Hyperpolarizability of Water at the Air-Vapor Interface: Numerical Modeling Questions Standard Experimental Approximations

In this article, we investigate the molecular first hyperpolarizability of water molecules nearby the liquid-vapor interface. The hyperpolarizability of each molecule is calculated at the quantum level within an explicit, inhomogeneous electrostatic embedding. We report that the average molecular first hyperpolarizability tensor depends on the distance relative to the interface, but it practically respects the Kleinman symmetry everywhere in the liquid. Within this numerical approach, based on the dipolar approximation, the water layer contributing to the Surface Second Harmonic Generation (S-SHG) intensity is less than a nanometer. We show that within this interfacial layer, the common assumption considering a single, constant hyperpolarizability for all water molecules is not supported by our data: hyperpolarizability fluctuations are expected to impact the S-SHG intensity. These results represent a step forward the molecular interpretation of experimental S-SHG signal of aqueous interfaces.