Quantum-Coherent Electronic Energy Transfer: Did ... - ACS Publications

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Quantum-Coherent Electronic Energy Transfer: Did Nature Think of It First? Gregory D. Scholes* Department of Chemistry, Institute for Optical Sciences and Centre for Quantum Information and Quantum Control, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6 Canada

ABSTRACT Recent research suggests that electronic energy transfer in complex biological and chemical systems can involve quantum coherence, even at ambient temperature conditions. It is particularly notable that this phenomenon has been found in some photosynthetic proteins. The role of these proteins in photosynthesis is introduced. The meaning of quantum-coherent energy transfer is explained, and it is compared to F€ orster energy transfer. Broad, interdisciplinary questions for future work are noted. For example, how can chemists use quantum coherence in synthetic systems (perhaps in organic photovoltaics)? Why did certain photosynthetic organisms evolve to use quantum coherence in light harvesting? Are these electronic excitations entangled?

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round 3.5 billion years ago plants and related photosynthetic organisms worked out how to capture energy from sunlight and use it to drive life-sustaining biochemical processes. In the process, they transformed a primitive Earth's inhospitable CO2-rich atmosphere to the life-supporting mix of gases that we know today. It is suggested by satellite imaging studies that photosynthetic organisms presently convert CO2 into 105 billion tons of biomass annually.1 Precisely how the lightinitiated chain of events in photosynthetic solar energy conversion by plants, algae, and certain bacteria works has been the subject of countless investigations over the past century.2-8

these recent discoveries suggest is that, rather than being constrained by classical probability laws, some antenna proteins are able to employ interference of quantum amplitudes to steer energy transfer. The discovery changes the way we think about limits for how fast and how far excitation energy can be transferred. It challenges researchers to address the theory of energy transfer in the most difficult limit of the averaging problem, when electronic coupling between chromophores has a similar magnitude to exciton-bath coupling. As chemists, we are impelled to work out how we can design chemical systems that direct energy using quantum interference of pathways that we would “wire” together using electronic structure. The aims of this perspective are to explain what quantum-coherent energy transfer means and what the implications are for biophysics and chemistry. Natural light-harvesting antenna systems are a prominent component in the photosynthetic machinery.18,19 Numerous highly absorptive molecules, bound onto a protein scaffold, capture sunlight and funnel that energy to power reaction centers;specialized biological solar cells. While reaction center architecture is basically conserved across a multiplicity of photosynthetic species, lightharvesting antennae exhibit remarkable diversity as well as the ability to adapt to local light conditions and to regulate the operation of reaction centers, Figure 1. Researchers are learning that arrangements of the light-absorbing molecules are not random but are carefully positioned to optimize flow of energy from the point where sunlight is absorbed to a reaction center. Typically, that energy funnel

How the light-initiated chain of events in photosynthetic solar energy conversion by plants, algae, and certain bacteria works has been the subject of countless investigations over the past century.

Nature's solar cells have been improved through billions of years of evolution. It is therefore not so surprising that plants, algae, and other photosynthetic organisms have developed tricks that lie behind their success. It has emerged recently that one of these strategies;at least for some organisms;is to use quantum coherence to direct energy flow from molecule to molecule through antenna proteins.3,9-11 What

r 2010 American Chemical Society

Received Date: September 28, 2009 Accepted Date: October 28, 2009 Published on Web Date: January 07, 2010

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DOI: 10.1021/jz900062f |J. Phys. Chem. Lett. 2010, 1, 2–8


Scheme 1. Measuring Quantum Coherence Using Two-Dimensional Photon Echo Spectroscopya

