Vibrational Modes of C₆₀ Molecule

Abstract

The purpose of this article lies in a qualitative understanding of the vibrational excitation of C₆₀ molecule. In this paper we look upon a C₆₀ molecule as a 2-dimensional lattice with the icosahedral symmetry and then start with the analysis ofthe infinitesimal oscillation of a spherical elastic membrane, i.e., a 2-dimensional version of the Debye model. The analysis of the model turns out to be successfully carried out on a basis of the Riemannian geometry. We next approximate the vibration of C₆₀ molecule by that of a spherical membrane partially discretized in an icosahedral-symmetric way. The whole process described is expected to help understand a qualitative aspect of the existing results of the computer simulation. Finally it may be noteworthy that the method here developed is easily applicable to a variety of fullerenes.