  This is the first in a series of two papers investigating the effect of
electron-phonon coupling in two-dimensional Fourier transformed electronic
spectroscopy. We present a series of one- and two-dimensional nonlinear
spectroscopic techniques for studying a dye molecule in solution. Ultrafast
laser pulse excitation of an electronic transition coupled to vibrational modes
induces a propagating vibrational wave packet that manifests itself in
oscillating signal intensities and line-shapes. For the two-dimensional
electronic spectra we can attribute the observed modulations to periodic
enhancement and decrement of the relative amplitudes of rephasing and
non-rephasing contributions to the total response. Different metrics of the
two-dimensional signals are shown to relate to the frequency-frequency
correlation function which provides the connection between experimentally
accessible observations and the underlying microscopic molecular dynamics. A
detailed theory of the time-dependent two-dimensional spectral line-shapes is
presented in the accompanying paper [T. Mancal et al., arXiv:1003.xxxx].
