Frenkel Exciton Model Research Articles

Excitonic Approach for Nonadiabatic Dynamics: Extending Beyond the Frenkel Exciton Model.

We report the formulation and implementation of an extended Frenkel exciton model (EFEM) designed for simulating the dynamics of multichromophoric systems, taking into account the possible presence of interchromophore charge transfer states, as well as other states in which two chromophores are simultaneously excited. Our approach involves constructing a Hamiltonian based on calculations performed on monomers and selected dimers within the multichromophoric aggregate. Nonadiabatic molecular dynamics is addressed using a surface hopping approach, while the electronic wave functions and energies required for constructing the EFEM are computed utilizing the semiempirical floating occupation molecular orbitals-configuration interaction (FOMO-CI) electronic structure method. To validate our approach, we simulate the singlet fission process in a trimer of 2,5-bis(fluorene-9-ylidene)-2,5-dihydrothiophene (ThBF) molecules, embedded in their crystal environment, comparing the results of the EFEM to the standard "supermolecule" approach.

Electronic Couplings versus Thermal Fluctuations in the Internal Conversion of Perylene Diimides: The Battle to Localize the Exciton.

Energy transfer processes among units of light-harvesting homo-oligomers impact the efficiency of these materials as components in organic optoelectronic devices such as solar cells. Perylene diimide (PDI), a prototypical dye, features exceptional light absorption and highly tunable optical and electronic properties. These properties can be modulated by varying the number of PDI units and linkers between them. Herein, atomistic nonadiabatic excited state molecular dynamics is used to explore the energy transfer during the internal conversion of acetylene and diacetylene bridged dimeric and trimeric PDIs. Our simulations reveal a significant impact of the bridge type on the transient exciton localization/delocalization between units of PDI dimers. After electronic relaxation, larger exciton delocalization occurs in the PDI dimer connected by the diacetylene bridge with respect to the one connected by the shorter acetylene bridge. These changes can be rationalized by the Frenkel exciton model. We outline a technique for deriving parameters for this model using inputs provided by nonadiabatic dynamics simulations. Frenkel exciton description reveals an interplay between the relative strengths of the diagonal and off-diagonal disorders. Moreover, atomistic simulations and the Frenkel exciton model of the PDI trimer systems corroborate in detail the localization properties of the exciton on the molecular units during the internal conversion to the lowest-energy excited state when the units become effectively decoupled. Overall, atomistic nonadiabatic simulations in combination with the Frenkel exciton model can serve as a predictive framework for analyzing and predicting desired exciton traps in PDI-based oligomers designed for organic electronics and photonic devices.

PigmentHunter: A point-and-click application for automated chlorophyll-protein simulations.

Chlorophyll proteins (CPs) are the workhorses of biological photosynthesis, working together to absorb solar energy, transfer it to chemically active reaction centers, and control the charge-separation process that drives its storage as chemical energy. Yet predicting CP optical and electronic properties remains a serious challenge, driven by the computational difficulty of treating large, electronically coupled molecular pigments embedded in a dynamically structured protein environment. To address this challenge, we introduce here an analysis tool called PigmentHunter, which automates the process of preparing CP structures for molecular dynamics (MD), running short MD simulations on the nanoHUB.org science gateway, and then using electrostatic and steric analysis routines to predict optical absorption, fluorescence, and circular dichroism spectra within a Frenkel exciton model. Inter-pigment couplings are evaluated using point-dipole or transition-charge coupling models, while site energies can be estimated using both electrostatic and ring-deformation approaches. The package is built in a Jupyter Notebook environment, with a point-and-click interface that can be used either to manually prepare individual structures or to batch-process many structures at once. We illustrate PigmentHunter's capabilities with example simulations on spectral line shapes in the light harvesting 2 complex, site energies in the Fenna-Matthews-Olson protein, and ring deformation in photosystems I and II.

Spatial Correlations Drive Long-Range Transport and Trapping of Excitons in Single H-Aggregates: Experiment and Theory.

