The effect of static disorder on the center line slope in 2D electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) is a powerful tool for investigating the dynamics of complex systems. However, analyzing the resulting spectra can be challenging, and thus may require the use of theoretical modeling techniques. The center line slope (CLS) method is one of such approaches, which aims to extract the time correlation function (TCF) from 2DES with minimal error. Since static disorder is widely observed in complex systems, it may be interesting to ask whether the CLS approach still work in the presence of the static disorder. In this paper, the effect of the static disorder on the TCF obtained through the CLS method is investigated. It is found that the steady-state value of the CLS increases monotonically with respect to the static disorder, which suggests that the amplitude of the static disorder can be determined using the CLS in the long-time limit. Additionally, as the static disorder rises, the decay rate of the CLS first decreases to a certain value and remains at this value until the static disorder is sufficiently large. Afterward, the CLS begins to fluctuate significantly and thus results in obtaining the decay rate through the CLS method unreliable. Based on these discoveries, we propose a method to fix the error and obtain the TCF. Our findings may pave the way for obtaining reliable system-bath information by analyzing 2DES in the practical situations.