tion (GGA) of the density functional theory. The spin-orbit coupling is included from pseu- dopotentials, and the convergence with respect to cutoff energy and K-points sampling are well checked. From the calculated Bloch eigen functions of ground state, maximally localized Wannier functions can be constructed $^{16}$. Such Wannier functions are used to construct the low energy effective Hamiltonian H$_{LDA}$ for free-standing slab of Bi$_{2}$Se$_{3}$ film. Adding proper Zeeman term into effective Hamiltonian, ferromagnetic ordering and QAH effects are studied without free parameters. 34 S. Sanvito, G. Theurich, and N.A. Hill, J. Supercond. 15 , 85 (2002). 14