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.

Two-dimensional electronic spectroscopy of the Qx to Qy relaxation of chlorophylls a in photosystem II core complex.

Using two-dimensional electronic spectroscopy, we measured the Qx to Qy transfer dynamics of the chlorophyll a (Chl a) manifold in the photosystem II (PSII) monomeric core complex from Arabidopsis thaliana. A PSII monomeric core consists of 35 Chls a and no Chl b, thus allowing for a clear window to study Chl a Qx dynamics in a large pigment-protein complex. Initial excitation in the Qx band results in a transfer to the Qy band in less than 60 fs. Upon the ultrafast transfer, regardless of the excitation frequency within the Qx band, the quasi-transient absorption spectra are very similar. This observation indicates that Chl a's Qx to Qy transfer is not frequency selective. Using a simple model, we determined that this is not due to the lifetime broadening of the ultrafast transfer but predominantly due to a lack of correlation between the PSII core complex's Chl a Qx and Qy bands. We suggest the origin to be the intrinsic loss of correlation during the Qx to Qy internal conversion as observed in previous studies of molecular Chl a dissolved in solvents.

Ultrafast excitation quenching by the oxidized photosystem II reaction center.

Photosystem II (PSII) is the pigment-protein complex driving the photoinduced oxidation of water and reduction of plastoquinone in all oxygenic photosynthetic organisms. Excitations in the antenna chlorophylls are photochemically trapped in the reaction center (RC) producing the chlorophyll-pheophytin radical ion pair P+ Pheo-. When electron donation from water is inhibited, the oxidized RC chlorophyll P+ acts as an excitation quencher, but knowledge on the kinetics of quenching is limited. Here, we used femtosecond transient absorption spectroscopy to compare the excitation dynamics of PSII with neutral and oxidized RC (P+). We find that equilibration in the core antenna has a major lifetime of about 300 fs, irrespective of the RC redox state. Two-dimensional electronic spectroscopy revealed additional slower energy equilibration occurring on timescales of 3-5 ps, concurrent with excitation trapping. The kinetics of PSII with open RC can be described well with previously proposed models according to which the radical pair P+ Pheo- is populated with a main lifetime of about 40 ps, which is primarily determined by energy transfer between the core antenna and the RC chlorophylls. Yet, in PSII with oxidized RC (P+), fast excitation quenching was observed with decay lifetimes as short as 3 ps and an average decay lifetime of about 90 ps, which is shorter than the excited-state lifetime of PSII with open RC. The underlying mechanism of this extremely fast quenching prompts further investigation.

Two-Dimensional Electronic Spectroscopy of a Minimal Photosystem I Complex Reveals the Rate of Primary Charge Separation.

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.

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.

Revealing the excitation energy transfer network of Light-Harvesting Complex II by a phenomenological analysis of two-dimensional electronic spectra at 77 K.

Energy equilibration in light-harvesting antenna systems normally occurs before energy is transferred to a reaction center. The equilibration mechanism is a characteristic of the excitation energy transfer (EET) network of the antenna. Characterizing this network is crucial in understanding the first step of photosynthesis. We present our phenomenology-based analysis procedure and results in obtaining the excitonic energy levels, spectral linewidths, and transfer-rate matrix of Light-Harvesting Complex II directly from its 2D electronic spectra recorded at 77 K with waiting times between 100 fs to 100 ps. Due to the restriction of the models and complexity of the system, a unique EET network cannot be constructed. Nevertheless, a recurring pattern of energy transfer with very similar overall time scales between spectral components (excitons) is consistently obtained. The models identify a "bottleneck" state in the 664-668 nm region although with a relatively shorter lifetime (∼4-6 ps) of this state compared to previous studies. The model also determines three terminal exciton states at 675, 677-678, and 680-681 nm that are weakly coupled to each other. The excitation energy equilibration between the three termini is found to be independent of the initial excitation conditions, which is a crucial design for the light-harvesting complexes to ensure the energy flow under different light conditions and avoid excitation trapping. We proposed two EET schemes with tentative pigment assignments based on the interpretation of the modeling results together with previous structure-based calculations and spectroscopic observables.

