In this paper the normal mode of vibrational energy levels of ethylene & benzene molecules are studied by U(2) Lie algebra. Its application to ethylene & benzene are presented with fewer algebraic fitting parameters. Here each 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 normal modes of vibrational energy levels of these molecules are calculated and hence compared by considering the local Hamiltonian of Morse potential using the U(2) algebra.
