Two-dimensional spectroscopy of coupled vibrations with the optimized mean-trajectory approximation.

The optimized mean-trajectory (OMT) approximation is a semiclassical representation of the nonlinear vibrational response function used to compute multidimensional infrared spectra. In this method, response functions are calculated from a sequence of classical trajectories linked by discontinuities representing the effects of radiation-matter interactions, thus providing an approximation to quantum dynamics using classical inputs. This approach was previously formulated and assessed numerically for a single anharmonic degree of freedom. Our previous work is generalized here in two respects. First, the derivation of the OMT is extended to any number of coupled anharmonic vibrations by determining semiclassical approximations for pairs of double-sided Feynman diagrams. Second, an efficient numerical procedure is developed for calculating two-dimensional infrared spectra of coupled anharmonic vibrations in the OMT approximation. The OMT approximation is shown to reproduce the fundamental features of the quantum response function including both coherence and population dynamics.