Excitation transfer and trapping kinetics in plant photosystem I probed by two-dimensional electronic spectroscopy.

Photosystem I is a robust and highly efficient biological solar engine. Its capacity to utilize virtually every absorbed photon's energy in a photochemical reaction generates great interest in the kinetics and mechanisms of excitation energy transfer and charge separation. In this work, we have employed room-temperature coherent two-dimensional electronic spectroscopy and time-resolved fluorescence spectroscopy to follow exciton equilibration and excitation trapping in intact Photosystem I complexes as well as core complexes isolated from Pisum sativum. We performed two-dimensional electronic spectroscopy measurements with low excitation pulse energies to record excited-state kinetics free from singlet-singlet annihilation. Global lifetime analysis resolved energy transfer and trapping lifetimes closely matches the time-correlated single-photon counting data. Exciton energy equilibration in the core antenna occurred on a timescale of 0.5 ps. We further observed spectral equilibration component in the core complex with a 3-4 ps lifetime between the bulk Chl states and a state absorbing at 700 nm. Trapping in the core complex occurred with a 20 ps lifetime, which in the supercomplex split into two lifetimes, 16 ps and 67-75 ps. The experimental data could be modelled with two alternative models resulting in equally good fits-a transfer-to-trap-limited model and a trap-limited model. However, the former model is only possible if the 3-4 ps component is ascribed to equilibration with a "red" core antenna pool absorbing at 700 nm. Conversely, if these low-energy states are identified with the P700 reaction centre, the transfer-to-trap-model is ruled out in favour of a trap-limited model.

Two-dimensional electronic-Raman spectroscopy.

We present a new technique, two-dimensional electronic-Raman spectroscopy (2DER), which combines femtosecond stimulated Raman spectroscopy and a pulse-shaper-assisted 2D spectroscopic scheme for the actinic pump. The 2DER spectrum presents the initial actinic excitation wavelength with nanometer spectral resolution in the first axis and the detected stimulated Raman spectra in the second axis. We measured the correlation of the electronic and vibrational states in the photosynthetic accessory pigment ß-carotene and reveal its photoexcited state manifold.

Glass formation of a DMSO-water mixture probed with a photosynthetic pigment.

Despite their extensive industrial usage, glass-forming liquids are not fully understood, and methods to investigate their dynamical heterogeneity are sought after. Here we show how the appearance of a second component in the visible absorption spectrum of a photosynthetic pigment upon cooling can be used to probe the glass transition of a dimethylsulfoxide-water mixture. The changes in the relative ratio of the two components with respect to temperature follow a sigmoid curve, and we show that the second component arises due to protonation of the pigment at low temperatures. Furthermore, from visible transient absorption spectra we show that, unlike the first component, the dynamics of the second component slows down significantly at lower temperatures, suggesting that there are two distinct environments with fast and slow fluctuations. Our results therefore enable a new method to characterize the dynamical heterogeneity of glass-forming liquids.

Simplified expressions that incorporate finite pulse effects into coherent two-dimensional optical spectra.

We derive general expressions that incorporate finite pulse envelope effects into a coherent two-dimensional optical spectroscopy (2DOS) technique. These expressions are simpler and less computationally intensive than the conventional triple integral calculations needed to simulate 2DOS spectra. The simplified expressions involving multiplications of arbitrary pulse spectra with 2D spectral response function are shown to be exactly equal to the conventional triple integral calculations of 2DOS spectra if the 2D spectral response functions do not vary with population time. With minor modifications, they are also accurate for 2D spectral response functions with quantum beats and exponential decay during population time. These conditions cover a broad range of experimental 2DOS spectra. For certain analytically defined pulse spectra, we also derived expressions of 2D spectra for arbitrary population time dependent 2DOS spectral response functions. Having simpler and more efficient methods to calculate experimentally relevant 2DOS spectra with finite pulse effect considered will be important in the simulation and understanding of the complex systems routinely being studied by using 2DOS.

Interplay of hole transfer and host-guest interaction in a molecular dyad and triad: ensemble and single-molecule spectroscopy and sensing applications.

