Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons, and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue has still not been solved, in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-nuclear wave function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via positiondependent corrections to the bare nuclear masses.
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On the Mass of Atoms in Molecules: Beyond the Born-Oppenheimer Approximation
Arne Scherrer, Federica Agostini, Daniel Sebastiani, E. K. U. Gross & Rodolphe Vuilleumier
PHYSICAL REVIEW X 25 août 2017