High-order Moller-Plesset perturbation calculations have been carried out for several small molecules and compared to full configuration interaction (FCI) results. The convergence of the Moller-Plesset series is found to depend crucially on the one-electron basis sets. Addition of diffuse basis functions leads in some cases to divergent behavior of the Moller-Plesset series, even for highly single reference dominated systems as Ne and HF. The results thus questions the usefulness of higher-order perturbation calculations as a vehicle for obtaining arbitrary accuracy of quantum chemical calculations and raises the fundamental theoretical question : When does Moller-Plesset perturbation theory converge for many-electron systems in extended basis sets? 1996 American Institute of Physics.