Diatoms contribute about 40% of marine primary photoproduction, owing their success, in part, to a specialized light-harvesting antenna built from fucoxanthin-chlorophyll a/c-binding proteins (FCPs). Photosystem I (PSI) in the marine diatom Thalassiosira pseudonana contains up to 13 FCPI subunits. The mechanisms by which PSI maintains photochemical efficiency with a large antenna are not well understood. Here, we investigate the excitation energy transfer dynamics in PSI-FCPI from T. pseudonana using time-resolved spectroscopy and structure-based exciton modeling. Two-dimensional electronic spectroscopy shows that spectral equilibration in PSI-FCPI occurs mainly within 1 ps. Exciton migration between FCPI and PSI takes similar to 10 ps. The rapid inter-subunit energy transfer is contributed by (1) strongly coupled chlorophyll dimers in Lhcr-type FCPI, acting as red-shifted excitonic "gateway" states, and (2) hierarchical organization with strongly connected FCPI "hubs" carrying energy from neighboring FCPIs to the core. The findings can inform the design of bio-inspired light-harvesting systems.

The blend of polymeric donor PM6 and non-fullerene acceptor Y6 is high performing as both an active layer in organic photovoltaics and as a nanoparticulate photocatalyst for the renewable production of hydrogen gas. Despite the high performance of PM6:Y6 blends, many aspects of the photophysics of this material remain unclear. Here we present a detailed spectroscopic analysis of bulk heterojunction PM6:Y6 nanoparticles for photocatalytic hydrogen evolution over 11 orders of magnitude in time, ranging from tens of femtoseconds to hundreds of microseconds. We find that the excitation of Y6 primarily results in the formation of charges first in Y6 domains, followed by diffusion of Y6 holes to PM6 domains. Upon excitation of PM6, charges are generated through two mechanisms: (1) energy transfer to Y6 followed by exciton dissociation and back hole transfer to PM6, and (2) electron transfer to Y6 facilitated by an interfacial charge-transfer state. We use kinetic modelling to confirm these mechanisms and determine the rates of formation and recombination of charges. We also investigate the PM6:Y6 nanoparticles under photocatalytic conditions, and show that the Pt co-catalyst can accept both Y6 electrons and Y6 holes on relatively fast (<100 ps) timescales, and that the sacrificial electron donor ascorbic acid scavenges holes from both components on picosecond and microsecond timescales. The results highlight the critical importance of rapid free polaron formation in Y6 domains, and point towards harnessing this property of the Y-series and other non-fullerene acceptors to develop industrially viable organic hydrogen-evolution photocatalysts.

Cross peaks on 2D optical spectra are indicative of interactions between molecular excitonic states. Currently, the two conventional assignments of cross peaks are direct coupling and population transfer between excitonic states. Here, we show that there is another possible source of cross peaks. We theoretically demonstrate that for a model comprising two nondirectly interacting excitons or two-level systems (TLSs), cross peaks can arise if there is a complex-valued or quantum frequency-gap cross-correlation function between the two TLSs. Considering only real-valued or classical cross-correlation functions will result in no cross peaks. We derive and validate the mathematical expressions describing such cross peaks. We then simulate the 2D electronic spectra of an example model system comprising nondirectly interacting TLSs whose quantum cross-correlation functions arise from coupling to a common overdamped Brownian oscillator mode. We show that there are clear observational differences between such quantum correlation cross peaks with conventional direct coupling and population transfer cross peaks.

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.

