Two-dimensional electronic spectra from trajectory-based dynamics: pure-state Ehrenfest, spin-mapping, and mean classical path approaches

Two-dimensional electronic spectroscopy (2DES) provides a detailed picture of electronically nonadiabatic dynamics that can be interpreted with the aid of simulations. Here, we develop and contrast trajectory-based nonadiabatic dynamics approaches for simulating 2DES spectra. First, we argue that an improved pure-state Ehrenfest approach can be constructed by decomposing the initial coherence into a sum of equatorial pure states that contain equal contributions from the states in the coherence. We then use this framework to show how one can obtain a more accurate, but computationally more expensive, approximation to the third-order 2DES response function by replacing Ehrenfest dynamics with spin mapping during the pump-probe delay time. We end by comparing and contrasting the accuracy of these methods and the simpler mean classical path approximation in reproducing the exact linear, pump-probe, and 2DES spectra of two Frenkel exciton models: a coupled dimer system and the Fenna-Matthews-Olson (FMO) complex.