  The physics of manganites is often described within an effective two-band
tight-binding (TB) model for the Mn e_g electrons, which apart from the kinetic
energy includes also a local "Hund's rule" coupling to the t_{2g} core spin and
a local coupling to the Jahn-Teller (JT) distortion of the oxygen octahedra. We
test the validity of this model by comparing the energy dispersion calculated
for the TB model with the full Kohn-Sham band-structure calculated within the
local spin-density approximation (LSDA) to density functional theory. We
analyze the effect of magnetic order, JT distortions, and "GdFeO_3-type"
tilt-rotations of the oxygen octahedra. We show that the hopping amplitudes are
independent of magnetic order and JT distortions, and that both effects can be
described with a consistent set of model parameters if hopping between both
nearest and next-nearest neighbors is taken into account. We determine a full
set of model parameters from the density functional theory calculations, and we
show that both JT distortions and Hund's rule coupling are required to obtain
an insulating ground state within LSDA. Furthermore, our calculations show that
the "GdFeO_3-type" rotations of the oxygen octahedra lead to a substantial
reduction of the hopping amplitudes but to no significant deviation from the
simple TB model.
