Absence of Metallization in Solid Molecular Hydrogen

Being the simplest element with just one electron and proton the electronic structure of the Hydrogen atom is known exactly. However, this does not hold for the complex interplay between them in a solid and in particular not at high pressure that is known to alter the crystal as well as the electronic structure. Back in 1935 Wigner and Huntington predicted that at very high pressure solid molecular hydrogen would dissociate and form an atomic solid that is metallic. In spite of intense research efforts the experimental realization, as well as the theoretical determination of the crystal structure has remained elusive. Here we present a computational study showing that the distorted hexagonal P6$_3$/m structure is the most likely candidate for Phase III of solid hydrogen. We find that the pairing structure is very persistent and insulating over the whole pressure range, which suggests that metallization due to dissociation may precede eventual bandgap closure. Due to the fact that this not only resolve one of major disagreement between theory and experiment, but also excludes the conjectured existence of phonon-driven superconductivity in solid molecular hydrogen, our results involve a complete revision of the zero-temperature phase diagram of Phase III.

💡 Research Summary

The paper addresses the long‑standing question of whether solid molecular hydrogen becomes metallic under extreme compression, and if so, by what mechanism. Historically, Wigner and Huntington (1935) predicted that at sufficiently high pressure hydrogen would dissociate into an atomic metallic solid. Yet, despite decades of experimental and theoretical work, the crystal structure of Phase III (above ~150 GPa) and its electronic character have remained ambiguous.

The authors begin by reproducing earlier semilocal density‑functional theory (DFT) calculations using the Perdew‑Burke‑Ernzerhof (PBE) functional. They examine five candidate structures that have been proposed for Phase III: C2/c, Cmca‑12, Pbcn, C2, and the distorted hexagonal P6₃/m. At the semilocal level, the enthalpy hierarchy reproduces previous results: C2/c is most stable up to ~290 GPa, after which the band gap of C2/c closes and the system is predicted to transform into the metallic Cmca‑12 phase. However, semilocal DFT notoriously underestimates band gaps by roughly 50 %, leading to an artificially low metallization pressure.

To overcome this limitation, the authors employ two higher‑level electronic‑structure methods: (i) a hybrid functional (PBE0) that mixes 25 % exact Hartree‑Fock exchange with the PBE exchange‑correlation, and (ii) many‑body perturbation theory within the G₀W₀ approximation as implemented in the Yambo code. Hybrid DFT partially restores the derivative discontinuity (Δ_XC) missing in local and semilocal functionals, thereby widening the fundamental gap and stabilizing insulating phases relative to metallic ones. The G₀W₀ calculations provide an independent, quasiparticle‑level assessment of the gaps.

The results are striking. All candidate structures exhibit substantially larger gaps when evaluated with hybrid DFT, and the G₀W₀ gaps confirm this trend. In particular, the P6₃/m structure retains a gap of >2 eV even at 500 GPa, implying that it remains insulating throughout the entire pressure range traditionally assigned to Phase III. Moreover, the enthalpy differences shift dramatically: whereas semilocal DFT placed the metallic Cmca‑12 structure close to the ground state, hybrid DFT raises its enthalpy by ~8 meV per proton, rendering it unstable. Conversely, P6₃/m becomes the lowest‑enthalpy phase across the whole pressure window, and C2/c, while still competitive, is consistently higher in energy than P6₃/m once exchange‑correlation non‑locality is accounted for.

The authors also discuss zero‑point vibrational energy (ZPE). Although ZPE is sizable for hydrogen, the differences between the candidate structures largely cancel, especially at high pressure, and ZPE tends to favor more symmetric configurations. This further supports the stability of the P6₃/m phase, which features a slightly distorted hcp lattice of H₂ molecules and exhibits spontaneous electronic polarization that explains its infrared‑active vibron mode—consistent with experimental IR observations of Phase III.

Two metallization pathways are considered. The first involves band‑gap closure while the system remains molecular; the second requires molecular dissociation followed by a transition to an atomic metallic phase (e.g., I4₁/amd). The hybrid DFT and G₀W₀ results indicate that the first pathway does not occur below ~500 GPa; the gap never closes in the molecular phases. Consequently, metallization is expected only after dissociation, at pressures around 490 GPa, in agreement with recent theoretical estimates of the dissociation pressure. This conclusion also implies that electron‑phonon coupling in a molecular metallic phase—previously invoked to predict high‑Tc superconductivity—is unlikely, as the molecular phase never becomes metallic.

By reconciling the previously contradictory theoretical predictions (many of which found metallic Cmca‑12 or other metallic candidates) with experimental observations (e.g., the onset of opacity around 320 GPa), the paper provides a coherent picture: Phase III is best described by the P6₃/m structure, which remains an insulator up to the point where hydrogen finally dissociates into an atomic metallic state. This revision of the zero‑temperature phase diagram eliminates the need for a phonon‑driven superconducting molecular phase and narrows the pressure window for any putative quantum liquid metallic hydrogen.

Overall, the study demonstrates that high‑accuracy electronic‑structure methods—hybrid functionals and GW—are essential for reliable predictions of phase stability and electronic properties in extreme‑pressure hydrogen. It sets a new benchmark for future theoretical and experimental investigations of this fundamental system.