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.

Two-photon Absorption and Photoionization of a Bacterial Phytochrome.

Phytochromes constitute a family of photosensory proteins that are utilized by various organisms to regulate several physiological processes. Phytochromes bind a bilin pigment that switches its isomeric state upon absorption of red or far-red photons, resulting in protein conformational changes that are sensed by the organism. Previously, the ultrafast dynamics in bacterial phytochrome was resolved to atomic resolution by time-resolved serial femtosecond X-ray diffraction (TR-SFX), showing extensive changes in its molecular conformation at 1 picosecond delay time. However, the large excitation fluence of mJ/mm2 used in TR-SFX questions the validity of the observed dynamics. In this work, we present an excitation-dependent ultrafast transient absorption study to test the response of a related bacterial phytochrome to excitation fluence. We observe excitation power-dependent sub-picosecond dynamics, assigned to the population of high-lying excited state Sn through resonantly enhanced two-photon absorption, followed by rapid internal conversion to the low-lying S1 state. Inspection of the long-lived spectrum under high fluence shows that in addition to the primary intermediate Lumi-R, spectroscopic signatures of solvated electrons and ionized chromophore radicals are observed. Supported by numerical modelling, we propose that under excitation fluences of tens of µJ/mm2 and higher, bacterial phytochrome partly undergoes photoionization from the Sn state in competition with internal conversion to the S1 state in 300 fs. We suggest that the extensive structural changes of related, shorter bacterial phytochrome, lacking the PHY domain, resolved from TR-SFX may have been affected by the ionized species. We propose approaches to minimize the two-photon absorption process by tuning the excitation spectrum away from the S1 absorption or using phytochromes exhibiting minimized or shifted S1 absorption.

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.

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.

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.

Ultrafast Excitation Energy Transfer Dynamics in the LHCII-CP29-CP24 Subdomain of Plant Photosystem II.

We measure the two-dimensional electronic spectra of the LHCII(M)-CP29-CP24 complex in photosystem II (PSII) and provide the first study of the ultrafast excitation energy transfer (EET) processes of an asymmetric and native light-harvesting assembly of the antenna of PSII. With comparisons to LHCII, we observe faster energy equilibrations in the intermediate levels of the LHCII(M)-CP29-CP24 complex at 662 and 670 nm. Notably, the putative "bottleneck" states in LHCII exhibit faster effective dynamics in the LHCII(M)-CP24-CP29 complex, with the average lifetime shortening from 2.5 ps in LHCII to 1.2 ps in the bigger assembly. The observations are supported by high-level structure-based calculations, and the accelerated dynamics can be attributed to the structural change of LHCII(M) in the bigger complex. This study shows that the biological functioning structures of the complexes are important to understand the overall EET dynamics of the PSII supercomplex.

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.

Electron Transfer Quenching of Rhodamine 6G by N-Methylpyrrole Is an Unproductive Process in the Photocatalytic Heterobiaryl Cross-Coupling Reaction.

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.

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.

An Exciton Dynamics Model of Bryopsis corticulans Light-Harvesting Complex II.

Bryopsis corticulans is a marine green macroalga adapted to the intertidal environment. It possesses siphonaxanthin-binding light-harvesting complexes of photosystem II (LHCII) with spectroscopic properties markedly different from the LHCII in plants. By applying a phenomenological fitting procedure to the two-dimensional electronic spectra of the LHCII from B. corticulans measured at 77 K, we can extract information about the excitonic states and energy-transfer processes. The fitting method results in well-converged parameters, including excitonic energy levels with their respective transition dipole moments, spectral widths, energy-transfer rates, and coupling properties. The 2D spectra simulated from the fitted parameters concur very well with the experimental data, showing the robustness of the fitting method. An excitonic energy-transfer scheme can be constructed from the fitting parameters. It shows the rapid energy transfer from chlorophylls (Chls) b to a at subpicosecond time scales and a long-lived state in the Chl b region at around 659 nm. Three weakly connected terminal states are resolved at 671, 675, and 677 nm. The lowest state is higher in energy than that in plant LHCII, which is probably because of the fewer number of Chls a in a B. corticulans LHCII monomer. Modeling based on existing Hamiltonians for the plant LHCII structure with two Chls a switched to Chls b suggests several possible Chl a-b replacements in comparison with those of plant LHCII. The adaptive changes result in a slower energy equilibration in the complex, revealed by the longer relaxation times of several exciton states compared to those of plant LHCII. The strength of our phenomenological fitting method for obtaining excitonic energy levels and energy-transfer network is put to the test in systems such as B. corticulans LHCII, where prior knowledge on exact assignment and spatial locations of pigments are lacking.

Observing the Fluctuation Dynamics of Dative Bonds Using Two-Dimensional Electronic Spectroscopy.

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.

Hierarchical Equations of Motion Simulation of Temperature-Dependent Two-Dimensional Electronic Spectroscopy of the Chlorophyll a Manifold in LHCII.

We simulated two-dimensional electronic spectra (2DES) of the chlorophyll a manifold of light-harvesting complex II (LHCII) at various temperatures (77, 110, 150, 190, 230, 273, and 293 K) using the hierarchical equations of the motion-phase matching approach. We confirm the main excitation energy transfer pathways assignments within the chlorophyll a manifold of LHCII measured in a recent work (J. Phys. Chem. B 2019, 123, 6765-6775). The calculated transfer rates are also in general agreement with the measured rates. We also provided theoretical confirmation for the experimental assignments, as uphill and downhill energy transfer processes, of 2D spectral features that were reported in recent experimental reports. These temperature-dependent features were also ascertained to follow the detailed-balance principle.

Spectral tuning of light-harvesting complex II in the siphonous alga Bryopsis corticulans and its effect on energy transfer dynamics.

Light-harvesting complex II (LHCII) from the marine green macroalga Bryopsis corticulans is spectroscopically characterized to understand the structural and functional changes resulting from adaptation to intertidal environment. LHCII is homologous to its counterpart in land plants but has a different carotenoid and chlorophyll (Chl) composition. This is reflected in the steady-state absorption, fluorescence, linear dichroism, circular dichroism and anisotropic circular dichroism spectra. Time-resolved fluorescence and two-dimensional electronic spectroscopy were used to investigate the consequences of this adaptive change in the pigment composition on the excited-state dynamics. The complex contains additional Chl b spectral forms - absorbing at around 650 nm and 658 nm - and lacks the red-most Chl a forms compared with higher-plant LHCII. Similar to plant LHCII, energy transfer between Chls occurs on timescales from under hundred fs (mainly from Chl b to Chl a) to several picoseconds (mainly between Chl a pools). However, the presence of long-lived, weakly coupled Chl b and Chl a states leads to slower exciton equilibration in LHCII from B. corticulans. The finding demonstrates a trade-off between the enhanced absorption of blue-green light and the excitation migration time. However, the adaptive change does not result in a significant drop in the overall photochemical efficiency of Photosystem II. These results show that LHCII is a robust adaptable system whose spectral properties can be tuned to the environment for optimal light harvesting.

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.

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.

Temperature Dependence of the Energy Transfer in LHCII Studied by Two-Dimensional Electronic Spectroscopy.

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 ∼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 ∼5 ps at 295 K 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.

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.

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.