Ab initiodescription of second-harmonic generation from crystal surfaces

We propose an ab initio framework to derive the dielectric and the second-order susceptibility tensors for crystal surfaces. The single-surface response is extracted from a supercell scheme. We evaluate macroscopic quantities, taking into account the local fields. The first- and second-order susceptibilities are evaluated within time-dependent density functional theory, in the long-wavelength limit. We apply our formalism to the calculation of the second-harmonic generation for clean and hydrogenated silicon surfaces. The agreement with measured second-order susceptibility components is significantly better, illustrating the importance of local-field effects.