AUTOMATED CONFORMATIONAL-ANALYSIS FROM CRYSTALLOGRAPHIC DATA .5. RECOGNITION OF SPECIAL POSITIONS IN CONFORMATIONAL SPACE IN SYMMETRY-MODIFIED CLUSTERING ALGORITHMS

This paper reports an extension to algorithms for the conformational classification of symmetrical chemical fragments on the basis of torsion-angle descriptors [Allen, Doyle & Taylor (1991). Acta Cryst. B47, 29-40, 41-49, 50-61]. The algorithms take account of 2D topological symmetry and bring all cluster centroids into a single asymmetric unit of conformational space. In some cases, however, mean conformational geometries show marginal distortions from ideal symmetric forms, i.e. the centroid lies close to a special symmetry position in conformational space. Here we examine a number of methods by which this proximity can be recognized. A simple, general solution is adopted based on the torsional dissimilarities, D(C(c),C(c')), between a given cluster centroid (C(c)) and each of its symmetry equivalents (C(c)). Symmetry-related clusters, c', are coalesced with the original cluster, c, if D(C(c),C(c')) less-than-or-equal-to MULT x (D(c))max, where (D(c))max is the maximum dissimilarity between any fragment in c and the centroid C(c). MULT is normally unity, but can be altered in practical applications. This procedure yields the 'order' of the symmetrized cluster (i.e. the number of symmetry variants that have been coalesced) and hence the multiplicity of the special position. The implications of cluster coalescence in the generation of statistical descriptors for the torsion-angle distributions is considered. The procedures are illustrated by application to a trial data set of six-membered carbocycles.