Qualitative Insights into the Transport Properties of Hückel/Möbius (Anti)Aromatic Compounds: Application to Expanded Porphyrins

Expanded porphyrins have been recently identified as promising candidates for conductance switching based on aromaticity and molecular topology changes. However, the factors that control electron transport switching across the metal-molecule-metal junction still need to be elucidated. For this reason, the transport properties of Hückel/Möbius (anti)aromatic compounds are investigated thoroughly in this work to gain qualitative understanding into the conductivity of these unique macrocycles. Starting from a polyene model, a simple counting rule is developed to predict the occurrence of quantum interference around the Fermi level at the Hückel level of theory. Next, the different approximations of Hückel theory are lifted, enabling the exploration of the influence of each of these approximations on the transport properties of expanded porphyrins. Along the way, a detailed study on the relationship between the conductance and aromaticity/topology has been undertaken. Even though it has been proposed that the π-conjugated systems of expanded porphyrins can be approximated as polyene macrocycles based on the "annulene model", it turns out that the distortion induced by the pyrrole rings to the electronic structure of the expanded porphyrins causes the simple counting rule for the prediction of quantum interference developed for polyenes to fail in some specific situations. Nevertheless, our back-of-the-envelope approach enables an intuitive rationalization of most of the transport properties of expanded porphyrins. Our conclusions cast further doubt on the proposed negative relationship between conductance and aromaticity and highlight the importance of the connectivity on determining the shape of the transmission functions of the different states. We hope that the new insights provided here will offer experimentalists a road map toward the design of functional, multidimensional electronic switches based on expanded porphyrins.