Theoretical Vibrational Spectra of Carbon Fullerenes

This article investigates the stretching vibrational modes of carbon fullerenes (C₂₄, C₂₈, C₃₂, and C₅₀) by using one-dimensional U(2) algebra. Considering the molecular symmetry, the model Hamiltonian is constructed which is able to describe the fundamental “stretching modes” of the physical system with less number of algebraic parameters. The calculated energies find an excellent agreement with the theoretical data of harmonic force constant calculation.