d bond lengths of planar reference conformations. The torsion angles p hi(j) are accurately described using the AS RP coordinates, the sigma deviations amounting 0.3 degrees for MM2 and 0.5 degrees for X-ray geo metries. The DE relationships describe worse the variation with the CP RP coordinates of the phi(j) angles and of the AS RP coordinates. How ever, the accuracy of these relationships is greatly improved when the finite puckering effects are taken into account by substituting the q (2) and q(3) amplitudes for functions in both q2 and q3 with only four lambda parameters to be determined. Very accurate equations between t he AS and CP RP coordinates are so obtained which permit one to analyz e quantitatively the relation between the conformational spaces spanne d by both kinds of RP coordinates.