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 five-orbital tight-binding fit of the full density functional theory band structure for BaFe2As2 including the kz dispersions. We compare the five-orbital spin fluctuation model to one previously studied for LaOFeAs and calculate the random-phase approximation enhanced susceptibility. Using the fluctuation ex- change 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=?. 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.
