The equilibrium geometry of N2O, NO and N2 molecules have been calculated on the computational levels of density functional theory. The Murrell-Sorbie analytic potential energy function of NO and N2 molecules have been derived through the least-square fitting to ab initio data. Similarly, the harmonic frequency has been calculated and the analytic potential energy function of linear molecule N2O isomer is derived by many-body expansion theory for the first time.