  To obtain an effective many-body model of graphene and related materials from
first principles we calculate the partially screened frequency dependent
Coulomb interaction. In graphene, the effective on-site (Hubbard) interaction
is U_00 = 9.3 eV in close vicinity to the critical value separating conducting
graphene from an insulating phase emphasizing the importance of non-local
Coulomb terms. The nearest-neighbor Coulomb interaction strength is computed to
U_01 = 5.5 eV. In the long wavelength limit, we find the effective background
dielectric constant of graphite to be \epsilon = 2.5 in very good agreement
with experiment.

Mesoscale and Nanoscale Physics;Materials Science;Strongly Correlated Electrons