First-Principles Investigation of Stability and Superconductivity in Magnesium Hexahydride Under High Pressures

This study explores the structural, mechanical, vibrational, and superconducting properties of magnesium hexahydride (MgH₆) under high pressure using first-principles density functional theory (DFT) with the generalized gradient approximation (GGA-PBE). Phonon dispersion calculations, performed via density functional perturbation theory (DFPT), reveal that MgH₆ achieves dynamic stability above 295 GPa, as evidenced by the absence of imaginary frequencies in the vibrational spectrum. While imaginary modes persist at lower pressures (150–290 GPa), their localized nature ensures minimal impact on the overall electron–phonon coupling strength. The calculated elastic constants satisfy the Born-Huang criteria, confirming mechanical stability across the 150–400 GPa range. By solving the Migdal-Eliashberg equations with a Coulomb pseudopotential (μ^* = 0.136), we predict a maximum superconducting critical temperature (\({T}_{C}\)) of 238 K at 290 GPa. This peak \({T}_{C}\) correlates with enhanced coupling from phonon softening near the stability threshold, underscoring the interplay between dynamic stability and superconductivity. Our results highlight MgH₆ as a promising high-temperature superconductor and provide insights into the stabilization mechanisms of hydrogen-rich compounds under extreme conditions.