Pyramidalization: Geometrical interpretation of the pi-orbital axis vector (POAV) in three-dimensions.

The pi-orbital axis vector (POAV) analysis provides a measure of the orientation (and hybridization) of pi-orbitals in formally sp sup 2 hybridized organic molecules which deviate from planarity. In the present note we provide a geometrical interpretation of the pi-orbital axis vectors themselves, in terms of the underlying sigma-skeleton. It is shown that the POAV may be expressed in terms of the vector areas of the three triangles formed by the three sigma-bonds at the conjugated atom in question. The construction makes it clear that the term pyramidalization provides an apt description of the process accompanying deviations from planarity in conjugated organic molecules. The analysis allows a connection to be established between the POAV approach and previous theories of molecular structure.