Two-dimensional Electronic Spectra Research Articles

Phase-modulated rapid-scanning fluorescence-detected two-dimensional electronic spectroscopy.

We present a rapid-scanning approach to fluorescence-detected two-dimensional electronic spectroscopy that combines acousto-optic phase-modulation with digital lock-in detection. This approach shifts the signal detection window to suppress 1/f laser noise and enables interferometric tracking of the time delays to allow for correction of spectral phase distortions and accurate phasing of the data. This use of digital lock-in detection enables acquisition of linear and nonlinear signals of interest in a single measurement. We demonstrate the method on a laser dye, measuring the linear fluorescence excitation spectrum as well as rephasing, non-rephasing, and absorptive fluorescence-detected two-dimensional electronic spectra.

Dynamic Stark Effect in Two-Dimensional Spectroscopy Revealing Modulation of Ultrafast Charge Separation in Bacterial Reaction Centers by an Inherent Electric Field.

Despite extensive study, mysteries remain regarding the highly efficient ultrafast charge separation processes in photosynthetic reaction centers (RCs). In this work, transient Stark signals were found to be present in ultrafast two-dimensional electronic spectra recorded for purple bacterial RCs at 77 K. These arose from the electric field that is inherent to the intradimer charge-transfer intermediate of the bacteriochlorophyll pair (P), PA+PB-. By comparing three mutated RCs, a correlation was found between the efficient formation of PA+PB- and a fast charge separation rate. Importantly, the energy level of P* was changed due to the Stark shift, influencing the driving force for P* → P+BA- electron transfer and hence its rate. Furthermore, the orientation and amplitude of the inherent electric field varied in different ways upon different mutation, leading to contrasting changes in the rates. This mechanism of modulation provides a solution to a long-lasting inconsistency between experimental observations and activation energy theory.

Modeling and Simulating the Excited-State Dynamics of a System with Condensed Phases: A Machine Learning Approach

Simulating the irreversible quantum dynamics of exciton- and electron-transfer problems poses a nontrivial challenge. Because the irreversibility of the system dynamics is a result of quantum thermal activation and dissipation caused by the surrounding environment, it is necessary to include infinite environmental degrees of freedom in the simulation. Because the capabilities of full quantum dynamics simulations that include the surrounding molecular degrees of freedom are limited, employing a system-bath model is a practical approach. In such a model, the dynamics of excitons or electrons are described by a system Hamiltonian, while the other degrees of freedom that arise from the environmental molecules are described by a harmonic oscillator bath (HOB) and system-bath interaction parameters. By extending on a previous study of molecular liquids [ J. Chem. Theory Comput. 2020, 16, 2099], here, we construct a system-bath model for exciton- and electron-transfer problems by means of a machine learning approach. We determine both the system and system-bath interaction parameters, including the spectral distribution of the bath, using the electronic excitation energies obtained from a quantum mechanics/molecular mechanics (QM/MM) simulation that is conducted as a function of time. Using the analytical expressions of optical response functions, we calculate linear and two-dimensional electronic spectra (2DES) for indocarbocyanine dimers in methanol. From these results, we demonstrate the capability of our approach to elucidate the nonequilibrium exciton dynamics of a quantum system in a nonintuitive manner.

A quantum Langevin equation approach for two-dimensional electronic spectra of coupled vibrational and electronic dynamics.

We present an efficient method to simulate two-dimensional (2D) electronic spectra of condensed-phase systems with an emphasis on treating quantum nuclear wave packet dynamics explicitly. To this end, we combine a quantum Langevin equation (QLE) approach for dissipation and a perturbative scheme to calculate three-pulse photon-echo polarizations based on wave packet dynamics under the influence of external fields. The proposed dynamical approach provides a consistent description of nuclear quantum dynamics, pulse-overlap effects, and vibrational relaxation, enabling simulations of 2D electronic spectra with explicit and non-perturbative treatment of coupled electronic-nuclear dynamics. We apply the method to simulate 2D electronic spectra of a displaced-oscillator model in the condensed phase and discuss the spectral and temporal evolutions of 2D signals. Our results show that the proposed QLE approach is capable of describing vibrational relaxation, decoherence, and vibrational coherence transfer, as well as their manifestations in spectroscopic signals. Furthermore, vibrational quantum beats specific for excited-state vs ground-state nuclear wave packet dynamics can also be identified. We anticipate that this method will provide a useful tool to conduct theoretical studies of 2D spectroscopy for strong vibronically coupled systems and to elucidate intricate vibronic couplings in complex molecular systems.

