  We present density functional theory calculations of phosphorus dopants in
bulk silicon and of several properties relating to their use as spin qubits for
quantum computation. Rather than a mixed pseudopotential or a Heitler-London
approach, we have used an explicit treatment for the phosphorus donor and
examined the detailed electronic structure of the system as a function of the
isotropic doping fraction, including lattice relaxation due to the presence of
the impurity. Doping electron densities and spin densities are examined in
order to study the properties of the dopant electron as a function of the
isotropic doping fraction. Doping potentials are also calculated for use in
calculations of the scattering cross-sections of the phosphorus dopants, which
are important in the understanding of electrically detected magnetic resonance
experiments. We find that the electron density around the dopant leads to
non-spherical features in the doping potentials, such as trigonal lobes in the
(001) plane at energy scales of +12 eV near the nucleus and of -700 meV
extending away from the dopants. These features are generally neglected in
effective mass theory and will affect the coupling between the donor electron
and the phosphorus nucleus. Our density functional calculations reveal detail
in the densities and potentials of the dopants which are not evident in
calculations that do not include explicit treatment of the phosphorus donor
atom and relaxation of the crystal lattice. These details can also be used to
parameterize tight-binding models for simulation of large-scale devices.
