Fourth order expressions for the electronic absorption lineshape of molecular excitons

The line shape of electronic absorption spectroscopy reflects the information on quantum dynamical processes accompanying the electronic excitation, and its accurate description is an important component for validating theoretical models and assumptions. The present work provides detailed expressions for the absorption line shape of molecular excitons that are valid up to the fourth order of exciton-bath interactions within the quantum master equation approach. These expressions can serve as the basis for developing general and systematic methods to model the line shape for a broad class of molecular exciton systems and environments. For the bath model of linearly coupled harmonic oscillators, more detailed expressions employing the spectral densities of the bath are presented. These expressions are then tested for a linear aggregate of identical chromophores each coupled to the harmonic oscillator bath. Calculation results for a super-Ohmic spectral density with exponential cutoff demonstrate the feasibility of calculations and also offer insights into the utility and difficulty of going beyond the second order approximation.