Sum-frequency generation spectroscopy of the libration mode at the air/water interface: Electric quadrupole effects

Based on ab initio molecular dynamics simulations and quantum chemistry calculations, we compute the sum-frequency generation (SFG) spectroscopy of the interfacial water libration mode by incorporating the electric dipole, electric quadrupole, and magnetic dipole contributions. The results demonstrate that the electric quadrupole contribution dominates the spectrum, while the magnetic dipole contribution is non-negligible. In contrast, the electric dipole contribution is minimal due to the weak polarizability derivative. These findings are consistent with experimental SFG spectroscopy featuring a prominent peak at 834 cm⁻¹, which can only be accurately reproduced when both the electric quadrupole and magnetic dipole terms are included. The dominance of the electric quadrupole effect is attributed to the delocalized electron density distribution inherent to librational motion, which extends beyond individual water molecules via hydrogen-bonding networks.