  We have performed ab initio calculations within the density-functional theory
for Ga_{1-x}Mn_xAs diluted semiconductors. Total energy results unambiguously
show that a quasi-localized down-spin hole, with strong p-like character,
surrounds the fully polarized Mn up-spin d^5-electrons. Calculations indicate
that the holes form an essentially dispersionless impurity band, thus rendering
effective-mass descriptions of hole states open to challenge. We obtain
estimates both for the s = 1/2 hole and S = 5/2 Mn exchange coupling, and for
the distance dependence of the effective Mn-Mn exchange interaction. Results
demonstrate that the effective Mn-Mn coupling is always ferromagnetic, thus
non-RKKY, and intermediated by the antiferromagnetic coupling of each Mn spin
to the holes.

Materials Science;Strongly Correlated Electrons