  Superconductivity in novel bismuth-sulphur superconductors has attracted
large research efforts, both experimental and theoretical, but a consensus on
the nature of superconductivity in these materials has yet to be reached. Using
density functional theory for superconductors, we study the electron-phonon
pairing mechanism in LaO$_{0.5}$F$_{0.5}$BiS$_2$. We first confirm the presence
of a commensurate charge density wave instability, in accordance with previous
studies. Using a recently developed integration scheme for the electron-phonon
coupling, we found that its strength is much lower than previously calculated,
due to improved density of state calculations. We finally conclude that
conventional phonon-mediated pairing cannot explain the high superconducting
transition temperatures observed in this material.
