Conspectus: The role of coherences, or coherently excited superposition states, in complex condensed-phase systems has been the topic of intense interest and debate for a number of years. In many cases, coherences have been utilized as spectators of ultrafast dynamics or for identifying couplings between electronic states. In rare cases, they have been found to drive excited state dynamics directly. Interestingly though, the utilization of coherences as a tool for high-detail vibronic spectroscopy has largely been overlooked until recently, despite their encoding of key information regarding molecular structure, electronically sensitive vibrational modes, and intermolecular interactions. Furthermore, their detection in the time domain makes for a highly comprehensive spectroscopic technique wherein the phase and dephasing times are extracted in addition to amplitude and intensity, an element not afforded in analogous frequency domain "steady-state" measurements. However, practical limitations arise in disentangling the large number of coherent signals typically accessed in broadband nonlinear spectroscopic experiments, often complicating assignment of the origin and type of coherences generated.Two-dimensional electronic spectroscopy (2DES) affords an avenue by which to disperse and decompose the large number of coherent signals generated in nonlinear experiments, facilitating the assignment of various types of quantum coherences. 2DES takes advantage of the broad bandwidth necessary for achieving the high time resolution desired for ultrafast dynamics and coherence generation by resolving the excitation axis to detect all excitation channels independently. This feature is beneficial for following population dynamics such as electronic energy transfer, and 2DES has become the choice method for such studies. Simultaneously, coherences arise as oscillations at well-defined coordinates across the 2D map often atop those evolving population signals. By isolating the coherent contribution to the 2DES data and Fourier transforming along the population time, a 3D spectral representation of the coherent 2D data is generated, and coherences are then ordered by their oscillation frequency, ν2. Individual coherences can then be selected by their frequency and evaluated via their distinct "2D coherence" spectra, yielding a significantly more distinctive set of spectroscopic signatures over other 1D methodologies and single-point 2DES analysis. Given that coherences of different origin result in unique 2D coherence spectra, these characteristics can be catalogued and compared directly against experiment for prompt assignment, a strategy not afforded by traditional 2DES analysis. In this Account, a structure-driven time-independent spectral model is discussed and employed to compare the 2D fingerprints of various coherences to experimental 2D coherence spectra. The frequency-domain approach can easily integrate ab initio derived vibronic parameters, and its correspondence with experimental coherence spectra of a model compound is demonstrated. Several examples and applications are discussed herein, from 2D Franck-Condon analysis of a model compound, to identifying the signatures of interpigment vibronic coupling in a photosynthetic light-harvesting complex. The 3D spectral approach to 2DES provides remarkable spectroscopic detail, in turn leading to new insights in molecular structure and interactions, which complement the time-resolved dynamics simultaneously recorded. The approach presented herein has the potential to distill down the convoluted set of nonlinear signals appearing in 2D coherent spectra, making the technique more amenable to high-detail vibronic spectroscopy in inherently complex condensed phase systems.
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