Continuous symmetry of C60 fullerene and its derivatives

TL;DR

This paper investigates the symmetry of C60 fullerene, revealing that despite formal symmetry lowering to Ci, continuous symmetry measures show it remains nearly Ih, explaining its spectral properties and stability.

Contribution

The study introduces continuous symmetry analysis to demonstrate that C60's formal Ci symmetry is nearly Ih, providing new insights into its electronic spectra and stability.

Findings

C60's formal Ci symmetry is 99.99% Ih according to continuous symmetry measures.

Continuous symmetry analysis explains the optical spectra of fullerene derivatives.

C60 maintains a high degree of symmetry stability despite formal symmetry lowering.

Abstract

Conventionally, the Ih symmetry of fullerene C60 is accepted which is supported by numerous calculations. However, this conclusion results from the consideration of the molecule electron system, of its odd electrons in particular, in a close-shell approximation without taking the electron spin into account. Passing to the open-shell approximation has lead to both the energy and the symmetry lowering up to Ci. Seemingly contradicting to a high-symmetry pattern of experimental recording, particularly concerning the molecule electronic spectra, the finding is considered in the current paper from the continuous symmetry viewpoint. Exploiting both continuous symmetry measure and continuous symmetry content, was shown that formal Ci symmetry of the molecule is by 99.99% Ih. A similar continuous symmetry analysis of the fullerene monoderivatives gives a reasonable explanation of a large variety of their optical spectra patterns within the framework of the same C1 formal symmetry exhibiting a strong stability of the C60 skeleton.