  Discovery of superconductivity in the impurity band formed by heavy doping of
boron into diamond (C:B) as well as doping of boron into silicon (Si:B) has
provided a rout for the possibility of new families of superconducting
materials. Motivated by the special role played by copper atoms in high
temperature superconducting materials where essentially Cu $d$ orbitals are
responsible for a variety of correlation induced phases, in this paper we
investigate the effect of substitutional doping of Cu into diamond. Our
extensive first principle calculations averaged over various geometries based
on density functional theory, indicates the formation of a mid-gap band, which
mainly arises from the $t_{2g}$ and $4p$ states of Cu. For impurity
concentrations of more than $\sim 1%, the effect of $2p$ bands of neighboring
carbon atoms can be ignored. Based on our detailed analysis, we suggest a two
band model for the mid-gap states consisting of a quarter-filled hole like
$t_{2g}$ band, and a half-filled band of $4p$ states. Increasing the
concentration of the Cu impurity beyond $\sim 5%, completely closes the
spectral gap of the host diamond.
