Third-order nonlinear optical response and energy transfer in static disordered systems

Understanding Carotenoid Dynamics via the Vibronic Energy Relaxation Approach

Carotenoids are an integral part of natural photosynthetic complexes, with tasks ranging from light harvesting to photoprotection. Their underlying energy deactivation network of optically dark and bright excited states is extremely efficient: after excitation of light with up to 2.5 eV of photon energy, the system relaxes back to ground state on a time scale of a few picoseconds. In this article, we summarize how a model based on the vibrational energy relaxation approach (VERA) explains the main characteristics of relaxation dynamics after one-photon excitation with special emphasis on the so-called S* state. Lineshapes after two-photon excitation are beyond the current model of VERA. We outline this future line of research in our article. In terms of experimental method development, we discuss which techniques are needed to better describe energy dissipation effects in carotenoids and within the first solvation shell.

Efficient Simulation of Three-Pulse Photon-Echo Signals with Application to the Determination of Electronic Coupling in a Bacterial Photosynthetic Reaction Center

A time-nonlocal quantum master equation coupled with a perturbative scheme to evaluate the third-order polarization in the phase-matching direction k(s) = -k(1) + k(2) + k(3) is used to efficiently simulate three-pulse photon-echo signals. The present method is capable of describing photon-echo peak shifts including pulse overlap and bath memory effects. In addition, the method treats the non-Markovian evolution of the density matrix and the third-order polarization in a consistent manner, thus is expected to be useful in systems with rapid and complex dynamics. We apply the theoretical method to describe one- and two-color three-pulse photon-echo peak shift experiments performed on a bacterial photosynthetic reaction center and demonstrate that, by properly incorporating the pulse overlap effects, the method can be used to describe simultaneously all peak shift experiments and determine the electronic coupling between the localized Q(y) excitations on the bacteriopheophytin (BPhy) and accessory bateriochlorophyll (BChl) in the reaction center. A value of J = 250 cm(-1) is found for the coupling between BPhy and BChl.

Measuring Electronic Coupling in the Reaction Center of Purple Photosynthetic Bacteria by Two-Color, Three-Pulse Photon Echo Peak Shift Spectroscopy

One- and two-color, three-pulse photon echo peak shift spectroscopy (1C and 2C3PEPS) was used to estimate the electronic coupling between the accessory bacteriochlorophyll (B) and the bacteriopheophytin (H) in the reaction center of the purple photosynthetic bacterium Rhodobacter sphaeroides as approximately 170 +/- 30 cm-1. This is the first direct experimental determination of this parameter; it is within the range of values found in previously published calculations. The 1C3PEPS signal of the Qy band of the bacteriochlorophyll B shows that it is weakly coupled to nuclear motions of the bath, whereas the 1C3PEPS signal of the Qy band of the bacteriopheophytin, H, shows that it is more strongly coupled to the bath, but has minimal inhomogeneous broadening. Our simulations capture the major features of the data with the theoretical framework developed in our group to separately calculate the response functions and population dynamics.

One- and Two-Color Photon Echo Peak Shift Studies of Photosystem I

Wavelength-dependent one- and two-color photon echo peak shift spectroscopy was performed on the chlorophyll Qy band of trimeric photosystem I from Thermosynechococcus elongatus. Sub-100 fs energy transfer steps were observed in addition to longer time scales previously measured by others. In the main PSI absorption peak (675-700 nm), the peak shift decays more slowly with increasing wavelength, implying that energy transfer between pigments of similar excitation energy is slower for pigments with lower site energies. In the far-red region (715 nm), the decay of the peak shift is more rapid and is complete by 1 ps, a consequence of the strong electron-phonon coupling present in this spectral region. Two-color photon echo peak shift data show strong excitonic coupling between pigments absorbing at 675 nm and those absorbing at 700 nm. The one- and two-color peak shifts were simulated using the previously developed energy transfer model (J. Phys. Chem. B 2002, 106, 10251; Biophysical Journal 2003, 85, 140). The simulations agree well with the experimental data. Two-color photon echo peak shift is shown to be far more sensitive to variations in the molecular Hamiltonian than one-color photon echo peak shift spectroscopy.

