Probing Photosynthetic Energy and Charge Transfer with Two-Dimensional Electronic Spectroscopy

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.

Theoretical model of femtosecond coherence spectroscopy of vibronic excitons in molecular aggregates

When used as pump pulses in transient absorption spectroscopy measurements, femtosecond laser pulses can produce oscillatory signals known as quantum beats. The quantum beats arise from coherent superpositions of the states of the sample and are best studied in the Fourier domain using Femtosecond Coherence Spectroscopy (FCS), which consists of one-dimensional amplitude and phase plots of a specified oscillation frequency as a function of the detection frequency. Prior works have shown ubiquitous amplitude nodes and π phase shifts in FCS from excited-state vibrational wavepackets in monomer samples. However, the FCS arising from vibronic-exciton states in molecular aggregates have not been studied theoretically. Here, we use a model of vibronic-exciton states in molecular dimers based on displaced harmonic oscillators to simulate FCS for dimers in two important cases. Simulations reveal distinct spectral signatures of excited-state vibronic-exciton coherences in molecular dimers that may be used to distinguish them from monomer vibrational coherences. A salient result is that, for certain relative orientations of the transition dipoles, the key resonance condition between the electronic coupling and the frequency of the vibrational mode may yield strong enhancement of the quantum-beat amplitude and, perhaps, also cause a significant decrease of the oscillation frequency to a value far lower than the vibrational frequency. Future studies using these results will lead to new insights into the excited-state coherences generated in photosynthetic pigment-protein complexes.

Ultrabroadband two-dimensional electronic spectroscopy in the pump-probe geometry using conventional optics

We report ultrabroadband two-dimensional electronic spectroscopy (2D ES) measurements obtained in the pump-probe geometry using conventional optics. A phase-stabilized Michelson interferometer provides the pump-pulse delay interval, τ1, necessary to obtain the excitation-frequency dimension. Spectral resolution of the probe beam provides the detection-frequency dimension, ω3. The interferometer incorporates active phase stabilization via a piezo stage and feedback from interference of a continuous-wave reference laser detected in quadrature. To demonstrate the method, we measured a well-characterized laser dye sample and obtained the known peak structure. The vibronic peaks are modulated as a function of the waiting time, τ2, by vibrational wave packets. The interferometer simplifies ultrabroadband 2D ES measurements and analysis.

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

Perturbed free induction decay obscures early time dynamics in two-dimensional electronic spectroscopy: The case of semiconductor nanocrystals

Two-dimensional electronic spectroscopy (2DES) has recently been gaining popularity as an alternative to the more common transient absorption spectroscopy due to the combination of high frequency and time resolution of 2DES. In order to advance the reliable analysis of population dynamics and to optimize the time resolution of the method, one has to understand the numerous field matter interactions that take place at an early and negative time. These interactions have historically been discussed in one-dimensional spectroscopy as coherent artifacts and have been assigned to both resonant and non-resonant system responses during or before the pulse overlap. These coherent artifacts have also been described in 2DES but remain less well-understood due to the complexity of 2DES and the relative novelty of the method. Here, we present 2DES results in two model nanocrystal samples, CdSe and CsPbI₃. We demonstrate non-resonant signals due to solvent response during the pulse overlap and resonant signals, which we assign to perturbed free induction decay (PFID), both before and during the pulse overlap. The simulations of the 2DES response functions at early and negative time delays reinforce the assignment of the negative time delay signals to PFID. Modeling reveals that the PFID signals will severely distort the initial picture of the resonant population dynamics. By including these effects in models of 2DES spectra, one is able to push forward the extraction of early time dynamics in 2DES.

Probing DNA structural heterogeneity by identifying conformational subensembles of a bicovalently bound cyanine dye

DNA is a re-configurable, biological information-storage unit, and much remains to be learned about its heterogeneous structural dynamics. For example, while it is known that molecular dyes templated onto DNA exhibit increased photostability, the mechanism by which the structural dynamics of DNA affect the dye photophysics remains unknown. Here, we use femtosecond, two-dimensional electronic spectroscopy measurements of a cyanine dye, Cy5, to probe local conformations in samples of single-stranded DNA (ssDNA-Cy5), double-stranded DNA (dsDNA-Cy5), and Holliday junction DNA (HJ-DNA-Cy5). A line shape analysis of the 2D spectra reveals a strong excitation-emission correlation present in only the dsDNA-Cy5 complex, which is a signature of inhomogeneous broadening. Molecular dynamics simulations support the conclusion that this inhomogeneous broadening arises from a nearly degenerate conformer found only in the dsDNA-Cy5 complex. These insights will support future studies on DNA's structural heterogeneity.

High-resolution two-dimensional electronic spectroscopy reveals the homogeneous line profile of chromophores solvated in nanoclusters

Doped clusters in the gas phase provide nanoconfined model systems for the study of system-bath interactions. To gain insight into interaction mechanisms between chromophores and their environment, the ensemble inhomogeneity has to be lifted and the homogeneous line profile must be accessed. However, such measurements are very challenging at the low particle densities and low signal levels in cluster beam experiments. Here, we dope cryogenic rare-gas clusters with phthalocyanine molecules and apply action-detected two-dimensional electronic spectroscopy to gain insight into the local molecule-cluster environment for solid and superfluid cluster species. The high-resolution homogeneous linewidth analysis provides a benchmark for the theoretical modelling of binding configurations and shows a promising route for high-resolution molecular two-dimensional spectroscopy.

