  The electronic structure of the doped manganites Pr$_{1-x}$Ca$_x$MnO$_3$ was
calculated by the LSDA+U method which takes into account the local Coulomb
interaction between d-electrons of transition metal ions. In contrast to the
standard local spin density approximation (LSDA) no Jahn-Teller lattice
distortions are needed to reproduce the experimentally observed orbital
ordering in the undoped PrMnO$_3$. The correct ground state : a charge and
orbital ordered antiferromagnetic insulator, was obtained for
Pr$_{1/2}$Ca$_{1/2}$MnO$_3$. The results are in good agreement with the neutron
diffraction data.
