  Band structure calculations for Ba_2Cu_3O_4Cl_2 within the local density
approximation (LDA) are presented. The investigated compound is similar to the
antiferromagnetic parent compounds of cuprate superconductors but contains
additional Cu_B atoms in the planes. Within the LDA, metallic behavior is found
with two bands crossing the Fermi surface (FS). These bands are built mainly
from Cu 3d_{x^2-y^2} and O 2p_{x,y} orbitals, and a corresponding tight-binding
(TB) model has been parameterized. All orbitals can be subdivided in two sets
corresponding to the A- and B-subsystems, respectively, the coupling between
which is found to be small. To describe the experimentally observed
antiferromagnetic insulating state, we propose an extended Hubbard model with
the derived TB parameters and local correlation terms characteristic for
cuprates. Using the derived parameter set we calculate the exchange integrals
for the Cu_3O_4 plane. The results are in quite reasonable agreement with the
experimental values for the isostructural compound Sr_2Cu_3O_4Cl_2.
