On the mass of atoms in molecules: Beyond the Born-Oppenheimer approximation

Abstract

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 to include 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 still is not 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 position-dependent corrections to the bare nuclear masses. This maintains an adiabatic-like point of view: the nuclear degrees of freedom feel the presence of the electrons via a single potential energy surface, whereas the inertia of electrons is accounted for and the total mass of the system is recovered. This constitutes a general framework for describing the mass acquired by slow degrees of freedom due to the inertia of light, bounded particles. We illustrate it with a model of proton transfer, where the light particle is the proton, and with corrections to the vibrational spectra of molecules. Inclusion of the light particle inertia allows to gain orders of magnitude in accuracy.

References in corpus (3)

• The adiabatic limit of the exact factorization of the electron-nuclear wave function
• Classical nuclear motion coupled to electronic non-adiabatic transitions
• Accurate \textit{ab initio} vibrational energies of methyl chloride

Cited by in corpus (20)

• On the Numerical Solution of the Exact Factorization Equations
• Shedding Light on Correlated Electron-Photon States using the Exact Factorization
• High accuracy water potential energy surface for the calculation of infrared spectra
• Quantum-classical nonadiabatic dynamics of Floquet driven systems
• Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states
• Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation
• Non-adiabatic mass-correction functions and rovibrational states of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\text{u}}^{+}$)
• Anyonic molecules in atomic fractional quantum Hall liquids: a quantitative probe of fractional charge and anyonic statistics
• Non-adiabatic mass correction to the rovibrational states of molecules. Numerical application for the H${}_2^{+}$ molecular ion
• Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation
• Non-adiabatic mass correction for excited states of molecular hydrogen: improvement for the outer-well $H\bar{H}{}^1{\Sigma }_{\mathrm{g}}^{+}$ term values
• H${}_3^{+}$ as a five-body problem described with explicitly correlated Gaussian basis sets
• Vibronic mass computation for the $EF$-$GK$-$H\bar{H}$ ${}^1{\Sigma }_{\text{g}}^{+}$ manifold of molecular hydrogen
• Density Matrix Renormalization Group Study of a One Dimensional Diatomic Molecule beyond the Born-Oppenheimer Approximation
• Ehrenfest dynamics implemented in the all-electron package exciting
• Dynamical response of noncollinear spin systems at constrained magnetic moments
• Electronic decoherence along a single nuclear trajectory
• Quantum covariant derivative
• Exactly factorized molecular Kohn-Sham density functional theory
• Rototranslational sum rules for nuclear dynamics via traveling pseudopotentials