Tight-binding study of the anomalous phonon spectrum of barium

The long-range contribution to the phonon dynamical matrix for bcc Ba is calculated from first principles using a perturbative tight-binding formulation of the electron-ion interaction. This contribution gives rise to excellent agreement with the anomalous neutron-scattering spectrum in which the longitudinal mode is found to lie at lower frequencies than the transverse mode in the [100] direction. The short-range contribution is treated within a force-constant model and is not responsible for anomalous behavior in the spectrum. In addition, p-d and d-d mixing terms in the electron-phonon matrix elements form the majority contribution to the dynamical matrix, suggesting that Ba behaves as a transition metal with regard to its electron-phonon interaction. This is similar to previous results obtained from nonperturbative calculations of the total crystal energy. © 1988 The American Physical Society.