Algebraic Hamiltonian of SO~2 molecule is classified using coherent state. The potential energy surface is derived from classical Hamiltonian. We proposed a new transformation for introducing the bond angle to the potential energy surface. We calculated the force constants and dissociation energy using this potential energy surface, and create the surface figure and its contour. These results are in good agreement with previous results. This method can be easily extended to polyatomic molecules.

Key words: SULFUR DIOXIDE, POTENTIAL ENERGY SURFACES, LIE ALGEBRA, VIBRATIONAL STATE, EXCITED STATE