Theoretical modeling of interface specific vibrational spectroscopy: Methods and applications to aqueous interfaces

A unified description of the experimental and theoretical considerations that are necessary to describe sum frequency generation (SFG) line shapes theoretically in the context of extant measurements and simulations is reviewed. A general theory of nonlinear polarization starting with the Nth order formulas and specializing to second-order processes are also presented. Also, relevant considerations concerning optical experiments at interfaces including the origin and importance of Fresnel factors and the phenomenological expression for the measured second-order intensity in terms of the signal field are discussed. Formal expressions for dipolar, quadrupolar, and static field-induced third-order contributions to the sum frequency signal and the theoretical simulations and results of aqueous interfaces are also included in the review. Additionally, time domain SFG techniques are shown to extend the abilities of SFG spectroscopy to probe interfacial vibrations in new novel ways. Theoretical and experimental measurements of both the real and imaginary parts of the SFG signal show great promise in helping unravel complex SFG line shapes.