Two-dimensional optical three-pulse photon echo spectroscopy. II. Signatures of coherent electronic motion and exciton population transfer in dimer two-dimensional spectra

Using the nonperturbative approach to the calculation of nonlinear optical spectra developed in a foregoing paper [Mancal et al., J. Chem. Phys. 124, 234504 (2006), preceding paper], calculations of two-dimensional electronic spectra of an excitonically coupled dimer model system are presented. The dissipative exciton transfer dynamics is treated within the Redfield theory and energetic disorder within the molecular ensemble is taken into account. The manner in which the two-dimensional spectra reveal electronic couplings in the aggregate system and the evolution of the spectra in time is studied in detail. Changes in the intensity and shape of the peaks in the two-dimensional relaxation spectra are related to the coherent and dissipative dynamics of the system. It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.

Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra

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].

Three-pulse photon echo of an excitonic dimer modeled via Redfield theory

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.

A reduced density-matrix theory of absorption line shape of molecular aggregate

A theory for the absorption line shape of molecular aggregates in condensed phase is formulated based on a reduced density-matrix approach. Intermolecular couplings in the aggregates are assumed to be weak (Förster type of energy transfer mechanism). The spin-Boson model is employed to include the effect of electron-phonon coupling. Using the projection operator technique, we derive kinetic equations for the reduced electronic density matrix associated with the absorption spectrum. General expressions of time-dependent rate constants in the kinetic equations are derived by using the cumulant expansion technique. The resulting time-dependent kinetic equations are solved numerically. We illustrate the applicability of the present theory by calculating the line shape of a dimer (a pair of donor and acceptor of energy transfer). For a J-aggregate type of molecular pair (with excitonic redshift), a tail appears on the blue side of the absorption spectrum due to the existence of inhomogeneity in electronic state mixing which is originated from the electron-phonon coupling.

The integrated photon echo and solvation dynamics. II. Peak shifts and two-dimensional photon echo of a coupled chromophore system

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.

Probing correlated spectral motion: Two-color photon echo study of Nile blue

We performed two-color three-pulse photon echo peak shift experiments on Nile blue in ethylene glycol and acetonitrile to determine the role of solvent dynamics in correlated spectral motion. The system was pumped near the absorption maximum and the correlation between the initial state and the final state was probed at a number of wavelengths, from the absorption maximum to the fluorescence maximum. In addition to solvent dynamics, we found that strongly coupled intramolecular vibrations generated correlations between different spectral regions. The inertial solvent response was found for both solvents to have a time scale on the order of 100-145 fs. This response contributed half of the solvent interaction strength for acetonitrile, but less than a third for ethylene glycol. Several diffusive time scales were observed: 500 fs and 2.5 ps for acetonitrile, and 1, 15, and 100 ps for ethylene glycol. A single description of the solvation dynamics was insufficient to quantitatively describe the dynamics at all probe wavelengths, which could indicate different dynamics in the ground and excited states or the presence of an additional contribution to the signal from the excited-state absorption.

Long-range resonance energy transfer in molecular systems

The current state of understanding of molecular resonance energy transfer (RET) and recent developments in the field are reviewed. The development of more general theoretical approaches has uncovered some new principles underlying RET processes. This review brings many of these important new concepts together into a generalization of Förster's original theory. The conclusions of studies investigating the various approximations in Förster theory are summarized. Areas of present and future activity are discussed. The review covers Förster theory for donor-acceptor pairs and electronic coupling for singlet-singlet, triplet-triplet, and superexchange-mediated energy transfer. This includes the transition density picture of Coulombic coupling as well as electronic coupling between molecular aggregates (excitons). Spectral overlaps and ensemble energy transfer rates in disordered aggregates, the role of dielectric properties of the medium, weak versus strong coupling, and new models for energy transfer in complex molecular assemblies are also described.