Quantum Effects Stabilize Hydrogen Phases up to 700 GPa, Resolving High-Pressure Discrepancies

The behaviour of hydrogen under extreme pressure remains a significant challenge in condensed matter physics, with predictions often varying depending on the computational methods employed. Stefano Racioppi and Eva Zurek, from the State University of New York at Buffalo, alongside Racioppi’s affiliation with the University of Cambridge, now present a detailed reanalysis of hydrogen’s cold phase diagram between 400 and 700 GPa. Their work demonstrates that commonly used computational methods may overestimate the importance of quantum effects, potentially leading to inaccurate predictions of hydrogen’s structure at high pressure. By employing more advanced computational techniques, the researchers find that molecular phases of hydrogen are stable at significantly higher pressures than previously thought, bringing theoretical predictions into closer agreement with both experimental observations and highly accurate calculations. This research clarifies the role of computational approximations and provides a more reliable foundation for understanding the behaviour of hydrogen under the immense pressures found within planetary interiors.

They employed Density Functional Theory (DFT) calculations, utilizing meta-GGA functionals like R2SCAN and SCAN0, and compared the results to those obtained with the more common PBE functional. This approach aimed to address known limitations of standard DFT methods when applied to hydrogen, particularly errors arising from electron-electron interactions and inaccurate descriptions of bonding. Scientists performed calculations on several candidate phases, including the molecular Cmca-12 and Cmca-4 structures, as well as the atomic I41/amd and C2/c phases, to assess their stability at high pressures.

The team meticulously calculated phonon spectra using R2SCAN, revealing that dynamical instabilities and anharmonic signatures previously predicted with PBE vanished, suggesting these effects stemmed from functional deficiencies rather than genuine quantum effects. This detailed analysis involved assessing the curvature of the potential energy surface near equilibrium, which is critical for accurately determining both phase stability and bonding characteristics. To further investigate bonding behavior, researchers conducted bonding analysis, demonstrating that PBE artificially weakens intramolecular hydrogen-hydrogen bonds while enhancing intermolecular interactions through charge delocalization. In contrast, the meta-GGA functionals preserved a more localized molecular character, providing a more realistic description of bonding. This research demonstrates the critical role of accurately describing the potential energy surface, particularly its curvature near equilibrium, for assessing both phase stability and bonding in hydrogen at extreme pressures.

High-Pressure Hydrogen Phases Stabilized by Meta-GGA

This work presents a detailed investigation into the high-pressure behavior of hydrogen, revisiting its cold phase diagram between 400 and 700 GPa using advanced computational methods. Researchers employed meta-GGA functionals, specifically R2SCAN and SCAN0, and compared the results with the more common PBE functional to assess the impact of exchange-correlation approximations on predicted phase stability. Calculations reveal that the molecular phases Cmca-4, Cmca-12, and C2/c are stabilized to significantly higher pressures than previously predicted by PBE, bringing the computational results into closer agreement with diffusion Monte Carlo calculations and experimental observations of band-gap closure near 425 GPa. Specifically, at 507 GPa, PBE predicts the atomic I41/amd phase to have the lowest energy, whereas the meta-GGA calculations demonstrate that molecular phases remain stable at higher pressures. The team performed a comprehensive search for new stable phases using the R2SCAN-L functional, exploring unit cells containing up to 32 atoms, but found no additional competitive structures. Phonon spectra calculated with R2SCAN show a significant improvement over previous GGA-level calculations, with dynamical instabilities and anharmonic signatures vanishing, suggesting these effects stemmed from functional deficiencies rather than genuine nuclear quantum effects.

R2SCAN Corrects High-Pressure Hydrogen Stability

This research presents a detailed investigation into the behaviour of high-pressure hydrogen phases, employing advanced computational methods to refine our understanding of its stability and bonding characteristics. Scientists accurately modelled the behaviour of hydrogen under extreme pressure, demonstrating that commonly used computational approaches can overestimate the instability of molecular phases. By utilizing meta-GGA functionals, specifically R2SCAN, the team found that previously predicted instabilities and anharmonic effects diminish, suggesting these arose from limitations in the computational methods rather than inherent properties of hydrogen itself. The study reveals that standard approximations tend to artificially weaken the bonds within hydrogen molecules and exaggerate interactions between them, leading to inaccurate predictions of phase stability.

In contrast, the meta-GGA approach preserves a more realistic molecular character, indicating that molecular phases of hydrogen can remain stable at higher pressures than previously thought. The team highlights the importance of accurately modelling the potential energy surface of hydrogen, particularly its curvature, for correctly assessing both its dynamic behaviour and bonding properties under extreme conditions. The authors acknowledge that while their calculations improve the understanding of hydrogen’s behaviour, the inclusion of anharmonic motion remains relevant for describing its dynamics at finite temperatures. Future work should continue to refine these models to fully capture the complex interplay between pressure, bonding, and thermal effects in this fundamental material. This research provides a more reliable foundation for both theoretical predictions and the interpretation of experimental observations in the field of high-pressure physics.