Abstract: By means of a deeper investigation of geminal N-electron basis set, the expansion formula of geminal N-electron basis set in terms of Slater determinants is obtained, in which the expansion coefficients are given explicity. As a direct result, the Hartree-Fock ab initio calculations can be taken as the starting point in the application of the geminal N-electron basis set for practical use.

Key words: Symplectic group, Geminal, N-electron basis, Slater determinant