  We report density functional calculations of the electronic structure, Fermi
surface, phonon spectrum and electron--phonon coupling for newly discovered
superconductor LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$. Significant similarity between
LaO$_{0.5}$F$_{0.5}$BiS$_{2}$ and LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$ is found, i.e.
there is a strong Fermi surface nesting at ($\pi $,$\pi $,0), which results in
unstable phonon branches. Combining the frozen phonon total energy calculations
and an anharmonic oscillator model, we find that the quantum fluctuation
prevents the appearance of static long--range order. The calculation shows that
LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$ is highly anisotropic, and same as
LaO$_{0.5}$F$_{0.5}$BiS$_{2}$, this compound is also a conventional
electron-phonon coupling induced superconductor.

Superconductivity