Understanding the interaction of single chromophores with nanoparticles remains a challenging task in nanoscience. Here the authors provide insight into the interaction between isolated base-free phthalocyanine molecules and He and Ne nanoclusters in the gas phase using high-resolution two-dimensional spectroscopy.

Deciphering Photoinduced Charge Transfer Dynamics in a Cross-Linked Graphene-Dye Nanohybrid

The search for synthetic materials that mimic natural photosynthesis by converting solar energy into other more useful forms of energy is an ever-growing research endeavor. Graphene-based materials, with their exceptional electronic and optical properties, are exemplary candidates for high-efficiency solar energy harvesting devices. High photoactivity can be conveniently achieved by functionalizing graphene with small molecule organic semiconductors whose band-gaps can be tuned by structural modification, leading to interactions between the π-conjugated electronic systems in both the semiconductor and graphene. Here we investigate the ultrafast transient optical properties of a cross-linked graphene-dye (diphenyl-dithiophenediketopyrrolopyrrole) nanohybrid material, in which oligomers of the organic semiconductor dye are covalently bound to a random network of few-layer graphene flakes, and compare the results to those obtained for the reference dye monomer. Using a combination of ultrafast transient absorption and two-dimensional electronic spectroscopy, we provide substantial evidence for photoinduced charge transfer that occurs within 18 ps in the nanohybrid system. Notably, subpicosecond photoinduced torsional relaxation observed in the constituent dye monomer is absent in the cross-linked nanohybrid system. Through density functional theory calculations, we compare the competing effects of covalent bonding, increasing conjugation length, and the presence of multiple graphene flakes. We find evidence that the observed ultrafast charge transfer process occurs through a superexchange mechanism in which the oligomeric dye bridge provides virtual states enabling charge transfer between graphene-dye covalent bond sites.

Hidden vibronic and excitonic structure and vibronic coherence transfer in the bacterial reaction center

We report two-dimensional electronic spectroscopy (2DES) experiments on the bacterial reaction center (BRC) from purple bacteria, revealing hidden vibronic and excitonic structure. Through analysis of the coherent dynamics of the BRC, we identify multiple quasi-resonances between pigment vibrations and excitonic energy gaps, and vibronic coherence transfer processes that are typically neglected in standard models of photosynthetic energy transfer and charge separation. We support our assignment with control experiments on bacteriochlorophyll and simulations of the coherent dynamics using a reduced excitonic model of the BRC. We find that specific vibronic coherence processes can readily reveal weak exciton transitions. While the functional relevance of such processes is unclear, they provide a spectroscopic tool that uses vibrations as a window for observing excited state structure and dynamics elsewhere in the BRC via vibronic coupling. Vibronic coherence transfer reveals the upper exciton of the “special pair” that was weakly visible in previous 2DES experiments.

Core-Valence Attosecond Transient Absorption Spectroscopy of Polyatomic Molecules

Tracing ultrafast processes induced by interaction of light with matter is often very challenging. In molecular systems, the initially created electronic coherence becomes damped by the slow nuclear rearrangement on a femtosecond timescale which makes real-time observations of electron dynamics in molecules particularly difficult. In this work, we report an extension of the theory underlying the attosecond transient absorption spectroscopy (ATAS) for the case of molecules, including a full account for the coupled electron-nuclear dynamics in the initially created wave packet, and apply it to probe the oscillations of the positive charge created after outer-valence ionization of the propiolic acid molecule. By taking advantage of element-specific core-to-valence transitions induced by x-ray radiation, we show that the resolution of ATAS makes it possible to trace the dynamics of electron density with atomic spatial resolution.

Spectral Diffusion of Excitons in 3,4,9,10-Perylenetetracarboxylic-diimide (PTCDI) Thin Films

In this work, we study spectral diffusion of molecular excitons in thin films of 3,4,9,10-perylenetetracarboxylic-diimide by using two-dimensional electronic spectroscopy (2DES). Temperature dependence of the spectral diffusion is studied from 105 to 471 K by analyzing the center line slope (CLS) of the ground-state bleach in the 2DES signal. A significant acceleration of the decay of the CLS with increasing the temperature is observed, which cannot be explained by a linear system-bath coupling model with a harmonic bath. We propose an anharmonic coupling model as the underlying mechanism, in which the exciton energy gap fluctuations by a high-frequency intramolecular vibration are enhanced by coupling with a low-frequency phonon mode.

