Non-adiabatic mass-correction functions and rovibrational states of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\text{u}}^{+}$)

Abstract

The mass-correction functions in the second-order non-adiabatic Hamiltonian are computed for the ${}^4$He${}_2^{+}$ molecular ion using the variational method, floating explicitly correlated Gaussian functions, and a general coordinate-transformation formalism. When non-adiabatic rovibrational energy levels are computed using these (coordinate-dependent) mass-correction functions and a highly accurate potential energy and diagonal Born-Oppenheimer correction curve, significantly improved theoretical results are obtained for the nine rotational and two rovibrational intervals known from high-resolution spectroscopy experiments.

References in corpus (11)

• Nonadiabatic corrections to rovibrational levels of H${}_2$
• Nonadiabatic corrections to the wave function and energy
• On the mass of atoms in molecules: Beyond the Born-Oppenheimer approximation
• Pre-Born-Oppenheimer Molecular Structure Theory
• The time-dependent Born-Oppenheimer approximation
• On the Calculation of Resonances in Pre-Born-Oppenheimer Molecular Structure Theory
• Elimination of the Translational Kinetic Energy Contamination in pre-Born-Oppenheimer Calculations
• Non-adiabatic mass correction to the rovibrational states of molecules. Numerical application for the H${}_2^{+}$ molecular ion
• Generalized elimination of the global translation from explicitly correlated Gaussian functions
• Precision measurement of the rotational energy-level structure of the three-electron molecule He${}_2^{+}$
• Relativistic Kinetic-Balance Condition for Explicitly Correlated Basis Functions

Cited by in corpus (18)

• Non-adiabatic, Relativistic, and Leading-order QED Corrections for Rovibrational Intervals of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\mathrm{u}}^{+}$)
• Precision measurement of the ionization energy and quantum defects of 39K I
• Precision Measurements in Few-Electron Molecules: The Ionization Energy of Metastable ${}^4$He${}_2$ and the First Rotational Interval of ${}^4$He${{}_2}^{+}$
• Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules
• Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states
• Precise computation of rovibronic resonances of molecular hydrogen: $EF{}^1{\Sigma }_{\mathrm{g}}^{+}$ inner-well rotational states
• Non-adiabatic mass correction to the rovibrational states of molecules. Numerical application for the H${}_2^{+}$ molecular ion
• On the Breit interaction in an explicitly correlated variational Dirac-Coulomb framework
• 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
• Lower bounds on par with upper bounds for few-electron atomic energies
• Ab initio potential energy curves, scattering lengths, and rovibrational levels of the He${}_2^{+}$ molecular ion in excited electronic states
• Characterization of the electronic ground state of He${}_2^{+}$ by high-resolution photoelectron spectroscopy
• High-Precision Quantum Dynamics of He${}_2$ over the b ${}^3{\Pi }_{\mathrm{g}}$-c ${}^3{\Sigma }_{\mathrm{g}}^{+}$ Electronic Subspace by including Non-adiabatic, Relativistic and QED Corrections and Couplings
• Precision Spectroscopy of the Fine Structure in the $\mathbf{a}{}^3{\mathbf{\Sigma }}_{\mathbf{u}}^{+}(\mathbf{v}=0)$ and $\mathbf{c}{}^3{\mathbf{\Sigma }}_{\mathbf{g}}^{+}(\mathbf{v}=4)$ States of the Helium Dimer
• Rovibrational computations for He${}_2^{+}$ X ${\Sigma }_{\mathrm{u}}^{+}$ including non-adiabatic, relativistic and QED corrections
• Rovibrational computations for the He${}_2$ a ${}^3{\Sigma }_{\mathrm{u}}^{+}$ state including non-adiabatic, relativistic, and QED corrections