AUTOMATED CONFORMATIONAL-ANALYSIS FROM CRYSTALLOGRAPHIC DATA .6. PRINCIPAL-COMPONENT ANALYSIS FOR N-MEMBERED CARBOCYCLIC RINGS (N = 4,5,6) - SYMMETRY CONSIDERATIONS AND CORRELATIONS WITH RING-PUCKERING PARAMETERS

Representative samples of four-, five- and six-membered carbocycles have been retrieved from the Cambridge Structural Database and have been used to fill, by symmetry expansion, the hyperdimensional conformation spaces spanned by the intra-annular torsion angles for these ring systems. The resulting distributions have been probed by principal-component analysis (PCA). For cyclobutane, all of the sample variance can be described in terms of a single coordinate [or principal component (PC)] which maps the degree of pucker about the ring diagonal. In the case of cyclopentane two equally important PC's fully describe the sample variance, and together they map the pseudorotation itinerary which interconverts the envelope and twist conformations of this ring. For cyclopentenes, however, a single PC (accounting for almost 80% of sample variance) maps the extent of ring pucker, whilst a second PC (accounting for the remaining 20% of variance) is found to describe minor torsional distortions away from 0-degrees about the double bond. PCA for six-membered carbocycles (cyclohexanes and cyclohexenes) reveals three PC's: one mapping the interconversion of enantiomeric chair conformers, and two that describe the pseudorotational interchange between boat and twist-boat forms. For all three ring systems the reduction in dimensionality as a consequence of the PCA is compared to, and is shown to be consistent with, the dimension reduction inherent in the Cremer-Pople (CP) description of ring pucker [Cremer & Pople (1975). J. Am. Chem. Soc. 97, 1354-1358]. The results for five-membered rings are also shown to be fully consistent with the alternative Altona-Sundaralingam (AS) analysis [Altona & Sundaralingam (1972). J. Am. Chem. Soc. 94, 8205-8212]. The influence of outliers on the PCA is illustrated, and the results of the study are used to highlight the potentials (and pitfalls) of PCA for conformational analysis and conformational mapping.