Computation of Time-Resolved Nonlinear Electronic Spectra From Classical Trajectories

A variety of time-resolved spectroscopic techniques employing femtosecond pump and probe pulses are nowadays widely used to unravel the fundamental mechanisms of photophysical and photochemical processes in molecules and materials. Theoretical support based on first-principles electronic-structure calculations is essential for the interpretation of the observed time and frequency resolved signals. Accurate calculations of nonlinear spectroscopic signals based on a quantum wave-packet description of the nonadiabatic excited-state dynamics have been demonstrated for diatomic and triatomic molecules. For polyatomic molecules with many nuclear degrees of freedom, quasi-classical trajectory descriptions of the excited-state dynamics are more practical. While the computation of time-dependent electronic population probabilities with quasi-classical trajectory methods has become routine, the simulation of time and frequency resolved pump-probe signals is more challenging. This article presents a theoretical framework for first-principles simulations of various femtosecond signals that is based on the third-order polarization and the quasi-classical implementation of the doorway-window approximation. The latter approximation is applicable for non-overlapping pump and probe pulses that are reasonably short on the characteristic time scale of the system dynamics. Apart from a systematic derivation of the theory, explicit computational protocols for the calculation of pump-probe signals are provided. Transient absorption pump-probe spectroscopy with UV pump and UV or X-ray probe pulses, two-dimensional electronic spectroscopy, and femtosecond time-resolved photoelectron spectroscopy are considered as specific examples. Recent applications of these computational methods to prototypical chromophores are briefly reviewed.