Multipartite quantum entanglement evolution in photosynthetic complexes

We investigate the evolution of entanglement in the Fenna-Matthew-Olson (FMO) complex based on simulations using the scaled hierarchical equations of motion approach. We examine the role of entanglement in the FMO complex by direct computation of the convex roof. We use monogamy to give a lower bound for entanglement and obtain an upper bound from the evaluation of the convex roof. Examination of bipartite measures for all possible bipartitions provides a complete picture of the multipartite entanglement. Our results support the hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways. In addition, we note that the structure of multipartite entanglement is quite simple, suggesting that there are constraints on the mixed state entanglement beyond those due to monogamy.     

Laser pulse control of exciton dynamics in a biological chromophore complex

Femtosecond laser pulse control of exciton dynamics in a biological chromophore complex is studied theoretically. The computations use the optimal control theory specified to open quantum systems and formulated in the framework of the rotating wave approximation. Based on the laser pulse induced formation of an excitonic wave packet the possibility to localize excitation energy at a certain chromophore within a photosynthetic antenna system (FMO complex of green bacteria) is investigated. Details of exciton dynamics driven by a polarization shaped pulse are discussed.     

Excitation energy transfer pathways in light‐harvesting proteins: Modeling with PyFREC

Excitation energy transfer (EET) determines the fate of sunlight energy absorbed by light‐harvesting proteins in natural photosynthetic systems and photovoltaic cells. As previously reported (D. Kosenkov, J. Comput. Chem. 2016, 37(19), 1847), PyFREC software enables computation of electronic couplings between organic molecules with a molecular fragmentation approach. The present work reports implementation of direct fragmentation‐based computation of the electronic couplings and EET rates in pigment–protein complexes within the Förster theory in PyFREC. The new feature enables assessment of EET pathways in a wide range of photosynthetic complexes, as well as artificial molecular architectures that include light‐harvesting proteins or tagged fluorescent biomolecules. The developed methodology has been tested analyzing EET in the Fenna–Matthews–Olson (FMO) pigment–protein complex. The pathways of excitation energy transfer in FMO have been identified based on the kinetics studies. © 2017 Wiley Periodicals, Inc.     

Multipartite entanglement in the Fenna-Matthews-Olson (FMO) pigment-protein complex

We investigate multipartite states in the Fenna-Matthews-Olson (FMO) pigment-protein complex of the green sulfur bacteria using a Lorentzian spectral density of the phonon reservoir fitted with typical parameter estimates of the species, Prosthecochloris aestuarii. The evolution of the entanglement measure of the excitonic W qubit states is evaluated in the picosecond time range, showing increased revivals in the non-Markovian regime. Similar trends are observed in the evolution dynamics of the Meyer-Wallach measure of the N-exciton multipartite state, with results showing that multipartite entanglement can last from 0.5 to 1 ps, between the bacteriochlorophylls of the FMO complex. The teleportation and quantum information splitting fidelities associated with the Greenberger-Horne-Zeilinger and W-like resource states formed by the excitonic qubit channels of the FMO complex show that revivals in fidelities increase with the degree of non-Markovian strength of the decoherent environment. Quantum information processing tasks involving teleportation followed by the decodification process involving W-like states of the FMO complex may play a critical role during coherent oscillations at physiological temperatures.     

Quantum tunneling effect in entanglement dynamics

Quantum tunneling effect in entanglement dynamics between two coupled particles with separable Gaussian initial state is investigated using entangled trajectory molecular dynamics method in terms of the reduced‐density linear entropy. It has been presented through showing distinguish contribution of single trajectory to linear entropy between classical trajectory and entangled trajectory with same initial state. We find that quantum tunneling effect makes single trajectory's contribution remarkably decrease under quantum dynamics compared to classical dynamics. The nonlocality of quantum entanglement is presented, and the energy transfer between two coupled particles through quantum correlations and classical ones is also discussed in the end. © 2015 Wiley Periodicals, Inc.     

Protonic delocalization and quantum correlations in the H-bond dynamics of G–C and κ–π DNA base pairs

A new base pair (called κ–π) of Watson–Crick type, with a H -bond pattern different from that in A –T and G –C base pairs, has been recently synthesized and shown to be stable and incorporable into duplex DNA and RNA by polymerases. This new basepair, which contains three H -bonds, is compared with G –C , in the framework of modern dynamical theory of quantum nonlocality and quantum correlations. Connection with the traditional treatment of proton transfer in DNA base pairs, which uses the adiabatic approximation, is explicitly made. As a result, the dynamics of the H -bond pattern of G –C is shown to exhibit a specific quantum mechanical phase stability, which is clearly missing in the case of κ–π. This finding is discussed and illustrated, also in connection with recent quantum chemical calculations of proton transfers in DNA base pairs. Additionally, certain speculations concerning the “evolutionary advantage” of G –C with respect to κ–π are briefly considered. © 1993 John Wiley & Sons, Inc.     

