  We study the gate voltage induced gap that occurs in graphene bilayers using
\textit{ab initio} density functional theory. Our calculations confirm the
qualitative picture suggested by phenomenological tight-binding and continuum
models. We discuss enhanced screening of the external interlayer potential at
small gate voltages, which is more pronounced in the \textit{ab initio}
calculations, and quantify the role of crystalline inhomogeneity using a
tight-binding model self-consistent Hartree calculation.
