Generic rules for achieving room-temperature superconductivity in ternary hydrides with clathrate structures

The discovery of superconductors with higher superconducting transition temperatures (${T}_{\mathrm{c}}$'s) at ambient physical conditions is a perpetual drive in fundamental studies and for practical applications. Here we conceptualize two generic rules for achieving this goal surrounding metal hydride superconductors. Rule 1: the metal skeletons should be composed of elements with an effective valency of 3 for efficient electron donation to hydrogen. Rule 2: the fractional occupancy of the metal ions should be $\ensuremath{\sim}0.4$ for maximal chemical squeezing on hydrogen. Guided by these rules, and based on first-principles approaches, we predict a collection of new hydride superconductors, including the representative examples of ${\mathrm{CaHfH}}_{12}$, with ${T}_{\mathrm{c}}$ of $\ensuremath{\sim}360$ K at 300 GPa, and ${\mathrm{CaZrH}}_{12}$, with ${T}_{\mathrm{c}}$ of $\ensuremath{\sim}290$ K at 200 GPa. These findings are expected to be instrumental in predictive discoveries of new high-${T}_{\mathrm{c}}$ hydride superconductors at lower pressures.