Two-dimensional Electronic Spectra Research Articles

Theory of 2D electronic spectroscopy of water soluble chlorophyll-binding protein (WSCP): Signatures of Chl b derivate.

We investigate how electronic excitations and subsequent dissipative dynamics in the water soluble chlorophyll-binding protein (WSCP) are connected to features in two-dimensional (2D) electronic spectra, thereby comparing results from our theoretical approach with experimental data from the literature. Our calculations rely on third-order response functions, which we derived from a second-order cumulant expansion of the dissipative dynamics involving the partial ordering prescription, assuming a fast vibrational relaxation in the potential energy surfaces of excitons. Depending on whether the WSCP complex containing a tetrameric arrangement of pigments composed of two dimers with weak excitonic coupling between them binds the chlorophyll variant Chl a or Chl b, the resulting linear absorption and circular dichroism spectra and particularly the 2D spectra exhibit substantial differences in line shapes. These differences between Chl a WSCP and Chl b WSCP cannot be explained by the slightly modified excitonic couplings within the two variants. In the case of Chl a WSCP, the assumption of equivalent dimer subunits facilitates a reproduction of substantial features from the experiment by the calculations. In contrast, for Chl b WSCP, we have to assume that the sample, in addition to Chl b dimers, contains a small but distinct fraction of chemically modified Chl b pigments. The existence of such Chl b derivates has been proposed by Pieper et al. [J. Phys. Chem. B 115, 4042 (2011)] based on low-temperature absorption and hole-burning spectroscopy. Here, we provide independent evidence.

Observation of Dark States in Two-Dimensional Electronic Spectra of Chlorosomes.

Observations of low-lying dark states in several photosynthetic complexes challenge our understanding of the mechanisms behind their efficient energy transfer processes. Computational models are necessary for providing novel insights into the nature and function of dark states, especially since these are not directly accessible in spectroscopy experiments. Here, we will focus on signatures of dark-type states in chlorosomes, a light-harvesting complex from green sulfur bacteria well-known for uniting a broad absorption band with very efficient energy transfer. In agreement with experiments, our simulations of two-dimensional electronic spectra capture the ultrafast exciton transfer occurring in 100s of femtoseconds within a single chlorosome cylinder. The sub-100 fs process corresponds to relaxation within the single-excitation manifold in a single chlorosome tube, where all initially created populations in the bright exciton states are quickly transferred to dark-type exciton states. Structural inhomogeneities on the local scale cause a redistribution of the oscillator strength, leading to the emergence of these dark-type exciton states, which dominate ultrafast energy transfer. The presence of the dark-type exciton states suppresses energy loss from an isolated chlorosome via fluorescence quenching, as observed experimentally. Our results further question whether relaxation to dark-exciton states is a leading process or merely competes with transfer to the baseplate within the photosynthetic apparatus of green sulfur bacteria.

Electric Field Susceptibility of Chlorophyll c Leads to Unexpected Excitation Dynamics in the Major Light-Harvesting Complex of Diatoms.

Diatoms are one of the most abundant photosynthetic organisms on earth and contribute largely to atmospheric oxygen production. They contain fucoxanthin and chlorophyll-a/c binding proteins (FCPs) as light-harvesting complexes with a remarkable adaptation to the fluctuating light on ocean surfaces. To understand the basis of the photosynthetic process in diatoms, the excitation energy funneling within FCPs must be probed. A state-of-the-art multiscale analysis within a quantum mechanics/molecular mechanics framework has been employed. To this end, the chlorophyll (Chl) excitation energies within the FCP complex from the diatom Phaeodactylum tricornutum have been determined. The Chl-c excitation energies were found to be 5-fold more susceptible to electric fields than those of Chl-a pigments and thus are significantly lower in FCP than in organic solvents. This finding challenges the general belief that the excitation energy of Chl-c is always higher than that of Chl-a in FCP proteins and reveals that Chl-c molecules are much more sensitive to electric fields within protein scaffolds than in Chl-a pigments. The analysis of the linear absorption spectrum and the two-dimensional electronic spectra of the FCP complex strongly supports these findings and allows us to study the excitation transfer within the FCP complex.

Artificial-Intelligence-Enhanced On-the-Fly Simulation of Nonlinear Time-Resolved Spectra.

Time-resolved spectroscopy is an important tool for unraveling the minute details of structural changes in molecules of biological and technological significance. The nonlinear femtosecond signals detected for such systems must be interpreted, but it is a challenging task for which theoretical simulations are often indispensable. Accurate simulations of transient absorption or two-dimensional electronic spectra are, however, computationally very expensive, prohibiting the wider adoption of existing first-principles methods. Here, we report an artificial-intelligence-enhanced protocol to drastically reduce the computational cost of simulating nonlinear time-resolved electronic spectra, which makes such simulations affordable for polyatomic molecules of increasing size. The protocol is based on the doorway-window approach for the on-the-fly surface-hopping simulations. We show its applicability for the prototypical molecule of pyrazine for which it produces spectra with high precision with respect to ab initio reference while cutting the computational cost by at least 95% compared to pure first-principles simulations.