Understanding radiative transitions and relaxation pathways in plexcitons

Summary Molecular aggregates on plasmonic nanoparticles have emerged as attractive systems for the studies of polaritonic light-matter states, called plexcitons. Such systems are tunable, scalable, easy to synthesize, and offer sub-wavelength confinement, all while giving access to the ultrastrong light-matter coupling regime, promising a plethora of applications. However, the complexity of these materials prevented the understanding of their excitation and relaxation phenomena. Here, we follow the relaxation pathways in plexcitons and conclude that while the metal destroys the optical coherence, the molecular aggregate coupled to surface processes significantly contributes to the energy dissipation. We use two-dimensional electronic spectroscopy with theoretical modeling to assign the different relaxation processes to either molecules or metal nanoparticle. We show that the dynamics beyond a few femtoseconds has to be considered in the language of hot electron distributions instead of the accepted lower and upper polariton branches and establish the framework for further understanding.

Finite-Temperature, Anharmonicity, and Duschinsky Effects on the Two-Dimensional Electronic Spectra from Ab Initio Thermo-Field Gaussian Wavepacket Dynamics.

Accurate description of finite-temperature vibrational dynamics is indispensable in the computation of two-dimensional electronic spectra. Such simulations are often based on the density matrix evolution, statistical averaging of initial vibrational states, or approximate classical or semiclassical limits. While many practical approaches exist, they are often of limited accuracy and difficult to interpret. Here, we use the concept of thermo-field dynamics to derive an exact finite-temperature expression that lends itself to an intuitive wavepacket-based interpretation. Furthermore, an efficient method for computing finite-temperature two-dimensional spectra is obtained by combining the exact thermo-field dynamics approach with the thawed Gaussian approximation for the wavepacket dynamics, which is exact for any displaced, distorted, and Duschinsky-rotated harmonic potential but also accounts partially for anharmonicity effects in general potentials. Using this new method, we directly relate a symmetry breaking of the two-dimensional signal to the deviation from the conventional Brownian oscillator picture.

Insights into Photosynthetic Energy Transfer Gained from Free-Energy Structure: Coherent Transport, Incoherent Hopping, and Vibrational Assistance Revisited.

Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring the possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and the criteria by which the necessity of the vibrational assistance is considered.

Explicit environmental and vibronic effects in simulations of linear and nonlinear optical spectroscopy.

Accurately simulating the linear and nonlinear electronic spectra of condensed phase systems and accounting for all physical phenomena contributing to spectral line shapes presents a significant challenge. Vibronic transitions can be captured through a harmonic model generated from the normal modes of a chromophore, but it is challenging to also include the effects of specific chromophore-environment interactions within such a model. We work to overcome this limitation by combining approaches to account for both explicit environment interactions and vibronic couplings for simulating both linear and nonlinear optical spectra. We present and show results for three approaches of varying computational cost for combining ensemble sampling of chromophore-environment configurations with Franck-Condon line shapes for simulating linear spectra. We present two analogous approaches for nonlinear spectra. Simulated absorption spectra and two-dimensional electronic spectra (2DES) are presented for the Nile red chromophore in different solvent environments. Employing an average Franck-Condon or 2DES line shape appears to be a promising method for simulating linear and nonlinear spectroscopy for a chromophore in the condensed phase.

Regarding expressions of the oscillatory patterns in the 2D spectra of a displaced oscillator model

There have been many efforts recently in analyzing the oscillation patterns in a two-dimensional electronic spectrum to characterize vibronic couplings. A displaced oscillator model with a four-level vibronic system (4LvS) is a commonly used model to approximate such phenomena. Although this model is related to an electronic two-level system coupled to a harmonic oscillator (2LScHO) model, there has not been a formal study to connect the two models. Here, we show explicitly that the former is a special case of the latter. We provide a detailed description of how the expressions for the 2D spectral peak amplitudes of the 4LvS model can be derived from the electronic 2LScHO model at T=0K. We also demonstrate that the two-dimensional Fourier maps of the 4LvS model are still good representatives of the more general electronic 2LScHO model at T≠0K.

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.

Exciton delocalization length in chlorosomes investigated by lineshape dynamics of two-dimensional electronic spectra.

