Measuring Molecular Reorientation at Liquid Surfaces with Time-Resolved Sum-Frequency Spectroscopy: A Theoretical Framework

A theoretical framework is presented for the design and analysis of ultrafast time- and polarization-resolved surface vibrational spectroscopy, aimed at elucidating surface molecular reorientational motion in real time. Vibrational excitation with linearly polarized light lifts the azimuthal symmetry of the surface transition-dipole distribution, causing marked, time-dependent changes in the surface sum-frequency generation (SFG) intensity. The subsequent recovery of the SFG signal generally reflects both vibrational relaxation and reorientational motion of surface molecules. We present experimental schemes that allow direct quantification of the time scale of surface molecular reorientational diffusive motion.