Dynamic localization of electronic excitation in photosynthetic complexes revealed with chiral two-dimensional spectroscopy

The development and applications of multidimensional biomolecular spectroscopy illustrated by photosynthetic light harvesting

The parallel and synergistic developments of atomic resolution structural information, new spectroscopic methods, their underpinning formalism, and the application of sophisticated theoretical methods have led to a step function change in our understanding of photosynthetic light harvesting, the process by which photosynthetic organisms collect solar energy and supply it to their reaction centers to initiate the chemistry of photosynthesis. The new spectroscopic methods, in particular multidimensional spectroscopies, have enabled a transition from recording rates of processes to focusing on mechanism. We discuss two ultrafast spectroscopies - two-dimensional electronic spectroscopy and two-dimensional electronic-vibrational spectroscopy - and illustrate their development through the lens of photosynthetic light harvesting. Both spectroscopies provide enhanced spectral resolution and, in different ways, reveal pathways of energy flow and coherent oscillations which relate to the quantum mechanical mixing of, for example, electronic excitations (excitons) and nuclear motions. The new types of information present in these spectra provoked the application of sophisticated quantum dynamical theories to describe the temporal evolution of the spectra and provide new questions for experimental investigation. While multidimensional spectroscopies have applications in many other areas of science, we feel that the investigation of photosynthetic light harvesting has had the largest influence on the development of spectroscopic and theoretical methods for the study of quantum dynamics in biology, hence the focus of this review. We conclude with key questions for the next decade of this review.

Coarse-Grained Approach to Simulate Signatures of Excitation Energy Transfer in Two-Dimensional Electronic Spectroscopy of Large Molecular Systems

Two-dimensional electronic spectroscopy (2DES) has proven to be a highly effective technique in studying the properties of excited states and the process of excitation energy transfer in complex molecular assemblies, particularly in biological light-harvesting systems. However, the accurate simulation of 2DES for large systems still poses a challenge because of the heavy computational demands it entails. In an effort to overcome this limitation, we devised a coarse-grained 2DES method. This method encompasses the treatment of the entire system by dividing it into distinct weakly coupled segments, which are assumed to communicate predominantly through incoherent exciton transfer. We first demonstrate the efficiency of this method through simulation on a model dimer system, which demonstrates a marked improvement in calculation efficiency, with results that exhibit good concordance with reference spectra calculated with less approximate methods. Additionally, the application of this method to the light-harvesting antenna 2 (LH2) complex of purple bacteria showcases its advantages, accuracy, and limitations. Furthermore, simulating the anisotropy decay in LH2 induced by energy transfer and its comparison with experiments confirm that the method is capable of accurately describing dynamical processes in a biologically relevant system. This method presented lends itself to an extension that accounts for the effect of intrasegment relaxation processes on the 2DES spectra, which for computational efficiency are ignored in the implementation reported here. It is envisioned that the method will be employed in the future to accurately and efficiently calculate 2D spectra of more extensive systems, such as photosynthetic supercomplexes.

Transient Chiral Dynamics in the Fenna-Matthews-Olson Complex Revealed by Two-Dimensional Circular Dichroism Spectroscopy

Chirality plays a pivotal role across scientific disciplines with profound implications spanning light-matter interactions, molecular recognition, and natural evolutionary processes. This study delves into the active influence of molecular chirality on exciton energy transfer within photosynthetic protein complexes, focusing on the Fenna-Matthews-Olson (FMO) complex. Employing two-dimensional circular dichroism (2DCD) spectroscopy, we investigate the transient chiral dynamics of excitons during energy transfer processes within the FMO complex. Our approach, incorporating pulse information into population dynamics based on the third-order response function, facilitates the calculation of 2DCD spectra and dynamics. This enables the extraction of chiral contributions to excitonic energy transfer and the examination of electronic wave functions. We demonstrate that 2DCD spectra offer excitation energies that are better resolved than those from conventional two-dimensional electronic spectroscopy. These findings deepen our understanding of exciton energy transfer mechanisms in natural photosynthesis, emphasizing the potential of 2DCD spectroscopy as a powerful tool for unraveling the chiral contribution to exciton dynamics.

