Extension and Quantification of the Fries Rule and Its Connection to Aromaticity: Large-Scale Validation by Wave-Function-Based Resonance Analysis

The Fries rule is a simple, intuitive tool to predict the most dominant Kekule structures of polycyclic aromatic hydrocarbons (PAHs), which is valuable for understanding the structure, stability, reactivity, and aromaticity of these conjugated compounds. However, it still remains an empirical hypothesis, with limited qualitative applications. Herein, we verify, generalize, and quantify the Fries rule based on the recently developed resonance analysis of the DFT wave functions of over 1500 PAH and fullerene molecules with over a billion Kekule structures. The extended rules, counting the numbers of electrons within all rings (not just sextets), are able to rank the relative importance of all Kekule structures for all considered systems. The statistically meaningful quantification also opens a way to evaluate ring aromaticity based on the resonance theory, which generally agrees well with conventional aromaticity descriptors. Furthermore, we propose a purely graph-based aromaticity indicator nicely applicable to PAHs and fullerenes, with no need of any quantum chemistry calculations, so that it can make valuable predictions for molecular properties that are related to local aromaticity.

Automated summary

The Fries rule, a simple and intuitive tool for predicting dominant Kekule structures of PAHs, has been verified, generalized, and quantified based on resonance analysis of over 1500 PAH and fullerene molecules. The extended rules, counting the numbers of electrons within all rings, can rank the relative importance of Kekule structures for all considered systems. The study also proposes a graph-based aromaticity indicator applicable to PAHs and fullerenes, which does not require any quantum chemistry calculations and can predict molecular properties related to local aromaticity.