Surface populations as a model for the distance-dependence of the interfacial refractive index

Vibrational sum frequency spectra provide information about interfaces that is sensitive to the orientation of molecules, their electronic environment, and the local electric fields. Here, we use molecular dynamics simulations in order to study a surfactant, para-cyanophenol, at the air-water interface. The volume fractions of water and the organic surfactant are considered at various points over the nanometer-scale region in a Lorentz-Lorenz model. We find that the calculated ratios of nonlinear susceptibility tensor elements are in agreement with experimental data only when this depth profile was considered. We also use these data to evaluate the ratio of the C-N hyperpolarizability tensor elements in the interfacial region.