The orbital and charge ordering in Pr_{1-x}Ca_xMnO_3 (x=0 and 0.5) from   the ab initio calculations
  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. 
V. I. Anisimov, I. S. Elfimov, M. A. Korotin (Institute of Metal   Physics, Ekaterinburg, Russia) and K. Terakura (JRCAT, Ts...