Maximum radius of convergence (MAXRc) perturbation theory [(2000) Journal of Chemical Physics 112:6997] is tested on the beryllium and neon atoms using calculations that are truncated in high orders. Calculations are also performed on the ground-state potential-energy curves of H2 and HF. The neon atom calculations use the 3-21G basis set with added diffuse s and p functions. All other calculations use the STO-3G minimum basis set. MAXRc perturbation theory consistently performs well. The Epstein–Nesbet and Møller–Plesset perturbative expansions frequently diverge or exhibit slow convergence compared to the expansions obtained from MAXRc.