Fast delocalization leads to robust long-range excitonic transfer in a large quantum chlorosome model

Large Scale Simulations of Photosynthetic Antenna Systems: Interplay of Cooperativity and Disorder

Large-scale simulations of light-matter interaction in natural photosynthetic antenna complexes containing more than one hundred thousands of chlorophyll molecules, comparable with natural size, have been performed. Photosynthetic antenna complexes present in Green sulfur bacteria and Purple bacteria have been analyzed using a radiative non-Hermitian Hamiltonian, well-known in the field of quantum optics, instead of the widely used dipole-dipole Frenkel Hamiltonian. This approach allows us to study ensembles of emitters beyond the small volume limit (system size much smaller than the absorbed wavelength), where the Frenkel Hamiltonian fails. When analyzed on a large scale, such structures display superradiant states much brighter than their single components. An analysis of the robustness to static disorder and dynamical (thermal) noise shows that exciton coherence in the whole photosynthetic complex is larger than the coherence found in its parts. This provides evidence that the photosynthetic complex as a whole plays a predominant role in sustaining coherences in the system even at room temperature. Our results allow a better understanding of natural photosynthetic antennae and could drive experiments to verify how the response to electromagnetic radiation depends on the size of the photosynthetic antenna.

Contrasting packing modes for tubular assemblies in chlorosomes

The largest light-harvesting antenna in nature, the chlorosome, is a heterogeneous helical BChl self-assembly that has evolved in green bacteria to harvest light for performing photosynthesis in low-light environments. Guided by NMR chemical shifts and distance constraints for Chlorobaculum tepidum wild-type chlorosomes, the two contrasting packing modes for syn-anti parallel stacks of BChl c to form polar 2D arrays, with dipole moments adding up, are explored. Layered assemblies were optimized using local orbital density functional and plane wave pseudopotential methods. The packing mode with the lowest energy contains syn-anti and anti-syn H-bonding between stacks. It can accommodate R and S epimers, and side chain variability. For this packing, a match with the available EM data on the subunit axial repeat and optical data is obtained with multiple concentric cylinders for a rolling vector with the stacks running at an angle of 21° to the cylinder axis and with the BChl dipole moments running at an angle ß ∼ 55° to the tube axis, in accordance with optical data. A packing mode involving alternating syn and anti parallel stacks that is at variance with EM appears higher in energy. A weak cross-peak at -6 ppm in the MAS NMR with 50 kHz spinning, assigned to C-181, matches the shift of antiparallel dimers, which possibly reflects a minor impurity-type fraction in the self-assembled BChl c.

Low-Frequency Oscillations of Bacteriochlorophyll Oligomers in Chlorosomes of Photosynthetic Green Bacteria

In green photosynthetic bacteria, light is absorbed by bacteriochlorophyll (BChl) c/d/e oligomers, which are located in chlorosomes - unique structures created by Nature to collect the energy of very weak light fluxes. Using coherent femtosecond spectroscopy at cryogenic temperature, we detected and studied low-frequency vibrational motions of BChl c oligomers in chlorosomes of the green bacteria Chloroflexus (Cfx.) aurantiacus. The objects of the study were chlorosomes isolated from the bacterial cultures grown under different light intensity. It was found that the Fourier spectrum of low-frequency coherent oscillations in the Qy band of BChl c oligomers depends on the light intensity used for the growth of bacteria. It turned out that the number of low-frequency vibrational modes of chlorosomes increases as illumination under which they were cultivated decreases. Also, the frequency range within which these modes are observed expands, and frequencies of the most modes change. Theoretical modeling of the obtained data and analysis of the literature led to conclusion that the structural basis of Cfx. aurantiacus chlorosomes are short linear chains of BChl c combined into more complex structures. Increase in the length of these chains in chlorosomes grown under weaker light leads to the observed changes in the spectrum of vibrations of BChl c oligomers. This increase is an effective mechanism for bacteria adaptation to changing external conditions.

