  Comparison of periodic B dopants with a random alloy of substitional boron in
diamond is carried out using several supercells and the coherent potential
approximation (CPA) for the random alloy case. The main peak in the B local
density of states is shifted to lower binding energy compared to the
corresponding C peak in intrinsic diamond. In supercells, this shows up as
strongly B-character bands split from bulk C bands away from the zone center,in
an energy region around -1 eV. Even for a 4*4*4 supercell (BC$_{127}$), effects
of the dopant order are evident in the form of primarily B-character bands just
below the Fermi level at the supercell zone boundary. The bands resulting from
the CPA are of continuous mixed C-B character. They resemble virtual crystal
bands, but broadened somewhat reflecting the disorder-induced lifetime, and are
consistent with angle-resolved photoemission band maps. The B character is 1.7
times larger than for C (per atom) near the top of the valence bands for CPA,
and roughly the same for supercells. CPA results are particularly useful since
they characterize the wavevector and energy dependence of disorder broadening.
