Transient Chiral Dynamics in the Fenna-Matthews-Olson Complex Revealed by Two-Dimensional Circular Dichroism Spectroscopy

Chirality plays a pivotal role across scientific disciplines with profound implications spanning light-matter interactions, molecular recognition, and natural evolutionary processes. This study delves into the active influence of molecular chirality on exciton energy transfer within photosynthetic protein complexes, focusing on the Fenna-Matthews-Olson (FMO) complex. Employing two-dimensional circular dichroism (2DCD) spectroscopy, we investigate the transient chiral dynamics of excitons during energy transfer processes within the FMO complex. Our approach, incorporating pulse information into population dynamics based on the third-order response function, facilitates the calculation of 2DCD spectra and dynamics. This enables the extraction of chiral contributions to excitonic energy transfer and the examination of electronic wave functions. We demonstrate that 2DCD spectra offer excitation energies that are better resolved than those from conventional two-dimensional electronic spectroscopy. These findings deepen our understanding of exciton energy transfer mechanisms in natural photosynthesis, emphasizing the potential of 2DCD spectroscopy as a powerful tool for unraveling the chiral contribution to exciton dynamics.

Quantum Interferometric Pathway Selectivity in Difference-Frequency-Generation Spectroscopy

Even-order spectroscopies such as sum-frequency generation (SFG) and difference-frequency generation (DFG) can serve as direct probes of molecular chirality. Such signals are usually given by the sum of several interaction pathways that carry different information about matter. Here we focus on DFG, involving impulsive optical-optical-IR interactions, where the last IR pulse probes vibrational transitions in the ground or excited electronic state manifolds, depending on the interaction pathway. Spectroscopy with classical light can use phase matching to select the two pathways. In this theoretical study, we propose a novel quantum interferometric protocol that uses entangled photons to isolate individual pathways. This additional selectivity originates from engineering the state of light using a Zou-Wang-Mandel interferometer combined with coincidence detection.

Experimental implementations of two-dimensional fourier transform electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Probing chirality fluctuations in molecules by nonlinear optical spectroscopy

Symmetry breaking caused by geometric fluctuations can enable processes that are otherwise forbidden. An example is a perylene bisimide dyad whose dipole moments are perpendicular to each other. Förster-type energy transfer is thus forbidden at the equilibrium geometry since the dipolar coupling vanishes. Yet, fluctuations of the geometric arrangement have been shown to induce finite energy transfer that depends on the dipole variance, rather than the mean. We demonstrate an analogous effect associated with chirality symmetry breaking. In its equilibrium geometry, this dimer is non-chiral. The linear chiral response which depends on the average geometry thus vanishes. However, we show that certain 2D chiral optical signals are finite due to geometric fluctuations. Furthermore, the correlation time of these fluctuations can be experimentally revealed by the waiting time dependence of the 2D signal.

Aggregation-induced emission on benzothiadiazole dyads with large third-order optical nonlinearity

Two kinds of D-A molecular of (4-(4-(9H-carbazol-9-yl)phenyl))-7-nitrobenzothiadiazole (BSC) and 4-((4-(9H-carbazol-9-yl)phenyl)ethynyl)-7-nitrobenzothiadiazole (BEC) containing carbazole moieties as the donor were synthesized. X-ray crystal data elucidated the multiple intermolecular interactions. They exhibit distinctly different self-assembly behaviours. The nonlinear optical properties were studied using the top-hat Z-scan technique at 532 nm with a 21 ps pulse. The results indicate that they exhibit large third-order nonlinear absorption effects. The nonlinear absorption coefficients α2 fitting the experimental data are 6.3 × 10(-12) m W(-1) for BSC and 3.6 × 10(-11) m W(-1) for BEC. The time-resolved pump-probe results show that both nonlinear absorption and nonlinear refraction of BEC in CH2Cl2 solution have rapid optical responses, which indicate the nonlinear absorption and nonlinear refraction mechanism are excited-state nonlinear. Moreover, both of these two compounds are observed to be aggregation-induced emission (AIE) active. The aggregates of the well-formed one-dimensional microrods of BEC and BSC endow the material with potential applications in the field of optical devices.

