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

Abstract

The expression for the McMillan-Hopfield constant $\ensuremath{\eta}=N({E}_{F})〈{I}^{2}〉$ within the rigid-muffin-tin approximation (RMTA) is reinterpreted in terms of single-channel electron-ion matrix elements ${I}_{l,l+1}^{2}$ and angular-momentum-character fractions ${f}_{l}$ of the electronic states at the Fermi level. Reexamination of Nb- and V-based $A15$ compounds suggests that ${I}_{l,l+1}^{2}$ 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 $\ensuremath{\eta}$ within RMTA are discussed.