Characterization of the ultrafast spectral diffusion and vibronic coherence of TIPS-pentacene using 2D electronic spectroscopy

TIPS-pentacene is a small-molecule organic semiconductor that is widely used in optoelectronic devices. It has been studied intensely owing to its ability to undergo singlet fission. In this study, we aim to develop further understanding of the coupling between the electronic and nuclear degrees of freedom of TIPS-pentacene (TIPS-Pn). We measured and analyzed the 2D electronic spectra of TIPS-Pn in solutions. Using center line slope (CLS) analysis, we characterized the frequency-fluctuation correlation function of the 0-0 vibronic transition. Strong oscillations in the CLS values were observed for up to 5 ps with a frequency of 264 cm^-1, which are attributable to a large vibronic coupling with the TIPS-Pn ring-breathing vibrational mode. In addition, detailed analysis of the CLS values allowed us to retrieve two spectral diffusion lifetimes, which are attributed to the inertial and diffusive dynamics of solvent molecules. Amplitude beating analysis also uncovered couplings with another vibrational mode at 1173 cm^-1. The experimental results can be described using the displaced harmonic oscillator model. By comparing the CLS values of the simulated data with the experimental CLS values, we estimated a Huang-Rhys factor of 0.1 for the ring-breathing vibrational mode. The results demonstrated how CLS analysis can be a useful method for characterizing the strength of vibronic coupling.

Excitonic structure and charge separation in the heliobacterial reaction center probed by multispectral multidimensional spectroscopy

Photochemical reaction centers are the engines that drive photosynthesis. The reaction center from heliobacteria (HbRC) has been proposed to most closely resemble the common ancestor of photosynthetic reaction centers, motivating a detailed understanding of its structure-function relationship. The recent elucidation of the HbRC crystal structure motivates advanced spectroscopic studies of its excitonic structure and charge separation mechanism. We perform multispectral two-dimensional electronic spectroscopy of the HbRC and corresponding numerical simulations, resolving the electronic structure and testing and refining recent excitonic models. Through extensive examination of the kinetic data by lifetime density analysis and global target analysis, we reveal that charge separation proceeds via a single pathway in which the distinct A₀ chlorophyll a pigment is the primary electron acceptor. In addition, we find strong delocalization of the charge separation intermediate. Our findings have general implications for the understanding of photosynthetic charge separation mechanisms, and how they might be tuned to achieve different functional goals.

The primary energy conversion step in photosynthesis, charge separation, takes place in the reaction center. Here the authors investigate the heliobacterial reaction center using multispectral two-dimensional electronic spectroscopy, identifying the primary electron acceptor and revealing the charge separation mechanism.

Insights into Photosynthetic Energy Transfer Gained from Free-Energy Structure: Coherent Transport, Incoherent Hopping, and Vibrational Assistance Revisited

Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring the possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and the criteria by which the necessity of the vibrational assistance is considered.

Unraveling the internal conversion process within the Q-bands of a chlorophyll-like-system through surface-hopping molecular dynamics simulations

The non-radiative relaxation process within the Q-bands of chlorophylls represents a crucial preliminary step during the photosynthetic mechanism. Despite several experimental and theoretical efforts performed in order to clarify the complex dynamics characterizing this stage, a complete understanding of this mechanism is still far to be reached. In this study, non-adiabatic excited-state molecular dynamic simulations have been performed to model the non-radiative process within the Q-bands for a model system of chlorophylls. This system has been considered in the gas phase and then, to have a more representative picture of the environment, with implicit and mixed implicit-explicit solvation models. In the first part of this analysis, absorption spectra have been simulated for each model in order to guide the setup for the non-adiabatic excited-state molecular dynamic simulations. Then, non-adiabatic excited-state molecular dynamic simulations have been performed on a large set of independent trajectories and the population of the Q_x and Q_y states has been computed as the average of all the trajectories, estimating the rate constant for the process. Finally, with the aim of investigating the possible role played by the solvent in the Q_x-Q_y crossing mechanism, an essential dynamic analysis has been performed on the generated data, allowing one to find the most important motions during the simulated dynamics.

Observation of Ultrafast Coherence Transfer and Degenerate States with Polarization-Controlled Two-Dimensional Electronic Spectroscopy

Optical spectroscopy is a powerful tool to interrogate quantum states of matter. We present simulation results for the cross-polarized two-dimensional electronic spectra of the light-harvesting system LH2 of purple bacteria. We identify a spectral feature on the diagonal, which we assign to ultrafast coherence transfer between degenerate states. The implication for the interpretation of previous experiments on different systems and the potential use of this feature are discussed. In particular, we foresee that this kind of feature will be useful for identifying mixed degenerate states and for identifying the origin of symmetry breaking disorder in systems like LH2. Furthermore, this may help identify both vibrational and electronic states in biological systems such as proteins and solid-state materials such as hybrid perovskites.

Two-dimensional electronic Stark spectroscopy of a photosynthetic dimer

Stark spectroscopy, which measures changes in the linear absorption of a sample in the presence of an external DC electric field, is a powerful experimental tool for probing the existence of charge-transfer (CT) states in photosynthetic systems. CT states often have small transition dipole moments, making them insensitive to other spectroscopic methods, but are particularly sensitive to Stark spectroscopy due to their large permanent dipole moment. In a previous study, we demonstrated a new experimental method, two-dimensional electronic Stark spectroscopy (2DESS), which combines two-dimensional electronic spectroscopy (2DES) and Stark spectroscopy. In order to understand how the presence of CT states manifest in 2DESS, here, we perform computational modeling and calculations of 2DESS as well as 2DES and Stark spectra, studying a photosynthetic dimer inspired by the photosystem II reaction center. We identify specific cases where qualitatively different sets of system parameters produce similar Stark and 2DES spectra but significantly different 2DESS spectra, showing the potential for 2DESS to aid in identifying CT states and their coupling to excitonic states.

