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Physical Review B

Two-dimensional electronic spectroscopy of an excitonically coupled dimer

Pär Kjellberg, Ben Brüggemann, Tõnu Pullerits

Published Jul 26, 2006• 115 citations
Publisher

Abstract

The two-dimensional three-pulse photon echo signals from a dimer system are investigated in detail. A perturbative approach is used to calculate the response of the system via a numerical propagation of the density matrix in exciton state representation. Exciton vibrational coupling is modeled by Redfield relaxation theory. The main goal of this paper is to dissect the two-dimensional spectrum of the dimer to give better understanding of how the dynamics influence the spectral features. We will show how different Liouville pathways lead to the appearance/disappearance of diagonal and cross peaks. The inclusion of a Gaussian shaped electric field will be contrasted to the use of delta-pulses in the impulsive limit. The impulsive limit is found to be a satisfactory approximation at long population times, while at shorter times, in the pulse-overlap region, more realistic electric fields are called for.

DOI
10.1103/physrevb.74.024303

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The Journal of Chemical Physics•May 8, 2002•12 citations
The two-dimensional three-pulse photon echo signals from a dimer system are investigated in detail. A perturbative approach is used to calculate the response of the system via a numerical propagation of the density matrix in exciton state representation. Exciton vibrational coupling is modeled by Redfield relaxation theory. The main goal of this paper is to dissect the two-dimensional spectrum of the dimer to give better understanding of how the dynamics influence the spectral features. We will show how different Liouville pathways lead to the appearance/disappearance of diagonal and cross peaks. The inclusion of a Gaussian shaped electric field will be contrasted to the use of delta-pulses in the impulsive limit. The impulsive limit is found to be a satisfactory approximation at long population times, while at shorter times, in the pulse-overlap region, more realistic electric fields are called for.
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.
We employ multi-level Redfield theory and the equation-of-motion phase-matching approach to model two-dimensional electronic photon-echo signals of a vibronic dimer weakly coupled to an uncorrelated harmonic bath. The vibronic manifold of the dimer is formed by Franck-Condon active vibrational modes (one mode per monomer). We study the effect of the coupled exciton-vibrational dynamics on the two-dimensional photon-echo profiles. Our main focus is the relationship of the system coherences to the oscillatory behavior of the cross-peak intensities with population time. The work represents the first step towards detailed understanding of oscillative signatures in two-dimensional electronic photon-echo signals of vibronic oligomers.
Signatures of chemical exchange and spectral diffusion in 2D photon-echo line shapes of molecular aggregates are studied using model calculations for a dimer whose Hamiltonian parameters are stochastically modulated. Cross peaks induced by chemical exchange and by exciton transport have different dynamics and distinguish two models which have the same absorption spectrum (a two-state jump bath modulation model of a dimer and a four-state jump bath model of a single chromophore). Slow Gaussian-Markovian spectral diffusion of a symmetric dimer induces new peaks which are damped as the dipole moment is equilibrated. These effects require an explicit treatment of the bath and may not be described by lower-level theories such as the Redfield equations, which eliminate the bath.
The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].
A theoretical description of one- and two-color photon echo peak shifts (PEPS) and two-dimensional (2D) photon echo spectrum (PES) of a coupled chromophore system are presented. The effects of population relaxation in the one-exciton states on both the PEPS and the 2D PES are investigated. For values of time T shorter than the population relaxation time, a finite two-color peak shift magnitude and nonzero cross peaks in the 2D PES provide evidence of electronic coupling between the chromophores. These two distinct observables, i.e., PEPS and off-diagonal peaks, both originate from the electronic coupling. However, it is shown that the PEPS and 2D PES methods can provide complementary information on the structure-dependent nonlinear optical responses of coupled chromophore systems.
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.