  Despite the wealth of experimental data on the Fe-pnictide compounds of the
KFe2As2-type, K = Ba, Ca, or Sr, the main theoretical work based on
multiorbital tight-binding models has been restricted so far to the study of
the related 1111 compounds. This can be ascribed to the more three dimensional
electronic structure found by ab initio calculations for the 122 materials,
making this system less amenable to model development. In addition, the more
complicated Brillouin zone (BZ) of the body-centered tetragonal symmetry does
not allow a straightforward unfolding of the electronic band structure into an
effective 1Fe/unit cell BZ. Here we present an effective 5-orbital
tight-binding fit of the full DFT band structure for BaFeAs including the kz
dispersions. We compare the 5-orbital spin fluctuation model to one previously
studied for LaOFeAs and calculate the RPA enhanced susceptibility. Using the
fluctuation exchange approximation to determine the leading pairing
instability, we then examine the differences between a strictly two dimensional
model calculation over a single kz cut of the BZ and a completely three
dimensional approach. We find pairing states quite similar to the 1111
materials, with generic quasi-isotropic pairing on the hole sheets and nodal
states on the electron sheets at kz = 0 which however are gapped as the system
is hole doped. On the other hand, a substantial kz dependence of the order
parameter remains, with most of the pairing strength deriving from processes
near kz = pi. These states exhibit a tendency for an enhanced anisotropy on the
hole sheets and a reduced anisotropy on the electron sheets near the top of the
BZ.
