Which Redfield theory is the most accurate for simulating 2D electronic spectra?

Two-dimensional electronic spectra (2DES) contain a wealth of information about electronic structure and excited-state dynamics. Experimental 2DES spectra are often congested with many overlapping peaks, making it difficult to extract informative details without simulations. Here, we evaluated the accuracy of 2DES spectra calculated using three theoretical approaches: the standard Redfield theory, the Redfield theory with the secular approximation (Lindblad master equation), and the coherent modified Redfield theory (CMRT). These methods are based on the Markovian quantum master equation, are computationally inexpensive, and can be applied to simulate 2DES spectra of large multichromophoric systems. They are, however, approximate and based on the second-order perturbation theory. Redfield and Lindblad methods are Markovian, while CMRT partially accounts for the non-Markovian effects. Therefore, a careful assessment of their accuracy is needed. We benchmark these methods on 2DES spectra of a molecular trimer coupled to a dissipative environment, which is a non-trivial extension of a previously extensively studied dimer as it enables coherence-to-coherence and more population-to-coherence and population relaxation pathways compared to the dimer. We show that in the Markovian regime, all methods produce accurate spectra. In the non-Markovian regime, Redfield and Lindbladian dynamics are not accurate, although both methods perform very reasonably for the zero waiting time 2DES spectra. At longer waiting times, both methods are no longer accurate but 2DES from the Lindblad dynamics agree better with the exact spectra than 2DES from the standard Redfield theory. CMRT was found to provide a very good agreement with the exact spectra for all system and bath parameters considered here.