Absence of superconductivity in iron polyhydrides at high pressures

The recently reported formation of the new iron polyhydride FeH${}_{5}$ at megabar pressures raised hopes about its potential high-$T$${}_{c}$ superconductivity because of an alleged layer of dense metallic hydrogen. Using electronic structure calculations, the present work shows that FeH${}_{5}$ displays no conventional superconductivity, since the electronic states at the Fermi level do not exhibit appreciable electron-phonon coupling. Superconductivity may be attained by partially filling empty Fe--H hybrid bands by adding more electrons, but critical temperatures would remain relatively low, because the $d$-metal bonding, and not the metallic hydrogen, dominates the electrons and phonons involved in the superconducting pairing.