Biomimetic Nanoarchitectures for Light Harvesting: Self-Assembly of Pyropheophorbide-Peptide Conjugates

The biological light-harvesting process offers an unlimited source of inspiration. The high level of control, adaptation capability, and efficiency challenge humankind to create artificial biomimicking nanoarchitectures with the same performances to respond to our energy needs. Here, in the extensive search for design principles at the base of efficient artificial light harvesters, an approach based on self-assembly of pigment-peptide conjugates is proposed. The solvent-driven and controlled aggregation of the peptide moieties promotes the formation of a dense network of interacting pigments, giving rise to an excitonic network characterized by intense and spectrally wide absorption bands. The ultrafast dynamics of the nanosystems studied through two-dimensional electronic spectroscopy reveals that the excitation energy is funneled in an ultrafast time range (hundreds of femtoseconds) to a manifold of long-living dark states, thus suggesting the considerable potentiality of the systems as efficient harvesters.

Exploiting chemistry and molecular systems for quantum information science

The power of chemistry to prepare new molecules and materials has driven the quest for new approaches to solve problems having global societal impact, such as in renewable energy, healthcare and information science. In the latter case, the intrinsic quantum nature of the electronic, nuclear and spin degrees of freedom in molecules offers intriguing new possibilities to advance the emerging field of quantum information science. In this Perspective, which resulted from discussions by the co-authors at a US Department of Energy workshop held in November 2018, we discuss how chemical systems and reactions can impact quantum computing, communication and sensing. Hierarchical molecular design and synthesis, from small molecules to supramolecular assemblies, combined with new spectroscopic probes of quantum coherence and theoretical modelling of complex systems, offer a broad range of possibilities to realize practical quantum information science applications.

Aromaticity-Photovoltaic Property Relationship of Triphenylamine-Based D-π-A Dyes: Leads from DFT Calculations

D-π-A-based dyes find a wide range of applications in molecular electronics and photovoltaics in general and dye-sensitized solar cells (DSSC) in particular. We speculated whether there exists a relationship between the degree of aromaticity of the π-spacers used in the D-π-A type dyes and their structural, electronic, energetic, photophysical, and intramolecular charge transfer properties. Triphenylamine (TPA) and cyanoacrylic acid (CAA) have been chosen as the donor and acceptor, respectively. In order to carry out the investigation systematically the π-spacers have been logically chosen based on their experimental resonance energies, which follows the order, furan < pyrrole < thiophene < pyridine < benzene. All the properties have been discussed based on the degree of aromaticity of the π-spacers. Geometric properties such as dihedral angles and bond lengths have been discussed extensively. Energy levels of the frontier molecular orbitals, electrochemical properties, namely, ground and excited state oxidation potentials (GSOP/ESOP), and change in Gibbs free energy for electron injection and regeneration (ΔG_inj/ΔG_reg) have also been evaluated. Photophysical properties like wavelength of maximum absorption (λ_max), oscillator strength (f), light harvesting efficiency (LHE), and intramolecular charge transfer properties, viz., charge transfer distance (D_CT), fraction of charge transferred (q_CT), and change in dipole moment (μ_CT) have been assessed. The adsorption characteristics of dye with (TiO₂)₉ nanocluster have been studied along with their optical properties. Results reveal that the nature of the relationship between the aforementioned properties and the extent of aromaticity of the π-spacers is inherently multifaceted. It thus turns out that it is highly difficult to quantify the relationship. These properties of D-π₁-π₂-A molecules can be regarded to be arising from two groups, namely, π-spacers with lower and higher resonance energies. This results in a natural trade-off in selection of competing properties. The qualitative aromaticity photovoltaic property relationship thus obtained may serve as a guide to tailor-design various properties of D-π-A type dyes for application in the intramolecular charge transfer devices.

Interference among Multiple Vibronic Modes in Two-Dimensional Electronic Spectroscopy

Vibronic coupling between electronic and vibrational states in molecules plays a critical role in most photo-induced phenomena. Many key details about a molecule’s vibronic coupling are hidden in linear spectroscopic measurements, and therefore nonlinear optical spectroscopy methods such as two-dimensional electronic spectroscopy (2D ES) have become more broadly adopted. A single vibrational mode of a molecule leads to a Franck–Condon progression of peaks in a 2D spectrum. Each peak oscillates as a function of the waiting time, and Fourier transformation can produce a spectral slice known as a ‘beating map’ at the oscillation frequency. The single vibrational mode produces a characteristic peak structure in the beating map. Studies of single modes have limited utility, however, because most molecules have numerous vibrational modes that couple to the electronic transition. Interactions or interference among the modes may lead to complicated peak patterns in each beating map. Here, we use lineshape-function theory to simulate 2D ES arising from a system having multiple vibrational modes. The simulations reveal that the peaks in each beating map are affected by all of the vibrational modes and therefore do not isolate a single mode, which was anticipated.

