## Information

Responsable Physico-Chimie Théorique

**Rodolphe VUILLEUMIER**

## Prix et distinctions

## Dernière publication

### 2017

## Professeurs invités

# On the Mass of Atoms in Molecules: Beyond the Born-Oppenheimer Approximation

**On the Mass of Atoms in Molecules: Beyond the Born-Oppenheimer Approximation, ***PHYSICAL REVIEW X, ***25 août 2017**

The Born-Oppenheimer (BO), or adiabatic, treatment of the coupled motion of electrons and nuclei in molecular systems is among the most fundamental approximations in condensed matter physics and chemical physics. Based on the hypothesis that part of the system, usually electrons or protons, evolves on a much shorter time scale than the rest, i.e., (heavy) nuclei, the BO approximation allows one to visualize molecules as a set of nuclei moving on a single potential energy surface that represents the effect of the electrons in a given eigenstate. Yet, it is an approximation, yielding the correct dynamics only in the limit of infinite nuclear masses. For instance, when compared to highly accurate molecular spectroscopy measurements, theoretical predictions might deviate from experimentally observed behavior.

Conceptually, we have resolved a well-known fundamental inconsistency of the BO approximation. In a translationally invariant problem, the center of mass moves as a free particle with mass that equals the total mass of the systems, i.e., nuclei and electrons, not only the nuclear mass. This feature is naturally built in the theory and corrects for a deficiency of the BO approximation, providing exactly the missing mass of the electrons. From amore practical point of view, our approach is very general and can be applied whenever a “factorization” of the underlying physical problem is possible, e.g., in the case of proton and oxygen atoms or in the case of electrons and nuclei.

Consultez le communiqué associé à cet article : Corriger l’approximation de Born-Oppenheimer !

**PHYSICAL REVIEW X** 25 août 2017

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.

**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