Dependence of Hess-Schaad resonance energy on Kekulé structures

Abstract

The Hess-Schaad resonance energy is defined as RE = E - Eref where E is the total π-electron energy and Eref is the reference energy computed by adding double- and single-bond contributions pertaining to some Kekulé structure. Therefore RE depends on the Kekulé structure considered. We show that in the case of benzenoid molecules the number of only one double-bond type determines RE. Furthermore, RE is a monotonically increasing function of the number of double bonds of type 3-3 or 2-2, and a monotonically decreasing function of the number of double bonds of type 2-3. This implies that RE is maximal if the respective Kekulé structure has the greatest possible number of double bonds of type 3-3, or the greatest possible number of double bonds of type 2-2, or the smallest possible number of double bonds of type 2-3.