Topological aspects of matters and Langlands program

The Langlands program is a vast mathematical projection linking number theory and geometry. In high-energy physics, a connection with mirror symmetry has been suggested in string theory, but it has been little studied in low-energy physics. In the framework of the Langlands program, we present a unified description of the integer and fractional quantum Hall effect and the duality found in the fractal nature of the energy spectrum of two-dimensional Bloch electrons, statistical physics, and quantum computation. The new unified view of existing dualism presented in this paper raises the entirely new question of how each theory of physics is connected as a piece of the Langlands program.

Quantum dynamics simulations of the 2D spectroscopy for exciton polaritons.

We develop an accurate and numerically efficient non-adiabatic path-integral approach to simulate the non-linear spectroscopy of exciton-polariton systems. This approach is based on the partial linearized density matrix approach to model the exciton dynamics with explicit propagation of the phonon bath environment, combined with a stochastic Lindblad dynamics approach to model the cavity loss dynamics. Through simulating both linear and polariton two-dimensional electronic spectra, we systematically investigate how light-matter coupling strength and cavity loss rate influence the optical response signal. Our results confirm the polaron decoupling effect, which is the reduced exciton-phonon coupling among polariton states due to the strong light-matter interactions. We further demonstrate that the polariton coherence time can be significantly prolonged compared to the electronic coherence outside the cavity.

Ultrafast Anisotropy Decay Reveals Structure and Energy Transfer in Supramolecular Aggregates.

Chlorosomes from green bacteria perform the most efficient light capture and energy transfer, as observed among natural light-harvesting antennae. Hence, their unique functional properties inspire developments in artificial light-harvesting and molecular optoelectronics. We examine two distinct organizations of the molecular building blocks as proposed in the literature, demonstrating how these organizations alter light capture and energy transfer, which can serve as a mechanism that the bacteria utilize to adapt to changes in light conditions. Spectral simulations of polarization-resolved two-dimensional electronic spectra unravel how changes in the helicity of chlorosomal aggregates alter energy transfer. We show that ultrafast anisotropy decay presents a spectral signature that reveals contrasting energy pathways in different chlorosomes.

Electronic–Vibrational Resonance Does Not Significantly Alter Steady-State Transport in Natural Light-Harvesting Systems

Oscillations in time-dependent two-dimensional electronic spectra appear as evidence of quantum coherence in light-harvesting systems related to electronic-vibrational resonant interactions. Nature, however, takes place in a non-equilibrium steady-state; therefore, the relevance of these arguments to the natural process is unclear. Here, we examine the role of intramolecular vibrations in the non-equilibrium steady-state of photosynthetic dimers in the natural scenario of incoherent light excitation. Specifically, we analyze the PEB dimer in the cryptophyte algae PE545 antenna protein. It is found that vibrations resonant with the energy difference between exciton states only marginally increase the quantum yield and the imaginary part of the intersite coherence that is relevant for transport compared to non-resonant vibrations in the natural non-equilibrium steady-state. That is, the electronic-vibrational resonance interaction does not significantly enhance energy transport under natural incoherent light excitation conditions.

Manifestation of Hydrogen Bonding and Exciton Delocalization on the Absorption and Two-Dimensional Electronic Spectra of Chlorosomes.

Chlorosomes are supramolecular aggregates that contain thousands of bacteriochlorophyll molecules. They perform the most efficient ultrafast excitation energy transfer of all natural light-harvesting complexes. Their broad absorption band optimizes light capture. In this study, we identify the microscopic sources of the disorder causing the spectral width and reveal how it affects the excited state properties and the optical response of the system. We combine molecular dynamics, quantum chemical calculations, and response function calculations to achieve this goal. The predicted linear and two-dimensional electronic spectra are found to compare well with experimental data reproducing all key spectral features. Our analysis of the microscopic model reveals the interplay of static and dynamic disorder from the molecular perspective. We find that hydrogen bonding motifs are essential for a correct description of the spectral line shape. Furthermore, we find that exciton delocalization over tens to hundreds of molecules is consistent with the two-dimensional electronic spectra.

Calculating nonlinear response functions for multidimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion.

We present a methodology for simulating multidimensional electronic spectra of molecular aggregates with coupling of electronic excitation to a structured environment using the stochastic non-Markovian quantum state diffusion (NMQSD) method in combination with perturbation theory for the response functions. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise. We demonstrate that our approach shows fast convergence with respect to the number of stochastic trajectories, providing a promising technique for numerical calculation of two-dimensional electronic spectra of large molecular aggregates.

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 vibronic spectroscopy with semiclassical thermofield dynamics.

Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational-electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.

Correlated spectral fluctuations quantified by line shape analysis of fifth-order two-dimensional electronic spectra.