Transient chiral dynamics revealed by two-dimensional circular dichroism spectroscopy

Chirality has been considered as one of the key factors in the evolution of life in nature. It is important to uncover how chiral potentials of molecular systems play vital role in fundamental photochemical processes. Here, we investigate the role of chirality in photoinduced energy transfer in a model dimeric system, where the monomers are excitonically coupled. To observe transient chiral dynamics and energy transfer, we employ circularly polarized laser pulses in two-dimensional electronic spectroscopy to construct the two-dimensional circular dichroism (2DCD) spectral maps. Tracking time-resolved peak magnitudes in 2DCD spectra allows one to identify chirality induced population dynamics. The dynamics of energy transfer is revealed by the time-resolved kinetics of cross peaks. However, the differential signal of 2DCD spectra shows the magnitude of cross peaks is dramatically reduced at initial waiting time, which indicates the weak chiral interactions between two monomers. The downhill energy transfer is resolved by presenting a strong magnitude of cross peak in 2DCD spectra after long waiting time. The chiral contribution towards coherent and incoherent energy-transfer pathways in the model dimer system is further examined via control of excitonic couplings between two monomers. Applications are made to study the energy-transfer process in the Fenna-Matthews-Olson complex. Our work uncovers the potential of 2DCD spectroscopy to resolve the chiral-induced interactions and population transfers in excitonically coupled systems.

Circularly Polarized Light Probes Excited-State Delocalization in Rectangular Ladder-type Pentaphenyl Helices

Ladder-type pentaphenyl chromophores have a rigid, planar π-system and show bright fluorescence featuring pronounced vibrational structure. Such moieties are ideal for studying interchromophoric interactions and delocalization of electronic excitations. We report the synthesis of helical polymers with a rigid square structure based on spiro-linked ladder-type pentaphenyl units. The variation of circular dichroism with increasing chain length provides direct evidence for delocalization of electronic excitations over at least 10 monomeric units. The change in the degree of circular polarization of the fluorescence across the vibronic side bands shows that vibrational motion can localize the excitation dynamically to almost one single unit through breakdown of the Born-Oppenheimer approximation. The dynamic conversion between delocalized and localized excited states provides a new paradigm for interpreting circular dichroism in helical polymers such as proteins and polynucleic acids.

Neumann's principle based eigenvector approach for deriving non-vanishing tensor elements for nonlinear optics

Physical properties are commonly represented by tensors, such as optical susceptibilities. The conventional approach of deriving non-vanishing tensor elements of symmetric systems relies on the intuitive consideration of positive/negative sign flipping after symmetry operations, which could be tedious and prone to miscalculation. Here, we present a matrix-based approach that gives a physical picture centered on Neumann's principle. The principle states that symmetries in geometric systems are adopted by their physical properties. We mathematically apply the principle to the tensor expressions and show a procedure with clear physical intuition to derive non-vanishing tensor elements based on eigensystems. The validity of the approach is demonstrated by examples of commonly known second and third-order nonlinear susceptibilities of chiral/achiral surfaces, together with complicated scenarios involving symmetries such as D6 and Oh symmetries. We then further applied this method to higher-rank tensors that are useful for 2D and high-order spectroscopy. We also extended our approach to derive nonlinear tensor elements with magnetization, which is critical for measuring spin polarization on surfaces for quantum information technologies. A Mathematica code based on this generalized approach is included that can be applied to any symmetry and higher order nonlinear processes.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

Multiscale conformational dynamics probed by time-resolved circular dichroism from seconds to picoseconds

Time-resolved circular dichroism has been developed for a few decades to investigate rapid conformational changes in (bio)molecules. In our group, we have come up with several experimental set-ups allowing us to study pico-nanosecond local phenomena in molecular systems as well as much slower effects occurring in proteins and DNA in the folding processes. After an overview of the worldwide realizations in this domain, we present emblematic experiments that we have carried out, spanning time domain from picoseconds to seconds.

Steering Triplet-Triplet Annihilation Upconversion through Enantioselective Self-Assembly in a Supramolecular Gel

Research on chiral selection and recognition not only is of fundamental importance in resolving the origin of biological homochirality, but also is instructive in the fabrication of controlled molecular organization in supramolecular systems to modulate their chirality-related functional properties. Here we report an enantioselective assembly process between a chiral energy donor and two enantiomeric energy acceptors, which further results in chirality-controlled energy transfer and enantioselective triplet-triplet annihilation upconversion (TTA-UC). It is found that the chiral energy donor Pd(II) octaethylporphyrin derivative PdOEP-LG12 (R_D) can selectively coassemble with the chiral energy acceptor LGAn (R_A) with the same chiral scaffold but tends to form segregation with the energy acceptor DGAn (S_A) with the opposite chiral scaffold in a thermodynamic equilibrium state. Thus, the coassembly of R_A/R_D shows more effective triplet-triplet energy transfer (TTET) and stronger upconverted luminescence and upconverted circularly polarized luminescence in comparison to the segregation of S_A/R_D. The establishment of such an enantioselective TTA-UC system highlights the applications of chirality-regulated triplet fusion in optoelectronic materials.

