Linear absorption is the most basic optical spectroscopy technique that provides information about the electronic and vibrational degrees of freedom of molecular systems. In simulations of absorption lineshapes, often diagonal fluctuations are included using the cumulant expansion, and the off-diagonal fluctuations are accounted for either perturbatively, or phenomenologically. The accuracy of these methods is limited and their range of validity is still questionable. In this work, a systematic study of several such methods is presented by comparing the lineshapes with exact results. It is demonstrated that a non-Markovian theory for off-diagonal fluctuations, termed complex time dependent Redfield theory, gives good agreement with exact lineshapes over a wide parameter range. This theory is also computationally efficient. On the other hand, accounting for the off-diagonal fluctuations using the modified Redfield lifetimes was found to be inaccurate.

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