Calculations of vibrationally resonant sum- and difference-frequency-generation spectra of chiral molecules in solutions: three-wave-mixing vibrational optical activity.

Determining absolute configuration of chiral molecule can be achieved by using vibrational optical activity (VOA) measurement methods, such as vibrational circular dichroism and Raman optical activity (ROA). Recently, vibrationally resonant sum frequency generation and difference frequency generation utilizing circularly polarized beams were theoretically studied and shown that they can be alternative and complementary VOA measurement techniques [S. Cheon and M. Cho, Phys. Rev. A 71, 013808 (2005); J. Phys. Chem. A 113, 2438 (2009)]. Even for randomly oriented chiral molecules in solutions, the sum- and difference-frequency-generation signals induced by linearly polarized incident beams with mutually perpendicular polarization directions can be nonzero and are determined by the optical activity hyperpolarizability given by a product of antisymmetric Raman tensor and vibrational transition dipole. If one of the beams involved in the three-wave-mixing processes is circularly polarized and if the difference signal is measured, not only the same optical activity hyperpolarizability but also that including electric quadrupole-ROA tensor are required to determine the signals. Here, we carried out quantum chemistry calculations to obtain these quantities for a representative chiral molecule, (S)-methyl lactate, and numerically simulated the corresponding spectra. It is shown that the circular polarization three-wave-mixing signal intensities are quantitatively similar to those of the linear polarization three-wave-mixing signals, respectively, and that they are sensitive to the absolute configuration of chiral molecule. The calculation results thus suggest that these two novel techniques will be of use in studying molecular chirality even in time domain, once polarization-modulated ultrashort pulses are used to carry out circular polarization three-wave-mixing experiments.