  Equilibrium crystal structures for La0.5Ca0.5MnO3 have been calculated using
hybrid exact exchange and density functional methods. Two distinct ground
states with either conventional checkerboard charge ordering or Zener polaron
formation are found depending on the proportion of exact exchange used. The
checkerboard state has mixed x^2-y^2, 3x^2-r^2 and 3y^2-r^2 orbital ordering
and CE-type magnetic order while the Zener polaron state has 3x^2-r^2 and
3y^2-r^2 ordering and A-type magnetic order.