Synergistic Approach of Ultrafast Spectroscopy and Molecular Simulations in the Characterization of Intramolecular Charge Transfer in Push-Pull Molecules

The comprehensive characterization of Intramolecular Charge Transfer (ICT) stemming in push-pull molecules with a delocalized π-system of electrons is noteworthy for a bespoke design of organic materials, spanning widespread applications from photovoltaics to nanomedicine imaging devices. Photo-induced ICT is characterized by structural reorganizations, which allows the molecule to adapt to the new electronic density distribution. Herein, we discuss recent photophysical advances combined with recent progresses in the computational chemistry of photoactive molecular ensembles. We focus the discussion on femtosecond Transient Absorption Spectroscopy (TAS) enabling us to follow the transition from a Locally Excited (LE) state to the ICT and to understand how the environment polarity influences radiative and non-radiative decay mechanisms. In many cases, the charge transfer transition is accompanied by structural rearrangements, such as the twisting or molecule planarization. The possibility of an accurate prediction of the charge-transfer occurring in complex molecules and molecular materials represents an enormous advantage in guiding new molecular and materials design. We briefly report on recent advances in ultrafast multidimensional spectroscopy, in particular, Two-Dimensional Electronic Spectroscopy (2DES), in unraveling the ICT nature of push-pull molecular systems. A theoretical description at the atomistic level of photo-induced molecular transitions can predict with reasonable accuracy the properties of photoactive molecules. In this framework, the review includes a discussion on the advances from simulation and modeling, which have provided, over the years, significant information on photoexcitation, emission, charge-transport, and decay pathways. Density Functional Theory (DFT) coupled with the Time-Dependent (TD) framework can describe electronic properties and dynamics for a limited system size. More recently, Machine Learning (ML) or deep learning approaches, as well as free-energy simulations containing excited state potentials, can speed up the calculations with transferable accuracy to more complex molecules with extended system size. A perspective on combining ultrafast spectroscopy with molecular simulations is foreseen for optimizing the design of photoactive compounds with tunable properties.

Measuring Ultrafast Spectral Diffusion and Correlation Dynamics by Two-Dimensional Electronic Spectroscopy

The frequency fluctuation correlation function (FFCF) measures the spectral diffusion of a state's transition while the frequency fluctuation cross-correlation function (FXCF) measures the correlation dynamics between the transitions of two separate states. These quantities contain a wealth of information on how the chromophores or excitonic states interact and couple with its environment and with each other. We summarize the experimental implementations and theoretical considerations of using two-dimensional electronic spectroscopy to characterize FFCFs and FXCFs. Applications can be found in systems such as the chlorophyll pigment molecules in light-harvesting complexes and CdSe nanomaterials.

Ligand-Enhanced Energy Transport in Nanocrystal Solids Viewed with Two-Dimensional Electronic Spectroscopy

We examine CdSe NCs functionalized with the exciton-delocalizing ligand phenyldithiocarbamate (PDTC) using two-dimensional electronic spectroscopy (2DES). PDTC forms hybrid molecular orbitals with CdSe's valence band that relax hole spatial confinement and create potential for enhanced exciton migration in NC solids. We find PDTC broadens the intrinsic line width of individual NCs in solution by ∼30 meV, which we ascribe to modulation of NC band edge states by ligand motion. In PDTC-exchanged solids, photoexcited excitons are mobile and rapidly move to low-energy NC sites over ∼30 ps. We also find placing excitons into high-energy states can accelerate their rate of migration by over an order of magnitude, which we attribute to enhanced spatial delocalization of these states that improves inter-NC wave function overlap. Our work demonstrates that NC surface ligands can actively facilitate inter-NC energy transfer and highlights principles to consider when designing ligands for this application.

Optical Gain from Biexcitons in CsPbBr3 Nanocrystals Revealed by Two-dimensional Electronic Spectroscopy

Perovskite semiconductor nanocrystals (NCs) exhibit highly efficient optical gain, which is promising for laser applications. However, the intrinsic mechanism of optical gain in perovskite NCs, particularly whether more than one exciton per NCs is required, remains poorly understood. Here, we use two-dimensional electronic spectroscopy to resonantly probe the interplay between near-band-edge transitions during the buildup of optical gain in CsPbBr₃ NCs. We find compelling evidence to conclude that optical gain in CsPbBr₃ NCs is generated through stimulated emission from strongly interacting biexcitons. The threshold is largely determined by the competition between stimulated emission from biexcitons and excited-state absorption from single exciton to biexciton states. The findings in this work may guide future explorations of NC materials with low-threshold optical gain.

