Non-Born–Oppenheimer effects predicted by translation-free nuclear orbital plus molecular orbital method

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.