Describing long-range energy transport is a crucial step, both toward deepening our knowledge on natural light-harvesting systems and toward developing novel photoactive materials. Here, we combine experiment and theory to resolve and reproduce energy transport on pico- to nanosecond time scales in single H-type supramolecular nanofibers based on carbonyl-bridged triarylamines (CBT). Each nanofiber shows energy transport dynamics over long distances up to ∼1 μm, despite exciton trapping at specific positions along the nanofibers. Using a minimal Frenkel exciton model including disorder, we demonstrate that spatial correlations in the normally distributed site energies are crucial to reproduce the experimental data. In particular, we can observe the long-range and subdiffusive nature of the exciton dynamics as well as the trapping behavior of excitons in specific locations of the nanofiber. This trapping behavior introduces a net directionality or asymmetry in the exciton dynamics as observed experimentally.

Energy transfer from two luteins to chlorophylls in light-harvesting complex II study by using exciton models with phase correction.

In light-harvesting complex II of plants, the two lutein pigments (LUT1 and LUT2) are always paired and an energy transfer pathway between them is believed to exist. However, it remains unclear whether this pathway is essential for the energy transfer between carotenoids and chlorophylls. In this work, we performed hybrid quantum mechanics/molecular mechanics simulations with Frenkel exciton models to investigate this energy transfer. The results show that the energy transfer pathways between the S2 state of LUT1 and CLAs are not affected by LUT2 S2. The energy transfer between LUT and chlorophyll-a (CLA) also follows a resonance mechanism. The two LUTs have different energy transfer pathways according to their energy gaps and coupling strengths with each CLA. The present work sheds light on the energy transfer pathways involved in the two LUTs.

Simulation of exciton spectra in disordered supramolecular polymers: exciton localization in cisoid indolenine squaraine hexamers.

In order to understand the effects of disorder and defects in oligomers and polymers on the localization of excitons, we investigated the spectral properties of the squaraine B hexamer using long range corrected tight-binding TDDFT (lc-TDDFTB) and Frenkel-exciton model based calculations. Employing classical molecular dynamics, the cisoid indolenine squaraine hexamers helix was propagated in DCM and acetone to obtain ensembles of realistic structures, which naturally exhibit considerable disorder. The trajectories together with several model squaraine systems were studied to show the profound effects of disorder in the superstructure and disorder of the local monomer geometry on optical properties like absorption and exciton localization. We further compared lc-TDDFTB and exciton theory derived spectral data to related experimental data on absorption, exciton transfer and localization in squaraine polymers and oligomers.

Intraband Exciton Transitions in Photosynthetic Complexes Revealed by Novel Five-Wave-Mixing Spectroscopy.

We calculate the χ(4) optical response of an oriented photosystem II reaction center of purple bacteria described by the Frenkel exciton model using nonlinear exciton equations (NEE). This approach treats each chromophore as an anharmonic oscillator and provides an intuitive quasiparticle picture of nonlinear spectroscopic signals of interacting excitons. It provides a computationally powerful description of nonlinear spectroscopic signals that avoids complete diagonalization of the total Hamiltonian. Expressions for the second- and the fourth-order nonlinear signals are derived. The NEE have been successfully employed in the past to describe even-order-wave-mixing. Here, we extend them to aggregates with broken inversion symmetries. Even-order susceptibilities require the introduction of permanent dipoles, which allow to directly probe low-frequency intraband transitions of excitons.

Data-driven insights into the fluorescence of asphaltene aggregates using extended Frenkel exciton model

The origin of the fluorescence redshift during asphaltene aggregation remains debated due to the great diversity of asphaltene molecules, while the extended Frenkel exciton model provided a theoretical framework for studying multi-chromophore systems, such as asphaltene aggregates. We investigated the fluorescence energy of hundreds of asphaltene dimers based on 133 experimental revealed asphaltene monomer structures. Our result shows that the dimer's fluorescence energy is always lower than both of its monomers regardless of its intermolecular conformation, with its redshift dominated by superexchange. The dimer oscillator strength predominantly depends on the monomer with the lower fluorescence energy, and the involvement of charge-transfer states and the cancellation between monomer transition dipole moments suppressed the fluorescence especially when two monomers have similar fluorescence energy. The above-mentioned findings hold for all asphaltene dimers despite their diversity, which offers a theoretical interpretation for comprehending the relationship between asphaltene aggregation and its fluorescence variation. Furthermore, this work provides theoretical guidance to other research areas related to organic planar conjugated systems with multiple chromophores.

