The simulation of multidimensional vibrational spectroscopy of condensed-phase systems including nuclear quantum effects is challenging since full quantum-mechanical calculations are still intractable for large systems comprising many degrees of freedom. Here, we apply the recently developed double Kubo transform (DKT) methodology in combination with ring-polymer molecular dynamics (RPMD) for evaluating multi-time correlation functions [K. A. Jung et al., J. Chem. Phys. 148, 244105 (2018)], providing a practical method for incorporating nuclear quantum effects in nonlinear spectroscopy of condensed-phase systems. We showcase the DKT approach in the simulation of the fifth-order two-dimensional (2D) Raman spectroscopy of Lennard-Jones liquids as a prototypical example, which involves nontrivial nonlinear spectroscopic observables of systems described by anharmonic potentials. Our results show that the DKT can faithfully reproduce the 2D Raman response of liquid xenon at high temperatures, where the system behaves classically. In contrast, liquid neon at low temperatures exhibits moderate but discernible nuclear quantum effects in the 2D Raman response compared to the responses obtained with classical molecular dynamics approaches. Thus, the DKT formalism in combination with RPMD simulations enables simulations of multidimensional optical spectroscopy of condensed-phase systems that partially account for nuclear quantum effects.
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