Femtosecond Exciton Relaxation in Chlorosomes of the Photosynthetic Green Bacterium Chloroflexus aurantiacus

Process of photosynthesis in the green bacteria Chloroflexus (Cfx.) aurantiacus starts from absorption of light by chlorosomes, peripheral antennas consisting of thousands of bacteriochlorophyll c (BChl c) molecules combined into oligomeric structures. In this case, the excited states are formed in BChl c, energy of which migrates along the chlorosome towards the baseplate and further to the reaction center, where the primary charge separation occurs. Energy migration is accompanied by non-radiative electronic transitions between the numerous exciton states, that is, exciton relaxation. In this work, we studied dynamics of the exciton relaxation in Cfx. aurantiacus chlorosomes using differential femtosecond spectroscopy at cryogenic temperature (80 K). Chlorosomes were excited by 20-fs light pulses at wavelengths in the range from 660 to 750 nm, and differential (light-dark) absorption kinetics were measured at a wavelength of 755 nm. Mathematical analysis of the obtained data revealed kinetic components with characteristic times of 140, 220, and 320 fs, which are responsible for exciton relaxation. As the excitation wavelength decreased, the number and relative contribution of these components increased. Theoretical modelling of the obtained data was carried out based of the cylindrical model of BChl c. Nonradiative transitions between the groups of exciton bands were described by a system of kinetic equations. The model that takes into account energy and structural disorder of chlorosomes turned out to be the most adequate.

Ring-shaped self-assembly of a naphthalene-linked chlorophyll dimer

Light-harvesting antennas, for example the LH2 complex in purple bacteria, sophisticatedly align chlorophyll molecules in a cyclic fashion by using protein scaffolds. However, artificial preparation of the circular LH antenna model without any templates has not been reported. We demonstrated the construction of ring-shaped supramolecules by self-assembly of a semisynthetic chlorophyll dimer through a transformation from wavy fiber-like aggregates.

Diagrammatic quantum Monte Carlo toward the calculation of transport properties in disordered semiconductors

A new diagrammatic quantum Monte Carlo approach is proposed to deal with the imaginary time propagator involving both dynamic disorder (i.e., electron–phonon interactions) and static disorder of local or nonlocal nature in a unified and numerically exact way. The establishment of the whole framework relies on a general reciprocal-space expression and a generalized Wick’s theorem for the static disorder. Since the numerical cost is independent of the system size, various physical quantities, such as the thermally averaged coherence, Matsubara one-particle Green’s function, and current autocorrelation function, can be efficiently evaluated in the thermodynamic limit (infinite in the system size). The validity and performance of the proposed approach are systematically examined in a broad parameter regime. This approach, combined with proper numerical analytic continuation methods and first-principles calculations, is expected to be a versatile tool toward the calculation of various transport properties, such as mobilities in realistic semiconductors involving multiple electronic energy bands, high-frequency optical and low-frequency acoustic phonons, different forms of dynamic and static disorders, and anisotropy.

Q-band hyperchromism and B-band hypochromism of bacteriochlorophyll c as a tool for investigation of the oligomeric structure of chlorosomes of the green photosynthetic bacterium Chloroflexus aurantiacus

Chlorosomes of green photosynthetic bacteria are the most amazing example of long-range ordered natural light-harvesting antennae. Chlorosomes are the largest among all known photosynthetic light-harvesting structures (~ 10⁴-10⁵ pigments in the aggregated state). The chlorosomal bacteriochlorophyll (BChl) c/d/e molecules are organized via self-assembly and do not require proteins to provide a scaffold for efficient light harvesting. Despite numerous investigations, a consensus regarding the spatial structure of chlorosomal antennae has not yet been reached. In the present work, we studied hyperchromism/hypochromism in the chlorosomal BChl c Q/B absorption bands of the green photosynthetic bacterium Chloroflexus (Cfx.) aurantiacus. The chlorosomes were isolated from cells grown under different light intensities and therefore, as we discovered earlier, they had different sizes of both BChl c antennae and their unit building blocks. We have shown experimentally that the Q-/B-band hyperchromism/hypochromism is proportional to the size of the chlorosomal antenna. We explained theoretically these findings in terms of excitonic intensity borrowing between the Q and B bands for the J-/H-aggregates of the BChls. The theory developed by Gülen (Photosynth Res 87:205-214, 2006) showed the dependence of the Q-/B-band hyperchromism/hypochromism on the structure of the aggregates. For the model of exciton-coupled BChl c linear chains within a unit building block, the theory predicted an increase in the hyperchromism/hypochromism with the increase in the number of molecules per chain and a decrease in it with the increase in the number of chains. It was previously shown that this model ensured a good fit with spectroscopy experiments and approximated the BChl c low packing density in vivo. The presented experimental and theoretical studies of the Q-/B-band hyperchromism/hypochromism permitted us to conclude that the unit building block of Cfx. aurantiacus chlorosomes comprises of several short BChl c chains.This conclusion is in accordance with previous linear and nonlinear spectroscopy studies on Cfx. aurantiacus chlorosomes.

