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Multi-dimensional spectroscopy represents a particularly insightful tool forinvestigating the interplay of nuclear and electronic dynamics, which plays animportant role in a number of photophysical processes and photochemicalreactions. Here we present a coherent state representation of the vibronicdynamics and of the resulting response functions for the widely used linearlydisplaced oscillator model. Analytical expressions are initially derived forthe case of third-order response functions in an N-level system, with groundstate initialization of the oscillator (zero-temperature limit). The resultsare then generalized to the case of M-th order response functions, witharbitrary M. The formal derivation is translated into a simple recipe, wherebythe explicit analytical expressions of the response functions can be deriveddirectly from the Feynman diagrams. We further generalize to the whole set ofinitial coherent states, which form an overcomplete basis. This allows one inprinciple to derive the dependence of the response functions on arbitraryinitial states of the vibrational modes and is here applied to the case ofthermal states. Finally, a non-Hermitian Hamiltonian approach is used toinclude in the above expressions the effect of vibrational relaxation.

Vibrational response functions for multidimensional electronic spectroscopy in the adiabatic regime: a coherent-state approach