Uncovering Clar's aromatic π -sextet rule in the Hubbard model using Maximum Probability Domain Partitions

Abstract

Clar's aromatic $\pi$ -sextet rule is a widely used qualitative method for assessing the electronic structure of polycyclic benzenoid hydrocarbons. Unfortunately, many of the quantum chemical concordances for this rule have a limited range of applicability. Here, we show that the fundamental probabilities associated with a distribution of electrons over domain partitions support Clar's rule in both mean-field and static correlation regimes. In particular, domain partitions that maximize those probabilities reflect the dominance of Clar structures in the electronic structure of these molecules. These findings suggest that extending methods that aim to maximize probabilities by deforming domain partitions could lead to novel quantum chemical underpinnings for many chemical concepts.

Keywords: Clar's rule; Hubbard model; Maximum Probability Domain Partitions.