DNA‐Organized Light‐Harvesting Antennae: Energy Transfer in Polyaromatic Stacks Proceeds through Interposed Nucleobase Pairs

DNA‐based light‐harvesting antennae with varying arrangements of light‐absorbing phenanthrene donor units and a pyrene acceptor dye were synthesized and tested for their light‐harvesting properties. Excitation of phenanthrene is followed by rapid transfer of the excitation energy to the pyrene chromophore. A block of six light‐absorbing phenanthrenes was separated from the site of the acceptor in a stepwise manner by an increasing number of intervening AT base pairs. Energy transfer occurs through interposed AT base pairs and is still detected when the phenanthrene antenna is separated by 5 AT base pairs.     

On the formation mechanism for electrically generated exciplexes in a carbazole–pyridine copolymer

Although carbazole‐containing copolymers are frequently used as hole‐transporting host materials for polymer organic light‐emitting diodes (OLEDs), they often suffer from the formation of undesired exciplexes when the OLED is operated. The reason why exciplexes sometimes form for electrical excitation, yet not for optical excitation is not well understood. Here, we use luminescence measurements and quantum chemical calculations to investigate the mechanism of such exciplex formation for electrical excitation (electroplex formation) in a carbazole–pyridine copolymer. Our results suggest that the exciplex is formed via a positively charged interchain precursor complex. This complex is stabilized by interactions that involve the nitrogen lone pairs on both chain segments. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

A stochastic surrogate Hamiltonian approach of coherent and incoherent exciton transport in the Fenna-Matthews-Olson complex

The capture and transduction of energy in biological systems is clearly necessary for life, and nature has evolved remarkable macromolecular entities to serve these purposes. The Fenna-Matthews-Olson (FMO) complex serves as an intermediate to transfer the energy from the chlorosome to the special pairs of different photo systems. Recent observations have both suggested the importance of coherent exciton transport within the FMO and motivated an elegant and appropriate theoretical construct for interpreting these observations. Here we employ a different approach to exciton transport in a relaxing environment, one based on the stochastic surrogate Hamiltonian method. With it, we calculate the quantum trajectories through the FMO complex both for the model involving seven bacteriochlorophylls that has been used before, and for one involving an eighth bacteriochlorophyll, which has been observed in some new and very important structural work. We find that in both systems, efficient energy transfer to the ultimate receptor occurs, but that because of the placement of, and energy relaxation among, the different bacteriochlorophyll subunits in the FMO complex, the importance of coherent oscillation that was discussed extensively for the seven site system is far less striking for the eight site system, effectively because of the weak mixing between the initial site and the remainder of the system. We suggest that the relevant spectral densities can be determinative for the energy transport route and may provide a new way to enhance energy transfer in artificial devices.     

Population and coherence dynamics in light harvesting complex II (LH2)

The electronic excitation population and coherence dynamics in the chromophores of the photosynthetic light harvesting complex 2 (LH2) B850 ring from purple bacteria (Rhodopseudomonas acidophila) have been studied theoretically at both physiological and cryogenic temperatures. Similar to the well-studied Fenna-Matthews-Olson (FMO) protein, oscillations of the excitation population and coherence in the site basis are observed in LH2 by using a scaled hierarchical equation of motion approach. However, this oscillation time (300 fs) is much shorter compared to the FMO protein (650 fs) at cryogenic temperature. Both environment and high temperature are found to enhance the propagation speed of the exciton wave packet yet they shorten the coherence time and suppress the oscillation amplitude of coherence and the population. Our calculations show that a long-lived coherence between chromophore electronic excited states can exist in such a noisy biological environment.     

Communication: Decoherence in a nonequilibrium environment: an analytically solvable model

We describe an analytically solvable model of quantum decoherence in a nonequilibrium environment. The model considers the effect of a bath driven from equilibrium by, for example, an ultrafast excitation of a quantum chromophore. The nonequilibrium response of the environment is represented by a nonstationary random function corresponding to the fluctuating transition frequency between two quantum states coupled to the surroundings. The nonstationary random function is characterized by a Fourier series with the phase of each term starting initially with a definite value across the ensemble but undergoing random diffusion with time. The decay of the off-diagonal density matrix element is shown to depend significantly on the particular pattern of initial phases of the terms in the Fourier series, or equivalently, the initial phases of bath modes coupled to the quantum subsystem. This suggests the possibility of control of quantum decoherence by the detailed properties of an environment that is driven from thermal equilibrium.     

