Bond Length Dependence of Cluster Expansions of Pi-Electron Energy

Abstract

There are two long established methods for representing the delocalized portion of the pi-electron energy of conjugated molecules in a simple local fashion. One, introduced by Hess and Schaad, can be used to provide a very accurate estimate of the energy of acyclic polyenes. Another, introduced originally by Herndon, has been successfully applied to the energy of aromatic ring systems. Both methods can be shown to be forms of cluster expansions, in which the energy of a molecule is expressed exactly as a sum of (successively smaller) contributions from successively larger molecular fragments. As such, it should in principle be possible to combine the methods to provide a consistent description of molecules of almost any structure. However past attempts to do so have yielded physically unreasonable results. It is shown that the key missing ingredient in these attempts is a failure to account for bond stretching and compression. When the energy changes associated with bond length changes are accounted for properly, the combined cluster expansion is quite successful in accounting for molecular pi electron energies in a very compact form.