Abstract: Based on the geometrical structure，feature table and irreducible representation of phosphate ion，

the vibration mode is analyzed. Then，according to selection rules of Raman spectroscopy，Raman activity of phosphate

ion is also discussed. Using the G matrix and F matrix of phosphate ion，we solve the prolonged equation of

simple positive vibration and got the Raman spectral frequency shift. By using the Demol3 program package under

the frame of density functional theory，the Raman vibration frequency shift for Phosphate ion are calculated and the

results are close to the data obtained above.

Key words:  , phosphate ion, group theory method, vibration mode, Raman vibration spectrum