Automated Conformational Analysis from Crystallographic Data. 2.* Symmetry-Modified and Complete-Linkage Clustering Algorithms for Three-Dimensional Recognition

The complete-linkage and Jarvis-Patrick clustering algorithms are used to identify discrete conformational subgroups for a chemical fragment from crystal structure data. Fragment conformations are defined by Nt torsion angles for N s occurrences of the fragment in the Cambridge Structural Database. Both algorithms are extensively modified to handle 2D topological symmetry of the fragment and the 3D conformational enantiomers which occur in crystal structures. The modified procedures ensure that symmetry equivalents of a given conformation are optimally superimposed in a unique cluster. A modified single-linkage algorithm, based on cluster centroids, is used to place the discrete clusters in a single asymmetric unit of conformational space. Principal-component analysis provides a graphical representation of the clustering process. The complete-linkage and Jarvis-Patrick algorithms may be preferable to single-linkage cluster analysis [Allen, Doyle & Taylor (1991). Aeta Cryst. B47, 29-40] since they minimize the effects of 'chaining' i.e. the linkage of major clusters through a chain of outlying observations. Both of the new algorithms have been tested using a trial data set of 222 six-membered carbocycles of known conformational complexity. The new algorithms are judged to provide a more effective conformational breakdown of the trial data set (in chemical terms) than that obtained with the single-linkage method alone.