How do the Hückel and Baird Rules Fade away in Annulenes?

• Main Authors: Irene Casademont-Reig, Eloy Ramos-Cordoba, Miquel Torrent-Sucarrat, Eduard Matito
• Format: Article
• Language: English
• Published: MDPI AG 2020-02-01
• Series: Molecules
• Subjects: annulenes; aromaticity; antiaromaticity; hückel rule; baird rule; density functional theory; delocalization error
• Online Access: https://www.mdpi.com/1420-3049/25/3/711

Two of the most popular rules to characterize the aromaticity of molecules are those due to H&#252;ckel and Baird, which govern the aromaticity of singlet and triplet states. In this work, we study how these rules fade away as the ring structure increases and an optimal overlap between <i>p</i> orbitals is no longer possible due to geometrical restrictions. To this end, we study the lowest-lying singlet and triplet states of neutral annulenes with an even number of carbon atoms between four and eighteen. First of all, we analyze these rules from the H&#252;ckel molecular orbital method and, afterwards, we perform a geometry optimization of the annulenes with several density functional approximations in order to analyze the effect that the distortions from planarity produce on the aromaticity of annulenes. Finally, we analyze the performance of three density functional approximations that employ different percentages of Hartree-Fock exchange (B3LYP, CAM-B3LYP and M06-2X) and Hartree-Fock. Our results reveal that functionals with a low percentage of Hartree-Fock exchange at long ranges suffer from severe delocalization errors that result in wrong geometrical structures and the overestimation of the aromatic character of annulenes.