Toward a simple molecular understanding of sum frequency generation at air-water interfaces

Second-order vibrational spectroscopies successfully isolate signals from interfaces, but they report on intermolecular structure in a complicated and indirect way. Here, we adapt a perspective on vibrational response developed for bulk spectroscopies to explore the microscopic fluctuations to which sum frequency generation (SFG), a popular surface-specific measurement, is most sensitive. We focus exclusively on inhomogeneous broadening of spectral susceptibilities for OH stretching of HOD as a dilute solute in D(2)O. Exploiting a simple connection between vibrational frequency shifts and an electric field variable, we identify several functions of molecular orientation whose averages govern SFG. The frequency dependence of these quantities is well captured by a pair of averages, involving alignment of OH and OD bonds with the surface normal at corresponding values of the electric field. The approximate form we obtain for SFG susceptibility highlights a dramatic sensitivity to the way a simulated liquid slab is partitioned for calculating second-order response.