  Maximally localized Wannier functions (MLWFs) based on Kohn-Sham
band-structures provide a systematic way to construct realistic, materials
specific tight-binding models for further theoretical analysis. Here, we
construct MLWFs for the Mn e_g bands in LaMnO_3, and we monitor changes in the
MLWF matrix elements induced by different magnetic configurations and
structural distortions. From this we obtain values for the local Jahn-Teller
and Hund's rule coupling strength, the hopping amplitudes between all nearest
and further neighbors, and the corresponding reduction due to the GdFeO_3-type
distortion. By comparing our results with commonly used model Hamiltonians for
manganites, where electrons can hop between two "e_g-like" orbitals located on
each Mn site, we find that the most crucial limitation of such models stems
from neglecting changes in the underlying Mn(d)-O(p) hybridization.
