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

Non-Hermitian Hamiltonian Approach for Two-Dimensional Coherent Spectra of Driven Systems

Two-dimensional coherent spectroscopy (2DCS) offers significant advantages in terms of high temporal and frequency resolutions and a signal-to-noise ratio. Until now, the response-function (RF) formalism has been the prevalent theoretical description. In this study, we compare the non-Hermitian Hamiltonian (NHH) method with the RF formalism in a three-level system with a constant control field. We obtain the signals from both approaches and compare their population dynamics and 2DCS. We propose quasi-Green functions for the NHH method, which allows all dominant Liouville paths to be inferred. We further simulated the 2DCS of Rh(CO)2C5H7O2 (RDC) dissolved in hexane with the NHH method, which is in good agreement with the previous experiments. Although the NHH method overestimates relaxations, it provides all important paths by analytical solutions, which are different from the four paths used in the RF formalism. Our results demonstrate that the NHH method is more suitable than the RF formalism for investigating the systems, including relaxation and control fields via the 2DCS.

Linear Dichroism Microscopy Resolves Competing Structural Models of a Synthetic Light-Harvesting Complex

The initial stages of photosynthesis in light-harvesting antennae, driven by excitonic energy transport, have inspired the design of artificial light-harvesting complexes. Double-walled nanotubes (DWNTs) formed from the cyanine dye C8S3 provide a robust, self-assembled system that mimics natural chlorosomes in both structure and optical properties. Two competing molecular packing models─bricklayer (BL) and herringbone (HB)─have been proposed to explain the structural and optical characteristics of these DWNTs. This study resolves the debate by combining theoretical analysis with advanced polarization-resolved wide-field photoluminescence microscopy. Quantum-classical simulations reveal reduced linear dichroism (LDr) as a decisive parameter for distinguishing between the models. Experimental measurements of single DWNTs yielded LDr values as high as 0.93, strongly favoring the BL model. The BL model's unique excitonic patterns, dominated by negative couplings among individual chromophores, generate superradiant exciton states with transition dipoles preferentially aligned along the nanotube axis. In contrast, the HB model's mixed positive and negative couplings produce destructive interference, leading to a weaker alignment of transition dipoles. Our approach deepens the understanding of the structure-property relationships in self-assembled systems and demonstrates the potential of slip-stacking engineering to fine-tune excitonic properties for artificial light-harvesting applications.

The first step of cyanine dye self-assembly: Dimerization

Self-assembling amphiphilic cyanine dyes, such as C8S3, are promising candidates for energy storage and optoelectronic applications due to their efficient energy transport properties. C8S3 is known to self-assemble in water into double-walled J-aggregates. Thus far, the molecular self-assembly steps remain shrouded in mystery. Here, we employ a multiscale approach to unravel the first self-assembly step: dimerization. Our multiscale approach combines molecular dynamics simulations with quantum chemistry calculations to obtain a Frenkel exciton Hamiltonian, which we then use in spectral calculations to determine the absorption and two-dimensional electronic spectra of C8S3 monomer and dimer systems. We model these systems solvated in both water and methanol, validating our model with experiments in methanol solution. Our theoretical results predict a measurable anisotropy decay upon dimerization, which is experimentally confirmed. Our approach provides a tool for the experimental probing of dimerization. Moreover, molecular dynamics simulations reveal that the dimer conformation is characterized by the interaction between the hydrophobic aliphatic tails rather than the π-π stacking previously reported for other cyanine dyes. Our results pave the way for future research into the mechanism of molecular self-assembly in similar light-harvesting complexes, offering valuable insights for understanding and optimizing self-assembly processes for various (nano)technological applications.