Energy Transfer Dynamics in Light-Harvesting Complex 2 Variants Containing Oxidized B800 Bacteriochlorophyll a

Excitation energy transfer (EET) in light-harvesting proteins is vital for photosynthetic activities. The pigment compositions and their organizations in these proteins are responsible for the EET functions. Thus, changing the pigment compositions in light-harvesting proteins contributes to a better understanding of EET mechanisms. In this study, we investigated the EET dynamics of two light-harvesting complex 2 (LH2) variants, in which nine B800 bacteriochlorophyll (BChl) a pigments were entirely or half converted to 3-acetyl chlorophyll (AcChl) a. The AcChl a pigments showed a Q_y band, which was blue-shifted by 107 nm from B800 BChl a in the two variants. EET from AcChl a to B850 BChl a was observed in both fully oxidized and half-oxidized LH2 variants, but the EET rates were lower than that from B800 to B850 BChl a. EET from AcChl a to the co-present B800 was barely detected in the half-oxidized LH2. The preferential EET from AcChl a to B850 instead of B800 was rationalized by little spectral overlap of AcChl a with B800 BChl a and the pigment geometry in the protein. The EET rate from B800 to B850 BChl a in the half-oxidized LH2 was analogous to that in native LH2, indicating that partial oxidation of B800 did not disturb the EET channel from the residual B800 to B850.

Fully Quantum Modeling of Exciton Diffusion in Mesoscale Light Harvesting Systems

It has long been a challenge to accurately and efficiently simulate exciton-phonon dynamics in mesoscale photosynthetic systems with a fully quantum mechanical treatment due to extensive computational resources required. In this work, we tackle this seemingly intractable problem by combining the Dirac-Frenkel time-dependent variational method with Davydov trial states and implementing the algorithm in graphic processing units. The phonons are treated on the same footing as the exciton. Tested with toy models, which are nanoarrays of the B850 pigments from the light harvesting 2 complexes of purple bacteria, the methodology is adopted to describe exciton diffusion in huge systems containing more than 1600 molecules. The superradiance enhancement factor extracted from the simulations indicates an exciton delocalization over two to three pigments, in agreement with measurements of fluorescence quantum yield and lifetime in B850 systems. With fractal analysis of the exciton dynamics, it is found that exciton transfer in B850 nanoarrays exhibits a superdiffusion component for about 500 fs. Treating the B850 ring as an aggregate and modeling the inter-ring exciton transfer as incoherent hopping, we also apply the method of classical master equations to estimate exciton diffusion properties in one-dimensional (1D) and two-dimensional (2D) B850 nanoarrays using derived analytical expressions of time-dependent excitation probabilities. For both coherent and incoherent propagation, faster energy transfer is uncovered in 2D nanoarrays than 1D chains, owing to availability of more numerous propagating channels in the 2D arrangement.

An Ab Initio Multiple Cloning Method for Non-Adiabatic Excited-State Molecular Dynamics in NWChem

The recently developed ab initio multiple cloning (AIMC) approach based on the multiconfigurational Ehrenfest (MCE) method provides a powerful and accurate way of describing the excited-state dynamics of molecular systems. The AIMC method is a controlled approximation to nonadiabatic dynamics with a particular strength in the proper description of decoherence effects because of the branching of vibrational wavepackets at a level crossing. Here, we report a new implementation of the AIMC algorithm in the open source NWChem computational chemistry program. The framework combines linear-response time-dependent density functional theory with Ehrenfest mean-field theory to determine the equations of motion for classical trajectories. The multidimensional wave function is decomposed into a superposition of Gaussian coherent states guided by Ehrenfest trajectories (i.e., MCE approach), which can clone with fully quantum mechanical amplitudes and phases. By using an efficient time-derivative based nonadiabatic coupling approach within the AIMC method, all observables are calculated on-the-fly in the nonadiabatic molecular dynamics process. As a representative example, we apply our implementation to study the ultrafast photoinduced electronic and vibrational energy transfer in a pyridine molecule. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer are discussed. This new AIMC implementation provides a high-level nonadiabatic molecular dynamics framework for simulating photoexcited dynamics in complex molecular systems and experimentally relevant ultrafast spectroscopic probes, such as nonlinear coherent optical and X-ray signals.