In a two-dimensional (2D) optical spectrum of a multilevel system, there are diagonal peaks and off-diagonal cross-peaks that correlate the different levels. The time-dependent properties of these diagonal peaks and cross-peaks contain much information about the dynamics of the multilevel system. The time-dependent diagonal peakshape that depends on the spectral diffusion dynamics of the associated transition and characterized by the frequency-fluctuation correlation function (FFCF) is well studied. However, the time-dependent peakshape of a cross-peak that provides the correlation dynamics between different transitions is much less studied or understood. We derived the third-order nonlinear response functions that describe the cross-peaks in a 2D electronic spectrum of a multilevel system that arise from processes sharing a common ground state and/or from internal conversion and population transfer. We can use the center line slope (CLS) analysis to characterize the cross-peaks in conjunction with the diagonal peaks. This allows us to recover the frequency-fluctuation cross-correlation functions (FXCFs) between two transitions. The FXCF and its subsidiary quantities such as the initial correlation and the initial covariance between different transitions are important for studying the correlation effects between states in complex systems, such as energy-transfer processes. Furthermore, knowledge of how various molecular processes over different timescales affect simultaneously different transitions can also be obtained from the measured FXCF. We validated and tested our derived equations and analysis process by studying, as an example, the 2D electronic spectra of metal-free phthalocyanine in solution. We measured and analyzed the diagonal peaks of the Qx and Qy transitions and the cross-peaks between these two transitions of this multilevel electronic system and obtained the associated FFCFs and FXCFs. In this model system, we measured negative components of FXCF over the tens of picosecond timescale. This suggests that in phthalocyanine, the Qx and Qy transitions coupling with the solvent molecule motion are anticorrelated to each other.

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.

We perform two-dimensional electronic spectroscopy on chlorophyll (Chl) a and b molecules in aprotic solvents of different Lewis basicity. By analyzing the ultrafast spectral diffusion dynamics of the Qy transition, we show that a certain timescale of the spectral diffusion dynamics is affected by the solvents' Lewis basicity. Control experiments with Chlorin-e6—a Chl molecule analog—and ab initio time-dependent density functional theory calculations confirm that we are directly probing the fluctuation dynamics of the dative bond between the solvent's lone pair and the Mg2+ center in Chls that is responsible for the Lewis basicity. The observation is indicative of dative bond length and angular fluctuations with timescales ranging between ∼30 and 150 ps and the dative bond-strength-dependent perturbation on the Qy transition frequency of Chls.

In the heterobiaryl cross-coupling reaction between aryl halides (Ar-X) and N-methylpyrrole (N-MP) catalyzed by rhodamine 6G (Rh6G+) under irradiation with visible light, a highly active and long-lived (millisecond time range) rhodamine 6G radical (Rh6G•) is formed upon electron transfer from N,N-diisopropylethylamine (DIPEA) to Rh6G+. In this study, we utilized steady-state and time-resolved spectroscopy techniques to demonstrate the existence of another electron-transfer process occurring from the relatively electron-rich N-MP to photoexcited Rh6G+ that was neglected in the previous reports. In this case, the radical Rh6G• formed is short-lived and undergoes rapid recombination (nanosecond time-range), rendering it ineffective in reducing Ar-X to aryl radicals Ar• that can subsequently be trapped by N-MP. This is further demonstrated via two model reactions involving 4'-bromoacetophenone and 1,3,5-tribromobenzene with insignificant product yields after visible-light irradiation in the absence of DIPEA. The unproductive quenching of photoexcited Rh6G+ by N-MP leads to a lower concentration of photocatalyst available for competitive charge transfer with DIPEA and hence decreases the efficiency of the cross-coupling reaction.

There have been many efforts recently in analyzing the oscillation patterns in a two-dimensional electronic spectrum to characterize vibronic couplings. A displaced oscillator model with a four-level vibronic system (4LvS) is a commonly used model to approximate such phenomena. Although this model is related to an electronic two-level system coupled to a harmonic oscillator (2LScHO) model, there has not been a formal study to connect the two models. Here, we show explicitly that the former is a special case of the latter. We provide a detailed description of how the expressions for the 2D spectral peak amplitudes of the 4LvS model can be derived from the electronic 2LScHO model at T=0K. We also demonstrate that the two-dimensional Fourier maps of the 4LvS model are still good representatives of the more general electronic 2LScHO model at T≠0K.

