Measuring the Spectral Diffusion of Chlorophyll a Using Two-Dimensional Electronic Spectroscopy

Coherence in Chemistry: Foundations and Frontiers

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

Full visible range two-dimensional electronic spectroscopy with high time resolution

Two-dimensional electronic spectroscopy (2DES) is a powerful method to study coherent and incoherent interactions and dynamics in complex quantum systems by correlating excitation and detection energies in a nonlinear spectroscopy experiment. Such dynamics can be probed with a time resolution limited only by the duration of the employed laser pulses and in a spectral range defined by the pulse spectrum. In the blue spectral range (<500 nm), the generation of sufficiently broadband ultrashort pulses with pulse durations of 10 fs or less has been challenging so far. Here, we present a 2DES setup based on a hollow-core fiber supercontinuum covering the full visible range (400-700 nm). Pulse compression via custom-made chirped mirrors yields a time resolution of <10 fs. The broad spectral coverage, in particular the extension of the pulse spectra into the blue spectral range, unlocks new possibilities for coherent investigations of blue-light absorbing and multichromophoric compounds, as demonstrated by a 2DES measurement of chlorophyll a.

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.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

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

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

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

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

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

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

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 Q_y 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 Q_y transition frequency of Chls.

Unravelling the Role of Water in Ultrafast Excited-State Relaxation Dynamics within Nano-Architectures of Chlorophyll a

Water plays a pivotal role in structural stability of supramolecular pigment assemblies designed for natural light harvesting (for example, chlorosome antenna complex) as well as their artificial analogs. However, the dynamic role of water in the context of excite-state relaxation has not been explored till date, which we report here. Using femtosecond transient absorption spectroscopy, we investigate the excited-state dynamics of two types of nano-scale assemblies of chlorophyll a with different structural motifs, rod-shaped and micellar assemblies, that depend on the water content. We show how water participates in excess energy dissipation by vibrational cooling of the non-thermally populated Q_y band at different rates in different types of clusters but exhibits no polar solvation dynamics. For the micelles, we observe a bifurcation of stimulated emission line shape, whereas a positive-to-negative switching of differential absorption is observed for the rods; both these observations are correlated with their specific structural aspects. Density functional theory calculations reveal two possible stable ground state geometries of dimers, accounting for the bifurcation of line shape in micelles. Thus, our study elucidates water-mediated structure-function relationship within these pigment assemblies.

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.

Vibronic structure of photosynthetic pigments probed by polarized two-dimensional electronic spectroscopy and ab initio calculations

Bacteriochlorophyll a (Bchl a) and chlorophyll a (Chl a) play important roles as light absorbers in photosynthetic antennae and participate in the initial charge-separation steps in photosynthetic reaction centers. Despite decades of study, questions remain about the interplay of electronic and vibrational states within the Q-band and its effect on the photoexcited dynamics. Here we report results of polarized two-dimensional electronic spectroscopic measurements, performed on penta-coordinated Bchl a and Chl a and their interpretation based on state-of-the-art time-dependent density functional theory calculations and vibrational mode analysis for spectral shapes. We find that the Q-band of Bchl a is comprised of two independent bands, that are assigned following the Gouterman model to Q x and Q y states with orthogonal transition dipole moments. However, we measure the angle to be ∼75°, a finding that is confirmed by ab initio calculations. The internal conversion rate constant from Q x to Q y is found to be 11 ps-1. Unlike Bchl a, the Q-band of Chl a contains three distinct peaks with different polarizations. Ab initio calculations trace these features back to a spectral overlap between two electronic transitions and their vibrational replicas. The smaller energy gap and the mixing of vibronic states result in faster internal conversion rate constants of 38-50 ps-1. We analyze the spectra of penta-coordinated Bchl a and Chl a to highlight the interplay between low-lying vibronic states and their relationship to photoinduced relaxation. Our findings shed new light on the photoexcited dynamics in photosynthetic systems where these chromophores are primary pigments.

Electronic Interactions in the Bacterial Reaction Center Revealed by Two-Color 2D Electronic Spectroscopy

The bacterial reaction center (BRC) serves as an important model system for understanding the charge separation processes in photosynthesis. Knowledge of the electronic structure of the BRC is critical for understanding its charge separation mechanism. While it is well-accepted that the "special pair" pigments are strongly coupled, the degree of coupling among other BRC pigments has been thought to be relatively weak. Here we study the W(M250)V mutant BRC by two-color two-dimensional electronic spectroscopy to correlate changes in the Q _x region with excitation of the Q _y transitions. The resulting Q _y-Q _x cross-peaks provide a sensitive measure of the electronic interactions throughout the BRC pigment network and complement one-color 2D studies in which such interactions are often obscured by energy transfer and excited-state absorption signals. Our observations should motivate the refinement of electronic structure models of the BRC to facilitate improved understanding of the charge separation mechanism.

