Triangle Counting Rule: An Approach to Forecast the Magnetic Properties of Benzenoid Polycyclic Hydrocarbons

TL;DR

This paper introduces the Triangle Counting Rule (TCR), a simple predictive method for the magnetic ground states of benzenoid polycyclic hydrocarbons, aiding the design of magnetic carbon nanostructures for quantum applications.

Contribution

The study develops the TCR based on graph analysis and extends existing theoretical rules, providing a new practical tool for predicting magnetic properties of BPHs.

Findings

Number of internal vertices correlates with open-shell character.

TCR extends Lieb's theorem and Ovchinnikov's rule.

Provides a database and predictive method for magnetic BPHs.

Abstract

Open-shell benzenoid polycyclic hydrocarbons (BPHs) are promising materials for future quantum applications. However, the search and realization of open-shell BPHs with desired properties is a challenging task due to the gigantic chemical space of BPHs, requiring new strategies for both theoretical understanding and experimental advancement. In this work, by building a structure database of BPHs through graphical enumeration, performing data-driven analysis, and combining tight-binding and mean-field Hubbard calculations, we discovered that the number of the internal vertices of the BPH graphs is closely correlated to their open-shell characters. We further established a series of simple rules, the triangle counting rule (TCR), to predict the magnetic ground state of BPHs. These findings not only provide a database of open-shell BPHs, but also extend the well-known Lieb's theorem and Ovchinnikov's rule and provide a straightforward method for designing open-shell carbon nanostructures. These insights may aid in the exploration of emerging quantum phases and the development of magnetic carbon materials for technology applications.