One and Two Dimensional Vibronic Spectra for an Exciton Dimer from Classical Trajectories

We extend the semiclassical optimized mean trajectory (OMT) procedure to calculate electronic spectra for a dimer with excitonic and vibronic interactions. The electronic part of the quantum Hamiltonian is expressed in the Miller-Meyer-Stock-Thoss form with one fictitious harmonic oscillator per electronic state, and the classical limit is taken, transforming a quantum Hamiltonian governing discrete states to an equivalent classical form. The ad hoc addition of classical nuclear degrees of freedom and electron-nuclear coupling yields a classical Hamiltonian with one degree of freedom per each electronic state and also per each nuclear motion. Semiclassical quantization is applied to this Hamiltonian through the OMT, originally developed to describe nuclear dynamics on a single potential surface and subsequently generalized to include electronic transitions. The accuracy and practicality of this trajectory-based method is assessed for an excitonically coupled dimer. The semiclassical one- and two-dimensional spectra are shown to compare well with quantum dynamical calculations performed with the hierarchical equations of motion method.