Multipolar electric and magnetic contributions to sum-frequency generation spectra reveal biaxial interfacial water structure

Liquid interfaces play central roles in biological and physicochemical processes. Sum-frequency-generation (SFG) spectroscopy is intrinsically interface-specific, but the insight gained from SFG spectra into molecular interfacial structure has been limited since spectral analysis is usually done within the electric-dipole approximation, neglecting higher-order multipole contributions. Here we introduce a general framework that includes electric and magnetic multipoles for calculating SFG spectra from molecular simulations, achieving quantitative agreement between predicted and experimental SFG spectra of the air-water interface. We show that the electric-dipole approximation breaks completely down in the water bending region and remains only qualitatively valid in the OH-stretch region. When accounting for multipole contributions, the analysis of the SFG bending band reveals pronounced biaxial water ordering in a triple-layer structure with a width of only about 0.8 nanometers. By resolving a fundamental limitation of the interpretation of SFG spectroscopy, our framework allows for the detailed extraction of interfacial molecular ordering from SFG spectra.