Multispectral multidimensional spectrometer spanning the ultraviolet to the mid-infrared

Multidimensional spectroscopy is the optical analog to nuclear magnetic resonance, probing dynamical processes with ultrafast time resolution. At optical frequencies, the technical challenges of multidimensional spectroscopy have hindered its progress until recently, where advances in laser sources and pulse-shaping have removed many obstacles to its implementation. Multidimensional spectroscopy in the visible and infrared (IR) regimes has already enabled respective advances in our understanding of photosynthesis and the structural rearrangements of liquid water. A frontier of ultrafast spectroscopy is to extend and combine multidimensional techniques and frequency ranges, which have been largely restricted to operating in the distinct visible or IR regimes. By employing two independent amplifiers seeded by a single oscillator, it is straightforward to span a wide range of time scales (femtoseconds to seconds), all of which are often relevant to the most important energy conversion and catalysis problems in chemistry, physics, and materials science. Complex condensed phase systems have optical transitions spanning the ultraviolet (UV) to the IR and exhibit dynamics relevant to function on time scales of femtoseconds to seconds and beyond. We describe the development of the Multispectral Multidimensional Nonlinear Spectrometer (MMDS) to enable studies of dynamical processes in atomic, molecular, and material systems spanning femtoseconds to seconds, from the UV to the IR regimes. The MMDS employs pulse-shaping methods to provide an easy-to-use instrument with an unprecedented spectral range that enables unique combination spectroscopies. We demonstrate the multispectral capabilities of the MMDS on several model systems.

Primary processes in the bacterial reaction center probed by two-dimensional electronic spectroscopy

In the initial steps of photosynthesis, reaction centers convert solar energy to stable charge-separated states with near-unity quantum efficiency. The reaction center from purple bacteria remains an important model system for probing the structure-function relationship and understanding mechanisms of photosynthetic charge separation. Here we perform 2D electronic spectroscopy (2DES) on bacterial reaction centers (BRCs) from two mutants of the purple bacterium Rhodobacter capsulatus, spanning the Q _y absorption bands of the BRC. We analyze the 2DES data using a multiexcitation global-fitting approach that employs a common set of basis spectra for all excitation frequencies, incorporating inputs from the linear absorption spectrum and the BRC structure. We extract the exciton energies, resolving the previously hidden upper exciton state of the special pair. We show that the time-dependent 2DES data are well-represented by a two-step sequential reaction scheme in which charge separation proceeds from the excited state of the special pair (P*) to P⁺H_A^- via the intermediate P⁺B_A^- When inhomogeneous broadening and Stark shifts of the B* band are taken into account we can adequately describe the 2DES data without the need to introduce a second charge-separation pathway originating from the excited state of the monomeric bacteriochlorophyll B_A*.

Ultrafast energy transfer within the photosystem II core complex

We report 2D electronic spectroscopy on the photosystem II core complex (PSII CC) at 77 K under different polarization conditions. A global analysis of the high time-resolution 2D data shows rapid, sub-100 fs energy transfer within the PSII CC. It also reveals the 2D spectral signatures of slower energy equilibration processes occurring on several to hundreds of picosecond time scales that are consistent with previous work. Using a recent structure-based model of the PSII CC [Y. Shibata, S. Nishi, K. Kawakami, J. R. Shen and T. Renger, J. Am. Chem. Soc., 2013, 135, 6903], we simulate the energy transfer in the PSII CC by calculating auxiliary time-resolved fluorescence spectra. We obtain the observed sub-100 fs evolution, even though the calculated electronic energy shows almost no dynamics at early times. On the other hand, the electronic-vibrational interaction energy increases considerably over the same time period. We conclude that interactions with vibrational degrees of freedom not only induce population transfer between the excitonic states in the PSII CC, but also reshape the energy landscape of the system. We suggest that the experimentally observed ultrafast energy transfer is a signature of excitonic-polaron formation.

Mechanistic insight into internal conversion process within Q-bands of chlorophyll a

The non-radiative relaxation of the excitation energy from higher energy states to the lowest energy state in chlorophylls is a crucial preliminary step for the process of photosynthesis. Despite the continuous theoretical and experimental efforts to clarify the ultrafast dynamics of this process, it still represents the object of an intense investigation because the ultrafast timescale and the congestion of the involved states makes its characterization particularly challenging. Here we exploit 2D electronic spectroscopy and recently developed data analysis tools to provide more detailed insights into the mechanism of internal conversion within the Q-bands of chlorophyll a. The measurements confirmed the timescale of the overall internal conversion rate (170 fs) and captured the presence of a previously unidentified ultrafast (40 fs) intermediate step, involving vibronic levels of the lowest excited state.

Triplet Separation Drives Singlet Fission after Femtosecond Correlated Triplet Pair Production in Rubrene

Singlet fission, a multistep molecular process in which one photon generates two triplet excitons, holds great technological promise. Here, by applying a combination of transient transmittance and two-dimensional electronic spectroscopy with 5 fs laser pulses, we resolve the full set of fission steps before the onset of spin dephasing. In addition to its role as a viable singlet fission material, single-crystalline rubrene is selected because its energetics and transition dipole alignment uniquely allow for the unambiguous identification of the various fission steps through their contributions to distinct spectroscopic features. The measurements reveal that the neighboring correlated triplet pair achieves its maximum population within 20 fs. Subsequent growth of the triplet signal on picosecond time scales is attributable to spatial separation of the triplets, proceeding nonadiabatically through weakly coupled but near-resonant states. As such, we provide evidence in crystalline rubrene for a singlet fission step that, until now, has not been convincingly observed.