A new molecular dyad consisting of a Cy5 chromophore and ferrocene (Fc) and a triad consisting of Cy5, Fc, and ß-cyclodextrin (CD) are synthesized and their photophysical properties investigated at both the ensemble and single-molecule levels. Hole transfer efficiency from Cy5 to Fc in the dyad is reduced upon addition of CD. This is due to an increase in the Cy5-Fc separation (r) when the Fc is encapsulated in the macrocyclic host. On the other hand, the triad adopts either a Fc-CD inclusion complex conformation in which hole transfer quenching of the Cy5 by Fc is minimal or a quasi-static conformation with short r and rapid charge transfer. Single-molecule fluorescence measurements reveal that r is lengthened when the triad molecules are deposited on a glass substrate. By combining intramolecular charge transfer and competitive supramolecular interaction, the triad acts as an efficient chemical sensor to detect different bioactive analytes such as amantadine hydrochloride and sodium lithocholate in aqueous solution and synthetic urine.

Energy transfer dynamics in trimers and aggregates of light-harvesting complex II probed by 2D electronic spectroscopy.

The pathways and dynamics of excitation energy transfer between the chlorophyll (Chl) domains in solubilized trimeric and aggregated light-harvesting complex II (LHCII) are examined using two-dimensional electronic spectroscopy (2DES). The LHCII trimers and aggregates exhibit the unquenched and quenched excitonic states of Chl a, respectively. 2DES allows direct correlation of excitation and emission energies of coupled states over population time delays, hence enabling mapping of the energy flow between Chls. By the excitation of the entire Chl b Qy band, energy transfer from Chl b to Chl a states is monitored in the LHCII trimers and aggregates. Global analysis of the two-dimensional (2D) spectra reveals that energy transfer from Chl b to Chl a occurs on fast and slow time scales of 240-270 fs and 2.8 ps for both forms of LHCII. 2D decay-associated spectra resulting from the global analysis identify the correlation between Chl states involved in the energy transfer and decay at a given lifetime. The contribution of singlet-singlet annihilation on the kinetics of Chl energy transfer and decay is also modelled and discussed. The results show a marked change in the energy transfer kinetics in the time range of a few picoseconds. Owing to slow energy equilibration processes, long-lived intermediate Chl a states are present in solubilized trimers, while in aggregates, the population decay of these excited states is significantly accelerated, suggesting that, overall, the energy transfer within the LHCII complexes is faster in the aggregated state.

Pathways of energy transfer in LHCII revealed by room-temperature 2D electronic spectroscopy.

We present here the first room-temperature 2D electronic spectroscopy study of energy transfer in the plant light-harvesting complex II, LHCII. Two-dimensional electronic spectroscopy has been used to study energy transfer dynamics in LHCII trimers from the chlorophyll b Qy band to the chlorophyll a Qy band. Observing cross-peak regions corresponding to couplings between different excitonic states reveals partially resolved fine structure at the exciton level that cannot be isolated by pump-probe or linear spectroscopy measurements alone. Global analysis of the data has been performed to identify the pathways and time constants of energy transfer. The measured waiting time (Tw) dependent 2D spectra are found to be composed of 2D decay-associated spectra with three timescales (0.3 ps, 2.3 ps and >20 ps). Direct and multistep cascading pathways from the high-energy chlorophyll b states to the lowest-energy chlorophyll a states have been resolved occurring on time scales of hundreds of femtoseconds to picoseconds.

Inhomogeneous energy transfer dynamics from iron-stress-induced protein A to photosystem I.

Cyanobacteria respond to iron limitation by producing the pigment-protein complex IsiA, forming rings associated with photosystem I (PSI). Initially considered a chlorophyll-storage protein, IsiA is known to act as an auxiliary light-harvesting antenna of PSI, increasing its absorption cross-section and reducing the need for iron-rich PSI core complexes. Spectroscopic studies have demonstrated efficient energy transfer from IsiA to PSI. Here we investigate the room-temperature excitation dynamics in isolated PSI-IsiA, PSI, IsiA monomer complexes and IsiA aggregates using two-dimensional electronic spectroscopy. Cross analyses of the data from these three samples allow us to resolve components of energy transfer between IsiA and PSI with lifetimes of 2-3 ps and around 20 ps. Structure-based Förster theory calculations predict a single major timescale of IsiA-PSI equilibration, that depends on multiple energy transfer routes between different IsiA subunits in the ring. Despite the experimentally observed lifetime heterogeneity, which is attributed to structural heterogeneity of the supercomplexes, IsiA is found to be a unique, highly efficient, membrane antenna complex in cyanobacteria.

