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Beyond the Electric Dipole Approximation: Electric and Magnetic Multipole Contributions Reveal Biaxial Water Structure from SFG Spectra at the Air-Water Interface

The interpretation of sum-frequency-generation (SFG) spectra has been severely limited by the absence of quantitative theoretical predictions of higher-order multipole contributions. Magnetic dipole and electric quadrupole contributions are determined by bulk properties but appear in all experimental SFG spectra, obscuring the connection between measured spectra and interfacial structure. We present the simulation-based framework to predict the full set of multipole spectral contributions. This framework also yields depth-resolved spectra, enabling the precise spatial localization of spectroscopic features. Applied to the air-water interface, our approach achieves quantitative agreement with experimental spectra for different polarization combinations in both the bending and stretching regions. Higher-order multipole contributions are crucial for correctly interpreting SFG spectra: in the bending band, the electric dipole and the magnetic dipole contributions have similar intensities, while the electric quadrupole contribution is significantly larger. In the OH-stretch region, the electric quadrupole contribution is found to be in large part responsible for the characteristic shoulder at 3600/cm. Crucially, subtracting the quadrupole and magnetic contributions isolates the second-order electric dipole susceptibility, which is a quantitative probe for interfacial molecular orientational anisotropy. This electric-dipole susceptibility reveals a pronounced biaxial ordering of water at the air-water interface. By resolving a fundamental limitation of the interpretation of SFG spectroscopy, our framework allows for the detailed extraction of interfacial water ordering from SFG spectra.