Redfield Treatment of Multipathway Electron Transfer in Artificial Photosynthetic Systems

Coherence effects on electron transfer in a series of symmetric and asymmetric two-, three-, four-, and five-site molecular model systems for photosystem I in cyanobacteria and green plants were studied. The total site energies of the electronic Hamiltonian were calculated using the density functional theory (DFT) formalism and included the zero point vibrational energies of the electron donors and acceptors. Site energies and couplings were calculated using a polarizable continuum model to represent various solvent environments, and the site-to-site couplings were calculated using fragment charge difference methods at the DFT level of theory. The Redfield formalism was used to propagate the electron density from the donors to the acceptors, incorporating relaxation and dephasing effects to describe the electron transfer processes. Changing the relative energies of the donor, intermediate acceptor, and final acceptor molecules in these assemblies has profound effects on the electron transfer rates as well as on the amplitude of the quantum oscillations observed. Increasing the ratio of a particular energy gap to the electronic coupling for a given pair of states leads to weaker quantum oscillations between sites. Biasing the intermediate acceptor energies to slightly favor one pathway leads to a general decrease in electron transfer yield.

Conformational Homogeneity in the Pr Isomer of Phytochrome Cph1

Numerous time-resolved studies of the P_r to P_fr photoisomerization in phytochrome Cph1 have revealed multiphasic excited-state decay kinetics. It remains unclear whether these kinetics arise from multiple ground-state conformational subpopulations or from a single ground-state conformation that undergoes an excited-state photoisomerization process-either branching on the excited state or relaxing through multiple sequential intermediates. Many studies have attempted to resolve this debate by fitting the measured dynamics to proposed kinetic models, arriving at different conclusions. Here we probe spectral signatures of ground-state heterogeneity of P_r. Two-dimensional electronic spectra display negligible inhomogeneous line broadening, and vibrational coherence spectra extracted from transient absorption measurements do not contain nodes and phase shifts at the fluorescence maximum. These spectroscopic results support the homogeneous model, in which the primary photochemical transformation of P_r to Lumi-R occurs adiabatically on the excited-state potential energy surface.

Two-Dimensional Electronic Stark Spectroscopy

Characterizing ultrafast energy and charge transfer is important for understanding a wide range of systems, from natural photosynthetic complexes to organic photovoltaics. Distinguishing the kinetic processes of energy transfer and charge separation in such systems is challenging due to the lack of clear spectral signatures of charge transfer states, which are typically nonradiative. Stark spectroscopy has proven to be a valuable method for uncovering charge transfer states. Here we extend the dimensionality of Stark spectroscopy to perform two-dimensional electronic Stark spectroscopy. We demonstrate the method on TIPS-pentacene in 3-methylpentane at 77 K. The additional frequency dimension of two-dimensional Stark spectroscopy promises to enable the identification of charge transfer states, their coupling to other charge transfer and exciton states, and their involvement in charge separation processes.

Two-Dimensional Spectroscopy of Chlorophyll a Excited-State Equilibration in Light-Harvesting Complex II

Excited-state relaxation dynamics and energy-transfer processes in the chlorophyll a (Chl a) manifold of the light-harvesting complex II (LHCII) were examined at physiological temperature using femtosecond two-dimensional electronic spectroscopy (2DES). The experiments were done under conditions free from singlet-singlet annihilation and anisotropic decay. Energy transfer between the different domains of the Chl a manifold was found to proceed on time scales from hundreds of femtoseconds to five picoseconds, before reaching equilibration. No component slower than 10 ps was observed in the spectral equilibration dynamics. We clearly observe the bidirectional (uphill and downhill) energy transfer of the equilibration process between excited states. This bidirectional energy flow, although implicit in the modeling and simulation of the EET processes, has not been observed in any prior transient absorption studies. Furthermore, we identified the spectral forms associated with the different energy transfer lifetimes in the equilibration process.

Fast, Accurate Simulation of Polaron Dynamics and Multidimensional Spectroscopy by Multiple Davydov Trial States

By employing the Dirac-Frenkel time-dependent variational principle, we study the dynamical properties of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling. A linear combination of the Davydov D1 (D2) ansatz, referred to as the "multi-D1 ansatz" ("multi-D2 ansatz"), is used as the trial state with enhanced accuracy but without sacrificing efficiency. The time evolution of the exciton probability is found to be in perfect agreement with that of the hierarchy equations of motion, demonstrating the promise the multiple Davydov trial states hold as an efficient, robust description of dynamics of complex quantum systems. In addition to the linear absorption spectra computed for both diagonal and off-diagonal cases, for the first time, 2D spectra have been calculated for systems with off-diagonal exciton-phonon coupling by employing the multiple D2 ansatz to compute the nonlinear response function, testifying to the great potential of the multiple D2 ansatz for fast, accurate implementation of multidimensional spectroscopy. It is found that the signal exhibits a single peak for weak off-diagonal coupling, while a vibronic multipeak structure appears for strong off-diagonal coupling.