Quantum interferometry and pathway selectivity in the nonlinear response of photosynthetic excitons

We propose a time-frequency resolved spectroscopic technique which employs nonlinear interferometers to study exciton-exciton scattering in molecular aggregates. A higher degree of control over the contributing Liouville pathways is obtained as compared to classical light. We show how the nonlinear response can be isolated from the orders-of-magnitude stronger linear background by either phase matching or polarization filtering. Both arise due to averaging the signal over a large number of noninteracting, randomly oriented molecules. We apply our technique to the Frenkel exciton model which excludes charge separation for the photosystem II reaction center. We show how the sum of the entangled photon frequencies can be used to select two-exciton resonances, while their delay times reveal the single-exciton levels involved in the optical process.

A Multiconfigurational Wave Function Implementation of the Frenkel Exciton Model for Molecular Aggregates.

We present an implementation of the Frenkel exciton model into the OpenMolcas program package enabling calculations of collective electronic excited states of molecular aggregates based on a multiconfigurational wave function description of the individual monomers. The computational protocol avoids using diabatization schemes and, thus, supermolecule calculations. Additionally, the use of the Cholesky decomposition of the two-electron integrals entering pair interactions enhances the efficiency of the computational scheme. The application of the method is exemplified for two test systems, that is, a formaldehyde oxime and a bacteriochlorophyll-like dimer. For the sake of comparison with the dipole approximation, we restrict our considerations to situations where intermonomer exchange can be neglected. The protocol is expected to be beneficial for aggregates composed of molecules with extended π systems, unpaired electrons such as radicals or transition metal centers, where it should outperform widely used methods based on time-dependent density functional theory.

An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra.

Linear and nonlinear electronic spectra provide an important tool to probe the absorption and transfer of electronic energy. Here, we introduce a pure state Ehrenfest approach to obtain accurate linear and nonlinear spectra that is applicable to systems with large numbers of excited states and complex chemical environments. We achieve this by representing the initial conditions as sums of pure states and unfolding multi-time correlation functions into the Schrödinger picture. By doing this, we show that one can obtain significant improvements in accuracy over the previously used projected Ehrenfest approach and that these benefits are particularly pronounced in cases where the initial condition is a coherence between excited states. While such initial conditions do not arise when calculating linear electronic spectra, they play a vital role in capturing multidimensional spectroscopies. We demonstrate the performance of our method by showing that it is able to quantitatively capture the exact linear, 2D electronic spectroscopy, and pump-probe spectra for a Frenkel exciton model in slow bath regimes and is even able to reproduce the main spectral features in fast bath regimes.

Compact and complete description of non-Markovian dynamics.

Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices to qubit decoherence in quantum technologies and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium, one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analog and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.

Intermolecular resonance energy transfer between two lutein pigments in light-harvesting complex II studied by frenkel exciton models.

The energy transfer pathways in light-harvesting complex II are complicated and the discovery of the energy transfer between the two luteins revealed an unelucidated important role of carotenoids in the energy flow. This energy transfer between the two S2 states of luteins was for the first time investigated using Frenkel exciton models, using a hybrid scheme of molecular mechanics and quantum mechanics. The results show the energy flow between the two luteins under the Förster resonance energy transfer mechanism. The energy transfer caused by energy level resonance occurs in configurations with small energy gaps. This energy transfer pathway is particularly sensitive to conformation. Moreover, according to the statistical characteristics of the data of the energy gaps and coupling values between LUTs, we proposed stochastic exciton Hamiltonian models to facilitate clarification of the energy transfer among pigments in antenna complexes.