Polaritons and excitons: Hamiltonian design for enhanced coherence

The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian-connections between sites (or molecules) made by electronic coupling-is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.

Dynamic Disorder Drives Exciton Transfer in Tubular Chlorosomal Assemblies

Chlorosomes stand out for their highly efficient excitation energy transfer (EET) in extreme low light conditions. Yet, little is known about the EET when a chlorosome is excited to a pure state that is an eigenstate of the exciton Hamiltonian. In this work, we consider the dynamic disorder in the intermolecular electronic coupling explicitly by calculating the electronic coupling terms in the Hamiltonian using nuclear coordinates that are taken from molecular dynamics simulation trajectories. We show that this dynamic disorder is capable of driving the evolution of the exciton, being a stationary state of the initial Hamiltonian. In particular, long-distance excitation energy transfer between domains of high exciton population and oscillatory behavior of the population in the site basis are observed, in line with two-dimensional electronic spectroscopy studies. We also found that in the high exciton population domains, their population variation is correlated with their overall coupling strength. Analysis in a reference state basis shows that such dynamic disorder, originating from thermal energy, creates a fluctuating landscape for the exciton and promotes the EET process. We propose such dynamic disorder as an important microscopic origin for the high efficient EET widely observed in different types of chlorosomes, bioinspired tubular aggregates, or other light-harvesting complexes.

Quantum Chemistry in the Age of Quantum Computing

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

Charge and energy transfer in large molecular assemblies: Quantum state diffusion with an adaptive basis

We show that the stochastic, wave-function based quantum state diffusion approach in combination with an adaptive basis is well suited to numerically treat the motion of an excitation in large molecular aggregates in the complicated regime where the transfer-time between molecules is comparable to the decoherence caused by environmental degrees of freedom.

Ultrafast excited-state dynamics in chlorosomes isolated from the photosynthetic filamentous green bacterium Chloroflexus aurantiacus

Bacteriochlorophyll (BChl) c pigments in the aggregated state are responsible for efficient light harvesting in chlorosomes of the filamentous anoxygenic photosynthetic bacterium, Chloroflexus (Cfx.) aurantiacus. Absorption of light creates excited states in the BChl c aggregates. After subpicosecond intrachlorosomal energy transfer, redistribution and relaxation, the excitation is transferred to the BChl a complexes and further to reaction centers on the picosecond time scale. In this work, the femtosecond excited state dynamics within BChl c oligomers of isolated Cfx. aurantiacus chlorosomes was studied by double difference pump-probe spectroscopy at room temperature. Difference (A^light  - A^dark ) spectra corresponding to excitation at 725 nm (blue side of the BChl c absorption band) were compared with those corresponding to excitation at 750 nm (red side of the BChl c absorption band). A very fast (time constant 70 ± 10 fs) rise kinetic component was found in the stimulated emission (SE) upon excitation at 725 nm. This component was absent at 750-nm excitation. These data were explained by the dynamical red shift of the SE due to excited state relaxation. The nature and mechanisms of the ultrafast excited state dynamics in chlorosomal BChl c aggregates are discussed.

Thousand-atom ab initio calculations of excited states at organic/organic interfaces: toward first-principles investigations of charge photogeneration

Predicting electronically excited states across electron-donor/electron acceptor interfaces is essential for understanding the charge photogeneration process in organic solar cells. However, organic solar cells are large and disordered systems, and their excited states cannot be easily accessed by conventional quantum chemistry approaches. Moreover, a large number of excited states must be obtained to fully understand the charge separation mechanism. Recently, we have developed a novel fragment-based excited state method which can efficiently calculate a large number of states in molecular aggregates. In this article, we demonstrate the large-scale excited-state calculations by investigating interfacial charge transfer (ICT) states across the electron-donor/electron acceptor interfaces. As the model systems, we considered the face-on and edge-on configurations of pentacene/C₆₀ bilayer heterojunction structures. These model structures contain approximately 1.8 × 10⁵ atoms, and their local interface regions containing 2000 atoms were treated quantum mechanically, embedded in the electrostatic potentials from the remaining parts. Therefore, the charge delocalization effect, structural disorder, and the resulting heterogeneous electrostatic and polarizable environments were taken into account in the excited-state calculations. The computed energies of the low-lying ICT states are in reasonable agreement with experimental estimates. By comparing the edge-on and face-on configurations of the pentacene/C₆₀ interfaces, we discuss the influence of interfacial morphologies on the energetics and charge delocalization of ICT states. In addition, we present the detailed characterization of excited states and highlight the importance of hybridization effects between pentacene excited states and ICT states. The large-scale ab initio calculations for the interface systems enabled the exploration of the ICT states, leading to first-principles investigation of the charge separation mechanism in organic solar cells.

