AbstractFirst principles methods are used to explicitly calculate the nonlinear susceptibility (χ⁽²⁾(2ω, ω, ω)) representing the second harmonic generation (SHG) of two dimensional semiconducting materials, namely transition metal dichalcogenides (TMDs) and Boron Nitride (BN). It is found that alloying TMDs improves their second harmonic response, with MoTeS alloys exhibiting the highest of all hexagonal alloys at low photon energies. Moreover, careful examination of the relationship between the concentration of Se in Mo_xSe_yS_z alloys shows that the SHG intensity can be tuned by modifying the stoichiometry. In addition, materials with curvature can have large second harmonic susceptibility. Of all the calculated monolayer structures, the hypothetical TMD Haeckelites NbSSe and Nb_0.5Ta_0.5S₂ exhibit the highest χ⁽²⁾, while one of the porous 3D structures constructed from 2D hBN exhibits a larger χ⁽²⁾ than known large band gap 3-D materials.