Nonadiabatic rotational states of the hydrogen molecule

Abstract

We present a new computational method for the determination of energy levels in four-particle systems like H${}_2$, HD, and HeH${}^{+}$ using explicitly correlated exponential basis functions and analytic integration formulas. In solving the Schrödinger equation, no adiabatic separation of the nuclear and electronic degrees of freedom is introduced. We provide formulas for the coupling between the rotational and electronic angular momenta, which enable calculations of arbitrary rotationally excited energy levels. To illustrate the high numerical efficiency of the method, we present results for various states of the hydrogen molecule. The relative accuracy to which we determined the nonrelativistic energy reached the level of $10^{-12}$-$10^{-13}$, which corresponds to an uncertainty of $10^{-7}$-$10^{-8}$ cm${}^{-1}$.

References in corpus (6)

• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• Complete ${\alpha }^{6}m$ corrections to the ground state of H${}_2$
• Relativistic corrections for the ground electronic state of molecular hydrogen
• Two-center two-electron integrals with exponential functions
• High-precision spectroscopy of the HD+ molecule at the 1-p.p.b. level
• Test of quantum chemistry in vibrationally-hot hydrogen molecules

Cited by in corpus (16)

• The full infrared spectrum of molecular hydrogen
• Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory
• Nonadiabatic QED correction to the dissociation energy of the hydrogen molecule
• Nonadiabatic relativistic correction in H${}_2$, D${}_2$, and HD
• Dissociation Energy of Molecular Hydrogen Isotopologues
• Hyperfine structure of the first rotational level in H${}_2$, D${}_2$ and HD molecules and the deuteron quadrupole moment
• Non-adiabatic, Relativistic, and Leading-order QED Corrections for Rovibrational Intervals of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\mathrm{u}}^{+}$)
• Precision measurement of the fundamental vibrational frequencies of tritium-bearing hydrogen molecules: T${}_2$, DT, HT
• All-order relativistic computations for atoms and molecules using an explicitly correlated Gaussian basis
• Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states
• Non-adiabatic mass correction to the rovibrational states of molecules. Numerical application for the H${}_2^{+}$ molecular ion
• Hyperfine components of all rovibrational quadrupole transitions in the H${}_2$ and D${}_2$ molecules
• Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations
• Nonrelativistic energy of tritium-containing hydrogen molecule isotopologues
• Vibronic mass computation for the $EF$-$GK$-$H\bar{H}$ ${}^1{\Sigma }_{\text{g}}^{+}$ manifold of molecular hydrogen
• Nonadiabatic corrections to electric quadrupole transition rates in H${}_2$