Optical response functions are known to reflect quantum dynamics in a superposition state and as such, lack a well-defined classical limit. In a previous paper we considered the importance of accounting for the quantum nature of the dynamics by comparing the linear absorption spectrum and homodyne-detected time-integrated two-pulse photon-echo signal as calculated via the semiclassical forward-backward approach, linearized semiclassical approach, and standard approach which is based on equilibrium ground state dynamics [Shi and Geva, J. Chem. Phys. 122, 064506 (2005)]. In the present paper, we extend the comparison to the case of heterodyne-detected and time-resolved nonlinear time-domain rephasing and nonrephasing signals generated in three-pulse experiments and the corresponding frequency-domain two-dimensional spectra. The comparison is performed in the context of a two-state chromophore solvated in a nonpolar liquid. It is shown that the inherent insensitivity of the standard method to the nonequilibrium dynamics on the excited state potential surface gives rise to two-dimensional spectra which are symmetrical relative to the diagonal. In contrast, accounting for the effect of nonequilibrium excited state dynamics, as is the case within the forward-backward and linearized semiclassical methods, is found to give rise to two-dimensional spectra that become increasingly asymmetrical relative to the diagonal as the waiting time between the second and third pulses becomes larger. It is argued that the emergence of the asymmetry provides a useful probe of nonequilibrium solvation on the excited state potential surface.
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