▎ 摘　　要

We use ab initio calculations to investigate the geometry, band structures, and optical properties of hydrogen functionalized graphene, where hydrogen atoms are attached periodically to A-site carbon atoms to form root 3 x root 3, 2 x 2, 3 x 3, 4 x 4, and 5 x 5 supercells. The adsorbed hydrogen atoms distort the carbon atoms vertically, with almost no modification of the in-plane structures. The ground states show ferromagnetic order, with a total energy of a few tens meV lower than the nonmagnetic ground state. The hydrogen adsorption opens a gap that depends on the supercell size. Optical conductivities are calculated and show fine structures at the band edge. Taking into account the spin-orbit coupling, the nonzero off-diagonal components of the conductivity predict Kerr and Faraday effects without an external magnetic field.