Ring Current in Anthracene and Phenanthrene: Correction to Hückel Parameters

Abstract

Excessive degeneracy in the ground state of the π-electron energy levels of anthracene was removed using the Hückel method by correcting the Coulomb integral of the four central carbon atoms. A further correction to the resonance integral was proposed based on the ring-current model, which describes the π-ring current flow along the molecule’s perimeter, by introducing a new parameter for the bridge carbon atoms expressed as a fraction of the resonance energy. The solution to the Hamiltonian was obtained based on the symmetry group theory, which provides the advantage of solving the determinant matrix or secular equations in a particular irreducible representation with a relatively small matrix dimension. The results were further analyzed to determine the bond order and bond length. The values of the harmonic oscillator model of aromaticity, GEO, and EN indices of aromaticity and their ratio for the central and outer rings of benzene were used to evaluate the validity of the correction. Applying the same method to phenanthrene as a topological analog of anthracene allows for an interesting comparison of the stabilities of the two molecules.