Fourth-order complex time-dependent Redfield theory for absorption line shapes

Simulations of the absorption line shapes of various molecular systems provide insights into experimental data and can be used as tests for different models. The second-order complex-time dependent Redfield (ctR) theory has been shown to possess an excellent combination of accuracy and numerical efficiency. Nonetheless, there are some cases where improvements in its accuracy are desirable. In this study, we have developed a fourth-order extension of the ctR theory (ctR4). By assuming an exponential decomposition of the bath correlation function, we have derived analytical expressions, thus avoiding costly numerical integration in the time domain. Our results show that the ctR4 approach can provide higher quality results for the Debye spectral density, even in the case when the reorganization energies of different molecules are slightly different. On the other hand, for the Ohmic spectral density with exponential cutoff, the ctR4 line shapes are more accurate only for small reorganization energies, while for the super-Ohmic spectral density, the original second-order theory provides better results. Moreover, for some parameter values, the ctR4 line shapes can exhibit negative features. Therefore, the original ctR theory remains preferable in practical calculations.