The vibron model and long molecular chains: Algebraic polyethylene and its first CH stretching overtone

We apply the algebraic (vibron) model to very long molecular chains, starting from n-alkanes molecules up to polyethylene. The infrared spectrum of CH stretches is computed in an algebraic basis and we obtain analytical formulas for both energy values and intensities of vibrational modes in the ν=2 overtone. We provide a simple, yet confident explanation of the main features of the IR spectrum of the polyethylene molecule in this energy range.