Superradiance of bacteriochlorophyll c aggregates in chlorosomes of green photosynthetic bacteria

Chlorosomes are the main light-harvesting complexes of green photosynthetic bacteria that are adapted to a phototrophic life at low-light conditions. They contain a large number of bacteriochlorophyll c, d, or e molecules organized in self-assembling aggregates. Tight packing of the pigments results in strong excitonic interactions between the monomers, which leads to a redshift of the absorption spectra and excitation delocalization. Due to the large amount of disorder present in chlorosomes, the extent of delocalization is limited and further decreases in time after excitation. In this work we address the question whether the excitonic interactions between the bacteriochlorophyll c molecules are strong enough to maintain some extent of delocalization even after exciton relaxation. That would manifest itself by collective spontaneous emission, so-called superradiance. We show that despite a very low fluorescence quantum yield and short excited state lifetime, both caused by the aggregation, chlorosomes indeed exhibit superradiance. The emission occurs from states delocalized over at least two molecules. In other words, the dipole strength of the emissive states is larger than for a bacteriochlorophyll c monomer. This represents an important functional mechanism increasing the probability of excitation energy transfer that is vital at low-light conditions. Similar behaviour was observed also in one type of artificial aggregates, and this may be beneficial for their potential use in artificial photosynthesis.

Two-dimensional electronic spectroscopy of bacteriochlorophyll a with synchronized dual mode-locked lasers

How atoms and electrons in a molecule move during a chemical reaction and how rapidly energy is transferred to or from the surroundings can be studied with flashes of laser light. However, despite prolonged efforts to develop various coherent spectroscopic techniques, the lack of an all-encompassing method capable of both femtosecond time resolution and nanosecond relaxation measurement has hampered various applications of studying correlated electron dynamics and vibrational coherences in functional materials and biological systems. Here, we demonstrate that two broadband (>300 nm) synchronized mode-locked lasers enable two-dimensional electronic spectroscopy (2DES) study of chromophores such as bacteriochlorophyll a in condensed phases to measure both high-resolution coherent vibrational spectrum and nanosecond electronic relaxation. We thus anticipate that the dual mode-locked laser-based 2DES developed and demonstrated here would be of use for unveiling the correlation between the quantum coherence and exciton dynamics in light-harvesting protein complexes and semiconducting materials.

Monitoring the evolution of intersite and interexciton coherence in electronic excitation transfer via wave-packet interferometry

We detail an experimental strategy for tracking the generation and time-development of electronic coherence within the singly excited manifold of an energy-transfer dimer. The technique requires that the two monomers have nonparallel electronic transition-dipole moments and that these possess fixed orientations in space. It makes use of two-dimensional wave-packet interferometry (WPI or whoopee) measurements in which the A, B, C, and D pulses have respective polarizations e, e, e, and e'. In the case of energy-transfer coupling that is weak or strong compared to electronic-nuclear interactions, it is convenient to follow the evolution of intersite or interexciton coherence, respectively. Under weak coupling, e could be perpendicular to the acceptor chromophore's transition dipole moment and the unit vector e' would be perpendicular to the donor's transition dipole. Under strong coupling, e could be perpendicular to the ground-to-excited transition dipole to the lower exciton level and e' would be perpendicular to the ground-to-excited transition dipole to the upper exciton level. If the required spatial orientation can be realized for an entire ensemble, experiments of the kind proposed could be performed by either conventional four-wave-mixing or fluorescence-detected WPI methods. Alternatively, fluorescence-detected whoopee experiments of this kind could be carried out on a single energy-transfer dimer of fixed orientation. We exhibit detailed theoretical expressions for the desired WPI signal, explain the physical origin of electronic coherence detection, and show calculated observed-coherence signals for model dimers with one, two, or three internal vibrational modes per monomer and both weak and strong energy-transfer coupling.

