A comprehensive theoretical study of MnS is conducted using linear response constrained density functional theory to determine the Hubbard $U$ parameter, structure searching to predict high-pressure phases, and first-principles calculations to investigate phase transition behavior and electronic structure. To validate the predicted high-pressure phases, theoretical x-ray diffraction patterns are compared with experimental data from the literature. Theoretical Raman and infrared spectra are also provided. Our findings predict a previously unreported hexagonal phase of MnS, revise its phase transition sequence, and elucidate the underlying physical mechanisms. With increasing pressure, MnS undergoes sequential phase transitions from the $Fm\overline{3}m$ phase to the $P{6}_3/mmc$ and further to the $Pnma$ structure, with the latter transition accompanied by Jahn-Teller distortion, spin crossover, and negative charge transfer. Both $P{6}_3/mmc$ and $Pnma$ phases exhibit antiferromagnetic order with prominent altermagnetic characteristics. These findings elucidate the lattice structures, electronic structures, and altermagnetism of MnS under high pressure, establishing essential theoretical foundations for altermagnetic materials.

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• Altermagnetism
• Electronic structure
• First-principles calculations
• High-pressure studies
• Structural phase transition
• Strongly correlated systems