Ultrafast Energy Transfer in a Diatom Photosystem II Supercomplex.

The light-harvesting complexes (LHCs) of diatoms, specifically fucoxanthin-Chl a/c binding proteins (FCPs), exhibit structural and functional diversity, as highlighted by recent structural studies of photosystem II-FCP (PSII-FCPII) supercomplexes from different diatom species. The excitation dynamics of PSII-FCPII supercomplexes isolated from the diatom Thalassiosira pseudonana was explored using time-resolved fluorescence spectroscopy and two-dimensional electronic spectroscopy at room temperature and 77 K. Energy transfer between FCPII and PSII occurred remarkably fast (<5 ps), emphasizing the efficiency of FCPII as a light-harvesting antenna. The presence of long-wavelength chlorophylls may further help concentrate excitations in the core complex and increase the efficiency of light harvesting. Structure-based calculations reveal remarkably strong excitonic couplings between chlorophylls in the FCP antenna and between FCP and the PSII core antenna that are the basis for the rapid energy transfer.

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.

Inter-subunit energy transfer processes in a minimal plant photosystem II supercomplex.

Photosystem II (PSII) is an integral part of the photosynthesis machinery, in which several light-harvesting complexes rely on inter-complex excitonic energy transfer (EET) processes to channel energy to the reaction center. In this paper, we report on a direct observation of the inter-complex EET in a minimal PSII supercomplex from plants, containing the trimeric light-harvesting complex II (LHCII), the monomeric light-harvesting complex CP26, and the monomeric PSII core complex. Using two-dimensional (2D) electronic spectroscopy, we measure an inter-complex EET timescale of 50 picoseconds for excitations from the LHCII-CP26 peripheral antenna to the PSII core. The 2D electronic spectra also reveal that the transfer timescale is nearly constant over the pump spectrum of 600 to 700 nanometers. Structure-based calculations reveal the contribution of each antenna complex to the measured inter-complex EET time. These results provide a step in elucidating the full inter-complex energy transfer network of the PSII machinery.

Measuring the Ultrafast Spectral Diffusion and Vibronic Coupling Dynamics in CdSe Colloidal Quantum Wells using Two-Dimensional Electronic Spectroscopy.

We measure the ultrafast spectral diffusion, vibronic dynamics, and energy relaxation of a CdSe colloidal quantum wells (CQWs) system at room temperature using two-dimensional electronic spectroscopy (2DES). The energy relaxation of light-hole (LH) excitons and hot carriers to heavy-hole (HH) excitons is resolved with a time scale of ∼210 fs. We observe the equilibration dynamics between the spectroscopically accessible HH excitonic state and a dark state with a time scale of ∼160 fs. We use the center line slope analysis to quantify the spectral diffusion dynamics in HH excitons, which contains an apparent sub-200 fs decay together with oscillatory features resolved at 4 and 25 meV. These observations can be explained by the coupling to various lattice phonon modes. We further perform quantum calculations that can replicate and explain the observed dynamics. The 4 meV mode is observed to be in the near-critically damped regime and may be mediating the transition between the bright and dark HH excitons. These findings show that 2DES can provide a comprehensive and detailed characterization of the ultrafast spectral properties in CQWs and similar nanomaterials.

Measuring the Ultrafast Correlation Dynamics of a Multilevel System Using the Center Line Slope Analysis in Two-Dimensional Electronic Spectroscopy.

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.

Purely absorptive fifth-order three-dimensional electronic spectroscopy.

We demonstrate a method to measure a purely absorptive fifth-order three-dimensional (3D) electronic spectrum based on a pulse-shaper assisted pump-probe beam geometry setup. The 3D spectra are measured as a function of two independently controlled population times. With phase-cycling and data processing, purely absorptive 3D spectra of chlorophyll a are obtained.