Rotation–vibration spectra of icosahedral molecules. II. Icosahedral symmetry, vibrational eigenfrequencies, and normal modes of buckminsterfullerene

Abstract

The icosahedral symmetry of molecules such as buckyball, B12H12−2, and C20H20, is analyzed using subgroup chain defined projection operators. The icosahedral analysis is used to determine the eigenvalues and eigenvectors of a classical spring mass model of buckyball. A spectrum of Raman and dipole active modes is given using the spring constants of benzene. Corresponding dipole active and Raman active normal modes are displayed stereographically. Several choices for springs constants are discussed and a comparison with spring mass systems of reduced symmetry is made.