What interactions can distort the orientational distribution of interfacial water molecules as probed by second harmonic and sum frequency generation?

Aqueous interfaces are omnipresent in nature. Nonlinear optical methods such as second harmonic and sum frequency generation (SHG/SFG) are valuable techniques to access molecular level information from these interfaces. In the interpretation of SHG and SFG data for both scattering and reflection mode experiments, the relation between the second-order hyperpolarizability tensor β(2), a molecular property, and the surface second-order susceptibility χ(2), a surface averaged property, plays a central role. To correctly describe the molecular details of the interface, it needs to be determined how molecules are oriented, and what the influence is of interfacial electrostatic fields and H-bonding on the orientational distribution. Here, we revisit the relations between β(2) and χ(2) and show, by means of a Boltzmann average, that significant energy differences are needed to generate measurable changes in the molecular orientational distribution at the interface. In practice, H-bonding and surface pressure such as applied in a Langmuir trough can be strong enough to alter the shape of the orientational distribution function of water. In contrast, electrostatic fields, such as those present in the Stern layer, will not have a significant impact on the shape of the orientational distribution function of water molecules.