Understanding the influence of disorder on the exciton dynamics and energy transfer in Zn-phthalocyanine H-aggregates

The photophysics of 9(19),16(17),23(24)-tri-tert-butyl-2-[ethynyl-(4-carboxymethyl)phenyl]phthalocyaninatozinc(ii) and its H-aggregates is studied in different solvents by means of ultrafast non-linear optical spectroscopy and computational modeling. In non-coordinating solvents, both stationary and time-resolved spectroscopies highlight the formation of extended molecular aggregates, whose dimension and spectral properties depends on the concentration. In all the explored experimental conditions, time-resolved transient absorption experiments show multi exponential decay of the signals. Additional insights into the excited state relaxation mechanisms of the system is obtained with 2D electronic spectroscopy, which is employed to compare the deactivation channels in the absence or presence of aggregates. In ethanol and diethylether, where only monomers are present, an ultrafast relaxation process among the two non-degenerate Q-states of the molecule is evidenced by the appearance of a cross peak in the 2D-maps. In chloroform or CCl4, where disordered H-aggregates are formed, an energy transfer channel among aggregates with different composition and size is observed, leading to the non-radiative decay towards the lower energy dark state of the aggregates. Efficient coupling between less and more aggregated species is highlighted in two-dimensional electronic spectra by the appearance of a cross peak. The kinetics and intensity of the latter depend on the concentration of the solution. Finally, the linear spectroscopic properties of the aggregate are reproduced using a simplified structural model of an extended aggregate, based on Frenkel Hamiltonian Calculations and on an estimate of the electronic couplings between each dimer composing the aggregate computed at DFT level.

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

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

Broadband 2D electronic spectrometer using white light and pulse shaping: noise and signal evaluation at 1 and 100 kHz

We have developed a broad bandwidth two-dimensional electronic spectrometer that operates shot-to-shot at repetition rates up to 100 kHz using an acousto-optic pulse shaper. It is called a two-dimensional white-light (2D-WL) spectrometer because the input is white-light supercontinuum. Methods for 100 kHz data collection are studied to understand how laser noise is incorporated into 2D spectra during measurement. At 100 kHz, shot-to-shot scanning of the delays and phases of the pulses in the pulse sequence produces a 2D spectrum 13-times faster and with the same signal-to-noise as using mechanical stages and a chopper. Comparing 100 to 1 kHz repetition rates, data acquisition time is decreased by a factor of 200, which is beyond the improvement expected by the repetition rates alone due to reduction in 1/f noise. These improvements arise because shot-to-shot readout and modulation of the pulse train at 100 kHz enables the electronic coherences to be measured faster than the decay in correlation between laser intensities. Using white light supercontinuum for the pump and probe pulses produces high signal-to-noise spectra on samples with optical densities <0.1 within a few minutes of averaging and an instrument response time of <46 fs thereby demonstrating that that simple broadband continuum sources, although weak, are sufficient to create high quality 2D spectra with >200 nm bandwidth.

Bacteriophytochrome Photoisomerization Proceeds Homogeneously Despite Heterogeneity in Ground State

Phytochromes are red/far-red photoreceptors that are widely distributed in plants and prokaryotes. Ultrafast photoisomerization of a double bond in a biliverdin cofactor or other linear tetrapyrrole drives their photoactivity, but their photodynamics are only partially understood. Multiexponential dynamics were observed in previous ultrafast spectroscopic studies and were attributed to heterogeneous populations of the pigment-protein complex. In this work, two-dimensional photon echo spectroscopy was applied to study dynamics of the bacteriophytochromes RpBphP2 and PaBphP. Two-dimensional photon echo spectroscopy can simultaneously resolve inhomogeneity in ensembles and fast dynamics by correlating pump wavelength with the emitted signal wavelength. The distribution of absorption and emission energies within the same state indicates an ensemble of heterogeneous protein environments that are spectroscopically distinct. However, the lifetimes of the dynamics are uniform across the ensemble, suggesting a homogeneous model involving sequential intermediates for the initial photodynamics of isomerization.

