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The Journal of Chemical Physics

Probing electronic coupling in excitonically coupled heterodimer complexes by two-color three-pulse photon echoes

Tomáš Mančal, Graham R. Fleming

Published Nov 16, 2004• 27 citations
Publisher

Abstract

Following the earlier work of Yang et al. [J. Chem. Phys. 110 (1999) 2983] analytical expressions for the downhill and uphill resonant two-color three-pulse photon echo peak shift (2C-3PEPS) of a heterodimer system are derived in the impulsive limit. It is shown how to obtain information about coupling between the components of the dimer from the combined one- and two-color peak shift measurements. Further analytical relations are derived which enable site specific information about the environment of the components, including the relative difference of the inhomogeneity and the difference between the energy-gap correlation functions on the heterodimer sites to be obtained. The simulations show only a very small influence of the laser pulse length on the measured values of coupling coefficient and other relevant quantities suggesting that current 2C-3PEPS measurements can find practical application in directly measuring couplings in excitonically coupled heterodimer complexes.

DOI
10.1063/1.1807816

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Following the earlier work of Yang et al. [J. Chem. Phys. 110 (1999) 2983] analytical expressions for the downhill and uphill resonant two-color three-pulse photon echo peak shift (2C-3PEPS) of a heterodimer system are derived in the impulsive limit. It is shown how to obtain information about coupling between the components of the dimer from the combined one- and two-color peak shift measurements. Further analytical relations are derived which enable site specific information about the environment of the components, including the relative difference of the inhomogeneity and the difference between the energy-gap correlation functions on the heterodimer sites to be obtained. The simulations show only a very small influence of the laser pulse length on the measured values of coupling coefficient and other relevant quantities suggesting that current 2C-3PEPS measurements can find practical application in directly measuring couplings in excitonically coupled heterodimer complexes.
A two-color photon echo peak shift measurement to probe the electronic coupling strength in molecular complexes is proposed. Exciton transfer between the electronic eigenstates is neglected and the baths associated with each monomer are assumed to be independent of each other. Within this simplified model, we derive a useful relation which can be used to estimate the electronic coupling strength via a combination of a normal one-color and the present two-color peak shift measurements. A simulation based on the cumulant expansion technique illustrates the validity of our suggestion.
Two-color three pulse photon echo peak shift spectroscopy (2C3PEPS) has been used to probe correlation in electronic transitions in two different regions of the electronic spectrum of a chromophore in the condensed phase. The 2C3PEPS can be done in an “uphill” or a “downhill” sense, where the first two interactions are of lower (higher) frequency than the final interaction with the radiation field. In both cases no correlation between the two spectral regions is observed at very short times. Different parts of the spectrum gain correlation owing to ultrafast solvent motion and the accompanying Stokes shift. We propose a model for the spectral shift that incorporates a conditional probability distribution for transition frequencies in the two spectral regions. The model qualitatively reproduces all the features of complete numerical simulations. Our results show that memory is partially conserved during the spectral diffusion process from the pump to the probe region. The downhill difference peak shift is very sensitive to the time scale of the inertial component of solvation and seems very promising for an accurate determination of this time scale.
We investigate the two-color three-pulse photon echo peak shift in a (left-right) binary system, where each component consists of a heterodimer. On the basis of the model, we find that the effect of the excitonic asymmetry between two components leads to an additional factor in the peak shift. A pseudo-rephasing and pseudo-free-induction-decay mechanism is proposed to explain the resultant negative peak shift, when the differences between the two left/right components have the opposite sign. In such a case, estimates of the electronic coupling strength via two- and one-color peak shift experiments lead to an underestimate of the coupling magnitude.
In this article the third-order response of an excitonically coupled dimer is studied. The three-pulse photon echo signals were calculated by extracting polarization components from the total polarization in the corresponding phase-matched directions. The total nonlinear response was obtained by numeric propagation of the density matrix, with the exciton-vibrational coupling modeled via Redfield relaxation theory. The full two-dimensional three-pulse photon echo signals and the peak shift were analyzed in terms of the density-matrix dynamics of coherence dephasing and population relaxation. The location of the two-exciton state was found to be essential for proper modeling of the three-pulse photon echo. In particular, an oscillation in the three-pulse photon echo peak shift is found if the two-exciton state is displaced. The oscillations can be related to the dynamics of the one-exciton coherences.
An understanding of chemical reactivity begins with an understanding of the dynamics involved regarding system-bath interactions. Spectroscopic studies of these interactions in condensed-phase multichromophoric systems are intricate and contain much information. Photon-echo spectroscopy has proven to be a useful tool for probing these interactions. A description of three-pulse photon-echo peak shift spectroscopy (3PEPS)--theory, experiment, and application--for the study of solvation and dynamics of nanoscale excitons is presented. Also, we discuss how two-dimensional photon-echo spectroscopy (2DPE) relates to 3PEPS and show how 3PEPS data can be extracted from 2D photon-echo data.
The two-dimensional (2D) temporal shape of the (degenerate) three-pulse photon-echo (3-PPE) polarization P(3)(t′,τ12,τ23=0) has been theoretically analyzed for a weakly interacting two-site system (TSS) in the presence of site inhomogeneous broadening. The TSS has been modeled in terms of two identical, energy-degenerate, excitonically coupled pairs of electronic states in the site-representation (i.e., two S0 and S1 states forming a 4-level system). The 2D time-domain signal S(t′,τ12,τ23=0) has been derived in a closed-form solution which allowed to formulate the analytical Fourier transform analog under sequential δ-pulse excitation. The resulting 2D PE signal in frequency–frequency space S(ωt′,ωτ12) is formed in the region of the resonant, optical carrier frequency by, generally, four peaks, arranged at the edges of a square with distances determined by the excitonic coupling. The two diagonal peaks are of one-exciton origin, while the two off-diagonal (cross) peaks involve two-exciton effects, too. The relative heights of the four peaks are in distinct relation with the mutual orientation of the site-localized transition dipoles, thus these 2D line shapes serving as a structural probe for resonantly interacting molecules. The shapes of the peaks reflect the ratio between homogeneous and inhomogeneous dephasings and can be used for structural studies of statically disordered systems of TSS. The semiclassical two-site model is intended to provide a preparatory platform for mimicking electronically coupled segmental pairs dispersed in energy and space along the strongly disordered main chain contour. The results of the model calculation are taken to discuss the potential and the limitations of 2D line shape echo-spectroscopy in the study of short-range coherences and electronic coupling in π-conjugated polymers.