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We investigate the electronic and phonon properties of hydrogen sulfide(SH$_3$) under ultrahigh pressure to elucidate the origin of its high-T$_c$superconductivity. Contrary to the prevailing belief that the metalized S-H$\sigma$ bond is responsible, our analysis, based on the anisotropicMigdal-Eliashberg equation and the crystal orbital Hamilton population (COHP)calculation, reveals that the H-H $\sigma$-antibonding states play a dominantrole in the large electron-phonon coupling that leads to the superconductingpairing in SH$_3$. Furthermore, by partially restricting the vibration of Satoms, we demonstrate that the S-H bonds provide subsidiary contributions tothe pairing interaction. These findings shed light on the importance of thepreviously overlooked H-H $\sigma^*$ bonds in driving high-T$_c$superconductivity in SH$_3$ and offer insights into the relationship betweenmetallic H-H covalent antibonding and high-T$_c$ superconductivity in otherhydrogen-rich materials under high pressure.

Microscopic resolution of superconducting electrons in ultrahigh-pressed hydrogen sulfide