Hund and anti-Hund rules in circular molecules

TL;DR

This paper investigates the validity of Hund's first rule in circular molecules using a perturbative extended Hubbard model, revealing conditions where anti-Hund behavior dominates and how electron count influences ground state spin multiplicity.

Contribution

It provides a theoretical analysis showing anti-Hund rules always apply at half-filling for 4N atom molecules and identifies conditions where Hund or anti-Hund ground states occur based on electron filling and interaction strengths.

Findings

Anti-Hund rule always applies at half-filling for 4N atom molecules.

Both singlet and triplet ground states are possible depending on electron count.

Long-range interactions influence the realization of Hund's rule in certain fillings.

Abstract

We study the validity of Hund's first rule for the spin multiplicity in circular molecules - made of real or artificial atoms such as quantum dots - by considering a perturbative approach in the Coulomb interaction in the extended Hubbard model with both on-site and long-range interactions. In this approximation, we show that an anti-Hund rule {\it always} defines the ground state in a molecule with $4N$ atoms at half-filling. In all other cases (i.e. number of atoms {\it not} multiple of four, or a $4N$ molecule away from half-filling) both the singlet and the triplet outcomes are possible, as determined {primarily} by the total number of electrons in the system. In some instances, the Hund rule is always obeyed and the triplet ground state is realized {\it mathematically} for any values of the on-site and long range interactions, while for other filling situations the singlet is also possible but only if the long-range interactions exceed a certain threshold, relatively to the on-site interaction.