Application of the Time-Domain Multichromophoric Fluorescence Resonant Energy Transfer Method in the NISE Programme

We present the implementation of the time-domain multichromophoric fluorescence resonant energy transfer (TC-MCFRET) approach in the numerical integration of the Schrödinger equation (NISE) program. This method enables the efficient simulation of incoherent energy transfer between distinct segments within large and complex molecular systems, such as photosynthetic complexes. Our approach incorporates a segmentation protocol to divide these systems into manageable components and a modified thermal correction to ensure detailed balance. The implementation allows us to calculate the energy transfer rate in the NISE program systematically and easily. To validate our method, we applied it to a range of test cases, including parallel linear aggregates and biologically relevant systems like the B850 rings from LH2 and the Fenna-Matthews-Olson complex. Our results show excellent agreement with previous studies, demonstrating the accuracy and efficiency of our TD-MCFRET method. We anticipate that this approach will be widely applicable to the calculation of energy transfer rates in other large molecular systems and will pave the way for future simulations of multidimensional electronic spectra.

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.

Photoelectrochemical Two-Dimensional Electronic Spectroscopy (PEC2DES) of Photosystem I: Charge Separation Dynamics Hidden in a Multichromophoric Landscape

We present a nonlinear spectroelectrochemical technique to investigate photosynthetic protein complexes. The PEC2DES setup combines photoelectrochemical detection (PEC) that selectively probes the protein photogenerated charges output with two-dimensional electronic spectroscopy (2DES) excitation that spreads the nonlinear optical response of the system in an excitation-detection map. PEC allows us to distinguish the contribution of charge separation (CS) from other de-excitation pathways, whereas 2DES allows us to disentangle congested spectral bands and evaluate the exciton dynamics (decays and coherences) of the photosystem complex. We have developed in operando phase-modulated 2DES by measuring the photoelectrochemical reaction rate in a biohybrid electrode functionalized with a plant photosystem complex I-light harvesting complex I (PSI-LHCI) layer. Optimizing the photoelectrochemical current signal yields reliable linear spectra unequivocally associated with PSI-LHCI. The 2DES signal is validated by nonlinear features like the characteristic vibrational coherence at 750 cm-1. However, no energy transfer dynamics is observed within the 450 fs experimental window. These intriguing results are discussed in the context of incoherent mixing resulting in reduced nonlinear contrast for multichromophoric complexes, such as the 160 chlorophyll PSI. The presented PEC2DES method identifies generated charges unlike purely optical 2DES and opens the way to probe the CS channel in multichromophoric complexes.

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.

PigmentHunter: A point-and-click application for automated chlorophyll-protein simulations

Chlorophyll proteins (CPs) are the workhorses of biological photosynthesis, working together to absorb solar energy, transfer it to chemically active reaction centers, and control the charge-separation process that drives its storage as chemical energy. Yet predicting CP optical and electronic properties remains a serious challenge, driven by the computational difficulty of treating large, electronically coupled molecular pigments embedded in a dynamically structured protein environment. To address this challenge, we introduce here an analysis tool called PigmentHunter, which automates the process of preparing CP structures for molecular dynamics (MD), running short MD simulations on the nanoHUB.org science gateway, and then using electrostatic and steric analysis routines to predict optical absorption, fluorescence, and circular dichroism spectra within a Frenkel exciton model. Inter-pigment couplings are evaluated using point-dipole or transition-charge coupling models, while site energies can be estimated using both electrostatic and ring-deformation approaches. The package is built in a Jupyter Notebook environment, with a point-and-click interface that can be used either to manually prepare individual structures or to batch-process many structures at once. We illustrate PigmentHunter's capabilities with example simulations on spectral line shapes in the light harvesting 2 complex, site energies in the Fenna-Matthews-Olson protein, and ring deformation in photosystems I and II.