Ultrafast Excitation Transfer in Cy5 DNA Photonic Wires Displays Dye Conjugation and Excitation Energy Dependency

DNA scaffolds enable base-pair-specific positioning of fluorescent molecules, allowing for nanometer-scale precision in controlling multidye interactions. Expanding on this concept, DNA-based molecular photonic wires (MPWs) allow for light harvesting and directional propagation of photonic energy on the nanometer scale. The most common MPW examples exploit Förster resonance energy transfer (FRET), and FRET between the same dye species (HomoFRET) was recently shown to increase the distance and efficiency at which MPWs can function. Although increased proximity between adjacent fluorophores can be used to increase the energy transfer efficiency, FRET assumptions break down as the distance between the dye molecules becomes comparable to their size (∼2 nm). Here we compare dye conjugation with single versus dimer Cy5 dye repeats as HomoFRET MPW components on a double-crossover DNA scaffold. At room temperature (RT) under low-light conditions, end-labeled uncoupled dye molecules provide optimal transfer, while the Cy5 dimers show ultrafast (<100 ps) nonradiative decay that severely limits their functionality. Of particular interest is the observation that through increased excitation fluence as well as cryogenic temperatures, the dimeric MPW shows suppression of the ultrafast decay, demonstrating fluorescence lifetimes similar to the single Cy5 MPWs. This work points to the complex dynamic capabilities of dye-based nanophotonic networks, where dye positioning and interactions can become critical, and could be used to extend the lengths and complexities of such dye-DNA devices, enabling multiparameter nanophotonic circuitry.

Solvent tuning of photochemistry upon excited-state symmetry breaking

The nature of the electronic excited state of many symmetric multibranched donor–acceptor molecules varies from delocalized/multipolar to localized/dipolar depending on the environment. Solvent-driven localization breaks the symmetry and traps the exciton in one branch. Using a combination of ultrafast spectroscopies, we investigate how such excited-state symmetry breaking affects the photochemical reactivity of quadrupolar and octupolar A–(π-D)_2,3 molecules with photoisomerizable A–π–D branches. Excited-state symmetry breaking is identified by monitoring several spectroscopic signatures of the multipolar delocalized exciton, including the S₂ ← S₁ electronic transition, whose energy reflects interbranch coupling. It occurs in all but nonpolar solvents. In polar media, it is rapidly followed by an alkyne–allene isomerization of the excited branch. In nonpolar solvents, slow and reversible isomerization corresponding to chemically-driven symmetry breaking, is observed. These findings reveal that the photoreactivity of large conjugated molecules can be tuned by controlling the localization of the excitation.

Symmetric multibranched donor-acceptor molecules are promising photoactive materials for diverse applications. Here the authors show that, in octupolar and quadrupolar dyes, excited-state symmetry breaking occurs efficiently in polar solvents only and results in a concentration of the excitation that may trigger fast photochemical reactions.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Unveiling Excited-State Chirality of Binaphthols by Femtosecond Circular Dichroism and Quantum Chemical Calculations

Time-resolved circular dichroism (TR-CD) is a powerful tool for probing conformational dynamics of biomolecules over large time scales that are crucial for establishing their structure-function relationship. However, such experiments, notably in the femtosecond regime, remain challenging due to their extremely weak signals, prone to polarization artifacts. By using binol and two bridged derivatives (PL1 and PL2) as chiral prototypes, we present here the first comprehensive study of this type in the middle UV, combining femtosecond TR-CD and quantum mechanical calculations (TD-DFT). We show that excitation of the three compounds induces large variations of their transient CD signals, in sharp contrast to those of their achiral transient absorption. We demonstrate that these variations arise from both the alteration of the electronic distribution and the dihedral angle in the excited state. These results highlight the great sensitivity of TR-CD detection to signals hardly accessible to achiral transient absorption.

Geometry Effects on Light-Harvesting Complex's Light Absorption and Energy Transfer in Purple Bacteria

Light-harvesting complexes (LHC) in photosynthetic organisms perform the major function of light absorption and energy transportation. Optical spectrum of LHC provides a detailed understanding of the molecular mechanisms involved in the excitation energy transfer (EET) processes, which has been widely studied. Here, we study how the geometric property of LHC in Rhodospirillum (Rs.) molischianum would affect its spectral characteristics and energy transfer process. By adopting the effective Hamiltonian and the dipole-dipole approximation, we calculate the exciton level structures for the LH2 ring and LH1 ring and the energy transfer time between different LHCs under various structural parameters and different rotational symmetries. Our numerical results show that the LHC's absorption peaks and the energy transfer time between different LHCs can be modified by changing the geometric configurations. Our study may be beneficial to the applications in designing highly efficient photovoltaic cell and other artificial photosynthetic systems.

