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Denser hydrogen inferred from first-principles simulations challenges Jupiter’s interior models

Cesare Cozza1,*,†, Kousuke Nakano2,3,*, Saburo Howard1, Hao Xie1,‡, Ravit Helled1, and Guglielmo Mazzola1,4,§

  • *These authors contributed equally to this work.
  • †Contact author: cesare.cozza@uzh.ch
  • ‡Contact author: qwexiehao@gmail.com
  • §Contact author: gmazzola@sissa.it
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Phys. Rev. Research 8, 013089 – Published 27 January, 2026

DOI: https://doi.org/10.1103/yrk6-ryps

Abstract

First-principles modeling of dense hydrogen is crucial in materials and planetary sciences. Despite its apparent simplicity, predicting the ionic and electronic structure of hydrogen is a formidable challenge, and it is connected with the insulator-to-metal transition, a century-old problem in condensed matter. Accurate simulations of liquid hydrogen are also essential for modeling gas giant planets. Here, we perform an exhaustive study of the equation of state of hydrogen using density functional theory (DFT) and quantum Monte Carlo simulations. We find that the pressure predicted by DFT may vary qualitatively when using different functionals. The predictive power of first-principles simulations is restored by validating each functional against higher-level wavefunction theories, represented by computationally intensive variational and diffusion Monte Carlo calculations. Our simulations provide evidence that hydrogen is denser at planetary conditions, compared to currently used equations of state. For Jupiter, this implies a lower bulk metallicity (i.e., a smaller mass of heavy elements). Our results further amplify the inconsistency between Jupiter’s atmospheric metallicity measured by the Galileo probe and the envelope metallicity inferred from interior models.

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Phys. Rev. Research 8, 013089– Published 27 January, 2026
  • Received 29 January 2025
  • Accepted 5 January 2026
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