A novel construction of complex-valued Gaussian processes with arbitrary spectral densities and its application to excitation energy transfer.

The recent experimental discoveries about excitation energy transfer (EET) in light harvesting antenna (LHA) attract a lot of interest. As an open non-equilibrium quantum system, the EET demands more rigorous theoretical framework to understand the interaction between system and environment and therein the evolution of reduced density matrix. A phonon is often used to model the fluctuating environment and convolutes the reduced quantum system temporarily.

Generic mechanism of optimal energy transfer efficiency: a scaling theory of the mean first-passage time in exciton systems.

An asymptotic scaling theory is presented using the conceptual basis of trapping-free subspace (i.e., orthogonal subspace) to establish the generic mechanism of optimal efficiency of excitation energy transfer in light-harvesting systems.

Optimal fold symmetry of LH2 rings on a photosynthetic membrane.

An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cells with rotational symmetry, extendable to the entire lattice for the global optimization of the EET network.

Molecular binoculars: how to spatially resolve environmental fluctuations by following two or more single-molecule spectral trails at a time.

We propose a novel type of spectral diffusion experiment that enables one to decouple spatial characteristics of the environmental fluctuations, such as their concentration, from the interaction with the chromophore. Traditional hole broadening experiments do not allow for such decoupling in the common case when the chromophore-environment interaction is scale invariant. Here we propose to simultaneously follow the spectral trails of a small number of nearby chromophores--two or more--which thereby sense a highly overlapping set of the fluctuations.

Thermally-limited exciton delocalization in superradiant molecular aggregates.

We present two-dimensional Fourier transform optical spectroscopy measurements of two types of molecular J-aggregate thin films and show that temperature-dependent dynamical effects govern exciton delocalization at all temperatures, even in the presence of significant inhomogeneity. Our results indicate that in the tested molecular aggregates, even when the static structure disorder dominates exciton dephasing dynamics, the extent of exciton delocalization may be limited by dynamical fluctuations, mainly exciton-phonon coupling. Thus inhomogeneous dephasing may mediate the exciton coherence time whereas dynamical fluctuations mediate the exciton coherence length.

Efficient energy transfer in light-harvesting systems: quantum-classical comparison, flux network, and robustness analysis.

Following the calculation of optimal energy transfer in thermal environment in our first paper [J. L. Wu, F.

Phase transition in the Jarzynski estimator of free energy differences.

The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the Jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements. Given a fixed number of measurements, the Jarzynski estimator is unbiased for sufficiently small systems. In these systems the directionality of time is poorly defined and the configurations that dominate the empirical average, but which are in fact typical of the reverse process, are sufficiently well sampled.

Theoretical description of quantum effects in multi-chromophoric aggregates.

Recent experiments on light-harvesting complexes have shown clear indication of coherent transport of excitations in these aggregates. We discuss the theoretical models that have been used to study energy transfer in molecular aggregates, beginning with the early models of Förster and Davydov and ending with the theoretical models of the present day.

Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting.

The effective absorption cross-section of a molecule (acceptor) can be greatly increased by associating it with a cluster of molecules that absorb light and transfer the excitation energy to the acceptor molecule. The basic mechanism of such light harvesting by Förster resonance energy transfer (FRET) is well established, but recent experiments have revealed a new feature whereby excitation is coherently shared among donor and acceptor molecules during FRET. In the present study, two-dimensional electronic spectroscopy was used to examine energy transfer at ambient temperature in a naturally occurring light-harvesting protein (PE545 of the marine cryptophyte alga Rhodomonas sp.

Reaction Event Counting Statistics of Biopolymer Reaction Systems with Dynamic Heterogeneity.

We investigate the reaction event counting statistics (RECS) of an elementary biopolymer reaction in which the rate coefficient is dependent on states of the biopolymer and the surrounding environment and discover a universal kinetic phase transition in the RECS of the reaction system with dynamic heterogeneity. From an exact analysis for a general model of elementary biopolymer reactions, we find that the variance in the number of reaction events is dependent on the square of the mean number of the reaction events when the size of measurement time is small on the relaxation time scale of rate coefficient fluctuations, which does not conform to renewal statistics. On the other hand, when the size of the measurement time interval is much greater than the relaxation time of rate coefficient fluctuations, the variance becomes linearly proportional to the mean reaction number in accordance with renewal statistics.

Correlated intermolecular coupling fluctuations in photosynthetic complexes.

The functioning and efficiency of natural photosynthetic complexes is strongly influenced by their embedding in a noisy protein environment, which can even serve to enhance the transport efficiency. Interactions with the environment induce fluctuations of the transition energies and couplings between the chlorophyll molecules, and due to the fact that different fluctuations will partially be caused by the same environmental factors, correlations between the various fluctuations will occur. We argue that fluctuations of the couplings should, in general, not be neglected, as these have a considerable impact on population transfer rates, decoherence rates, and the efficiency of photosynthetic complexes.

Is there elliptic distortion in the light harvesting complex 2 of purple bacteria?

Single molecule spectroscopy (SMS) revealed an unusually large Gap between two major exciton peaks of the B850 unit of light harvesting complex 2 (LH2), which could be explained assuming elliptic distortion or k = 2 symmetry modulation in the site excitation energy. On the basis of extensive simulation of the SMS data and ensemble line shape, we found that uniform modulation of k = 2 symmetry cannot explain the dependence of intensity ratios on the Gap of the two major peaks, which are available from SMS, nor the ensemble line shape. Alternative models of disorder with k = 1 and k = 2 symmetry correlation are shown to reproduce these data reasonably well and can even explain the Gap distribution when it is assumed that the lower major peak in the SMS line shape is an intensity weighted average of k = 1- and k = 0 states.

