Quantitative description of six-membered ring conformations following the IUPAC conformational nomenclature

Although several methods of quantitative conformational characterization exist in the literature, all these methods use a spherical polar coordinate representation which is in contrast to the qualitative description based on the IUPAC nomenclature. To bridge this gap this paper introduces a method to characterize six-membered ring conformations as a linear combination of ideal basic conformations. The linear combination coefficients are derived by projection of the vector of torsion angles onto those of ideal basic conformations. As the IUPAC nomenclature uses subscripts and superscripts to indicate atoms below and above the reference plane, the linear combination coefficients combined with the IUPAC name provide an instant visual image of the conformation. The method introduced here is based on endocyclic dihedral angles and requires only three dihedral angles for a full characterization, which is often available by NMR measurements for rigid conformations. We provide a table of equations to determine the missing dihedral angles based on redundancy conditions. The relationship between linear combinations and spherical representation similar to the well-known Cremer–Pople parameters is presented. In deriving the spherical conformational parameters we solved an inconsistency of previous definitions for spherical representation, namely that none of previous definitions place the intermediate halfchair or twistboat conformations exactly halfway between the pole (chair) and the equator (boat and twistboat) of the sphere as expected based on intuitive stereochemistry. To make our method generally available we provide an interface on the Internet that carries out all calculations described in the paper and allows the user to visualize, rotate and manipulate the ring (http://www.nrc.ca/ibs/6ring.html). By simplifying both the concepts and the access to carry out the calculations more experimental chemists can benefit from the description of ring conformation.