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We present a first-principles framework to compute sum-frequency generation (SFG) vibrational spectra of semiconductors and insulators. The method is based on density functional theory and the use of maximally localized Wannier functions to compute the response to electric fields, and it includes the effect of electric field gradients at surfaces. In addition, it includes quadrupole contributions to SFG spectra, thus enabling the verification of the dipole approximation, whose validity determines the surface specificity of SFG spectroscopy. We compute the SFG spectra of ice I_{h} basal surfaces and identify which spectra components are affected by bulk contributions. Our results are in good agreement with experiments at low temperature.

First-Principles Framework to Compute Sum-Frequency Generation Vibrational Spectra of Semiconductors and Insulators