A chlorosome, a photosynthetic light-harvesting complex found in green sulfur bacteria, is an aggregate of self-assembled pigments and is optimized for efficient light harvesting and energy transfer under dim-light conditions. In this highly-disordered aggregate, the absorption and transfer of photoexcitation energy are governed by the degree of disorder. To describe the disorder, the number of molecules forming excitons, which is termed exciton delocalization length (EDL), is a relevant parameter because the EDL sensitively changes with the disorder of the constituent molecules. In this work, we determined the EDL in chlorosomes using two-dimensional electronic spectroscopy (2D-ES). Since spectral features correlated with EDL are spread out in the two-dimensional (2D) electronic spectra, we were able to determine the EDL accurately without the effects of homogeneous and inhomogeneous line broadening. In particular, by taking advantage of the multi-dimensionality and the time evolution of 2D spectra, we not only determined the excitation frequency dependence of EDL but also monitored the temporal change of EDL. We found that the EDL is ∼7 at 77 K and ∼6 at 298 K and increases with the excitation frequency, with the maximum located well above the maximum of the absorption spectrum of chlorosomes. The spectral profile of EDL changes rapidly within 100 fs and becomes flat over time due to dephasing of initial exciton coherence. From the coherent oscillations superimposed on the decay of EDL, it was learned that high-frequency phonons are more activated at 298 K than at 77 K.

What do Bloch electrons in a magnetic field have to do with Apollonian packing of circles?

Integral Apollonian packing, the packing of circles with integer curvatures, where every circle is tangent to three other mutually tangent circles, is shown to encode the fractal structure of the energy spectrum of two-dimensional Bloch electrons in a magnetic field, known as the ‘Hofstadter butterfly’. In this Apollonian–butterfly-connection, the integer curvatures of the circles contain in a convoluted form, the topological quantum numbers of the butterfly graph—the quanta of the Hall conductivity. Nesting properties of these two fractals are described in terms of the Apollonian group and the conformal transformations. In this mapping, Farey tree hierarchy plays the central role, revealing how the geometry and the number theory are intertwined in the quantum mechanics of Bloch electrons in a magnetic field.

Spectroscopic response theory with classical mapping Hamiltonians.

Exact quantum dynamics with a time-independent Hamiltonian in a discrete state space can be computed using classical mechanics through the classical Meyer-Miller-Stock-Thoss mapping Hamiltonian. In order to compute quantum response functions from classical dynamics, we extend this mapping to a quantum Hamiltonian with time-dependence arising from a classical field. This generalization requires attention to time-ordering in quantum and classical propagators. Quantum response theory with the original quantum Hamiltonian is equivalent to classical response theory with the classical mapping Hamiltonian. We elucidate the structure of classical response theory with the mapping Hamiltonian, thereby generating classical versions of the two-sided quantum density operator diagrams conventionally used to describe spectroscopic processes. This formal development can provide a foundation for new semiclassical approximations to spectroscopic observables for models in which classical nuclear degrees of freedom are introduced into a mapping Hamiltonian describing electronic states. Calculations of the temperature-dependence of two-dimensional electronic spectra for an exciton dimer using two semiclassical approaches are compared with benchmark calculations using the hierarchical equations of motion method.

On-the-fly ab initio semiclassical evaluation of third-order response functions for two-dimensional electronic spectroscopy.

Ab initio computation of two-dimensional electronic spectra is an expanding field, whose goal is improving upon simple, few-dimensional models often employed to explain experiments. Here, we propose an accurate and computationally affordable approach, based on the single-trajectory semiclassical thawed Gaussian approximation, to evaluate two-dimensional electronic spectra. Importantly, the method is exact for arbitrary harmonic potentials with mode displacement, changes in the mode frequencies, and inter-mode coupling (Duschinsky effect), but can also account partially for the anharmonicity of the involved potential energy surfaces. We test its accuracy on a set of model Morse potentials and use it to study anharmonicity and Duschinsky effects on the linear and two-dimensional electronic spectra of phenol. We find that in this molecule, the anharmonicity effects are weak, whereas the Duschinsky rotation and the changes in the mode frequencies must be included in accurate simulations. In contrast, the widely used displaced harmonic oscillator model captures only the basic physics of the problem but fails to reproduce the correct vibronic lineshape.

Observation of Ultrafast Coherence Transfer and Degenerate States with Polarization-Controlled Two-Dimensional Electronic Spectroscopy.

Optical spectroscopy is a powerful tool to interrogate quantum states of matter. We present simulation results for the cross-polarized two-dimensional electronic spectra of the light-harvesting system LH2 of purple bacteria. We identify a spectral feature on the diagonal, which we assign to ultrafast coherence transfer between degenerate states. The implication for the interpretation of previous experiments on different systems and the potential use of this feature are discussed. In particular, we foresee that this kind of feature will be useful for identifying mixed degenerate states and for identifying the origin of symmetry breaking disorder in systems like LH2. Furthermore, this may help identify both vibrational and electronic states in biological systems such as proteins and solid-state materials such as hybrid perovskites.

