  The formal link between the linear combination of atomic orbitals approach to
density functional theory and two-center Slater-Koster tight-binding models is
used to derive an orthogonal $d$-band tight-binding model for iron with only
two fitting parameters. The resulting tight-binding model correctly predicts
the energetic ordering of the low energy iron-phases, including the
ferromagnetic BCC, antiferromagnetic FCC, HCP and topologically close-packed
structures. The energetics of test structures that were not included in the fit
are equally well reproduced as those included, thus demonstrating the
transferability of the model. The simple model also gives a good description of
the vacancy formation energy in the nonmagnetic FCC and ferromagnetic BCC iron
lattices.
