Vibrational coherence transfer illuminates dark modes in models of the FeFe hydrogenase active site

Understanding 2D-IR Spectra of Hydrogenases: A Descriptive and Predictive Computational Study

[NiFe] hydrogenases are metalloenzymes that catalyze the reversible cleavage of dihydrogen (), a clean future fuel. Understanding the mechanism of these biocatalysts requires spectroscopic techniques that yield insights into the structure and dynamics of the [NiFe] active site. Due to the presence of CO and ligands at this cofactor, infrared (IR) spectroscopy represents an ideal technique for studying these aspects, but molecular information from linear IR absorption experiments is limited. More detailed insights can be obtained from ultrafast nonlinear IR techniques like IRpump−IRprobe and two-dimensional (2D-)IR spectroscopy. However, fully exploiting these advanced techniques requires an in-depth understanding of experimental observables and the encoded molecular information. To address this challenge, we present a descriptive and predictive computational approach for the simulation and analysis of static 2D-IR spectra of [NiFe] hydrogenases and similar organometallic systems. Accurate reproduction of experimental spectra from a first-coordination-sphere model suggests a decisive role of the [NiFe] core in shaping the enzymatic potential energy surface. We also reveal spectrally encoded molecular information that is not accessible by experiments, thereby helping to understand the catalytic role of the diatomic ligands, structural differences between [NiFe] intermediates, and possible energy transfer mechanisms. Our studies demonstrate the feasibility and benefits of computational spectroscopy in the 2D-IR investigation of hydrogenases, thereby further strengthening the potential of this nonlinear IR technique as a powerful research tool for the investigation of complex bioinorganic molecules.

Tracking Energy Transfer across a Platinum Center

Rigid, conjugated alkyne bridges serve as important components in various transition-metal complexes used for energy conversion, charge separation, sensing, and molecular electronics. Alkyne stretching modes have potential for modulating charge separation in donor–bridge–acceptor compounds. Understanding the rules of energy relaxation and energy transfer across the metal center in such compounds can help optimize their electron transfer switching properties. We used relaxation-assisted two-dimensional infrared spectroscopy to track energy transfer across metal centers in platinum complexes featuring a triazole-terminated alkyne ligand of two or six carbons, a perfluorophenyl ligand, and two tri(p-tolyl)phosphine ligands. Comprehensive analyses of waiting-time dynamics for numerous cross and diagonal peaks were performed, focusing on coherent oscillation, energy transfer, and cooling parameters. These observables augmented with density functional theory computations of vibrational frequencies and anharmonic force constants enabled identification of different functional groups of the compounds. Computations of vibrational relaxation pathways and mode couplings were performed, and two regimes of intramolecular energy redistribution are described. One involves energy transfer between ligands via high-frequency modes; the transfer is efficient only if the modes involved are delocalized over both ligands. The energy transport pathways between the ligands are identified. Another regime involves redistribution via low-frequency delocalized modes, which does not lead to interligand energy transport.

Ultrafast vibrational excitation transfer on resonant antenna lattices revealed by two-dimensional infrared spectroscopy

High-quality lattice resonances in arrays of infrared antennas operating in an open-cavity regime form polariton states by means of strong coupling to molecular vibrations. We studied polaritons formed by carbonyl stretching modes of (poly)methyl methacrylate on resonant antenna arrays using femtosecond 2DIR spectroscopy. At a normal incidence of excitation light, doubly degenerate antenna-lattice resonances (ALRs) form two polariton states: a lower polariton and an upper polariton. At an off-normal incidence geometry of 2DIR experiments, the ALR degeneracy is lifted and, consequently, the polariton energies are split. We spectrally resolved and tracked the time-dependent evolution of a cross-peak signal associated with the excitation of reservoir states and the unidirectional transfer of the excess energy to lower polaritons. Bi-exponential decay of the cross-peak suggests that a reversible energy exchange between the bright and dark lower polaritons occurs with a characteristic transfer time of ∼200 fs. The cross-peak signal further decays within ∼800 fs, which is consistent with the relaxation time of the carbonyl stretching vibration and with the dephasing time of the ALR. An increase in the excitation pulse intensity leads to saturation of the cross-peak amplitude and a modification of the relaxation dynamics. Using quantum-mechanical modeling, we found that the kinetic scheme that captures all the experimental observations implies that only the bright lower polariton accepts the energy from the reservoir, suggesting that transfer occurs via a mechanism involving dipole–dipole interaction. An efficient reservoir-to-polariton transfer can play an important role in developing novel room-temperature quantum optical devices in the mid-infrared wavelength region.

Hidden vibronic and excitonic structure and vibronic coherence transfer in the bacterial reaction center

We report two-dimensional electronic spectroscopy (2DES) experiments on the bacterial reaction center (BRC) from purple bacteria, revealing hidden vibronic and excitonic structure. Through analysis of the coherent dynamics of the BRC, we identify multiple quasi-resonances between pigment vibrations and excitonic energy gaps, and vibronic coherence transfer processes that are typically neglected in standard models of photosynthetic energy transfer and charge separation. We support our assignment with control experiments on bacteriochlorophyll and simulations of the coherent dynamics using a reduced excitonic model of the BRC. We find that specific vibronic coherence processes can readily reveal weak exciton transitions. While the functional relevance of such processes is unclear, they provide a spectroscopic tool that uses vibrations as a window for observing excited state structure and dynamics elsewhere in the BRC via vibronic coupling. Vibronic coherence transfer reveals the upper exciton of the “special pair” that was weakly visible in previous 2DES experiments.