Two-dimensional electronic photon echo (2DPE) spectroscopy has recently emerged as a practical method for obtaining detailed insights into excited-state dynamics, as described elsewhere. 3,38-45 Information in 2DPE spectra includes the time evolution of coherent superpositions of the absorption bands, which provides a measure of quantum coherence.9 To illustrate this, let us consider a representative rephasing 2DPE spectrum for a population waiting time T. The data are plotted as the photon echo “emission” frequency ωt versus the conjugate frequency ωτ that represents excitation. They are plotted here on an arcsinh intensity scale to accentuate the representation of weak features in the cross-peaks. To follow the dynamics, a series of such spectra are recorded for various population times. The data shown here were recorded for an aqueous suspension of cryptophyte antenna proteins at 294 K (PC645 from Chroomonas CCMP270).11 (a) The linear absorption spectrum is projected along the diagonal of the 2DPE spectrum. Despite strong spectral line broadening, peaks along the diagonal (white line) can be identified with absorption bands in the linear spectrum, projected above and beside each 2DPE plot for reference. For example, the excitation of the absorption band labeled β can yield an emission at the same frequency in the photon echo, according to the double-sided Feynman diagram shown on the right-hand side of the panel. That signal (analogous to a bleach signal in pump-probe spectroscopy) yields a diagonal peak in the 2DPE spectrum, as indicated. (b, c) Off-diagonal peaks in 2DPE spectra can have a few different origins. They can mean, for example, that excitation of the absorption band R produces an excited-state population that relaxes incoherently to band β, perhaps by electronic energy transfer. Consequently a cross-peak in the lower diagonal would emerge with population time T. Crosspeaks can also provide signatures of coherent superposition states formed by the excitation pulse sequence. Two possible coherent superposition states are presented here, and depending on the corresponding off-diagonal component of the density matrix, |RæÆβ| or |βæÆR|, they can produce a 2DPE signal at the upper or lower cross-peak position, respectively. Notice that according to the representative Feynman diagrams that explain these signal contributions, an oscillating phase will be acquired during the population time T. This is the same kind of beating sound heard when two tuning forks of different frequency are rung simultaneously. The magnitude of the oscillation frequency is determined by the energy difference between the two absorption bands in the superposition state, but the sign of the oscillation is opposite for each peak in the pair of the cross-peaks. (d) Cross-peak intensity oscillations in 2DPE spectra reveal quantum coherence, particularly by the observation of anticorrelated oscillations as a function of T. As an illustration, we fit cross-peak intensities versus T to a sum of damped cosine functions and thereby isolate the oscillating component corresponding to the energy difference between R and β. The anticipated anticorrelation is clearly indicated. The damping time of the beats indicates the decoherence time for the superposition. a


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comprises ∼200 molecules, and energy is transferred via a sequence of quantum mechanical energy-transfer processes across a total distance of ∼20-100 nm with near-unit quantum efficiency.

The question usually asked at this point is, What makes quantum-coherent energy transfer possible? Here I will, instead, ask, Why would we not observe quantum-coherent energy transfer? In quantum mechanics, if we wish to compute the probability for excitation starting at molecule A and ending up at molecule B after a time interval t, we cannot solve the usual kinetics problem because that assumes a classical probability law. Instead, we must add the probability amplitudes calculated by considering each path leading from A to B, and then, we take the modulus squared of that sum.31 The important result of the quantum mechanical law is that each pathway carries a phase that dictates how competing pathways interfere.32 Such interference processes have the potential to optimize energy transfer by constructive interference or suppress it by destructive interference. The obvious pathways are those where excitation jumps among the molecules, including those in between and around A and B. The excitation can also resonate many times among a subset, or even all, of the molecules. Interference of strong backward-forward excitation resonance produces stationary electronic states known as molecular, or Frenkel, exciton states. There is a long history of the study of such states in photosynthetic proteins.33 Notable examples include the special pair in the reaction center of purple bacteria, the multimer model for photosystem II, chlorosome antennae from green sulfur bacteria, and, particularly, the B850 ring in the peripheral light-harvesting complex LH2 of purple bacteria.34 It turns out, however, that these quantum mechanical resonances over a length scale of nanometers rarely predominate. The reason boils down to additional interferences involving less obvious, though nonetheless very important, kinds of pathways. These pathways, which are usually treated using some sort of averaging procedure, consider the multitude of ways that the molecules can interact with the environment (e.g., the solvent, often called the “bath”) between excitation jumps.35 In the microscopic, time domain picture, these interactions cause the electronic transition energies to fluctuate, thus stochastically modulating resonance conditions between the molecules. In the usual, F€ orster, limit, coupling to the environment is much stronger, and therefore more favored, than the electronic coupling between the chromophores. The result is that each molecule has time to average over the whole distribution of transition energies, represented by its homogeneous line width, before transferring excitation. The definite phase relationships associating backward-forward resonance pathways for electronic excitation jumps are lost, and energy migration dynamics end up being incoherent and following classical probability laws. The time scale over which these phase relationships disappear, the decoherence time, is exceptionally rapid for large, complex molecules in liquid environments, usually just a few tens of femtoseconds. In accord with the notion that decoherence is a transition from quantum to classical, localization (or at least partial localization) of

