# Exchange rules for diradical {\pi}-conjugated hydrocarbons

## TL;DR

This paper develops rules to accurately predict zero mode states, spin multiplicity, and shell nature of planar pi-conjugated hydrocarbons, extending beyond traditional theorems using analytical, Hubbard model, and quantum chemistry methods.

## Contribution

It introduces a comprehensive set of rules for predicting electronic states and spin configurations in diradical pi-conjugated hydrocarbons, surpassing existing theorems.

## Key findings

- Rules accurately predict zero mode states and spin multiplicity.
- Analytical and computational methods validate the predictions.
- Extends understanding beyond Lieb's theorem and Ovchinnikov's rule.

## Abstract

A variety of planar {\pi}-conjugated hydrocarbons such as heptauthrene, Clar's goblet and, recently synthesized, triangulene have two electrons occupying two degenerate molecular orbitals. The resulting spin of the interacting ground state is often correctly anticipated as S = 1, extending the application of Hund's rules to these systems, but this is not correct in some instances. Here we provide a set of rules to correctly predict the existence of zero mode states, as well as the spin multiplicity of both the ground state and the low-lying excited states, together with their open- or closed-shell nature. This is accomplished using a combination of analytical arguments and configuration interaction calculations with a Hubbard model, both backed by quantum chemistry methods with a larger Gaussian basis set. Our results go beyond the well established Lieb's theorem and Ovchinnikov's rule, as we address the multiplicity and the open-/closed-shell nature of both ground and excited states.