Wigner and Huntington (1935) proposed that sufficiently compressed hydrogen would abandon its insulating molecular form for a monatomic metallic lattice, estimating roughly 250,000 atm (about 25 GPa) as a rough lower bound on the transition pressure and listing the then-unresolved issues: the correlation energy, the unknown compressibility of molecular hydrogen, uninvestigated layer-like lattices, the approximate zero-point energy, and nucleation of the new lattice. Modern first-principles theory has settled the quantitative side of this question: molecular hydrogen is predicted to dissociate near 500 GPa into a monatomic body-centered tetragonal metal, with planar layered structures stable at multi-terapascal pressures, and the correlation- and zero-point-energy limitations of 1935 are now treated with quantum Monte Carlo and coupled-cluster methods. Experiment has not delivered the phase: molecular hydrogen has been driven to a semimetallic molecular state above 350–425 GPa, but the only claimed observation of the monatomic Wigner–Huntington transition (Dias and Silvera, 2017) is disputed at the raw-data level and has never been reproduced; reviews in 2024–2026 concur that metallic hydrogen has not been experimentally realized. The open problem is this surviving open core: the unambiguous, reproducible synthesis and verification of monatomic metallic hydrogen, with pressure calibration and phase diagnosis robust against the recently documented optical limitations of diamond anvils near and above 500 GPa.

Background

At ambient pressure solid hydrogen is an insulating crystal of H2 molecules. The conjecture that extreme compression could break the molecules apart and delocalize the electrons dates to Wigner and Huntington (1935). "Metallic hydrogen" in this context means a phase in which the protons form a lattice without molecular units — the 1935 paper notes that any Bravais lattice (a crystal whose atoms are all translationally equivalent, one atom per primitive cell) of hydrogen would have metallic properties — so the target is a monatomic, atomic-metal form of the lightest element.

Wigner and Huntington computed the energy of a body-centered monatomic lattice of protons immersed in its electron gas as a function of the lattice constant, using the then-new perturbative theory of the dense electron gas. The correlation energy — the additional lowering of the energy beyond the independent-electron (Hartree–Fock) description, arising from electrons mutually avoiding one another — entered through Wigner's interpolation formula, and the zero-point energy of the protons (the residual vibrational energy that quantum mechanics forbids them from losing) was estimated in a Debye model, which approximates lattice vibrations as sound waves up to a cutoff frequency. They found that the monatomic minimum occurs at a density many times that of molecular solid hydrogen and lies well above the molecular ground state in energy, so that enormous compression would be needed to stabilize the metallic form; they quoted about 250,000 atm (25 GPa; 1 GPa is roughly 10,000 atmospheres) as a rough lower bound on the transition pressure. Their closing discussion flagged the issues that define this problem: the correlation energy might be underestimated for the highly modulated metallic wave functions; the compressibility of molecular hydrogen at high pressure was not experimentally known; "the chances are better, perhaps, for intermediate, layer-like lattices", which had not been investigated theoretically; the zero-point energy relied on the Debye approximation; and the need to nucleate a new lattice could greatly hinder the transition in practice.

Static high-pressure experiments use the diamond anvil cell (DAC), in which a micron-scale sample is squeezed between two diamond anvils; pressure is inferred from the Raman spectrum of the diamond edge or from calibrated markers. Compressed molecular hydrogen passes through a sequence of structural phases (denoted I, III, IV, V), tracked by Raman and infrared spectroscopy: the vibron (the intramolecular H2 stretch frequency) shifts and softens, and the electronic band gap narrows. Experiments have shown that molecular hydrogen becomes semimetallic — metallic in behavior while retaining H2 units — above about 350 GPa (Eremets et al., 2019), and that its direct band gap drops discontinuously from 0.6 eV to below 0.1 eV near 425 GPa (Loubeyre et al., 2020). These results realize a metallic but still molecular phase, not the monatomic Wigner–Huntington transition.

