Non-adiabatic mass correction to the rovibrational states of molecules. Numerical application for the H${}_2^{+}$ molecular ion

Abstract

General transformation expressions of the second-order non-adiabatic Hamiltonian of the atomic nuclei, including the kinetic-energy correction terms, are derived upon the change from laboratory-fixed Cartesian coordinates to general curvilinear coordinate systems commonly used in rovibrational computations. The kinetic-energy or so-called "mass-correction" tensor elements are computed with the stochastic variational method and floating explicitly correlated Gaussian functions for the H${}_2^{+}$ molecular ion in its ground electronic state. (Further numerical applications for the ${}^4$He${}_2^{+}$ molecular ion are presented in the forthcoming paper, Paper II.) The general, curvilinear non-adiabatic kinetic energy operator expressions are used in the examples and non-adiabatic rovibrational energies and corrections are determined by solving the rovibrational Schrödinger equation including the diagonal Born--Oppenheimer as well as the mass-tensor corrections.

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Cited by in corpus (12)

• Non-adiabatic, Relativistic, and Leading-order QED Corrections for Rovibrational Intervals of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\mathrm{u}}^{+}$)
• Towards breaking the curse of dimensionality in (ro)vibrational computations of molecular systems with multiple large-amplitude motions
• Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states
• Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules
• Precise computation of rovibronic resonances of molecular hydrogen: $EF{}^1{\Sigma }_{\mathrm{g}}^{+}$ inner-well rotational states
• Non-adiabatic mass-correction functions and rovibrational states of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\text{u}}^{+}$)
• Non-adiabatic mass correction for excited states of molecular hydrogen: improvement for the outer-well $H\bar{H}{}^1{\Sigma }_{\mathrm{g}}^{+}$ term values
• On the Breit interaction in an explicitly correlated variational Dirac-Coulomb framework
• Vibronic mass computation for the $EF$-$GK$-$H\bar{H}$ ${}^1{\Sigma }_{\text{g}}^{+}$ manifold of molecular hydrogen
• Variational Vibrational States of Methanol (12D)
• 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