Contrasting Modes of Self-Assembly and Hydrogen-Bonding Heterogeneity in Chlorosomes of Chlorobaculum tepidum

Chlorosome antennae form an interesting class of materials for studying the role of structural motifs and dynamics in nonadiabatic energy transfer. They perform robust and highly quantum-efficient transfer of excitonic energy while allowing for compositional variation and completely lacking the usual regulatory proteins. Here, we first cast the geometrical analysis for ideal tubular scaffolding models into a formal framework, to relate effective helical properties of the assembly structures to established characterization data for various types of chlorosomes. This analysis shows that helicity is uniquely defined for chlorosomes composed of bacteriochlorophyll (BChl) d and that three chiral angles are consistent with the nuclear magnetic resonance (NMR) and electron microscope data for BChl c, including two novel ones that are at variance with current interpretations of optical data based on perfect cylindrical symmetry. We use this information as a starting point for investigating dynamic and static heterogeneity at the molecular level by unconstrained molecular dynamics. We first identify a rotational degree of freedom, along the Mg-OH coordination bond, that alternates along the syn-anti stacks and underlies the (flexible) curvature on a larger scale. Because rotation directly relates to the formation or breaking of interstack hydrogen bonds of the O-H···O=C structural motif along the syn-anti stacks, we analyzed the relative fractions of hydrogen-bonded and the nonbonded regions, forming stripe domains in otherwise spectroscopically homogeneous curved slabs. The ratios 7:3 for BChl c and 9:1 for BChl d for the two distinct structural components agree well with the signal intensities determined by NMR. In addition, rotation with curvature-independent formation of stripe domains offers a viable explanation for the localization and dispersion of exciton states over two fractions, as observed in single chlorosome fluorescence decay studies.

Delocalized triplet state in porphyrin J-aggregates revealed by EPR spectroscopy

In this work, the electronic structure of the triplet state of self-assembled J-aggregates of tetrakis(4-sulfonatophenyl)porphyrin (TPPS) has been characterized by means of time-resolved electron paramagnetic resonance spectroscopy. Several insights into the triplet properties of the aggregate have been gained through comparison with the corresponding monomeric unit in both free base and acidified forms. Molecular distortions in the monomeric acidified TPPS cause variation in its zero-field splitting parameters and a redirection of triplet spin sublevel activity. The aggregation process does not alter the mechanism of triplet state population compared to the acidified monomer but it is accompanied by a further reduction in the zero-field splitting parameter D, which is possibly indicative of the formation of a delocalized triplet state species. The detection of a long-lived spin-polarized radical species also proves polaron generation and movement to a trap site in the J-aggregates.

Programmed coherent coupling in a synthetic DNA-based excitonic circuit

Natural light-harvesting systems spatially organize densely packed chromophore aggregates using rigid protein scaffolds to achieve highly efficient, directed energy transfer. Here, we report a synthetic strategy using rigid DNA scaffolds to similarly program the spatial organization of densely packed, discrete clusters of cyanine dye aggregates with tunable absorption spectra and strongly coupled exciton dynamics present in natural light-harvesting systems. We first characterize the range of dye-aggregate sizes that can be templated spatially by A-tracts of B-form DNA while retaining coherent energy transfer. We then use structure-based modelling and quantum dynamics to guide the rational design of higher-order synthetic circuits consisting of multiple discrete dye aggregates within a DX-tile. These programmed circuits exhibit excitonic transport properties with prominent circular dichroism, superradiance, and fast delocalized exciton transfer, consistent with our quantum dynamics predictions. This bottom-up strategy offers a versatile approach to the rational design of strongly coupled excitonic circuits using spatially organized dye aggregates for use in coherent nanoscale energy transport, artificial light-harvesting, and nanophotonics.

