Pi-Electrons in Three-Dimensions

Nonplanarity in conjugated organic molecules such as the bridged-annulenes, strained cycloalkenes, cyclophanes, pi-complexes of organometallic and surface-bound alkenes and aromatics and the transition states of most chemical transformations (particularly substitutions, additions, eliminations and pericyclic reactions), plays a fundamental role in determining their chemistry. The primary response of conjugated systems to nonplanarity is a change in the balance between the Sigma(sp2) and Pi(p) hybridization which is the rule in planar situations. In previous publications on this subject we have reported the development of the pi-orbital axis vector (POAV) analysis which preserves sigma-pi separability in nonplanar geometries by appeal to the orbital orthogonality relationships. It is the primary hypothesis of the POAV analys that the sigma-bonds lie along the internuclear axes of the molecule. Thus, after structural adjustment, the remaining dislocations are construed to occur among the pi-electrons. In the present paper a detailed analysis of these questions is presented in terms of electronic structure calculations on torsionally (C2) twisted ethylene. The results are in excellent agreement with the assumption and predictions of the POAV model and lend credence to the idea that torsionally twisted pi-systems may be adequately mapped onto a minimal sp basis set (for analytical purposes) by the POAV theory. In the second part of the paper a number of nonplanar conjugated systems are analyzed with the 3-dimensional (3D-) HMO theory. The 3D-HMO theory further quantities the POAV analysis by utilizing the local POAV hybrids to calculate overlap integrals between pairs of conjugated atoms. Suitably scaled, the overlap integrals provide reduced resonance integrals which allow a unified treatment of conjugated systems-planar and nonplanar. The natural definition of homoconjugation emerges from the analysis: the homoconjugate bond is characterized by an overlap integral between a pair of conjugated atoms in which the Ppi, Ppi contribution does not predominate.