Abstract

A connection is developed between typical characteristic polynomial coefficient sign patterns and Δ, the difference between the numbers of π-bonding and π-antibonding molecular orbitals for hydrocarbons. A link is revealed between Δ and dominant Sachs' subgraphs for the non-zero characteristic polynomial coefficient that is closest to the end of the polynomial. Through the intermediacy of the appropriate Sachs' subgraphs, the connection between a given Lewis structure and Δ is clarified. Exploiting the Sachs' subgraphs, one can redesign non-alternant hydrocarbon structures to alter π-system stability and, therefore, the kinetic stability of interesting molecules. A PM3 test of this methodology is provided in the accompanying paper.