Charge and energy transfer—the movement of electrons or excitations from one molecule to another—are the simplest chemical reactions.

We are interested in how charges and excitons move through disordered molecular assemblies such as photosynthetic complexes (see below) or organic semiconductors. These materials challenge existing theoretical treatments because they do not fall into any of the well-understood regimes, straddling both order and disorder, both classical and quantum transport.^{3}

A recent highlight is our development of generalised Marcus theory,^{23} a simple approach for describing the transfer of delocalised charges between two molecular aggregates, in terms of the properties of the component molecules.

Photosynthetic organisms harvest light using large antenna complexes containing chlorophyll molecules. The harvested energy is then transported to reaction centres, where it drives the first chemical steps of photosynthesis. Recent experiments have suggested that the energy transport can be partially coherent, challenging previous assumptions that quantum effects could be relevant in biological systems at room temperature.

We have shown that many of the quantum effects observed in photosynthetic complexes are side effects of the laser excitation and are not relevant to biological function in sunlight.^{11} As a consequence, describing energy transport in incoherent light is dramatically simplified, allowing us to rapidly screen hypothetical scenarios to determine whether natural light-harvesting architectures are already optimal or whether they could be improved.^{16, 19}

Our screening studies identified several quantum effects that are important even in incoherent light.^{16} In particular, we reported the most statistically significant quantum enhancement in a photosynthetic complex,^{19} showing that the light-harvesting apparatus of purple bacteria is more than five standard deviations more efficient than would be expected by chance, and that the enhancement is largely due to supertransfer, a cooperative enhancement of energy transfer due to coherent delocalisation.

We have also analysed the performance of reaction centres to understand why they adopted dimeric structures that have been conserved over billions of years of evolution. We found that the most probable explanation for the dimerism is that it deepened the excitonic trap in the special pair, possibly leading to considerable improvements in reaction-centre efficiency.^{28}

We are continuing our work on charge and energy transport—stay tuned or come join us!

Natasha Taylor and Ivan Kassal

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All photosynthetic organisms convert solar energy into chemical energy through charge separation in dimeric reaction centres. It is unknown why early reaction centres dimerised and completely displaced their monomeric ancestors. Here, we discuss several proposed explanations for reaction-centre dimerism and conclude—with only weak assumptions about the primordial dimerisation event—that the most probable explanation for the dimerism is that it arose because it enhanced light-harvesting efficiency by deepening the excitonic trap, i.e., by enhancing the rate of exciton transfer from an antenna complex and decreasing the rate of back transfer. This effect would have outweighed the negative effect dimerisation would have had on charge transfer within the reaction centre. Our argument implies that dimerisation likely occurred after the evolution of the first antennas, and it explains why the lower-energy state of the special pair is bright.

Natasha B. Taylor and Ivan Kassal

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Although Marcus theory is widely used to describe charge transfer in molecular systems, in its usual form it is restricted to transfer from one molecule to another. If a charge is delocalised across multiple donor molecules, this approach requires us to treat the entire donor aggregate as a unified supermolecule, leading to potentially expensive quantum-chemical calculations and making it more difficult to understand how the aggregate components contribute to the overall transfer. Here, we show that it is possible to describe charge transfer between groups of molecules in terms of the properties of the constituent molecules and couplings between them, obviating the need for expensive supermolecular calculations. We use the resulting theory to show that charge delocalisation between molecules in either the donor or acceptor aggregates can enhance the rate of charge transfer through a process we call supertransfer (or suppress it through subtransfer). The rate can also be enhanced above what is possible with a single donor and a single acceptor by judiciously tuning energy levels and reorganisation energies. We also describe bridge-mediated charge transfer between delocalised molecular aggregates. The equations of generalised Marcus theory are in closed form, providing qualitative insight into the impact of delocalisation on charge dynamics in molecular systems.

Sima Baghbanzadeh and Ivan Kassal

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The remarkable rotational symmetry of the photosynthetic antenna complexes of purple bacteria has long been thought to enhance their light harvesting and excitation energy transport. We study the role of symmetry by modeling hypothetical antennas whose symmetry is broken by altering the orientations of the bacteriochlorophyll pigments. We find that in both LH2 and LH1 complexes, symmetry increases energy transfer rates by enabling the cooperative, coherent process of supertransfer. The enhancement is particularly pronounced in the LH1 complex, whose natural geometry outperforms the average randomized geometry by 5.5 standard deviations, the most significant coherence-related enhancement found in a photosynthetic complex.

