  We employ a tight-binding parametrization based on the Slater Koster model in
order to fit the band structures of single-layer, bilayer and bulk black
phosphorus obtained from first-principles calculations. We find that our model,
which includes 9 or 17 parameters depending on whether overlap is included or
not, reproduces quite well the ab-initio band structures over a wide energy
range, especially the occupied bands. We also find that the inclusion of
overlap parameters improves the quality of the fit for the conduction bands. On
the other hand, hopping and on-site energies are consistent throughout the
different systems, which is an indication that our model is suitable for
calculations on multilayer black phosphorus and more complex situations in
which first-principles calculations become prohibitive, such as disordered
systems and heterostructures with a large lattice mismatch. We also discuss the
limitations of the model and how the fit procedure can be improved for a more
accurate description of bands in the vicinity of the Fermi energy.
