Algebraic techniques are examined as a computational tool for the analysis and interpretation of experimental rovibrational spectral of small and medium-sized molecules. These techniques are based on the idea of dynamical symmetry, which in turn, is expressed through the language of unitary Lie algebras. Within this framework, any specific mechanism relevant for the correct characterization of the molecular dynamics and spectroscopy can accounted. Here every C-C bond of the molecule is replaced by a corresponding Lie algebra and finally the Hamiltonian is constructed considering the interacting Casimir and Majorana operators. The fundamental vibrational energy levels of the carbon C60 and C70 clusters are then calculated using this Hamiltonian to fit the experimental results.