The nuclear orbital plus molecular orbital (NOMO) theory was developed in order to determine the nonadiabatic nuclear and electronic wave functions without Born-Oppenheimer (BO) approximation. In this study, the translational-free NOMO method is applied to one- and two-electron atomic systems of first-row elements (from H to Ne), which possess no vibrational and rotational motions. We compare the total-energy difference between MO and NOMO calculations with exact non-BO effects and show the importance of the separation of the translational motion for the accuracy of the non-BO effects. (c) 2006 Elsevier B.V. All rights reserved.