Hybridization and the orientation and alignment of .pi.-orbitals in nonplanar conjugated organic molecules: .pi.-orbital axis vector analysis (POAV2)

The concept of hybridization of atomic orbital basis functions to produce spatially directed wave functions with the orientation necessary for bond formation is fundamental to the modern understanding of the molecular and electronic structure of molecules. In the present article, we consider a bonding situation which has become increasingly important in recent years-nonplanar conjugated organic molecules, which are usually considered to possess formal sp2 hybridization. It is shown that with a single assumption, it is possible to obtain analytical solutions for the hybridization in such compounds which in turn leads directly to the orientation of the *-orbital axis vectors (POAV) and hence to a measure of n-orbital alignment and overlap in distorted *-electron systems of known geometry. The *-orbital axis vector (POAV) analysis provides a vivid picture of the *-bonding in nonplanar conjugated organic molecules and the manner in which the a-system has rehybridized and adjusted to facilitate the maintenance of favorable *-orbital overlap. The method is nonparametric and merely requires the atomic coordinates of the molecule or molecular fragment for its implementation (computer program POAV~ has been deposited with the Quantum Chemistry Program Exchange). The analysis is based on the sp hybrid orthogonality relationships and the geometry of the o-skeleton. As such the method provides the most logical and natural bridge between the a-r separability assumed in planar conjugated systems and the realistics of *-bonding in nonplanar situations. The analysis is not recommended in circumstances where the o-bond angles are less than looo, but with this proviso the method may be used with confidence. The general practice of quoting formal dihedral angles as a measure of *-orbital alignment or strain is strongly discouraged-such an approach is misleading, arbitrary, and equivocal. The POAV analysis has been used to provide insight into the electronic structure of a number of nonplanar conjugated organic systems of topical interest.