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) atC2v geometries (re, 1.5re and 2re). Atre, the RHF and UHF series rapidly converge, but at2re, 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.