Observation of Dark States in Two-Dimensional Electronic Spectra of Chlorosomes

Observations of low-lying dark states in several photosynthetic complexes challenge our understanding of the mechanisms behind their efficient energy transfer processes. Computational models are necessary for providing novel insights into the nature and function of dark states, especially since these are not directly accessible in spectroscopy experiments. Here, we will focus on signatures of dark-type states in chlorosomes, a light-harvesting complex from green sulfur bacteria well-known for uniting a broad absorption band with very efficient energy transfer. In agreement with experiments, our simulations of two-dimensional electronic spectra capture the ultrafast exciton transfer occurring in 100s of femtoseconds within a single chlorosome cylinder. The sub-100 fs process corresponds to relaxation within the single-excitation manifold in a single chlorosome tube, where all initially created populations in the bright exciton states are quickly transferred to dark-type exciton states. Structural inhomogeneities on the local scale cause a redistribution of the oscillator strength, leading to the emergence of these dark-type exciton states, which dominate ultrafast energy transfer. The presence of the dark-type exciton states suppresses energy loss from an isolated chlorosome via fluorescence quenching, as observed experimentally. Our results further question whether relaxation to dark-exciton states is a leading process or merely competes with transfer to the baseplate within the photosynthetic apparatus of green sulfur bacteria.

High-Resolution Frequency-Domain Spectroscopic and Modeling Studies of Photosystem I (PSI), PSI Mutants and PSI Supercomplexes

Photosystem I (PSI) is one of the two main pigment-protein complexes where the primary steps of oxygenic photosynthesis take place. This review describes low-temperature frequency-domain experiments (absorption, emission, circular dichroism, resonant and non-resonant hole-burned spectra) and modeling efforts reported for PSI in recent years. In particular, we focus on the spectral hole-burning studies, which are not as common in photosynthesis research as the time-domain spectroscopies. Experimental and modeling data obtained for trimeric cyanobacterial Photosystem I (PSI3), PSI3 mutants, and PSI3-IsiA18 supercomplexes are analyzed to provide a more comprehensive understanding of their excitonic structure and excitation energy transfer (EET) processes. Detailed information on the excitonic structure of photosynthetic complexes is essential to determine the structure-function relationship. We will focus on the so-called "red antenna states" of cyanobacterial PSI, as these states play an important role in photochemical processes and EET pathways. The high-resolution data and modeling studies presented here provide additional information on the energetics of the lowest energy states and their chlorophyll (Chl) compositions, as well as the EET pathways and how they are altered by mutations. We present evidence that the low-energy traps observed in PSI are excitonically coupled states with significant charge-transfer (CT) character. The analysis presented for various optical spectra of PSI3 and PSI3-IsiA18 supercomplexes allowed us to make inferences about EET from the IsiA18 ring to the PSI3 core and demonstrate that the number of entry points varies between sample preparations studied by different groups. In our most recent samples, there most likely are three entry points for EET from the IsiA18 ring per the PSI core monomer, with two of these entry points likely being located next to each other. Therefore, there are nine entry points from the IsiA18 ring to the PSI3 trimer. We anticipate that the data discussed below will stimulate further research in this area, providing even more insight into the structure-based models of these important cyanobacterial photosystems.

Electric Field Susceptibility of Chlorophyll c Leads to Unexpected Excitation Dynamics in the Major Light-Harvesting Complex of Diatoms

Diatoms are one of the most abundant photosynthetic organisms on earth and contribute largely to atmospheric oxygen production. They contain fucoxanthin and chlorophyll-a/c binding proteins (FCPs) as light-harvesting complexes with a remarkable adaptation to the fluctuating light on ocean surfaces. To understand the basis of the photosynthetic process in diatoms, the excitation energy funneling within FCPs must be probed. A state-of-the-art multiscale analysis within a quantum mechanics/molecular mechanics framework has been employed. To this end, the chlorophyll (Chl) excitation energies within the FCP complex from the diatom Phaeodactylum tricornutum have been determined. The Chl-c excitation energies were found to be 5-fold more susceptible to electric fields than those of Chl-a pigments and thus are significantly lower in FCP than in organic solvents. This finding challenges the general belief that the excitation energy of Chl-c is always higher than that of Chl-a in FCP proteins and reveals that Chl-c molecules are much more sensitive to electric fields within protein scaffolds than in Chl-a pigments. The analysis of the linear absorption spectrum and the two-dimensional electronic spectra of the FCP complex strongly supports these findings and allows us to study the excitation transfer within the FCP complex.