Alternative view of two-dimensional spectroscopy

Femtosecond two-dimensional (2D) spectroscopy has become a widely employed method for the investigation of the dynamics of complex chemical and biological systems. In 2D spectroscopy, the sample is excited with three phase-locked femtosecond pulses, and the signal is heterodyned with the local oscillator field. The 2D spectrum is obtained by double Fourier transform with respect to the time delay between the first two pulses and the time delay between the third pulse and the local oscillator field. We show that 2D optical signals can alternatively be measured and computationally simulated as four-wave-mixing signals generated by two femtosecond pulses and two one-sided continuous-wave (CW) pulses. The first femtosecond pulse and one-sided CW pulse create the doorway state, while the second femtosecond pulse and one-sided CW pulse create the window state. This picture relates 2D spectroscopy to other mixed time-frequency-domain techniques, which is useful for the interpretation of the corresponding signals. Moreover, it allows a computationally efficient evaluation of 2D spectra.

Relation between Dephasing Time and Energy Gap Fluctuations in Biomolecular Systems

Excitation energy and charge transfer are fundamental processes in biological systems. Because of their quantum nature, the effect of dephasing on these processes is of interest especially when trying to understand their efficiency. Moreover, recent experiments have shown quantum coherences in such systems. As a first step toward a better understanding, we studied the relationship between dephasing time and energy gap fluctuations of the individual molecular subunits. A larger set of molecular simulations has been investigated to shed light on this dependence. This set includes bacterio-chlorophylls in Fenna-Matthews-Olson complexes, the PE545 aggregate, the LH2 complexes, DNA, photolyase, and cryptochromes. For the individual molecular subunits of these aggregates it has been confirmed quantitatively that an inverse proportionality exists between dephasing time and average gap energy fluctuation. However, for entire complexes including the respective intermolecular couplings, such a relation still needs to be verified.

Simulation of femtosecond two-dimensional electronic spectra of conical intersections

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

Study of carotenoids in cyanobacteria by Raman spectroscopy

Cyanobacteria have established dominant aquatic populations around the world, generally in aggressive environments and under severe stress conditions, e.g., intense solar radiation. Several marine strains make use of compounds such as the polyenic molecules for their damage protection justifying the range of colours observed for these species. The peridinin/chlorophyll-a/protein complex is an excellent example of essential structures used for self-prevention; their systems allow to them surviving under aggressive environments. In our simulations, few protective dyes are required to the initial specimen defense; this is an important data concern the synthetic priority in order to supply adequate damage protection. Raman measurements obtained with 1064 and 514.5 nm excitations for Cylindrospermopsis raciborskii and Microcystis aeruginosa strains shows bands assignable to the carotenoid peridinin. It was characterized by bands at 1940, 1650, 1515, 1449, 1185, 1155 and 1000 cm(-1) assigned to ν(C=C=C) (allenic vibration), ν(C=C/CO), ν(C=C), δ(C-H, C-18/19), δ(C-H), ν(C-C), and ρ(C-CH3), respectively. Recognition by Raman spectroscopy proved to be an important tool for preliminaries detections and characterization of polyene molecules in several algae, besides initiate an interesting discussion about their synthetic priority.

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.

Dispersion-free continuum two-dimensional electronic spectrometer

Electronic dynamics span broad energy scales with ultrafast time constants in the condensed phase. Two-dimensional (2D) electronic spectroscopy permits the study of these dynamics with simultaneous resolution in both frequency and time. In practice, this technique is sensitive to changes in nonlinear dispersion in the laser pulses as time delays are varied during the experiment. We have developed a 2D spectrometer that uses broadband continuum generated in argon as the light source. Using this visible light in phase-sensitive optical experiments presents new challenges in implementation. We demonstrate all-reflective interferometric delays using angled stages. Upon selecting an ~180  nm window of the available bandwidth at ~10  fs compression, we probe the nonlinear response of broadly absorbing CdSe quantum dots and electronic transitions of Chlorophyll a.

Fifth-order three-dimensional electronic spectroscopy using a pump-probe configuration

We present the theoretical details and experimental demonstration of fifth-order three-dimensional (3D) electronic spectroscopy using a pump-probe beam geometry. This is achieved using a pulse shaper and appropriate phase cycling schemes. We show how 8-step and 27-step phase cycling schemes can measure purely absorptive 3D spectra as well as 3D spectra for the individual fifth-order processes that contribute to the purely absorptive spectrum. 3D spectra as a function of two separate controllable waiting time periods can be obtained. The peak shapes and positions of the peaks in the experimental measurement correspond well to theory.