Interpretation of Hund's multiplicity rule for the carbon atom

TL;DR

This paper uses quantum Monte Carlo methods to analyze Hund's multiplicity rule in the carbon atom, providing detailed insights into the electronic correlation and the energetic mechanism behind the rule.

Contribution

It offers a high-accuracy quantum Monte Carlo analysis of Hund's rule for carbon, clarifying the energetic origin of the rule with potential extension to heavier atoms.

Findings

Triplet state has greater electron-nucleus attraction than singlet.

Quantum Monte Carlo accurately accounts for electronic correlation.

Results support the mechanism proposed by Hartree-Fock and correlated studies.

Abstract

Hund's multiplicity rule is investigated for the carbon atom using quantum Monte Carlo methods. Our calculations give an accurate account of electronic correlation and obey the virial theorem to high accuracy. This allows us to obtain accurate values for each of the energy terms and therefore to give a convincing explanation of the mechanism by which Hund's rule operates in carbon. We find that the energy gain in the triplet with respect to the singlet state is due to the greater electron-nucleus attraction in the higher spin state, in accordance with Hartree-Fock calculations and studies including correlation. The method used here can easily be extended to heavier atoms.