Light-harvesting antennae exhibit remarkable diversity as well as the ability to adapt to local light conditions and to regulate the operation of reaction centers.

F€ orster's theory implies that the energy-transfer rate for each “hop” through an antenna complex (or any molecular assembly) is optimized by two main factors.20-22 First, donor-acceptor spectral overlap should be maximized by aligning the transition energies and narrowing the spectral line shapes. Second, the chromophores should be oriented in a particular way and brought as close together as possible. A problem, however, with closely proximate molecules in a large aggregate is that excited states can be more easily quenched, thereby suppressing long-range energy migration. A contemporary example of this “concentration quenching” is found in conjugated polymer films or aggregates.23 In the case of photosynthetic proteins, it has been realized for some time that there should be an optimum interchromophore spacing in photosynthetic proteins to maximize energy transfer while thwarting concentration quenching.24 However, is longrange energy migration substantially compromised by this trade-off? Recent studies of photosynthetic energy transfer in the Fenna-Matthews-Olsen (FMO) complex from green sulfur bacteria led to the surprising discovery that quantum coherence can help.9 My group and our collaborators have studied light-harvesting antenna proteins isolated from marine algae called cryptophytes, Figure 2. The chromophores, specifically tetrapyrroles, called bilins, in cryptophyte antenna proteins are arranged with average nearest-neighbor separations of ∼20 Å.13 In comparison, nearest-neighbor separations between chlorophyll molecules in the major higher plant peripheral antenna protein LHC-II are typically about half of that distance.29 Yet, cryptophyte antenna complexes are still able to collect incident light and transfer those excitations to reaction centers (photosystems I and II) with a quantum efficiency of >95%.30 How cryptophyte antenna complexes are still able to function with the same overall efficiency as LHC-II has puzzled me for some years, but recent twodimensional photon echo experiments, Scheme 1, suggest an answer. Quantum-coherence plays a role, even at physiological temperature, to “wire” the chromophores together in cryptophyte antennae, thereby compensating for the large interchromophore separations.11


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Figure 1. Structural models and absorption spectra of some representative photosynthetic light-harvesting antennae. These spectra were recorded at 77 K, but the spectra are similar at ambient temperature, owing to the significant inhomogeneous line broadening. Clockwise from left: (i) The peridinin-chlorophyll proteins (PCPs) of dinoflagellates contain eight blue-absorbing peridinin molecules and two chlorophyll-a molecules.12 (ii) The PE545 complex, typical of various cryptophyte antenna proteins, binds eight bilin chromophores with absorption energies that vary widely among species.13 (iii) The primary light-harvesting complex of higher plants, LHC-II, shown in the trimeric form. Each complex in the trimer binds eight chlorophyll-a and six chlorophyll-b chromophores as well as carotenoids used for photoprotection and regulation.14 (iv) The gigantic chlorosome antennae from green sulfur bacteria comprises ∼200 000 self-assembled bacteriochlorophyll-c chromophores.15 The FMO proteins (green balls) act as conduits for the excitation energy to be transferred from the antenna to the membrane-bound reaction center. (v) The LH2 complex from purple bacteria is notable for its beautiful nine-fold symmetry.16 It binds carotenoids and two rings of bacteriochlorophyll-a chomophores, 9 in the B800 ring and 18 in the B850 ring. Adapted from ref 17.

