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Ionization and Dissociation Energies of Molecular Hydrogen

Ioana Doran1, Charlaine Roth2, Nicolas Hölsch1, Maximilian Beyer2, Andrés Martínez de Velasco2, Vincent Barbé2, Mathieu Collombon2, Elmer Gründeman2, Julian J. Krauth2 et al.

Jinjun Liu1,*, Josef A. Agner1, Urs Hollenstein1, Andreas Osterwalder1,†, Hansjürg Schmutz1, Daniel Sprecher1, Andrea Wüest1,3, Wim Ubachs2, Christian Jungen3, Kjeld S. E. Eikema2,‡, and Frédéric Merkt1,4,5,§

  • *Permanent address: Department of Physics and Astronomy, University of Louisville, Louisville, Kentucky 40292, USA.
  • †Permanent address: Institute for Chemical Sciences and Engineering (ISIC), École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland.
  • ‡Contact author: k.s.e.eikema@vu.nl
  • §Contact author: frederic.merkt@phys.chem.ethz.ch
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Phys. Rev. X 16, 041032 – Published 5 November, 2026

DOI: https://doi.org/10.1103/42c4-pc1s

Abstract

Molecular hydrogen (H2) is the simplest neutral molecule, and its ionization and dissociation energies are key benchmarks for testing first-principles calculations of nonadiabatic, relativistic, quantum-electrodynamic, and finite-nuclear-size effects in molecules. To obtain improved H2 ionization and dissociation energies, we performed precision measurements of 15 transition frequencies in para-H2. They connect the X Σg+1(v=0,N=0) ground state, the long-lived EF 1Σg+(v=0,N=0) excited state, and several high members of the np and nd Rydberg series with principal quantum number n in the range between 48 and 70. These data lead to a 5 times more accurate value of the ionization energy of the ground state of para-H2, equivalent to a relative frequency accuracy of 5×10−11. Combined with a global network analysis of 45 energy intervals in para- and ortho-H2 that have been measured in the past three decades, we obtain statistically robust values for the ionization energy [EI(0,0)/(hc)=124 417.491 1573(58)  cm−1] and the dissociation energy [D0N=0=36 118.069 6646(58)  cm−1] of H2. These values have an unprecedented accuracy equivalent to 175 kHz. The network analysis also leads to improved term values and dissociation energies of the excited states involved in the analysis. By comparing the results with first-principles calculations of the level structures of H2 and H2+, a significantly reduced upper bound of 540 kHz is derived for putative beyond-the-standard-model contributions to the energy difference between para- and ortho-H2.

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Popular Summary

The ionization and dissociation energies of molecular hydrogen act as essential benchmarks for testing fundamental first-principles calculations of complex molecular structure. We determined these energies to a relative accuracy of 5×10−11 for the ionization frequency by performing precision measurements of fifteen transition frequencies in para-H2 using deep-ultraviolet, ultraviolet, and millimeter-wave spectroscopy. Combined with a global network analysis of forty-five energy intervals measured over three decades, we obtained statistically robust values for the ionization and dissociation energies of molecular hydrogen with an accuracy of 175 kHz. Furthermore, we established a substantially reduced upper bound for putative beyond-the-standard-model contributions to the energy difference between para-H2 and ortho-H2. Our results provide stringent benchmarks for calculations in two-electron systems and might eventually help resolve a persisting discrepancy between the experimental and theoretical ionization energies of metastable helium.

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Phys. Rev. X 16, 041032– Published 5 November, 2026
  • Received 28 April 2026
  • Accepted 31 August 2026
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