Watching the Interplay between Photoinduced Ultrafast Charge Dynamics and Nuclear Vibrations

Here is presented the ultrafast hole-electron dynamics of photoinduced metal to ligand charge-transfer (MLCT) states in a Ru(II) complex, [Ru(dcbpy)2(NCS)2]4- (dcbpy = 4,4'-dicarboxy-2,2'-bipyridine), a photoactive molecule employed in dye sensitized solar cells. Via cutting-edge computational techniques, a tailored computational protocol is here presented and developed to provide a detailed analysis of the electronic manifold coupled with nuclear vibrations to better understand the nonradiative pathways and the resulting overall dye performances in light-harvesting processes (electron injection). Thus, the effects of different vibrational modes were investigated on both the electronic levels and charge transfer dynamics through a theoretical-computational approach. First, the linear response time-dependent density functional (LR-TDDFT) formalism was employed to characterize excitation energies and spacing among electronic levels (the electronic layouts). Then, to understand the ultrafast (femtosecond) charge dynamics on the molecular scale, we relied on the nonperturbative mean-field quantum electronic dynamics via real-time (RT-) TDDFT. Three vibrational modes were selected, representative for collective nuclear movements that can have a significant influence on the electronic structure: two involving NCS- ligands and one involving dcbpy ligands. As main results, we observed that such MLCT states, under vibrational distortions, are strongly affected and a faster interligand electron transfer mechanism is observed along with an increasing MLCT character of the adiabatic electronic states approaching closer in energy due to the vibrations. Such findings can help both in providing a molecular picture of multidimensional vibro-electronic spectroscopic techniques, used to characterize ultrafast coherent and noncoherent dynamics of complex systems, and to improve dye performances with particular attention to the study of energy or charge transport processes and vibronic couplings.

Ultrafast Anisotropy Decay Reveals Structure and Energy Transfer in Supramolecular Aggregates

Chlorosomes from green bacteria perform the most efficient light capture and energy transfer, as observed among natural light-harvesting antennae. Hence, their unique functional properties inspire developments in artificial light-harvesting and molecular optoelectronics. We examine two distinct organizations of the molecular building blocks as proposed in the literature, demonstrating how these organizations alter light capture and energy transfer, which can serve as a mechanism that the bacteria utilize to adapt to changes in light conditions. Spectral simulations of polarization-resolved two-dimensional electronic spectra unravel how changes in the helicity of chlorosomal aggregates alter energy transfer. We show that ultrafast anisotropy decay presents a spectral signature that reveals contrasting energy pathways in different chlorosomes.

An efficient time-domain implementation of the multichromophoric Förster resonant energy transfer method

The excitation energy transfer (EET) process for photosynthetic antenna complexes consisting of subunits, each comprised of multiple chromophores, remains challenging to describe. The multichromophoric Förster resonance energy transfer theory is a popular method to describe the EET process in such systems. This paper presents a new time-domain method for calculating energy transfer based on the combination of multichromophoric Förster resonance energy transfer theory and the Numerical Integration of the Schrödinger Equation method. After validating the method on simple model systems, we apply it to the Light-Harvesting antenna 2 (LH2) complex, a light harvesting antenna found in purple bacteria. We use a simple model combining the overdamped Brownian oscillators to describe the dynamic disorder originating from the environmental fluctuations and the transition charge from the electrostatic potential coupling model to determine the interactions between chromophores. We demonstrate that with this model, both the calculated spectra and the EET rates between the two rings within the LH2 complex agree well with experimental results. We further find that the transfer between the strongly coupled rings of neighboring LH2 complexes can also be well described with our method. We conclude that our new method accurately describes the EET rate for biologically relevant multichromophoric systems, which are similar to the LH2 complex. Computationally, the new method is very tractable, especially for slow processes. We foresee that the method can be applied to efficiently calculate transfer in artificial systems as well and may pave the way for calculating multidimensional spectra of extensive multichromophoric systems in the future.