wave functions is needed if we wish concepts like “moving excitation” to make sense. The quantum-coherent energy transfer that is the focus of this Perspective occurs in an intermediate regime where there is a balance between interference among electronic resonances to give coherence and coupling to the environment causing decoherence. Phenomena existing within such a balance are fairly widely known and include, for example, band conduction in semiconductors and high Tc superconductivity.36 what really surprised researchers about the recent discoveries of quantum-coherent energy transfer is how long-lived the coherence is; hundreds of femtoseconds in complex biological systems and disordered conjugated polymers at temperatures between 77 and 293 K was unprecedented.9-11,37 Those observations have especially caught the attention of researchers


in the quantum information/quantum computing field because it hints that the usual prescriptions used for considering the role of the environment in decoherence may not be universal. Broad questions to be addressed in future work include the following: What is the role of the protein scaffold or molecular structural framework for protecting quantum

What really surprised researchers about the recent discoveries of quantum-coherent energy transfer is how long-lived the coherence is.

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Figure 2. Algae are plants lacking roots, stems, and leaves (thallophytes). They are found mainly in water but also in terrestrial environments including deserts.25 In most habitats, they are the primary producers in the food chain and “fix” about the same total quantity of CO2 annually as higher plants. Cryptophytes are one example of the numerous different algae. They are motile, unicellular algae that occur in a variety of aquatic environments, both marine and freshwater. (a) Electron micrograph of thinsectioned thylakoids from the cryptophyte Rhodomonas CS24 showing the lumens of the thylakoid sacs (vide infra), dark color, filled with the water-soluble PE545 antenna protein.26 (b) High-magnification electron micrograph of thylakoid membranes. (c) The characteristic bean-shaped form of Rhodomonas CS24 (9 μm 6 μm) is seen in this confocal fluorescence micrograph. The photosynthetic apparatus gives the red fluorescence. (d) A schematic, drawn approximately to scale, showing the arrangement of proteins involved in cryptophyte light-harvesting.27 The thylakoid membrane, colored green, is a flattened vesicle that hosts various photosynthetic proteins including photosystems I and II. Photosynthesis creates a chemical potential by establishing a proton gradient between the inside of the thylakoid (called the lumen) and the surrounding matrix (the stroma). The intrathylakoid space, lumen, contains the water-soluble antenna protein, PE545 in the case of Rhodomonas CS24. The micrographs are reproduced from ref 28.

coherence from decay? How can supramolecular or macromolecular chemical systems be designed to take advantage of quantum coherence in the intermediate regime? Are the excitations at different sites in these biological complexes entangled (in the Einstein-Podolsky-Rosen sense), and if so, how can experiment yield direct evidence for that hypothesis? A more demanding question is, Does the use of quantum-coherent energy transfer in light-harvesting proteins give certain organisms, the cryptophytes, for example, an evolutionary advantage? If so, what is that advantage? It is likely that a more subtle explanation than “photosynthesis works more efficiently” (as measured by oxygen evolution) may prove most satisfactory. For example, the photosynthetic efficiency is already strongly limited by slow reactions such as CO2 fixation, but being able to harvest light with a chromophore-lean antenna might confer benefits related to photoprotection, for example, by suppressing triplet-triplet energy transfer, or it may simplify biosynthesis of the antenna proteins. Clearly, there are many interesting and wide-ranging research questions for the future that will stimulate collaborations among


physical chemists, biologists, and physicists. The benefits will be the elucidation of insights into the light-initiated dynamics of very complex systems that were, until recently, unforeseen.

AUTHOR INFORMATION Corresponding Author: *E-mail: [email protected].

Biographies Greg Scholes obtained B.Sc. and Ph.D. (1994) degrees from the University of Melbourne. He was recently elected a Fellow of the Royal Society of Canada and serves as a Senior Editor for The Journal of Physical Chemistry. His present research focuses on elucidating the principles deciding electronic structure, optical properties, and photophysics of nanoscale systems by combining theory and ultrafast laser spectroscopy.

ACKNOWLEDGMENT The Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged for the support of this research.

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Quantum-Coherent Electronic Energy Transfer: Did ... - ACS Publications

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