Mino Yang

Influence of phonons on exciton transfer dynamics: comparison of the Redfield, Förster, and modified Redfield equations

Abstract The effect of the reorganization of phonons on exciton transfer dynamics is examined. Starting from a general quantum master equation, we obtain population transfer rates for the Redfield, the Forster, and the modified Redfield equations and compare the predictions of these three models over various ranges of parameters. It is shown that the validity of the traditional Redfield equation is justified by a broad spectrum of phonons rather than a small magnitude of electron–phonon coupling strength as is usually implied. The modified Redfield equation suggested by Zhang et al. [J. Chem. Phys. 108 (1998) 7763] is shown to have a wide range of applicability and to reduce numerically to the traditional Redfield equation and the Forster equation in the respective limiting cases.

Energy Transfer in Photosystem I of Cyanobacteria Synechococcus elongatus: Model Study with Structure-Based Semi-Empirical Hamiltonian and Experimental Spectral Density

We model the energy transfer and trapping kinetics in PSI. Rather than simply applying Förster theory, we develop a new approach to self-consistently describe energy transfer in a complex with heterogeneous couplings. Experimentally determined spectral densities are employed to calculate the energy transfer rates. The absorption spectrum and fluorescence decay time components of the complex at room temperature were reasonably reproduced. The roles of the special chlorophylls (red, linker, and reaction center, respectively) molecules are discussed. A formally exact expression for the trapping time is derived in terms of the intrinsic trapping time, mean first passage time to trap, and detrapping time. The energy transfer mechanism is discussed and the slowest steps of the arrival at the primary electron donor are found to contain two dominant steps: transfer-to-reaction-center, and transfer-to-trap-from-reaction-center. The intrinsic charge transfer time is estimated to be 0.8 approximately 1.7 ps. The optimality with respect to the trapping time of the calculated transition energies and the orientation of Chls is discussed.

Two-dimensional infrared spectroscopy and ultrafast anisotropy decay of water

We introduce a sparse-matrix algorithm that allows for the simulation of two-dimensional infrared (2DIR) spectra in systems with many coupled chromophores. We apply the method to bulk water, and our results are based on the recently developed ab initio maps for the vibrational Hamiltonian. Qualitative agreement between theory and experiment is found for the 2DIR spectra without the use of any fitting or scaling parameters in the Hamiltonian. The calculated spectra for bulk water are not so different from those for HOD in D(2)O, which we can understand by considering the spectral diffusion time-correlation functions in both cases. We also calculate the ultrafast anisotropy decay, which is dominated by population transfer, finding very good agreement with experiment. Finally, we determine the vibrational excitation diffusion rate, which is more than two orders of magnitude faster than the diffusion of the water molecules themselves.

Influence of intramolecular vibrations in third-order, time-domain resonant spectroscopies. II. Numerical calculations

We model recent experimental wavelength dependent Three Pulse Photon Echo Peak Shift (WD-3PEPS) and Transient Grating (WD-TG) signals considering both solvation dynamics and vibrational contributions. We present numerical simulations of WD-3PEPS and WD-TG signals of two probe molecules: Nile Blue and N,N-bisdimethylphenyl-2,4,6,8-perylenetetracarbonyl diamide to investigate the influence of intramolecular vibrations in the signals. By varying the excitation wavelength, we show that the different initial conditions for the vibrational wave packets significantly affect the signals, especially through the contributions associated with high frequency modes, often neglected in experimental analyses. We show that the temporal properties of both WD-TG and WD-3PEPS signals display sensitivities to both the excitation wavelength and the vibronic structure of the specific probe molecule used. Several mechanisms for generating vibronic modulations in the signals are discussed and their effects on the signals are des...

Kinetic theory of bimolecular reactions in liquid. III. Reversible association–dissociation: A+B⇄C

A theoretical formalism based on the fully renormalized kinetic theory is applied to a diffusion-influenced pseudo-first order reaction kinetics of reversible association–dissociation A+B⇄C including unimolecular decay processes. Linear response of the system, initially at equilibrium, to a thermal perturbation is examined and a rate kernel equation for the reactant concentrations is derived. The rate kernel has a hierarchical structure and the propagator appeared in the kernel expression is truncated by a disconnected approximation. When the unimolecular reactions are turned off, the response of the system not only shows the long-time power law of t−3/2 but also displays the proper behavior over the whole time region in accordance with previous computer simulation results. Moreover, it is shown that the amplitude of the long-time behavior predicted by previous workers is modified by a certain correction factor P which contains dynamical correlation effects. In this way, many-body complication inherent to...