Extracting the Frequency-Dependent Dynamic Stokes Shift from Two-Dimensional Electronic Spectra with Prominent Vibrational Coherences

The dynamic Stokes shift is a common means for characterizing ultrafast solvation dynamics of electronically excited states. Here we extract the excitation frequency-dependent dynamic Stokes shift from two-dimensional electronic spectra (2DES) of cresyl violet, a molecule with a well-defined vibronic progression. The extracted dynamic Stokes shift function, S(t), exhibits oscillatory behavior, and the oscillatory components are assigned to intramolecular vibrational modes through DFT and TD-DFT calculations. The well-characterized oscillations are incorporated into the fitting procedure of S(t). The excitation frequency dependence of the ultrafast response is examined through the analysis of S(t) obtained from slices taken at different excitation frequencies of the 2DES spectra. The extracted ultrafast timescales range from 36 to 98 fs, and we interpret the frequency dependence of the timescales in the context of other dynamic processes that also lead to lineshape changes in the 2DES spectrum, such as vibrational energy relaxation and spectral diffusion. Through comparison of the extracted timescales, we find that the fastest timescales are extracted over a range of excitation frequencies, where contributions from vibrational relaxation and spectral diffusion can be minimized.

A Nonperturbative Methodology for Simulating Multidimensional Spectra of Multiexcitonic Molecular Systems via Quasiclassical Mapping Hamiltonian Methods.

We present a new methodology for simulating multidimensional electronic spectra of complex multiexcitonic molecular systems within the framework of quasiclassical mapping Hamiltonian (QC/MH) methods. The methodology is meant to be cost-effective for molecular systems with a large number of nuclear degrees of freedom undergoing nonequilibrium nonadiabatic dynamics on multiple coupled anharmonic electronic potential energy surfaces, for which quantum-mechanically exact methods are not feasible. The methodology is based on a nonperturbative approach to field-matter interaction, which mimics the experimental measurement of those nonlinear time-resolved spectra via phase cycling and can accommodate laser pulses of arbitrary shape and intensity. The ability of different QC/MH methods to accurately simulate two-dimensional and pump-probe electronic spectra within the proposed methodology is compared in the context of a biexcitonic benchmark model that includes both the singly excited and doubly excited electronic states. The QC/MH methods compared include five variations of the linearized semiclassical (LSC) method and the mean-field (Ehrenfest) method. The results show that LSC-based methods are significantly more accurate than the mean-field method and can yield quantitatively accurate two-dimensional and pump-probe spectra when nuclear degrees of freedom can be treated as classical-like.

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.

Rapid acquisition of broadband two-dimensional electronic spectra by continuous scanning with conventional delay lines.

A passively phase-stable, broadband (∼7fs, >2000cm-1) two-dimensional (2D) electronic spectroscopy apparatus that achieves rapid acquisition rates by continuously-rather than step-wise-scanning the Fourier-transform dimension is demonstrated for the first time, to the best of our knowledge. This is made possible through use of a partially common path interferometer design in which the coherence time τ is sampled in a "rotating frame." Rapid, continuous scanning of τ increases the duty cycle of signal collection, rejects the majority of excitation pulse scatter, and enables the measurement of a complete 2D spectrum in 92 ms, which minimizes the influence of pulse intensity and delay fluctuations on the 2D spectrum. In practice, these improvements make possible the acquisition of hundreds of 2D spectra in tens of minutes, which opens the door to dense sampling of ultrafast relaxation dynamics and to generating extremely broadband 3D Fourier-transform spectra.

Quantum biology revisited.

Photosynthesis is a highly optimized process from which valuable lessons can be learned about the operating principles in nature. Its primary steps involve energy transport operating near theoretical quantum limits in efficiency. Recently, extensive research was motivated by the hypothesis that nature used quantum coherences to direct energy transfer. This body of work, a cornerstone for the field of quantum biology, rests on the interpretation of small-amplitude oscillations in two-dimensional electronic spectra of photosynthetic complexes. This Review discusses recent work reexamining these claims and demonstrates that interexciton coherences are too short lived to have any functional significance in photosynthetic energy transfer. Instead, the observed long-lived coherences originate from impulsively excited vibrations, generally observed in femtosecond spectroscopy. These efforts, collectively, lead to a more detailed understanding of the quantum aspects of dissipation. Nature, rather than trying to avoid dissipation, exploits it via engineering of exciton-bath interaction to create efficient energy flow.