Electronic structure and superconductivity in metal hexaborides

The electronic structure and the phonon modes of the superconducting cluster compounds La${\mathrm{B}}_6$ and Y${\mathrm{B}}_6$ are evaluated. They are used to calculate the Eliashberg function of both compounds within the rigid-muffin-tin approximation for electron-phonon coupling. The individual contributions from the different phonon branches are discussed. It turns out that nonlocal corrections to the electron-phonon coupling are essential for those modes where the ${\mathrm{B}}_6$ octahedras move as a whole. Omission of these corrections leads to a large overestimate of $\lambda$ and $T_c$.