Orientational Dynamics of Transition Dipoles and Exciton Relaxation in LH2 from Ultrafast Two-Dimensional Anisotropy

Light-harvesting complexes in photosynthetic organisms display fast and efficient energy transfer dynamics, which depend critically on the electronic structure of the coupled chromophores within the complexes and their interactions with their environment. We present ultrafast anisotropy dynamics, resolved in both time and frequency, of the transmembrane light-harvesting complex LH2 from Rhodobacter sphaeroides in its native membrane environment using polarization-controlled two-dimensional electronic spectroscopy. Time-dependent anisotropy obtained from both experiment and modified Redfield simulation reveals an orientational preference for excited state absorption and an ultrafast equilibration within the B850 band in LH2. This ultrafast equilibration is favorable for subsequent energy transfer toward the reaction center. Our results also show a dynamic difference in excited state absorption anisotropy between the directly excited B850 population and the population that is initially excited at 800 nm, suggesting absorption from B850 states to higher-lying excited states following energy transfer from B850*. These results give insight into the ultrafast dynamics of bacterial light harvesting and the excited state energy landscape of LH2 in the native membrane environment.

Recent advances in multidimensional ultrafast spectroscopy

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

Double-excitation manifold's effect on exciton transfer dynamics and the efficiency of coherent light harvesting

Dynamical dark states make the double-excitation manifold important in exciton transfer dynamics.

Electronic Delocalization, Vibrational Dynamics, and Energy Transfer in Organic Chromophores

The efficiency of materials developed for solar energy and technological applications depends on the interplay between molecular architecture and light-induced electronic energy redistribution. The spatial localization of electronic excitations is very sensitive to molecular distortions. Vibrational nuclear motions can couple to electronic dynamics driving changes in localization. The electronic energy transfer among multiple chromophores arises from several distinct mechanisms that can give rise to experimentally measured signals. Atomistic simulations of coupled electron-vibrational dynamics can help uncover the nuclear motions directing energy flow. Through careful analysis of excited state wave function evolution and a useful fragmenting of multichromophore systems, through-bond transport and exciton hopping (through-space) mechanisms can be distinguished. Such insights are crucial in the interpretation of fluorescence anisotropy measurements and can aid materials design. This Perspective highlights the interconnected vibrational and electronic motions at the foundation of nonadiabatic dynamics where nuclear motions, including torsional rotations and bond vibrations, drive electronic transitions.

Isolating the chiral contribution in optical two-dimensional chiral spectroscopy using linearly polarized light

The full development of mono- or multi-dimensional time-resolved spectroscopy techniques incorporating optical activity signals has been strongly hampered by the challenge of identifying the small chiral signals over the large achiral background. Here we propose a new methodology to isolate chiral signals removing the achiral background from two commonly used configurations for performing two-dimensional optical spectroscopy, known as BOXCARS and gradient assisted photon echo spectroscopy (GRAPES). It is found that in both cases an achiral signal from an isotropic system can be completely eliminated by small manipulations of the relative angles between the linear polarizations of the four input laser pulses. Starting from the formulation of a perturbative expansion of the signal in the angle between the beams and the propagation axis, we derive analytic expressions that can be used to estimate how to change the polarization angles of the four pulses to minimize achiral contributions in the studied configurations. The generalization to any other possible experimental configurations has also been discussed.

Communication: Coherences observed in vivo in photosynthetic bacteria using two-dimensional electronic spectroscopy

Energy transfer through large disordered antenna networks in photosynthetic organisms can occur with a quantum efficiency of nearly 100%. This energy transfer is facilitated by the electronic structure of the photosynthetic antennae as well as interactions between electronic states and the surrounding environment. Coherences in time-domain spectroscopy provide a fine probe of how a system interacts with its surroundings. In two-dimensional electronic spectroscopy, coherences can appear on both the ground and excited state surfaces revealing detailed information regarding electronic structure, system-bath coupling, energy transfer, and energetic coupling in complex chemical systems. Numerous studies have revealed coherences in isolated photosynthetic pigment-protein complexes, but these coherences have not been observed in vivo due to the small amplitude of these signals and the intense scatter from whole cells. Here, we present data acquired using ultrafast video-acquisition gradient-assisted photon echo spectroscopy to observe quantum beating signals from coherences in vivo. Experiments were conducted on isolated light harvesting complex II (LH2) from Rhodobacter sphaeroides, whole cells of R. sphaeroides, and whole cells of R. sphaeroides grown in 30% deuterated media. A vibronic coherence was observed following laser excitation at ambient temperature between the B850 and the B850(∗) states of LH2 in each of the 3 samples with a lifetime of ∼40-60 fs.

