  Using the quasiparticle self-consistent GW (QSGW) and local-density (LD)
approximations, we calculate the q-dependent static dielectric function, and
derive an effective 2D dielectric function corresponding to screening of point
charges. In the q-to-0 limit, the 2D function is found to scale approximately
as the square root of the macroscopic dielectric function. Its value is ~4, a
factor approximately 1.5 larger than predictions of Dirac model. Both kinds of
dielectric functions depend strongly on q, in contrast with the Dirac model.
The QSGW approximation is shown to describe QP levels very well, with small
systematic errors analogous to bulk sp semiconductors. Local-field effects are
rather more important in graphene than in bulk semiconductors.
