We present details of our effective computational methods based on the real-space finite-difference formalism to elucidate electronic and magnetic properties of the two-dimensional (2D) materials within the framework of the density functional theory. The real-space finite-difference formalism enables us to treat truly 2D computational models by imposing individual boundary condition on each direction. The formulae for practical computations under the boundary conditions specific to the 2D materials are derived and the electronic band structures of 2D materials are demonstrated using the proposed method. Additionally, we introduce other first-principles works on the MoS2 monolayer focusing on the modulation of electronic and magnetic properties originating from lattice defects.
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