Transferability and the electron-phonon interaction: A reinterpretation of the rigid-muffin-tin approximation

The expression for the McMillan-Hopfield constant $\eta =N\left(E_F\right)〈I^2〉$ within the rigid-muffin-tin approximation (RMTA) is reinterpreted in terms of single-channel electron-ion matrix elements $I_{l,l+1\mathrm{}}^2$ and angular-momentum-character fractions $f_l$ of the electronic states at the Fermi level. Reexamination of Nb- and V-based $A15\mathrm{}$ compounds suggests that $I_{l,l+1\mathrm{}}^2$ is more nearly an atomic property, and thus transferable from system to system, than other commonly used quantities. The fractions $f_l$ are dependent on bonding character and crystal structure but tend to be constant within a class of compounds. Criteria for increasing $\eta$ within RMTA are discussed.