Quantum Effects or Theoretical Artifacts? A Computational Reanalysis of Hydrogen at High-Pressure

The stability of high-pressure phases of hydrogen remains a central question in condensed matter physics, where both experimental observations and theoretical predictions are highly sensitive to methodological choices. Here, we revisit the cold phase diagram of hydrogen between 400 and 700 GPa using the meta-GGA functionals (R2SCAN and SCAN0) and compare the results with the more common PBE. At the meta-GGA level, molecular phases (Cmca-4, Cmca-12, and C2/c) are stabilized over the atomic I41/amd phase up to significantly higher pressures than predicted by GGA, in closer agreement with diffusion Monte Carlo calculations and experimental observations of band-gap closure near 425 GPa. Furthermore, phonon spectra calculated with R2SCAN show that the dynamical instabilities and anharmonic signatures previously predicted at the GGA level vanish, indicating that such effects may partly arise from functional deficiencies rather than genuine nuclear quantum effects. Bonding analysis reveals that PBE artificially weakens intramolecular H-H bonds and enhances intermolecular interactions through charge delocalization, whereas meta-GGA preserves a more localized molecular character. Anharmonic motion remains relevant for finite-temperature dynamics; however, we demonstrate that the accurate description of the potential energy surface - particularly its curvature near equilibrium - is pivotal for assessing both phase stability and bonding of hydrogen at high-pressure.