  We use first-principle calculations for transition metal impurities V, Cr,
Mn, Fe, Co and Ni in GaAs as well as Cr and Mn in GaN, GaP and GaSb to identify
the basic features of the electronic structure of these systems. The
microscopic details of the hole state such as the symmetry and the orbital
character, as well as the nature of the coupling between the hole and the
transition metal impurity are determined. This could help in the construction
of model Hamiltonians to obtain a description of various properties beyond what
current first-principle methods are capable of.