Spectral lineshapes in nonlinear electronic spectroscopy

We outline a computational approach for nonlinear electronic spectra, which accounts for the electronic energy fluctuations due to nuclear degrees of freedom and explicitly incorporates the fluctuations of higher excited states, induced by the dynamics in the photoactive state(s). This approach is based on mixed quantum-classical dynamics simulations. Tedious averaging over multiple trajectories is avoided by employing the linearly displaced Brownian harmonic oscillator to model the correlation functions. The present strategy couples accurate computations of the high-lying excited state manifold with dynamics simulations. The application is made to the two-dimensional electronic spectra of pyrene, a polycyclic aromatic hydrocarbon characterized by an ultrafast (few tens of femtoseconds) decay from the bright S2 state to the dark S1 state. The spectra for waiting times t2 = 0 and t2 = 1 ps demonstrate the ability of this approach to model electronic state fluctuations and realistic lineshapes. Comparison with experimental spectra [Krebs et al., New Journal of Physics, 2013, 15, 085016] shows excellent agreement and allows us to unambiguously assign the excited state absorption features.

Ultra-broadband 2D electronic spectroscopy of carotenoid-bacteriochlorophyll interactions in the LH1 complex of a purple bacterium

We investigate the excitation energy transfer (EET) pathways in the photosynthetic light harvesting 1 (LH1) complex of purple bacterium Rhodospirillum rubrum with ultra-broadband two-dimensional electronic spectroscopy (2DES). We employ a 2DES apparatus in the partially collinear geometry, using a passive birefringent interferometer to generate the phase-locked pump pulse pair. This scheme easily lends itself to two-color operation, by coupling a sub-10 fs visible pulse with a sub-15-fs near-infrared pulse. This unique pulse combination allows us to simultaneously track with extremely high temporal resolution both the dynamics of the photoexcited carotenoid spirilloxanthin (Spx) in the visible range and the EET between the Spx and the B890 bacterio-chlorophyll (BChl), whose Qx and Qy transitions peak at 585 and 881 nm, respectively, in the near-infrared. Global analysis of the one-color and two-color 2DES maps unravels different relaxation mechanisms in the LH1 complex: (i) the initial events of the internal conversion process within the Spx, (ii) the parallel EET from the first bright state S2 of the Spx towards the Qx state of the B890, and (iii) the internal conversion from Qx to Qy within the B890.

Ultrafast energy relaxation in single light-harvesting complexes

Energy relaxation in light-harvesting complexes has been extensively studied by various ultrafast spectroscopic techniques, the fastest processes being in the sub-100-fs range. At the same time, much slower dynamics have been observed in individual complexes by single-molecule fluorescence spectroscopy (SMS). In this work, we use a pump-probe-type SMS technique to observe the ultrafast energy relaxation in single light-harvesting complexes LH2 of purple bacteria. After excitation at 800 nm, the measured relaxation time distribution of multiple complexes has a peak at 95 fs and is asymmetric, with a tail at slower relaxation times. When tuning the excitation wavelength, the distribution changes in both its shape and position. The observed behavior agrees with what is to be expected from the LH2 excited states structure. As we show by a Redfield theory calculation of the relaxation times, the distribution shape corresponds to the expected effect of Gaussian disorder of the pigment transition energies. By repeatedly measuring few individual complexes for minutes, we find that complexes sample the relaxation time distribution on a timescale of seconds. Furthermore, by comparing the distribution from a single long-lived complex with the whole ensemble, we demonstrate that, regarding the relaxation times, the ensemble can be considered ergodic. Our findings thus agree with the commonly used notion of an ensemble of identical LH2 complexes experiencing slow random fluctuations.

