The Measure of Nonplanarity in Conjugated Organic Molecules: Which Structurally Characterized Molecule Displays the Highest Degree of Pyramidalization?.

The pathways of many organic chemical reactions involve pi- electron systems which undergo drastic deviations from planarity and the same situation prevails in the formation of the carbon spheriods such as icosahedral C sub 60. It is now becoming clear, however, that substantially nonplanar conjugated organic molecules can actually be isolated and subjected to (structural) characterization. Since interest in these compounds arose in many distinct connections, the nonplanarity has been assessed from a number of different standpoints. A measure which has found particular favor relates to the degree of pyramidalization, although this term has been used in many different connotations. It is of some interest to seek relations among these different measures and to inquire as to whether they lead to the same general scale of nonplanarity. It therefore seemed worthwhile to subject the various pyramidalization schemes to a rigorous analysis and to assess their predictive value. A set of vectors reciprocal to those pointing along the internuclear axes from a conjugated carbon atom are introduced. The resultant of the reciprocal vectors is shown to define the pi-orbital axis vector at a nonplanar conjugated atom. The quantities introduced in the transformation are sufficient to define all of the popular measures of pyramidalization in nonplanar conjugated organic molecules, and to allow comparisons between the different schemes. The measures of nonplanarity are divided according to isotropy, and it is shown that there is a high degree of correlation between the different scales of pyramidalization, particularly in the case of the isotropic analyses. The compound reported by Greene and coworkers in 1974, 9,9',10,10'- tetradehydrodianthracene (bold 2) is established as possessing the most pyramidalized carbon atoms of all structurally characterized molecules. All measures of pyramidalization concur with this assessment, and with the finding that the degree of pyramidalization in this compound surpasses that which is required in icosahedral C sub 60.