Dynamic localization of electronic excitation in photosynthetic complexes revealed with chiral two-dimensional spectroscopy

Time-resolved ultrafast optical probes of chiral dynamics provide a new window allowing us to explore how interactions with such structured environments drive electronic dynamics. Incorporating optical activity into time-resolved spectroscopies has proven challenging because of the small signal and large achiral background. Here we demonstrate that two-dimensional electronic spectroscopy can be adapted to detect chiral signals and that these signals reveal how excitations delocalize and contract following excitation. We dynamically probe the evolution of chiral electronic structure in the light-harvesting complex 2 of purple bacteria following photoexcitation by creating a chiral two-dimensional mapping. The dynamics of the chiral two-dimensional signal directly reports on changes in the degree of delocalization of the excitonic states following photoexcitation. The mechanism of energy transfer in this system may enhance transfer probability because of the coherent coupling among chromophores while suppressing fluorescence that arises from populating delocalized states. This generally applicable spectroscopy will provide an incisive tool to probe ultrafast transient molecular fluctuations that are obscured in non-chiral experiments.

Vibrational solvatochromism and electrochromism. II. Multipole analysis

Small infrared probe molecules have been widely used to study local electrostatic environment in solutions and proteins. Using a variety of time- and frequency-resolved vibrational spectroscopic methods, one can accurately measure the solvation-induced vibrational frequency shifts and the timescales and amplitudes of frequency fluctuations of such IR probes. Since the corresponding frequency shifts are directly related to the local electric field and its spatial derivatives of the surrounding solvent molecules or amino acids in proteins, one can extract information on local electric field around an IR probe directly from the vibrational spectroscopic results. Here, we show that, carrying out a multipole analysis of the solvatochromic frequency shift, the solvatochromic dipole contribution to the frequency shift is not always the dominant factor. In the cases of the nitrile-, thiocyanato-, and azido-derivatized molecules, the solvatochromic quadrupole contributions to the corresponding stretch mode frequency shifts are particularly large and often comparable to the solvatochromic dipole contributions. Noting that the higher multipole moment-solvent electric field interactions are short range effects in comparison to the dipole interaction, the H-bonding interaction-induced vibrational frequency shift can be caused by such short-range multipole-field interaction effects. We anticipate that the present multipole analysis method specifically developed to describe the solvatochromic vibrational frequency shifts will be useful to understand the intermolecular interaction-induced vibrational property changes and to find out a relationship between vibrational solvatochromism and electrochromism of IR probes in condensed phases.

Novel coherent two-dimensional optical spectroscopy probes of chirality exchange and fluctuations in molecules

We demonstrate how stochastic transitions between molecular configurations with opposite senses of chirality may be probed by 2D optical signals with specific pulse polarization configurations. The third-order optical response of molecular dimers (such as biphenyls) with dynamical axial chirality is calculated to order of k(2) in the wavevector of light. Spectroscopic signatures of equilibrium chirality fluctuations are predicted for three dynamical models (Ornstein-Uhlenbeck, two-state jump, and diffusion in double well) of the dihedral angle that controls the chirality.

Coherent control protocol for separating energy-transfer pathways in photosynthetic complexes by chiral multidimensional signals

Adaptive optimizations performed using a genetic algorithm are employed to construct optimal laser pulse configurations that separate spectroscopic features associated with the two main energy-transfer pathways in the third-order nonlinear optical response simulated for the Fenna-Matthews-Olson (FMO) photosynthetic complex from the green sulfur bacterium Chlorobium tepidum. Superpositions of chirality-induced tensor components in both collinear and noncollinear pulse configurations are analyzed. The optimal signals obtained by manipulating the ratios of various 2D spectral peaks reveal detailed information about the excitation dynamics.