Quantitative interpretation of the randomness in single enzyme turnover times.

Fluctuating turnover times of a single enzyme become observable with the advent of modern cutting-edge, single enzyme experimental techniques. Although the conventional chemical kinetics and its modern generalizations could provide a good quantitative description for the mean of the enzymatic turnover times, to our knowledge there has not yet been a successful quantitative interpretation for the variance or the randomness of the enzymatic turnover times. In this review, we briefly review several theories in this field, and compare predictions of these theories to the randomness parameter data reported for β-galactosidase enzyme.

Excitation energy transfer in a non-markovian dynamical disordered environment: localization, narrowing, and transfer efficiency.

The non-markovian effect of a fluctuating environment plays an important role in electronic excitation transfer in organic disordered media, such as light-harvesting systems and conjugated polymers. Stochastic Liouville equations (SLE) are used to study the interaction between excitons and the environment. We model the non-markovian environment phenomenologically with a dichotomic process.

Unified treatment of coherent and incoherent electronic energy transfer dynamics using classical electrodynamics.

Recent experiments on resonance energy transfer (RET) in photosynthetic systems have found evidence of quantum coherence between the donor and the acceptor. Under these conditions, Förster's theory of RET is no longer applicable and no theory of coherent RET advanced to date rivals the intuitive simplicity of Förster's theory. Here, we develop a framework for understanding RET that is based on classical electrodynamics but still captures the essence of the quantum coherence between the molecules.

Effect of correlation of local fluctuations on exciton coherence.

Recent experimental studies have shown both oscillations of exciton populations and long lasting coherence in multichromophoric systems such as photosynthetic light harvesting systems and conjugated polymers. It has been suggested that this quantum effect is due to correlations of the fluctuations of site energies among the closely packed chromophores in the protein environment. In addition to these, there is the strong possibility of correlations between site energies and transfer matrix elements.

Optimization of exciton trapping in energy transfer processes.

In this paper, we establish optimal conditions for maximal energy transfer efficiency using solutions for multilevel systems and interpret these analytical solutions with more intuitive kinetic networks resulting from a systematic mapping procedure. The mapping procedure defines an effective hopping rate as the leading order picture and nonlocal kinetic couplings as the quantum correction, hence leading to a rigorous separation of thermal hopping and coherent transfer useful for visualizing pathway connectivity and interference in quantum networks. As a result of these calculations, the dissipative effects of the surrounding environments can be optimized to yield the maximal efficiency, and modulation of the efficiency can be achieved using the cumulative quantum phase along any closed loops.

The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations.

The connection between work and changes in the Hamiltonian for a system with a time-dependent Hamiltonian has recently been called into question, casting doubt on the usefulness of the Jarzynski equality for calculating free energy changes. In this paper, we discuss the relationship between two possible definitions of free energy and show how some recent disagreements regarding the applicability of the Jarzynski equality are the result of different authors' using different definitions of free energy. Finally, in light of the recently raised doubts, we explicitly demonstrate that it is indeed possible to obtain physically relevant free energy profiles from molecular pulling experiments by using the Jarzynski equality and the results of Hummer and Szabo.

Beyond Förster resonance energy transfer in biological and nanoscale systems.

After photoexcitation, energy absorbed by a molecule can be transferred efficiently over a distance of up to several tens of angstroms to another molecule by the process of resonance energy transfer, RET (also commonly known as electronic energy transfer, EET). Examples of where RET is observed include natural and artificial antennae for the capture and energy conversion of light, amplification of fluorescence-based sensors, optimization of organic light-emitting diodes, and the measurement of structure in biological systems (FRET). Forster theory has proven to be very successful at estimating the rate of RET in many donor-acceptor systems, but it has also been of interest to discover when this theory does not work.

Practical model for imperfect conductometric molecular wire sensors.

We present a theoretical model for description of real polyreceptor molecular wire sensors (MWS), whose conductance signal may dramatically reduce upon analyte binding to one of the receptors coupled to the molecular wire but may not vanish as completely as assumed in the ideal MWS model. For the present nonideal MWS model, we establish the exact relationship between analyte concentration and the sensory signal intensity. It turns out that, whereas the Stern-Volmer curve of the ideal MWS always has a positive curvature, the Stern-Volmer curve of the imperfect MWS can have a negative curvature, consistent with experimental data.

Single-file dynamics with different diffusion constants.

We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two-particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF.

Diffusion of two particles with a finite interaction potential in one dimension.

We investigate the dynamics of two interacting diffusing particles in an infinite effectively one-dimensional system; the particles interact through a steplike potential of width b and height phi(0) and are allowed to pass one another. By solving the corresponding 2+1-variate Fokker-Planck equation, an exact result for the two-particle conditional probability density function (PDF) is obtained for arbitrary initial particle positions. From the two-particle PDF, we obtain the overtake probability, i.

Generic schemes for single-molecule kinetics. 1: Self-consistent pathway solutions for renewal processes.

In this paper, we discuss a strategy for reducing a complex single molecule kinetic process to a set of generic structures (motifs) that are building blocks for a general kinetic scheme. In general, these motifs have complex kinetics (i.e.

A unified theory for charge-carrier transport in organic crystals.

To characterize the crossover from bandlike transport to hopping transport in molecular crystals, we study a microscopic model that treats electron-phonon interactions explicitly. A finite-temperature variational method combining Merrifield's transformation with Bogoliubov's theorem is developed to obtain the optimal basis for an interacting electron-phonon system, which is then used to calculate the bandlike and hopping mobilities for charge carriers. Our calculations on the one dimensional (1D) Holstein model at T=0 K and finite temperatures show that the variational basis gives results that compared favorably to other analytical methods.