Abstract: The Schrodinger equation of many-electron atom is expressed in terms of hyperspherical ccordinates.Bsaed on the total wave function satisfying the Pauli principle, the coupled hyperradial differential equation is derived, which is similar to that of He atom.Symmetric basis functions are constructed for irreducible representation of S₃ permiitation group by applying the standard Young projection operator on nine-dimensional hyperspherical harmonics.We generdlize the HHGLmethod proposed by C.H.Deng to Li atom, and calculate firstly the ground-state eigenvalue, which qualitatively approaches to the experimental one.Morever, the slow convergence of the method for eigen energy is discussded.

Key words: Hypersplierical coordinate, Symmetric basis for irreducible representation of permutation group S₃, Hyperspherical harmonics, Generalized Laguerre function