Chiroptical nature of two-exciton states of light-harvesting complex: Doubly resonant three-wave-mixing spectroscopy

Photosynthetic light-harvesting complex is a coupled multichromophore system. Due to electronic couplings between neighboring chlorophylls in the complex, the one- and two-exciton states are delocalized and they can be written as linear combinations of singly and doubly excited configurations, respectively. Despite that the chiroptical properties of one-exciton states in such a multichromophore system have been investigated by using linear optical activity measurement techniques; those of two-exciton states have not been studied before due to a lack of appropriate measurement methods. Here, we present a theoretical description on chiroptical chi((2)) spectroscopy and show that it can be used to investigate such properties of a photosynthetic light-harvesting system, which is the Fenna-Matthews-Olson complex, consisting of seven bacteriochlorophylls in its protein subunit. To simulate the doubly resonant sum- and difference-frequency-generation spectra of the complex, one- and two-exciton transition dipoles were calculated. Carrying out quantum chemistry calculations of electronically excited states of a model bacteriochlorophyll system and taking into account the dipole-induced dipole electronic transition processes between the ground state and two-exciton states, we could calculate the two-dimensional sum-frequency-generation spectra revealing dominant second-order chiroptical transition pathways and involved one- and two-exciton states. It is believed that the present computational scheme and the theoretically proposed doubly resonant two-dimensional three-wave-mixing spectroscopy would be of use to shed light on the chiroptical natures of two-exciton states of arbitrary coupled multichromophore systems.

Computational vibrational spectroscopy of peptides and proteins in one and two dimensions

Vibrational spectroscopy provides direct information on molecular environment and motions but, its interpretation is often hampered by band broadening. Over the past decade, two-dimensional (2D) vibrational spectroscopy has emerged as a promising technique to overcome a number of difficulties associated with linear spectroscopy and provided significantly detailed information on the structure and dynamics of complex molecules in condensed phases. This Account reviews recently developed computational methods used to simulate 1D and 2D vibrational spectra. The central quantity to calculate in computational spectroscopy is the spectroscopic response function, which is the product of many contributing factors such as vibrational transition energies, transition moments, and their modulations by fluctuating local environment around a solute. Accurate calculations of such linear and nonlinear responses thus require a concerted effort employing a wide range of methods including electronic structure calculation (ESC) and molecular dynamics (MD) simulation. The electronic structure calculation can provide fundamental quantities such as normal-mode frequencies and transition multipole strengths. However, since the treatable system size is limited with this method, classical MD simulation has also been used to account for the dynamics of the solvent environment. To achieve chemical accuracy, these two results are combined to generate time series of fluctuating transition frequencies and transition moments with the distributed multipole analysis, and this particular approach has been known as the hybrid ESC/MD method. For coupled multichromophore systems, vibrational properties of each chromophore such as a peptide are individually calculated by electronic structure methods and the Hessian matrix reconstruction scheme was used to obtain local mode frequencies and couplings of constituting anharmonic oscillators. The spectra thus obtained, especially for biomolecules including polypeptides and proteins, have proven to be reliable and in good agreement with experimental spectra. An alternative to the hybrid method has also been developed, where the classical limit of the vibrational response function was considered. Its main attraction is the capability to obtain the spectra directly from a set of MD trajectories. A novel development along this direction has been achieved by using quantum mechanical/molecular mechanical (QM/MM) force fields for the accurate description of vibrational anharmonicity and chromophore polarization effects. The latter aspects are critical in the 2D case because classical force fields employing harmonic intramolecular potential cannot produce reliable 2D signal. We anticipate that the computational methods presented here will continue to evolve along with experimental advancements and will be of use to further elucidate ultrafast dynamics of chemical and biological systems.

Vibrational solvatochromism and electrochromism: coarse-grained models and their relationships

A theoretical description of vibrational solvatochromism and electrochromism is presented by using a coarse-grained model based on a distributed charge and multipole interaction theory. Solvatochromic frequency shift has been described by considering the interaction between distributed charges of a solute and electrostatic potential due to distributed charges of solvent molecules. Another approach was based on the expansion of the solvatochromic frequency shift in terms of solvent electric field and its gradient at distributed sites on solute. The relationship between these two approaches is elucidated and their validities are discussed. It is also shown that the distributed charge and multipole model for solvatochromism developed here can be used to describe vibrational Stark effects on frequency and transition dipole moment. The relationship between the vibrational Stark tuning rate and the parameters obtained from recent vibrational solvatochromism studies is clarified and used to determine the vibrational Stark tuning rates of a few stretching modes, which are then directly compared with experimentally measured values. We anticipate that the present theoretical model can be used to study a variety of vibrational solvatochromic and electrochromic phenomena and to extract critical information on local electrostatic environment around a small IR probe in solution or protein from linear and nonlinear IR spectroscopic studies.