Sima Baghbanzadeh and Ivan Kassal

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Photosynthetic complexes improve the transfer of excitation energy from peripheral antennas to reaction centers in several ways. In particular, a downward energy funnel can direct excitons in the right direction, while coherent excitonic delocalization can enhance transfer rates through the cooperative phenomenon of supertransfer. However, isolating the role of purely coherent effects is difficult because any change to the delocalization also changes the energy landscape. Here, we show that the relative importance of the two processes can be determined by comparing the natural light-harvesting apparatus with counterfactual models in which the delocalization and the energy landscape are altered. Applied to the example of purple bacteria, our approach shows that although supertransfer does enhance the rates somewhat, the energetic funnelling plays the decisive role. Because delocalization has a minor role (and is sometimes detrimental), it is most likely not adaptive, being a side-effect of the dense chlorophyll packing that evolved to increase light absorption per reaction center.

Elise Kenny and Ivan Kassal

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Excitonic couplings between (bacterio)chlorophyll molecules are necessary for simulating energy transport in photosynthetic complexes. Many techniques for calculating the couplings are in use, from the simple (but inaccurate) point-dipole approximation to fully quantum-chemical methods. We compared several approximations to determine their range of applicability, noting that the propagation of experimental uncertainties poses a fundamental limit on the achievable accuracy. In particular, the uncertainty in crystallographic coordinates yields an uncertainty of about 20% in the calculated couplings. Because quantum- chemical corrections are smaller than 20% in most biologically relevant cases, their considerable computational cost is rarely justified. We therefore recommend the electrostatic TrEsp method across the entire range of molecular separations and orientations because its cost is minimal and it generally agrees with quantum-chemical calculations to better than the geometric uncertainty. Understanding these uncertainties can guard against striving for unrealistic precision; at the same time, detailed benchmarks can allow important qualitative questions—which do not depend on the precise values of the simulation parameters—to be addressed with greater confidence about the conclusions..

Roberto J. León-Montiel, Ivan Kassal, and Juan P. Torres

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It has been argued that excitonic energy transport in photosynthetic complexes is efficient because of a balance between coherent evolution and decoherence, a phenomenon called environment-assisted quantum transport (ENAQT). Studies of ENAQT have usually assumed that the excitation is initially localized on a particular chromophore, and that it is transferred to a reaction center through a similarly localized trap. However, these assumptions are not physically accurate. We show that more realistic models of excitation and trapping can lead to very different predictions about the importance of ENAQT. In particular, although ENAQT is a robust effect if one assumes a localized trap, its effect can be negligible if the trapping is more accurately modeled as Forster transfer to a reaction center. Our results call into question the suggested role of ENAQT in the photosynthetic process of green sulfur bacteria and highlight the subtleties associated with drawing lessons for designing biomimetic light-harvesting complexes.

Ivan Kassal, Joel Yuen-Zhou, and Saleh Rahimi-Keshari

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Recent observations of coherence in photosynthetic complexes have led to the question of whether quantum effects can occur in vivo, not under femtosecond laser pulses but in incoherent sunlight and at steady state, and, if so, whether the coherence explains the high exciton transfer efficiency. We distinguish several types of coherence and show that although some photosynthetic pathways are partially coherent processes, photosynthesis in nature proceeds through stationary states. This distinction allows us to rule out several mechanisms of transport enhancement in sunlight. In particular, although they are crucial for understanding exciton transport, neither wavelike motion nor microscopic coherence, on their own, enhance the efficiency. By contrast, two partially coherent mechanisms—ENAQT and supertransfer—can enhance transport even in sunlight and thus constitute motifs for the optimisation of artificial sunlight harvesting. Finally, we clarify the importance of ultrafast spectroscopy in understanding incoherent processes.

Patrick Rebentrost, Masoud Mohseni, Ivan Kassal, Seth Lloyd, and Alán Aspuru-Guzik

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Transport phenomena at the nanoscale are of interest due to the presence of both quantum and classical behavior. In this work, we demonstrate that quantum transport efficiency can be enhanced by a dynamical interplay of the system Hamiltonian with pure dephasing induced by a fluctuating environment. This is in contrast to fully coherent hopping that leads to localization in disordered systems, and to highly incoherent transfer that is eventually suppressed by the quantum Zeno effect. We study these phenomena in the Fenna–Matthews–Olson protein complex as a prototype for larger photosynthetic energy transfer systems. We also show that the disordered binary tree structures exhibit enhanced transport in the presence of dephasing.