We have investigated the many-body effects in a molecular theory to determine simultaneously nuclear and electronic wave functions without the Born–Oppenheimer (BO) approximation. We first apply the many-body perturbation theory using the electron–nucleus and nucleus–nucleus interactions to the non-BO theory and show the importance of the electron–nucleus correlation rather than the nucleus–nucleus one. We next combine the non-BO theory with the coupled cluster double and Brueckner double methods using the one-electron plus one-nucleus excitation operators.
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Nakai et al. (2003) studied this question.