Theory and Simulation of the Environmental Effects on FMO Electronic Transitions

Long-lived quantum coherence has been experimentally observed in the Fenna-Matthews-Olson (FMO) light-harvesting complex. It is much debated which role thermal effects play and if the observed low-temperature behavior arises also at physiological temperature. To contribute to this debate we use molecular dynamics simulations to study the coupling between the protein environment and the vertical excitation energies of individual bacteriochlorophyll molecules in the FMO complex of the green sulphur bacterium Chlorobaculum tepidum. The so-called spectral densities, which account for the environmental influence on the excited state dynamics, are determined from temporal autocorrelation functions of the energy gaps between ground and first excited states of the individual pigments. Although the overall shape of the spectral density is found to be rather similar for all pigments, variations in their magnitude can be seen. Differences between the spectral densities for the pigments of the FMO monomer and FMO trimer are also presented.     

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.     

Energy transfer and fluorescence quenching in complexes of polymethine dyes with human serum albumin

Electronic excitation energy transfer (EET) between molecules of polymethine dyes bound to human serum albumin (HSA) has been established and studied by absorption and fluorescence spectroscopy as well as by fluorescence decay measurements. In this system, excitation of the donor dye molecule leads to fluorescence of the acceptor dye molecule, both bound to HSA, with donor fluorescence quenching by the acceptor. The short distance between the donor and the acceptor (25-28 A) revealed from the Forster model of EET as well as some spectroscopic data show that both molecules are probably located in the same binding domain of HSA. The role of HSA is to bring donor and acceptor molecules together to a distance adequate to achieve EET as well as to increase the donor and acceptor fluorescence quantum yields. Efficient quenching of the intrinsic HSA fluorescence by some polymethine dyes (oxonols) is observed. The experimental results fit well a model for the formation of a weakly fluorescent dye-HSA complex; the quencher in this complex should be located in the immediate vicinity of the HSA fluorophore group (Trp(214)).     

Dynamics of Tripartite Entanglement and Intramolecular Energy in Symmetric Trimer Molecule

The dynamics of tripartite entanglement and intramolecular energy for one harmonic-and two anharmonic-vibrational modes in a symmetric trimer molecule is studied for various ini-tial states, where the entanglement is quantified in terms of concurrence and the interacting energy among three modes is calculated to establish a link between entanglement and en-ergy. It is shown that the concurrence and the interacting energy behave dominantly positive correlation for the localized state in the anharmonic-vibrational mode, while they are domi-nantly anti-correlated for the localized state in the harmonic-vibrational mode. The relation between bipartite entanglement and the energy in a subsystem is discussed as well. Those are useful for quantum computing and quantum information in high dimensional states prepared in polyatomic molecules.     

Excitation energy transfer in multiporphyrin arrays with cyclic architectures: towards artificial light-harvesting antenna complexes

Since highly symmetric cyclic architecture of light-harvesting antenna complex LH2 in purple bacteria was revealed in 1995, there has been a renaissance in developing cyclic porphyrin arrays to duplicate natural systems in terms of high efficiency, in particular, in transferring excitation energy. This tutorial review highlights the mechanisms and rates of excitation energy transfer (EET) in a variety of synthetic cyclic porphyrin arrays on the basis of time-resolved spectroscopic measurements performed at both ensemble and single-molecule levels. Subtle change in structural parameters such as connectivity, distance, and orientation between neighboring porphyrin moieties exquisitely modulates not only the nature of interchromophoric interactions but also the rates and efficiencies of EET. The relationship between the structure and EET dynamics described here should assist a rational design of novel cyclic porphyrin arrays, more contiguous to real applications in artificial photosynthesis.     

Rapid and accurate assessment of GPCR–ligand interactions Using the fragment molecular orbital‐based density‐functional tight‐binding method

The reliable and precise evaluation of receptor–ligand interactions and pair‐interaction energy is an essential element of rational drug design. While quantum mechanical (QM) methods have been a promising means by which to achieve this, traditional QM is not applicable for large biological systems due to its high computational cost. Here, the fragment molecular orbital (FMO) method has been used to accelerate QM calculations, and by combining FMO with the density‐functional tight‐binding (DFTB) method we are able to decrease computational cost 1000 times, achieving results in seconds, instead of hours. We have applied FMO‐DFTB to three different GPCR–ligand systems. Our results correlate well with site directed mutagenesis data and findings presented in the published literature, demonstrating that FMO‐DFTB is a rapid and accurate means of GPCR–ligand interactions. © 2017 Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Excited States and Charge Separation in Membranes of the Green Sulfur Bacterium Prosthecochloris aestuarii

Time-resolved absorbance changes were measured in isolated membranes, depleted of chlorosomes, and in the Fenna-Matthews-Olson (FMO) complex of the green sulfur bacterium Prosthecochloris aestuarri. The isolated FMO complex showed a biphasic decay of excited bacteriochlorophyll a (BChl a) with time constants of about 80 and 1400 ps. Approximately the same time constants were observed upon excitation of isolated membranes together with a component of about 30 ps. It is concluded that the efficiency of energy transfer from the FMO to the core complex is very low, in agreement with earlier measurements of the efficiency of charge separation. The 30 ps decay component is ascribed to trapping of the excitation energy from the core BChl a by the reaction center.