Simulation of two-dimensional infrared Raman spectroscopy with application to proteins

Two-dimensional infrared Raman spectroscopy is a powerful technique for studying the structure and interaction in molecular and biological systems. Here, we present a new implementation of the simulation of the two-dimensional infrared Raman signals. The implementation builds on the numerical integration of the Schrödinger equation approach. It combines the prediction of dynamics from molecular dynamics with a map-based approach for obtaining Hamiltonian trajectories and response function calculations. The new implementation is tested on the amide-I region for two proteins, where one is dominated by α-helices and the other by β-sheets. We find that the predicted spectra agree well with experimental observations. We further find that the two-dimensional infrared Raman spectra at least of the studied proteins are much less sensitive to the laser polarization used compared to conventional two-dimensional infrared experiments. The present implementation and findings pave the way for future applications for the interpretation of two-dimensional infrared Raman spectra.

Manifestation of Hydrogen Bonding and Exciton Delocalization on the Absorption and Two-Dimensional Electronic Spectra of Chlorosomes

Chlorosomes are supramolecular aggregates that contain thousands of bacteriochlorophyll molecules. They perform the most efficient ultrafast excitation energy transfer of all natural light-harvesting complexes. Their broad absorption band optimizes light capture. In this study, we identify the microscopic sources of the disorder causing the spectral width and reveal how it affects the excited state properties and the optical response of the system. We combine molecular dynamics, quantum chemical calculations, and response function calculations to achieve this goal. The predicted linear and two-dimensional electronic spectra are found to compare well with experimental data reproducing all key spectral features. Our analysis of the microscopic model reveals the interplay of static and dynamic disorder from the molecular perspective. We find that hydrogen bonding motifs are essential for a correct description of the spectral line shape. Furthermore, we find that exciton delocalization over tens to hundreds of molecules is consistent with the two-dimensional electronic spectra.

Calculating Multidimensional Optical Spectra from Classical Trajectories

Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Computational spectroscopy of complex systems

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.

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.

Lessons from combined experimental and theoretical examination of the FTIR and 2D-IR spectroelectrochemistry of the amide I region of cytochrome c

Amide I difference spectroscopy is widely used to investigate protein function and structure changes. In this article, we show that the common approach of assigning features in amide I difference signals to distinct secondary structure elements in many cases may not be justified. Evidence comes from Fourier transform infrared (FTIR) and 2D-IR spectroelectrochemistry of the protein cytochrome c in the amide I range, in combination with computational spectroscopy based on molecular dynamics (MD) simulations. This combination reveals that each secondary structure unit, such as an alpha-helix or a beta-sheet, exhibits broad overlapping contributions, usually spanning a large part of the amide I region, which in the case of difference absorption experiments (such as in FTIR spectroelectrochemistry) may lead to intensity-compensating and even sign-changing contributions. We use cytochrome c as the test case, as this small electron-transferring redox-active protein contains different kinds of secondary structure units. Upon switching its redox-state, the protein exhibits a different charge distribution while largely retaining its structural scaffold. Our theoretical analysis suggests that the change in charge distribution contributes to the spectral changes and that structural changes are small. However, in order to confidently interpret FTIR amide I difference signals in cytochrome c and proteins in general, MD simulations in combination with additional experimental approaches such as isotope labeling, the insertion of infrared labels to selectively probe local structural elements will be required. In case these data are not available, a critical assessment of previous interpretations of protein amide I 1D- and 2D-IR difference spectroscopy data is warranted.