Photosystem I (PSI), found in all oxygenic photosynthetic organisms, uses solar energy to drive electron transport with nearly 100% quantum efficiency, thanks to fast energy transfer among antenna chlorophylls and charge separation in the reaction center. There is no complete consensus regarding the kinetics of the elementary steps involved in the overall trapping, especially the rate of primary charge separation. In this work, we employed two-dimensional coherent electronic spectroscopy to follow the dynamics of energy and electron transfer in a monomeric PSI complex from Synechocystis PCC 6803, containing only subunits A-E, K, and M, at 77 K. We also determined the structure of the complex to 4.3 Å resolution by cryoelectron microscopy with refinements to 2.5 Å. We applied structure-based modeling using a combined Redfield-Förster theory to compute the excitation dynamics. The absorptive 2D electronic spectra revealed fast excitonic/vibronic relaxation on time scales of 50-100 fs from the high-energy side of the absorption spectrum. Antenna excitations were funneled within 1 ps to a small pool of chlorophylls absorbing around 687 nm, thereafter decaying with 4-20 ps lifetimes, independently of excitation wavelength. Redfield-Förster energy transfer computations showed that the kinetics is limited by transfer from these red-shifted pigments. The rate of primary charge separation, upon direct excitation of the reaction center, was determined to be 1.2-1.5 ps-1. This result implies activationless electron transfer in PSI.

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.

Photosynthesis is a highly optimized process from which valuable lessons can be learned about the operating principles in nature. Its primary steps involve energy transport operating near theoretical quantum limits in efficiency. Recently, extensive research was motivated by the hypothesis that nature used quantum coherences to direct energy transfer. This body of work, a cornerstone for the field of quantum biology, rests on the interpretation of small-amplitude oscillations in two-dimensional electronic spectra of photosynthetic complexes. This Review discusses recent work reexamining these claims and demonstrates that interexciton coherences are too short lived to have any functional significance in photosynthetic energy transfer. Instead, the observed long-lived coherences originate from impulsively excited vibrations, generally observed in femtosecond spectroscopy. These efforts, collectively, lead to a more detailed understanding of the quantum aspects of dissipation. Nature, rather than trying to avoid dissipation, exploits it via engineering of exciton-bath interaction to create efficient energy flow.

The Frequency Fluctuation Correlation Function (FFCF) is a measure of the spectral diffusion dynamics of an electronic transition and details the interaction between the chromophore and its environment. The Frequency Fluctuation Cross-Correlation Function (FXCF) allows us to study how correlated, the transitions between different electronic transitions, are. These quantities contain a wealth of information on how the electronic transitions in chromophores and excitonic states interact and couple with their environment, and with each other. We summarize the experimental implementations and theoretical considerations of using ultrafast coherent two-dimensional electronic spectroscopy (2DES) to characterize FFCFs and FXCFs. In 2DES, the measured peakshapes of the electronic transitions are highly sensitive to the spectral diffusion and correlation dynamics [1]. One method that allows us to analyse these peakshapes is the Centre Line Slope (CLS) method [2]. We describe applications to systems such as the chlorophyll (Chl) molecules which are the major pigment molecules in the plant photosynthetic light harvesting machinery. We characterize the FFCFs of the Qy transition of Chl a and Chl b in various solvent environment [3,4]. The solvent dependence of the FFCF values and the relation of these values to the molecule's interaction with the solvent environment, will be discussed. Using similar methods, the FXCF between the Qx and Qy transitions of Chl a are measured. The results indicate that the Qx and Qy transitions have only minimal initial correlation, which decays to zero in a timescale of about 2 ps [5]. We also characterize the FFCFs of CdSe quantum dots (QD) and nanoplatelet (NPL) [6]. We found that no spectral diffusion dynamics occurs for the CdSe QDs. On the other hand, spectral diffusion was observed in the CdSe 5 mono-layers NPLs heavy-hole transition. The normalized Frequency Fluctuation Correlation Function (FFCF) of the CdSe NPLs heavy-hole transition was measured to have a major fast decay component at < 200 fs.

The molecule TIPS -Pentacene has gained a lot of attraction recently due to its ability to exhibit the singlet fission phenomenon, which has the potential of improving power conversion efficiency significantly in photovoltaic devices 1 .Therefore, investigating into the photophysical properties of this molecule can assist researchers in better understanding the singlet fission phenomenon.2D Electronic spectroscopy of TIPS -Pentacene in solution shown a strong beating at 265cm -1 in both the amplitude and the central line slope 2 , which corresponds to a breathing mode of the molecule.

