Additional Quantum Numbers for Electron Orbitals of Nanoparticles

TL;DR

This paper introduces additional quantum numbers necessary for uniquely classifying electron orbital states in large symmetrical nanoparticles, especially when IRs repeat, enhancing understanding of nanoparticle symmetry.

Contribution

It proposes using IR labels of intermediate subgroups for complete classification of electron states in symmetrical nanoparticles, addressing limitations of traditional quantum numbers.

Findings

Additional quantum numbers are needed for unambiguous labeling.

IR labels of intermediate subgroups help classify states with repeating IRs.

Examples with Oh and Ih groups illustrate the approach.

Abstract

It is shown that in large symmetrical nanoparticles additional quantum numbers are required to label unambiguously symmetry adapted linear combinations of the wave functions. It is obtained that the labels of irreducible representations (IRs) of intermediate subgroups (between the whole symmetry group and local subgroup) can be used for complete classification of states in the case of repeating IRs. The examples of Oh and Ih groups are considered and the connection of additional quantum numbers with local interactions is discussed