Publication
In a two-dimensional (2D) opticalspectrum of a multilevelsystem,there are diagonal peaks and off-diagonal cross-peaks that correlatethe different levels. The time-dependent properties of these diagonalpeaks and cross-peaks contain much information about the dynamicsof the multilevel system. The time-dependent diagonal peakshape thatdepends on the spectral diffusion dynamics of the associated transitionand characterized by the frequency-fluctuation correlationfunction (FFCF) is well studied. However, the time-dependent peakshapeof a cross-peak that provides the correlation dynamics between differenttransitions is much less studied or understood. We derived the third-ordernonlinear response functions that describe the cross-peaks in a 2Delectronic spectrum of a multilevel system that arise from processessharing a common ground state and/or from internal conversion andpopulation transfer. We can use the center line slope (CLS) analysisto characterize the cross-peaks in conjunction with the diagonal peaks.This allows us to recover the frequency-fluctuation cross-correlationfunctions (FXCFs) between two transitions. The FXCF and its subsidiaryquantities such as the initial correlation and the initial covariancebetween different transitions are important for studying the correlationeffects between states in complex systems, such as energy-transferprocesses. Furthermore, knowledge of how various molecular processesover different timescales affect simultaneously different transitionscan also be obtained from the measured FXCF. We validated and testedour derived equations and analysis process by studying, as an example,the 2D electronic spectra of metal-free phthalocyanine in solution.We measured and analyzed the diagonal peaks of the Q ( x ) and Q ( y ) transitions and the cross-peaks between these twotransitions of this multilevel electronic system and obtained theassociated FFCFs and FXCFs. In this model system, we measured negativecomponents of FXCF over the tens of picosecond timescale. This suggeststhat in phthalocyanine, the Q ( x ) and Q ( y ) transitionscoupling with the solvent molecule motion are anticorrelated to eachother.