Inverse Isotope Effect and the $x$ Dependence of the Superconducting Transition Temperature in $\mathrm{Pd}{\mathrm{H}}_x$ and $\mathrm{Pd}{\mathrm{D}}_x$

First-principles electronic—band-structure calculations and measured phonon properties are employed in a calculation of the concentration dependence of the superconducting transition temperatures for $\mathrm{Pd}{\mathrm{H}}_x$ and $\mathrm{Pd}{\mathrm{D}}_x$, including the inverse isotope effect. Excellent agreement with the experimental results is obtained. Our model also gives a qualitative understanding of the enhanced transition temperatures in the palladium-noble-metal hydrides.