Ultrafast exciton dynamics of J-aggregates in room temperature solution studied by third-order nonlinear optical spectroscopy and numerical simulation based on exciton theory

We report a study of the exciton dynamics in 1,1′-diethyl-3,3′-bis(sulforpropyl)-5,5′,6,6′ -tetrachlorobenzimidacarbocyanine (BIC) J-aggregates in water solution at room temperature by third-order nonlinear optical spectroscopy and numerical simulations based on exciton theory. The temporal profiles of the transient grating signals depend strongly on the excitation intensity as a result of exciton–exciton annihilation. On the other hand, the peak shift measurement gives information on the fluctuations of the transition frequency of the system. The peak shift decays with time constants of 26 and 128 fs. There is no finite peak shift on a longer time scale. The electronic state of J-aggregates is described by a Frenkel exciton Hamiltonian, and the exciton population relaxation processes is described by Redfield equations. Based on the numerical simulations, the peak shift data can only be explained even qualitatively when both exchange narrowing and exciton relaxation process are included in the model. The ...

The mechanism of energy transfer in the antenna of photosynthetic purple bacteria

Abstract The mechanism of energy transfer in the antenna system of purple bacteria is investigated by combination of photon echo spectroscopy and disordered exciton theory. In the B800 component of light harvesting complex 2 (LH2), a picture of incoherent hopping between monomers provides an excellent description of the photon echo data recorded as a function of excitation wavelength. In the B850 pigments of LH2, and to a somewhat greater extent in the B875 pigments of light harvesting complex 1 (LH1), the excitation is delocalized over several pigments. The observed dynamics correspond to relaxation between exciton states as a result of exciton–phonon coupling. Nonetheless, a picture of “hopping” between small groups of molecules provides a crude description of the motion of the excitation in B850, and B875. The electronic coupling required to simulate the experimental absorption spectrum and photon echo data is larger in LH1 than in LH2 (B850).

Kinetic theory of bimolecular reactions in liquid. I. Steady-state fluorescence quenching kinetics

A microscopic kinetic theory for steady-state fluorescence quenching reaction in liquid is formulated. Based on a linear reaction-Liouville equation for the distribution function in phase space, we derived a memory equation for the relaxation of singlet density function of reactants by use of Mori’s projection operator technique. The expression of the memory kernel is analyzed by the fully renormalized kinetic theory developed by Mazenko. The memory kernel includes the many-body information via a hierarchical structure of a propagator in that. This hierarchy is truncated by a disconnected approximation for the propagator governing the dynamics of an orthogonalized doublet field creating their initial correlation via a bimolecular interaction. This approximation is different from the dynamic superposition approximation for reduced distribution functions made in usual hierarchical approaches. As a result, the detailed description of reactant dynamics becomes available and the memory kernel consists of a geo...

Dynamic correlation effect in reversible diffusion-influenced reactions: Brownian dynamics simulation in three dimensions

A Brownian dynamics (BD) simulation for a pseudo-first-order diffusion-influenced reversible association–dissociation reaction of a target system in three dimensions with spherical symmetry is presented. The exact Green function for a reversible geminate dissociation that we obtained recently is utilized in the simulation. We compare the results of simulation with two successful theoretical predictions, the enhanced version of the superposition approximation approach (SA) and the more rigorous kinetic theoretical approach (KT). The KT predicts the correct power law behavior of ∼t−3/2 with a slightly higher amplitude in the long-time region, but it is in good agreement with the BD result in the transient region. On the other hand, a faster relaxation is observed in the transient region for the SA, but the correct power law behavior with numerically exact amplitude is predicted for the exact target system. An interesting interplay between the mobility of the system and the dynamic correlation effect incorpo...

Two-color three-pulse photon echoes as a probe of electronic coupling in molecular 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.