  Quantum beats in nonlinear spectroscopy of molecular aggregates are often
attributed to electronic phenomena of excitonic systems, while nuclear degrees
of freedom are commonly included into models as overdamped oscillations of bath
constituents responsible for dephasing. However, molecular systems are coupled
to various high-frequency molecular vibrations, which can cause the spectral
beats hardly distinguishable from those created by purely electronic
coherences. Models containing damped, undamped and overdamped vibrational modes
coupled to an electronic molecular transition are discussed in this paper in
context of linear absorption and two-dimensional electronic spectroscopy.
Analysis of different types of bath models demonstrates how do vibrations map
onto two-dimensional spectra and how the damping strength of the coherent
vibrational modes can be resolved from spectroscopic signals.