Two-dimensional optical spectroscopy (2DOS) is the optical version of the well-established 2D-NMR technique, e.g., COSY. With time resolution in the femtosecond regime, 2DOS is widely used to resolve the ultrafast frequency modulation dynamics, such as spectral diffusion, in various vibrational [1-2] and electronic [3-4] systems. Chlorophylls (Chls) a and b are two main types of photosynthetic pigments responsible for the light-harvesting and energy regulation of green plants on Earth. Here, we employ 2DOS to track the time evolution of the 2D peakshape (Fig. 1) and resolve the ultrafast spectral diffusion dynamics of the Chl Q y transition in various organic solvents. The obtained results suggest that Chls exhibit three different relaxation dynamics with the timescales of sub-picosecond (sub-ps), several ps and tens to hundreds of ps. The correlation between spectral diffusion timescales and the solvents’ Lewis basicity, together with the support of ab initio time-dependent density functional theory (TDDFT) calculations indicates that we are probing directly the the dative bond the solvent’s lone pair and the electrophilic Mg 2+ center of Chls. bond the solvent Lewis basicity. a time-resolved molecular chemical property – Lewis basicity.

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.

Light-harvesting complex II (LHCII) – the light-harvesting antenna of Photosystem II – is a naturally abundant system that plays an important role in photosynthesis. In this study, we present a phenomenological analysis of the excitonic energy transfer in LHCII using ultrafast two-dimensional electronic spectroscopy, that we find compares well with previous theoretical and experimental results.

We measured two-dimensional electronic spectra of light-harvesting complex II (LHCII) at various temperatures (77, 110, 150, 230, and 295 K) under conditions free from singlet-singlet annihilation. We elucidated the temperature-dependent excitation energy transfer dynamics in the Chl a manifold of LHCII. Global analysis revealed that the dynamics can be summarized in distinct time scales from 200 fs up to 15 ps. While the fastest dynamics with a decay time of similar to 0.2-0.3 ps are relatively temperature-independent, the lifetimes and relative contributions of slower components showed considerable temperature dependence. The slowest time scale of equilibration with the lowest-energy Chl a increased from similar to 5 ps at 295 K to similar to 15 ps at 77 K. The final excited state is independent of initial excitation at 230 K and above, whereas static energy disorder is apparent at lower temperatures. A clear temperature dependence of uphill energy transfer processes was also discerned, which is consistent with the detailed-balance condition.

Although most experiments are performed using a non-collinear beam geometry, multidimensional optical spectroscopy experiments can also be performed using collinear and partially collinear beam geometries. Phase cycling is an important procedure to enable multidimensional optical spectroscopy experiments to be performed in collinear and partially collinear beam geometries. In this chapter, we present the general theory of phase cycling and summarizes the development and applications of the phase cycling procedures in various multidimensional optical spectroscopies. These applications include fully collinear two dimensional optical spectroscopy, pump-probe geometry third order and fifth order two dimensional optical spectroscopies, and fifth order three dimensional optical spectroscopy.

Chlorophyll a (Chl a) and Chlorophyll b (Chl b) are major pigments in the photosynthetic machinery in green plants. Despite their similarities in chemical structures, the relaxation dynamics as observed in the ultrafast methods, such as pump probe and multidimensional spectroscopy, demonstrate a distinct kinetics. Here, we employ the ultrafast two-dimensional electronic spectroscopy (2DES) method to characterize the frequency fluctuation correlation function (FFCF) for Chl a and Chl b in various solvent environments, through the Centre Line Slope (CLS) method. We observe that the FFCF decay for both Chl a and Chl b in the methanol solvent environment has a similar to 40 ps component that is absent in aprotic solvents, tetrahydrofuran and diethyl ether. We observe also that Chl b exhibit higher values of inhomogeneous broadening than Chl a.