Spectroscopic Studies on Distorted Structure Nanomolecules by Using Lie Algebraic Model

We have applied Lie algebraic model to distorted structure molecules to determine the vibrational spectra of different stretching and bending vibrational modes. The the Lie algebraic model of the Hamiltonian expression is H = $E_0 + \sum_{i = 1}^{n} A_{i} C_{i} + \sum_{i < j}^{n} A_{ij} C_{ij} + \sum_{i < j}^{n} \lambda_{ij} M_{ij}$. By using the Lie algebraic method, the stretching vibrational energies of fullerene $(C_{80})$ are calculated in the one-dimensional [U(2)] framework. Using the model Hamiltonian so constructed, we have calculated the local mode vibrational energy levels of the fullerene $(C_{80})$ accurately.