SYMMETRY-MODIFIED CONFORMATIONAL MAPPING AND CLASSIFICATION OF THE MEDIUM RINGS FROM CRYSTALLOGRAPHIC DATA .1. CYCLOHEPTANE

Examples of (a) non-bridged and (b) bridged cycloheptane rings have been retrieved exhaustively from organic molecules in the Cambridge Structural Database. The 101 fragments of type (a) and 310 fragments of type (b) have been used to fill, by symmetry expansion, the hyperdimensional conformational space spanned by the intra-annular torsion angles. The resulting distributions have been examined by use of symmetry-adapted deformation coordinates, principal-component analysis (PCA) and symmetry-modified cluster analysis. The four-dimensional nature of conformational space is confirmed. The two independent pseudorotation pathways (chair-twist-chair and boat-twist-boat) can be seen to follow helical tracks on mutually orthogonal toroidal surfaces in four-dimensional space as predicted theoretically. The PCA yields four principal components, as two degenerate pairs, that can be correlated directly with the symmetry-adapted deformation modes. Cluster analysis of the conformations of non-bridged rings shows that the symmetrical low-energy forms are dominant (89%) with overall chair (C):twist-chair (TC):boat (B):twist-boat (TB) ratios of 30:48:10:1, although twelve C conformers are induced by small-ring fusion. For the bridged rings, C and B conformers dominate, with C:TC:B:TB ratios of 85:36:106:15, and distorted conformations are more frequently observed.