Polaronic effects at finite temperatures in the B850 ring of the LH2 complex

Energy transfer and relaxation dynamics in the B850 ring of LH2 molecular aggregates are described, taking into account the polaronic effects, by a stochastic time-dependent variational approach.

Vibronic resonances facilitate excited-state coherence in light-harvesting proteins at room temperature

Until recently it was believed that photosynthesis, a fundamental process for life on earth, could be fully understood with semiclassical models. However, puzzling quantum phenomena have been observed in several photosynthetic pigment-protein complexes, prompting questions regarding the nature and role of these effects. Recent attention has focused on discrete vibrational modes that are resonant or quasi-resonant with excitonic energy splittings and strongly coupled to these excitonic states. Here we unambiguously identify excited state coherent superpositions in photosynthetic light-harvesting complexes using a new experimental approach. Decoherence on the time scale of the excited state lifetime allows low energy (56 cm(-1)) oscillations on the signal intensity to be observed. In conjunction with an appropriate model, these oscillations provide clear and direct experimental evidence that the persistent coherences observed originate from quantum superpositions among vibronic excited states.

Circularly polarized luminescence spectroscopy reveals low-energy excited states and dynamic localization of vibronic transitions in CP43

Circularly polarized luminescence (CPL) spectroscopy is an established but relatively little-used technique that monitors the chirality of an emission. When applied to photosynthetic pigment assemblies, we find that CPL provides sensitive and detailed information on low-energy exciton states, reflecting the interactions, site energies and geometries of interacting pigments. CPL is the emission analog of circular dichroism (CD) and thus spectra explore the optical activity only of fluorescent states of the pigment-protein complex and consequently the nature of the lowest-energy excited states (trap states), whose study is a critical area of photosynthesis research. In this work, we develop the new approach of temperature-dependent CPL spectroscopy, over the 2-120 K temperature range, and apply it to the CP43 proximal antenna protein of photosystem II. Our results confirm strong excitonic interactions for at least one of the two well-established emitting states of CP43 named "A" and "B". Previous structure-based models of CP43 spectra are evaluated in the light of the new CPL data. Our analysis supports the assignments of Shibata et al. [Shibata et al. J. Am. Chem. Soc. 135 (2013) 6903-6914], particularly for the highly-delocalized B-state. This state dominates CPL spectra and is attributed predominantly to chlorophyll a's labeled Chl 634 and Chl 636 (alternatively labeled Chl 43 and 45 by Shibata et al.). The absence of any CPL intensity in intramolecular vibrational sidebands associated with the delocalized "B" excited state is attributed to the dynamic localization of intramolecular vibronic transitions.

On the accuracy of coherent modified Redfield theory in simulating excitation energy transfer dynamics

In this study, we investigate the accuracy of a recently developed coherent modified Redfield theory (CMRT) in simulating excitation energy transfer (EET) dynamics. The CMRT is a secular non-Markovian quantum master equation that is derived by extending the modified Redfield theory to treat coherence dynamics in molecular excitonic systems. Herein, we systematically survey the applicability of the CMRT in a large EET parameter space through the comparisons of the CMRT EET dynamics in a dimer system with the numerically exact results. The results confirm that the CMRT exhibits a broad applicable range and allow us to locate the specific parameter regimes where CMRT fails to provide adequate results. Moreover, we propose an accuracy criterion based on the magnitude of second-order perturbation to characterize the applicability of CMRT and show that the criterion summarizes all the benchmark results and the physics described by CMRT. Finally, we employ the accuracy criterion to quantitatively compare the performance of CMRT to that of a small polaron quantum master equation approach. The comparison demonstrates the complementary nature of these two methods, and as a result, the combination of the two methods provides accurate simulations of EET dynamics for the full parameter space investigated in this study. Our results not only delicately evaluate the applicability of the CMRT but also reveal new physical insights for factors controlling the dynamics of EET that should be useful for developing more accurate and efficient methods for simulations of EET dynamics in molecular aggregate systems.

Experimental implementations of two-dimensional fourier transform electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Electronic coherence and the kinetics of inter-complex energy transfer in light-harvesting systems

Comparison of inter-complex excitation energy transfer rates obtained in a general system (original, red) and in an alternative parameterization of the system that preserves static coherence while eliminating dynamic coherence (SCP, black) reveals that static coherence largely governs the kinetics of incoherent inter-complex EET in model light-harvesting networks, whereas dynamic coherence plays only a minor role.