An improved time correlation function (TCF) description of sum frequency generation (SFG) spectroscopy was developed and applied to theoretically describing the spectroscopy of the ambient water/vapor interface. A more general TCF expression than was published previously is presented-it is valid over the entire vibrational spectrum for both the real and imaginary parts of the signal. Computationally, earlier time correlation function approaches were limited to short correlation times that made signal processing challenging. Here, this limitation is overcome, and well-averaged spectra are presented for the three independent polarization conditions that are possible for electronically nonresonant SFG. The theoretical spectra compare quite favorably in shape and relative magnitude to extant experimental results in the O-H stretching region of water for all polarization geometries. The methodological improvements also allow the calculation of intermolecular SFG spectra. While the intermolecular spectrum of bulk water shows relatively little structure, the interfacial spectra (for polarizations that are sensitive to dipole derivatives normal to the interface--SSP and PPP) show a well-defined intermolecular mode at 875 cm(-1) that is comparable in intensity to the rest of the intermolecular structure, and has an intensity that is approximately one-sixth of the magnitude of the intense free O-H stretching peak. Using instantaneous normal mode methods, the resonance is shown to be due to a wagging mode localized on a single water molecule, almost parallel to the interface, with two hydrogens displaced normal to the interface, and the oxygen anchored in the interface. We have also uncovered the origin of another intermolecular mode at 95 cm(-1) for the SSP and PPP spectra, and at 220 cm(-1) for the SPS spectra. These resonances are due to hindered translations perpendicular to the interface for the SSP and PPP spectra, and translations parallel to the interface for the SPS spectra. Further, by examining the real and imaginary parts of the SFG signal, several resonances are shown to be due to a single spectroscopic species while the "donor" O-H region is shown to consist of three distinct species-consistent with an earlier experimental analysis.

The temperature dependence of the fifth-order Raman response function, R(5)(t1,t2), is calculated for fluid xenon by employing a recently developed time-correlation function (TCF) theory. The TCF theory expresses the two-dimensional (2D) Raman quantum response function in terms of a two-time, computationally tractable, classical TCF. The theory was shown to be in excellent agreement with existing exact classical MD calculations for liquid xenon as well as reproducing line shape characteristics predicted by earlier theoretical work. It is applied here to investigate the temperature dependence of the fifth-order Raman response function in fluid xenon. In general, the characteristic line shapes are preserved over the temperature range investigated (for the reduced temperature points T* = 0.5, 1.0, and 2.0); differences in the signal decay times and a large decline in intensity with decreasing temperature (and associated anharmonicity) are observed. In addition, there are some signature features that were not observed in earlier results for T* = 1. The most dramatic difference in line shape is observed for the polarization condition, xxzzxx, that shows a vibrational echo peak. In contrast, the fully polarized signal changes mainly in magnitude.