Abstract: Three simple spatially symmetric correlation functions exp[-α(r₁₊r₂₊r₃)](variable parameter a by E+3/2α²=0,constant α,2.76 and the nuclear charge z,respectively)are used to carry out the correlation-function hyperspherical-harmonic and generalized-Laguerre-function(CFHHGLF) calculations of the ground state lithium atom.With 215 symmetric bases of the two-dimensional irreducible representation for the permutation group S₃,constructed from nine-dimensional hyperspherical harmonics,the CFHHGLF calculations provide the best eigenenergy of -7.473122 a.u.as α=z,followed by α=2.76,-7.450788 a.u.,and the variable parameter α,-7.413668 a.u.,while from the convergence rate in the hyperradial direction,the variable parameter α generates the fastest convergence eigenenergy,and as α=.76 the eigenenergy slowly converges,as α=z the eigenenergy converges only when over 100 symmetry bases are taken into account.In view of the accuracy as well as the stability of the eigenenergy,symmetric exponent correlation function with α=z should be considered to obtain high precise eigenenergy in hyperspherical harmonic method.

Key words: Hyperspherical Harmonics, Correlation functions, Ground state of the lithium atom