Two-dimensional vibronic spectra from classical trajectories

We present a semiclassical procedure for calculating nonlinear optical spectra from a quantum Hamiltonian with discrete electronic states. The purely electronic Hamiltonian for N states is first mapped to the associated Meyer-Miller Hamiltonian for N quantum harmonic oscillators. The classical limit is then taken, and classical nuclear degrees of freedom are introduced. Spectra are calculated by propagating the classical analogs of transition dipole operators subject to semiclassical quantization conditions on action variables. This method generalizes the optimized-mean-trajectory approach, originally developed for nonlinear vibrational spectroscopy and subsequently extended to vibronic spectroscopy, to models with multiple interacting electronic states. Calculations for two electronic excited states with displaced harmonic nuclear potentials illustrate the implementation of this approach.