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.