Correlated spectral fluctuations were suggested to coordinate excitation transport inside natural light harvesting complexes. We demonstrate the capacities of 2D line shapes from fifth-order coherent electronic signals (R5-2D) to report on such fluctuations in molecular aggregates and present a stochastic approach to fluctuations in correlated site and bi-exciton binding energies in the optical dynamics of Frenkel excitons. The model is applied to R5-2D line shapes of a homodimer, and we show that the peak tilt dynamics are a measure for site energy disorder, inter-site correlation, and the strength of bi-exciton binding energy fluctuations.

The influence of a Hamiltonian vibration vs a bath vibration on the 2D electronic spectra of a homodimer.

We elucidate the influence of the system-bath boundary placement within an open quantum system, with emphasis on the two-dimensional electronic spectra, through the application of the hierarchical equations of motion formalism for an exciton system. We apply two different models, the Hamiltonian vibration model (HVM) and bath vibration model (BVM), to a monomer and a homodimer. In the HVM, we specifically include the vibronic states in the Hamiltonian capturing vibronic quenching, whereas in the BVM, all vibrational details are contained within the bath and described by an underdamped spectral density. The resultant spectra are analyzed in terms of energetic peak position and thermodynamic broadening precision in order to evaluate the efficacy of the two models. The HVM produces 2D spectra with accurate peak positional information, while the BVM is well suited to modeling dynamic peak broadening. For the monomer, both models produce equivalent spectra in the limit where additional damping associated with the underdamped vibration in the BVM approaches zero. This is supported by analytical results. However, for the homodimer, the BVM spectra are redshifted with respect to the HVM due to an absence of vibronic quenching in the BVM. The computational efficiency of the two models is also discussed in order to inform us of the most appropriate use of each method.

Coupling between Harmonic Vibrations Influences Quantum Beating Signatures in Two-Dimensional Electronic Spectra

Launching and tracking wavepacket dynamics with two-dimensional electronic spectroscopy (2DES) provides insight into the complex interactions that underlie coherent processes within photoactive materials. With the ever-growing interest in how electronic-vibrational (vibronic) interactions direct ultrafast photophysics, methods for translating 2DES results into meaningful descriptions of the molecular potential energy landscape must evolve correspondingly. The interpretation of quantum beatmaps, which provide direct insight into the intra- and interchromophoric couplings within a chemical system, frequently relies on physical models that account for a single nuclear coordinate. However, several recent works suggest that coupling between wavepackets borne from several different vibrational motions affects 2DES data in meaningful ways. We build upon these insights by directly comparing simulations using single- and multicomponent vibronic Hamiltonians against experimental 2DES results from the organic semiconductors terrylenediimide and ITIC, as well as the biomedical dyes methylene blue and Nile blue A. We show that the experimental beatmaps and Fourier power spectra are well-reproduced when both low- and high-frequency vibrational motions are included in the simulation. Moreover, we demonstrate that the interaction of harmonic wavepackets increases quantum beat amplitudes in the positive-frequency rephasing signals, which significantly complicates standard methods for separating ground- and excited-state vibrational coherence signatures from 2DES data. These findings illustrate that coupling between purely harmonic vibrational wavepackets can have significant and prevalent effects on experimental 2DES results.

Time-dependent simulation of photocurrent-detected two-dimensional spectroscopy of open systems

A new time-domain simulation protocol of two-dimensional electronic spectra with photocurrent detection is presented. Time-dependent density functional theory for open systems at finite temperature is applied to evaluate the photocurrent response to four laser pulses, and a non-perturbative phase-matching approach is implemented to extract the fourth-order photocurrent signal with a desired phase-matching condition. Simulations for an open three-level model indicates that transition dipoles interact resonantly with the incident pulses and that different sample-electrode couplings may be identified by appearance of different peaks/valleys in photocurrent spectra from different electrodes. Moreover, qualitative reproduction of experimental spectra of a PbS quantum dot photocell [Karki et al., Nat. Commun. 5(1), 5869 (2014)] reveals the stimulated electron dynamics.

Geometry, number theory, and the butterfly spectrum of two-dimensional Bloch electrons.

We take a deeper dive into the geometry and the number theory that underlay the butterfly graphs of the Harper and the generalized Harper models of Bloch electrons in a magnetic field. The root of the number theoretical characteristics of the fractal spectrum is traced to a close relationship between the Farey tree-the hierarchical tree that generates all rationals and the Wannier diagram-a graph that labels all the gaps of the butterfly graph. The resulting Farey-Wannier hierarchical lattice of trapezoids provides a geometrical representation of the nested pattern of butterflies in the butterfly graph. Some features of the energy spectrum, such as absence of some of the Wannier trajectories in the butterfly graph falling outside the number theoretical framework, can be stated as a simple rule of minimal violation of mirror symmetry. In a generalized Harper model, number theoretical framework prevails with the Farey-Wannier hierarchical lattice regrouping to form some hexagonal cells creating different species of butterflies.

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.