Based on the JahnTeller effect and quantum theory

the JahnTeller effect of Na-3 was studied with using the methods of group theory and symmetry analyses. The vibronic Hamiltonian of the E′e′ JahnTeller system was constructed. The Hamiltonian of the system was separated into two parts using unitary shift transformation

one part is the Hamiltonian of not having phonons excited

and the other part is the Hamiltonian of having phonons excited.The ground states and their energy of the system in each minimum were obtained

and the corresponding excited states and their energy in each minimum were also derived further. It was found that there were four potential energy minima on the potential energy surface of Na3. No matter which minimum the system was in

the original ground energy level of the system was split into two energy levels. The distortion leaded to that the symmetry of Na-3 was lowered to C 2v from D3h and the vibration frequency of system was split. After the distortion

the isotropy of Na-3 was destroyed and its anisotropy should appear.