On the theory side, the 1935 caveats have been systematically discharged. Density functional theory (DFT), the standard ab initio ground-state method, combined with random structure searching (computational sampling of many candidate crystal structures to locate the lowest-energy one), determined the zero-temperature ground states of atomic hydrogen (McMahon and Ceperley, 2011): including proton zero-point motion in the harmonic approximation, molecular hydrogen is predicted to dissociate into a monatomic body-centered tetragonal lattice (space group I41/amdI4_1/amd) near 500 GPa (rs≈1.225r_s \approx 1.225, where rsr_s is the mean inter-proton spacing in units of the Bohr radius), which persists to about 2.5 TPa; above that, an ...ABCABC... planar, graphite-like layered structure (remarkably similar to the ground state of lithium) is stable, compressing to face-centered cubic beyond about 5 TPa. The correlation-energy question is now addressed with many-body methods: quantum Monte Carlo (stochastic, near-exact treatment of electron correlation) drives molecular dynamics showing the liquid atomic phase stable near 300 GPa at 400 K (Attaccalite and Sorella, 2008), and coupled-cluster theory (a high-accuracy many-body electronic-structure method) benchmarked against diffusion Monte Carlo quantifies the molecular phases from 100 to 450 GPa (Liao et al., 2019). Reviews consolidate the picture (McMahon et al., 2012; Bonitz et al., 2024): the low-temperature molecular-to-monatomic boundary lies in the few-hundred-GPa range, with residual method-dependent spread of order tens to a hundred GPa.

Why the phase matters: Ashcroft (1968) predicted that metallic hydrogen would be a high-temperature superconductor; modern calculations predict superconducting critical temperatures TcT_c rising to several hundred kelvin in the atomic phase (McMahon and Ceperley, 2011). Giant planets such as Jupiter are composed largely of metallic hydrogen, and possible metastability of the phase after pressure release has been discussed since the 1935 nucleation remark.

The experimental frontier is now bounded by the diagnosis problem itself: the only claimed observation of the monatomic transition (Dias and Silvera, 2017, near 495 GPa) is disputed, the sample was lost, and it has never been reproduced. Moreover, recent measurements show that diamond anvils lose optical transparency under multimegabar compression, complicating all optical diagnostics of hydrogen near 500 GPa and beyond (Hilberer et al., 2026). Field reviews in 2024 and 2025 state plainly that metallic hydrogen has not been experimentally realized. The question that remains open is therefore no longer whether the metallic modification of hydrogen exists in principle — theory answers yes, near 500 GPa, in structures now known — but whether it can be produced and verified in the laboratory.

Problem Statement

The open problem is the experimental completion of the Wigner–Huntington question: whether the metallic modification of hydrogen can actually be produced. The quantitative theoretical prediction is already established — molecular solid hydrogen is expected to dissociate into a monatomic metallic solid near 500 GPa at low temperature (within an uncertainty band of roughly 400–600 GPa set by correlation, zero-point, and anharmonic effects), in a body-centered tetragonal structure, with layered planar structures stable at higher pressures — so the open target is not to re-derive the prediction but to realize the phase. Specifically: (1) synthesize the monatomic metallic phase of hydrogen under static compression, reaching and reliably calibrating the required pressure of order several hundred GPa; (2) verify unambiguously that the product is the atomic metallic phase rather than metallic molecular hydrogen — demonstrating molecular dissociation (e.g., disappearance of the H2 vibron — the intramolecular H2 stretch frequency — or structural/diffraction evidence of a monatomic lattice) together with metallic electronic behavior (finite DC conductivity, Drude-like (free-electron) reflectivity with the implied carrier density, or equivalent spectroscopic demonstration of band-gap closure plus dissociation); and (3) characterize the realized phase sufficiently to compare it with the predicted structure and transition conditions, including its response to decompression. These three components describe one objective — the realization and verification of the Wigner–Huntington metallic phase: a reproducible experimental demonstration with established pressure calibration, phase identity, and metallicity, together with a characterization of the realized phase, including its response to decompression. The target is elemental monatomic metallic hydrogen; metallization of the molecular solid, or metallic phases of hydrogen-rich compounds, is a different target.

References

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