On the convergence of the Møller-Plesset perturbation series

Møller-Plesset perturbation energies, up to as much as 48th order, have been calculated for H₂O (RHF and UHF framework) and NH₂ (UHF framework) atC_2v geometries (r_e, 1.5r_e and 2r_e). Atr_e, the RHF and UHF series rapidly converge, but at2r_e, the RHF series converges erratically with an energy at 43rd order within 10^–7 hartree of the exact value whereas the UHF series converges smoothly, but very slowly, and for H₂O has an error in excess of 10^–5 hartree at 48th order. The significance of these results is discussed.