Dark States in the Light-Harvesting complex 2 Revealed by Two-dimensional Electronic Spectroscopy

Energy transfer and trapping in the light harvesting antennae of purple photosynthetic bacteria is an ultrafast process, which occurs with a quantum efficiency close to unity. However the mechanisms behind this process have not yet been fully understood. Recently it was proposed that low-lying energy dark states, such as charge transfer states and polaron pairs, play an important role in the dynamics and directionality of energy transfer. However, it is difficult to directly detect those states because of their small transition dipole moment and overlap with the B850/B870 exciton bands. Here we present a new experimental approach, which combines the selectivity of two-dimensional electronic spectroscopy with the availability of genetically modified light harvesting complexes, to reveal the presence of those dark states in both the genetically modified and the wild-type light harvesting 2 complexes of Rhodopseudomonas palustris. We suggest that Nature has used the unavoidable charge transfer processes that occur when LH pigments are concentrated to enhance and direct the flow of energy.

Simulation of femtosecond two-dimensional electronic spectra of conical intersections

We have simulated femtosecond two-dimensional (2D) electronic spectra for an excited-state conical intersection using the wave-function version of the equation-of-motion phase-matching approach. We show that 2D spectra at fixed values of the waiting time provide information on the structure of the vibronic eigenstates of the conical intersection, while the evolution of the spectra with the waiting time reveals predominantly ground-state wave-packet dynamics. The results show that 2D spectra of conical intersection systems differ significantly from those obtained for chromophores with well separated excited-state potential-energy surfaces. The spectral signatures which can be attributed to conical intersections are discussed.

Optimal Energy Transfer in Light-Harvesting Systems

Photosynthesis is one of the most essential biological processes in which specialized pigment-protein complexes absorb solar photons, and with a remarkably high efficiency, guide the photo-induced excitation energy toward the reaction center to subsequently trigger its conversion to chemical energy. In this work, we review the principles of optimal energy transfer in various natural and artificial light harvesting systems. We begin by presenting the guiding principles for optimizing the energy transfer efficiency in systems connected to dissipative environments, with particular attention paid to the potential role of quantum coherence in light harvesting systems. We will comment briefly on photo-protective mechanisms in natural systems that ensure optimal functionality under varying ambient conditions. For completeness, we will also present an overview of the charge separation and electron transfer pathways in reaction centers. Finally, recent theoretical and experimental progress on excitation energy transfer, charge separation, and charge transport in artificial light harvesting systems is delineated, with organic solar cells taken as prime examples.

Two-Color Nonlinear Spectroscopy for the Rapid Acquisition of Coherent Dynamics

There has been considerable recent interest in the observation of coherent dynamics in photosynthetic systems by 2D electronic spectroscopy (2DES). In particular, coherences that persist during the "waiting time" in a 2DES experiment have been attributed to electronic, vibrational, and vibronic origins in various systems. The typical method for characterizing these coherent dynamics requires the acquisition of 2DES spectra as a function of waiting time, essentially a 3DES measurement. Such experiments require lengthy data acquisition times that degrade the signal-to-noise of the recorded coherent dynamics. We present a rapid and high signal-to-noise pulse-shaping-based approach for the characterization of coherent dynamics. Using chlorophyll a, we demonstrate that this method retains much of the information content of a 3DES measurement and provides insight into the physical origin of the coherent dynamics, distinguishing between ground and excited state coherences. It also enables high resolution determination of ground and excited state frequencies.

Critical assessment of the emission spectra of various photosystem II core complexes

We evaluate low-temperature (low-T) emission spectra of photosystem II core complexes (PSII-cc) previously reported in the literature, which are compared with emission spectra of PSII-cc obtained in this work from spinach and for dissolved PSII crystals from Thermosynechococcus (T.) elongatus. This new spectral dataset is used to interpret data published on membrane PSII (PSII-m) fragments from spinach and Chlamydomonas reinhardtii, as well as PSII-cc from T. vulcanus and intentionally damaged PSII-cc from spinach. This study offers new insight into the assignment of emission spectra reported on PSII-cc from different organisms. Previously reported spectra are also compared with data obtained at different saturation levels of the lowest energy state(s) of spinach and T. elongatus PSII-cc via hole burning in order to provide more insight into emission from bleached and/or photodamaged complexes. We show that typical low-T emission spectra of PSII-cc (with closed RCs), in addition to the 695 nm fluorescence band assigned to the intact CP47 complex (Reppert et al. J Phys Chem B 114:11884-11898, 2010), can be contributed to by several emission bands, depending on sample quality. Possible contributions include (i) a band near 690-691 nm that is largely reversible upon temperature annealing, proving that the band originates from CP47 with a bleached low-energy state near 693 nm (Neupane et al. J Am Chem Soc 132:4214-4229, 2010; Reppert et al. J Phys Chem B 114:11884-11898, 2010); (ii) CP43 emission at 683.3 nm (not at 685 nm, i.e., the F685 band, as reported in the literature) (Dang et al. J Phys Chem B 112:9921-9933, 2008; Reppert et al. J Phys Chem B 112:9934-9947, 2008); (iii) trap emission from destabilized CP47 complexes near 691 nm (FT1) and 685 nm (FT2) (Neupane et al. J Am Chem Soc 132:4214-4229, 2010); and (iv) emission from the RC pigments near 686-687 nm. We suggest that recently reported emission of single PSII-cc complexes from T. elongatus may not represent intact complexes, while those obtained for T. elongatus presented in this work most likely represent intact PSII-cc, since they are nearly indistinguishable from emission spectra obtained for various PSII-m fragments.