Effects of Heterogeneous Protein Environment on Excitation Energy Transfer Dynamics in the Fenna-Matthews-Olson Complex.

The Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria has been serving as a prototypical light-harvesting protein for studying excitation energy transfer (EET) dynamics in photosynthesis. The most widely used Frenkel exciton model for FMO complex assumes that each excited bacteriochlorophyll site couples to an identical and isolated harmonic bath, which does not account for the heterogeneous local protein environment. To better describe the realistic environment, we propose to use the recently developed multistate harmonic (MSH) model, which contains a globally shared bath that couples to the different pigment sites according to the atomistic quantum mechanics/molecular mechanics simulations with explicit protein scaffold and solvent. In this work, the effects of heterogeneous protein environment on EET in FMO complexes from Prosthecochloris aestuarii and Chlorobium tepidum, specifically including realistic spectral density, site-dependent reorganization energies, and system-bath couplings are investigated. Semiclassical and mixed quantum-classical mapping dynamics were applied to obtain the nonadiabatic EET dynamics in several models ranging from the Frenkel exciton model to the MSH model and their variants. The MSH model with realistic spectral density and site-dependent system-bath couplings displays slower EET dynamics than the Frenkel exciton model. Our comparative study shows that larger average reorganization energy, heterogeneity in spectral densities, and low-frequency modes could facilitate energy dissipation, which is insensitive to the static disorder in reorganization energies. The effects of the spectral densities and system-bath couplings along with the MSH model can be used to optimize EET dynamics for artificial light-harvesting systems.

Characterizing the excited states of large photoactive systems by exciton models

AbstractThe theoretical investigation of excited state for large photoactive systems plays the fundamental role in understanding various optical processes in material and biological system. Frenkel exciton (FE) model describing the excitation of the whole system as a collective effect of quasi‐particles of excitons, that is, bound electron–hole pairs, is well‐known as a simple but powerful theoretical scheme to present a clear and insightful physical picture for complicated excited state problems. In this mini‐review, we summarize our recent developments of quantum chemical methods based on exciton models and their related applications for large photoactive systems. It is shown that our developed ab initio renormalized exciton model (REM) and block interaction product state (BIPS) schemes provide new efficient and automatic low‐scaling excited state methods for both localized and delocalized excited states in large systems. Illustrative examples including simulations of both absorption and emission spectrum in large sized molecular aggregates, indicate the exciton model based methods provide promising computational tools for unravel the mechanism of photophysical and photochemical processes in large photoactive systems.

Optoelectronic properties of a self-assembling rigidly-linked BF2-curcuminoid bichromophore

We describe the synthesis and spectroscopic study of the bichromophoric molecule DA-meso consisting of two boron difluoride curcuminoid (BF2-curcuminoid) units tethered by the rigid diacetylenic bridge. This structural feature imparts the quadrupolar-like DA-meso with a strong ability to self-assemble in solution, which induces a profound change in the optical properties. The UV–vis absorption spectrum of the aggregate is characterized by the appearance of a redshifted band at low energy and its fluorescence emission occurs in the near infrared (λmax = 700 nm) with a low quantum yield (5%). This is in contradiction with the strong emission expected for J-aggregates considering the Frenkel exciton model. From concentration-dependent UV–vis absorption spectroscopy we demonstrate the formation of a dimer composed of four BF2-curcuminoid units. Single-crystal X-ray diffraction structure analysis and in-depth quantum chemical calculations based on density functional theory (DFT) and subsequent decomposition of the electronic excited states on a diabatic basis enable to discuss the geometry of the DA-meso dimer, and to establish the presence of excited states close in energy to that of the unperturbed monochromophore, which are not predicted by the classical Frenkel exciton model. Different dimer structures characterized by π-stacks of two and up to four chromophores are investigated, in which low-lying excited states with vanishing oscillator strength are found to be redshifted with respect to the lowest-energy allowed state of the aggregate. From these experimental and theoretical data, the spectral features of the DA-meso dimer are rationalized by considering the formation of a “non-fluorescent J-aggregate”, illustrating the trend in non-Kasha behavior observed for quadrupolar-like dyes.

