Thermal Population Fluctuations in Two-Dimensional Infrared Spectroscopy Captured with Semiclassical Mechanics

Time-resolved two-dimensional (2D) infrared spectra of the asymmetric stretch mode of solvated CO₂ show distinct features corresponding to ground- and excited-state thermal populations of the bend modes. The time-dependence of these peaks arises in part from solvent-driven thermal fluctuations in populations of the lower-frequency bend modes through their coupling to the higher-frequency asymmetric stretch. This observation illustrates the capacity of multidimensional vibrational spectroscopy to reveal details of the interactions among vibrational modes in condensed phases. The optimized mean-trajectory (OMT) method is a trajectory-based semiclassical approach to computing the vibrational response functions of multidimensional spectroscopy from a classical Hamiltonian. We perform an OMT calculation of the 2D vibrational spectrum for two coupled anharmonic modes, with the lower-frequency mode undergoing stochastic transitions in energy to mimic solvent-induced fluctuations in quantum populations. The semiclassical calculation reproduces the influence of thermal fluctuations in the low-frequency mode on the 2D spectrum of the high-frequency mode, as in measured spectra of solvated CO₂.