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The above analysis of a molecule with many (>3) torsional degrees of freedom is based on specially developed concepts and methods. First, the conformation of each PPh3-group and of each phenyl group is described by a single torsion angle, thus disregarding deviations from local C3vor C2v-symmetry, respectively. Second, the symmetry of the resulting 8-dimensional conformational space is taken into account. Symmetry implies among other things a periodic structure of this space due to the cycli~ nature of torsional coordinates. (MurrayRust, Burgi and Dunitz, Acta Cryst. A35 (1979) 703). This structure may be utilized by analyzing several, adjacent asymmetric units together (i.e. a data set containing an integer mUltiple of the original 62 data points) and by transforming torsion angles into appropriate sine and cosine values. Regions in conformational space which are densely populated with data points, were located using Ward's method of cluster analysis (Ward, J. Am. Stat. Ass. 58 (1963) 236) as implemented in SAS-procedure CLUSTER (SAS User's Guide: Statistics, SAS Institute Inc. (1982) Cary NC, USA). The clustering process treats every data point as a cluster, then joins neighboring clusters into new ones until all data points form a single cluster. For present purposes the process is intercepted, however: the final set of clusters is obtained with the following two criteria: (1) the set must conform to the symmetry of conformational space, and (2) a statistical clustering criterion must be a maximum.

acta crystallographica. section a, foundations of crystallography/acta crystallographica. section a

Interactions between diazonium groups and nucleophilic centres attached to the peri positions of naphthalenoid ring systems. Implications for the preferred direction of nucleophilic attack on N, N triple bonds