Variability of aggregation extent of light-harvesting pigments in peripheral antenna of Chloroflexus aurantiacus

The stationary ground state and femtosecond time-resolved absorption spectra as well as spectra of circular dichroism were measured at room temperature using freshly prepared samples of chlorosomes isolated from fresh cultures of the green bacterium Chloroflexus aurantiacus. Cultures were grown by using as inoculum the same seed culture but under different light conditions. All measured spectra clearly showed the red shift of BChl c Q_y bands (up to 5 nm) for low-light chlorosomes as compared to high-light ones, together with concomitant narrowing of these bands and increasing of their amplitudes. The sizes of the unit BChl c aggregates of the high-light-chlorosomes and the low-light ones were estimated. The fit of all experimental spectra was obtained within the framework of our model proposed before (Fetisova et al., Biophys J 71:995-101, 1996). The model assumes that a unit building block of the BChl c antenna has a form of a tubular aggregate of L = 6 linear single or double exciton-coupled pigment chains within a rod element, with the pigment packing density, approximating that in vivo. The simultaneous fit of all experimental spectra gave the number of pigments in each individual linear pigment chain N = 4 and N = 6 for the high-light and the low-light BChl c unit building blocks, respectively. The size of a unit building block in the BChl c antenna was found to vary from L × N = 24 to L × N = 36 exciton-coupled BChl c molecules being governed by the growth-light intensity. All sets of findings for Chloroflexus aurantiacus chlorosomes demonstrated the biologically expedient light-controlled variability, predicted by us, of the extent of BChl c aggregation within a unit building block in this antenna.

Coherent Dynamics of Mixed Frenkel and Charge-Transfer Excitons in Dinaphtho[2,3-b:2'3'-f]thieno[3,2-b]-thiophene Thin Films: The Importance of Hole Delocalization

Charge-transfer states in organic semiconductors play crucial roles in processes such as singlet fission and exciton dissociation at donor/acceptor interfaces. Recently, a time-resolved spectroscopy study of dinaphtho[2,3-b:2'3'-f]thieno[3,2-b]-thiophene (DNTT) thin films provided evidence for the formation of mixed Frenkel and charge-transfer excitons after the photoexcitation. Here, we investigate optical properties and excitation dynamics of the DNTT thin films by combining ab initio calculations and a stochastic Schrödinger equation. Our theory predicts that the low-energy Frenkel exciton band consists of 8-47% CT character. The quantum dynamics simulations show coherent dynamics of Frenkel and CT states in 50 fs after the optical excitation. We demonstrate the role of charge delocalization and localization in the mixing of CT states with Frenkel excitons as well as the role of their decoherence.

Quantum Chemical Studies of Light Harvesting

The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.

Probing ultrafast excitation energy transfer of the chlorosome with exciton–phonon variational dynamics

Excitation energy transfer of the chlorosome is investigated using exciton–phonon variational dynamics revealing ultrafast energy relaxation and exciton delocalization on a 100 fs scale.

Computing Nonequilibrium Conformational Dynamics of Structured Nucleic Acid Assemblies

Synthetic nucleic acids can be programmed to form precise three-dimensional structures on the nanometer-scale. These thermodynamically stable complexes can serve as structural scaffolds to spatially organize functional molecules including multiple enzymes, chromophores, and force-sensing elements with internal dynamics that include substrate reaction-diffusion, excitonic energy transfer, and force-displacement response that often depend critically on both the local and global conformational dynamics of the nucleic acid assembly. However, high molecular weight assemblies exhibit long time-scale and large length-scale motions that cannot easily be sampled using all-atom computational procedures such as molecular dynamics. As an alternative, here we present a computational framework to compute the overdamped conformational dynamics of structured nucleic acid assemblies and apply it to a DNA-based tweezer, a nine-layer DNA origami ring, and a pointer-shaped DNA origami object, which consist of 204, 3,600, and over 7,000 basepairs, respectively. The framework employs a mechanical finite element model for the DNA nanostructure combined with an implicit solvent model to either simulate the Brownian dynamics of the assembly or alternatively compute its Brownian modes. Computational results are compared with an all-atom molecular dynamics simulation of the DNA-based tweezer. Several hundred microseconds of Brownian dynamics are simulated for the nine-layer ring origami object to reveal its long time-scale conformational dynamics, and the first ten Brownian modes of the pointer-shaped structure are predicted.