Redox conditions correlated with vibronic coupling modulate quantum beats in photosynthetic pigment-protein complexes

Quantum coherences, observed as time-dependent beats in ultrafast spectroscopic experiments, arise when light-matter interactions prepare systems in superpositions of states with differing energy and fixed phase across the ensemble. Such coherences have been observed in photosynthetic systems following ultrafast laser excitation, but what these coherences imply about the underlying energy transfer dynamics remains subject to debate. Recent work showed that redox conditions tune vibronic coupling in the Fenna-Matthews-Olson (FMO) pigment-protein complex in green sulfur bacteria, raising the question of whether redox conditions may also affect the long-lived (>100 fs) quantum coherences observed in this complex. In this work, we perform ultrafast two-dimensional electronic spectroscopy measurements on the FMO complex under both oxidizing and reducing conditions. We observe that many excited-state coherences are exclusively present in reducing conditions and are absent or attenuated in oxidizing conditions. Reducing conditions mimic the natural conditions of the complex more closely. Further, the presence of these coherences correlates with the vibronic coupling that produces faster, more efficient energy transfer through the complex under reducing conditions. The growth of coherences across the waiting time and the number of beating frequencies across hundreds of wavenumbers in the power spectra suggest that the beats are excited-state coherences with a mostly vibrational character whose phase relationship is maintained through the energy transfer process. Our results suggest that excitonic energy transfer proceeds through a coherent mechanism in this complex and that the coherences may provide a tool to disentangle coherent relaxation from energy transfer driven by stochastic environmental fluctuations.

Ultrafast vibrational dynamics of a solute correlates with dynamics of the solvent

Two-dimensional infrared (2D-IR) spectroscopy is used to measure the spectral dynamics of the metal carbonyl complex cyclopentadienyl manganese tricarbonyl (CMT) in a series of linear alkyl nitriles. 2D-IR spectroscopy provides direct readout of solvation dynamics through spectral diffusion, probing the decay of frequency correlation induced by fluctuations of the solvent environment. 2D-IR simultaneously monitors intramolecular vibrational energy redistribution (IVR) among excited vibrations, which can also be influenced by the solvent through the spectral density rather than the dynamical friction underlying solvation. Here, we report that the CMT vibrational probe reveals solvent dependences in both the spectral diffusion and the IVR time scales, where each slows with increased alkyl chain length. In order to assess the degree to which solute-solvent interactions can be correlated with bulk solvent properties, we compared our results with low-frequency dynamics obtained from optical Kerr effect (OKE) spectroscopy-performed by others-on the same nitrile solvent series. We find excellent correlation between our spectral diffusion results and the orientational dynamics time scales from OKE. We also find a correlation between our IVR time scales and the amplitudes of the low-frequency spectral densities evaluated at the 90-cm^-1 energy difference, corresponding to the gap between the two strong vibrational modes of the carbonyl probe. 2D-IR and OKE provide complementary perspectives on condensed phase dynamics, and these findings provide experimental evidence that at least at the level of dynamical correlations, some aspects of a solute vibrational dynamics can be inferred from properties of the solvent.

Direct comparison of amplitude and geometric measures of spectral inhomogeneity using phase-cycled 2D-IR spectroscopy

Two-dimensional infrared (2D-IR) spectroscopy provides access to equilibrium dynamics with the extraction of the frequency-fluctuation correlation function (FFCF) from the measured spectra. Several different methods of obtaining the FFCF from experimental spectra, such as the center line slope (CLS), ellipticity, phase slope, and nodal line slope, all depend on the geometrical nature of the 2D line shape and necessarily require spectral extent in order to achieve a measure of the FFCF. Amplitude measures, on the other hand, such as the inhomogeneity index, rely only on signal amplitudes and can, in principle, be computed using just a single point in a 2D spectrum. With a pulse shaper-based 2D-IR spectrometer, in conjunction with phase cycling, we separate the rephasing and nonrephasing signals used to determine the inhomogeneity index. The same measured data provide the absorptive spectrum, needed for the CLS. Both methods are applied to two model molecular systems: tungsten hexacarbonyl (WCO₆) and methylcyclopentadienyl manganese tricarbonyl [Cp'Mn(CO)₃, MCMT]. The three degenerate IR modes of W(CO)₆ lack coherent modulation or noticeable intramolecular vibrational redistribution (IVR) and are used to establish a baseline comparison. The two bands of the MCMT tripod complex include intraband coherences and IVR as well as likely internal torsional motion on a few-picosecond time scale. We find essentially identical spectral diffusion, but faster, non-equilibrium dynamics lead to differences in the FFCFs extracted with the two methods. The inhomogeneity index offers an advantage in cases where spectra are complex and energy transfer can mimic line shape changes due to frequency fluctuations.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.