Algebraic theory of endohedrally confined diatomic molecules: application to H$_2$@C$_{60}$

TL;DR

This paper introduces a dynamical algebra-based model to describe the structure of endohedrally confined diatomic molecules, specifically applied to H₂@C₆₀, predicting spectral levels with few parameters.

Contribution

The paper develops a u(4)+u(3) algebraic framework combining vibron and center-of-mass degrees of freedom for confined molecules, applied to H₂@C₆₀.

Findings

Successfully describes H₂@C₆₀ spectrum with few parameters

Predicts new energy levels for endohedral molecules

Suggests reassigning quantum numbers for better data fit

Abstract

A simple and yet powerful approach for modeling the structure of endohedrally confined diatomic molecules is introduced. The theory, based on a u(4)+u(3) dynamical algebra, combines u(4), the vibron model dynamical algebra, with a u(3) dynamical algebra that models a spherically symmetric three dimensional potential. The first algebra encompasses the internal roto-vibrations degrees of freedom of the molecule, while the second takes into account the confined molecule center-of-mass degrees of freedom. A resulting subalgebra chain is connected to the underlying physics and the model is applied to the prototypical case of H2 caged in a fullerene molecule. The spectrum of the supramolecular complex H2@C60 is described with a few parameters and predictions for not yet detected levels are made. Our fits suggest that the quantum numbers of a few lines should be reassigned to obtain better agreement with data.