Plasmon-Enhanced Exciton Delocalization in Squaraine-Type Molecular Aggregates.

Enlarging exciton coherence lengths in molecular aggregates is critical for enhancing the collective optical and transport properties of molecular thin film nanostructures or devices. We demonstrate that the exciton coherence length of squaraine aggregates can be increased from 10 to 24 molecular units at room temperature when preparing the aggregated thin film on a metallic rather than a dielectric substrate. Two-dimensional electronic spectroscopy measurements reveal a much lower degree of inhomogeneous line broadening for aggregates on a gold film, pointing to a reduced disorder. The result is corroborated by simulations based on a Frenkel exciton model including exciton-plasmon coupling effects. The simulation shows that localized, energetically nearly resonant excitons on spatially well separated segments can be radiatively coupled via delocalized surface plasmon polariton modes at a planar molecule-gold interface. Such plasmon-enhanced delocalization of the exciton wave function is of high importance for improving the coherent transport properties of molecular aggregates on the nanoscale. Additionally, it may help tailor the collective optical response of organic materials for quantum optical applications.

Surface Hopping Dynamics with the Frenkel Exciton Model in a Semiempirical Framework.

We present an implementation of the Frenkel exciton model in the framework of the semiempirical floating occupation molecular orbitals-configuration interaction (FOMO-CI) electronic structure method, aimed at simulating the dynamics of multichromophoric systems, in which excitation energy transfer can occur, by a very efficient approach. The nonadiabatic molecular dynamics is here dealt with by the surface hopping method, but the implementation we proposed is compatible with other dynamical approaches. The exciton coupling is computed either exactly, within the semiempirical approximation considered, or by resorting to transition atomic charges. The validation of our implementation is carried out on the trans-azobenzeno-2S-phane (2S-TTABP), formed by two azobenzene units held together by sulfur bridges, taken as a minimal model of multichromophoric systems, in which both strong and weak exciton couplings are present.

Exciton dispersion in para-quaterphenyl: Significant molecular interactions beyond Coulomb coupling

We have experimentally determined the momentum dependence of the electronic excitation spectra of para-quaterphenyl single crystals. The parallel arrangement of para-quaterphenyl molecules results in a strong Coulomb coupling of the molecular excitons. Such crystals have been considered to be a very good realization of the Frenkel exciton model, including the formation of H-type aggregates. Our data reveal an unexpected exciton dispersion of the upper Davydov component, which cannot be rationalized in terms of inter-molecular Coulomb coupling of the excitons. A significant reduction of the nearest neighbor coupling due to additional charge-transfer processes is able to provide an explanation of the data. Furthermore, the spectral onset of the excitation spectrum, which represents a heavy exciton resulting from exciton–phonon coupling, also shows a clear dispersion, which had been unknown so far. Finally, an optically forbidden excitation about 1 eV above the excitation onset is observed.

Influence of solution phase environmental heterogeneity and fluctuations on vibronic spectra: Perylene diimide molecular chromophore complexes in solution.

Ensembles of ab initio parameterized Frenkel-exciton model Hamiltonians for different perylene diimide dimer systems are used, together with various dissipative quantum dynamics approaches, to study the influence of the solvation environment and fluctuations in chromophore relative orientation and packing on the vibronic spectra of two different dimer systems: a π-stacked dimer in aqueous solution in which the relative chromophore geometry is strongly confined by a phosphate bridge and a side-by-side dimer in dichloromethane involving a more flexible alkyne bridge that allows quasi-free rotation of the chromophores relative to one another. These entirely first-principles calculations are found to accurately reproduce the main features of the experimental absorption spectra, providing a detailed mechanistic understanding of how the structural fluctuations and environmental interactions influence the vibronic dynamics and spectroscopy of solutions of these multi-chromophore complexes.