Multichromophoric Systems Research Articles

Comparison of methods to study excitation energy transfer in molecular multichromophoric systems

We compare theoretical methods for calculating excitation energy transfer rates in multichromophoric systems. The employed methods are the multichromophoric Förster resonance energy transfer (MC-FRET), the numerical integration of the Schrödinger equation (NISE), and the Haken-Strobl-Reineker (HSR) model. As a reference, we use the numerically exact Hierarchy of Equations of Motion (HEOM). We examine these methods in various system and bath parameter regimes including the regime relevant to biological light-harvesting systems. We apply them to a model system of a monomeric donor coupled to a multichromophoric acceptor ring of varying size in two limiting configurations, namely symmetric and asymmetric. We find that the symmetric case is more sensitive to the approximations of the methods studied. The NISE method gives the most reasonable results throughout the parameter regimes tested, while still being computationally tractable.

Quantum Chemical Modeling of the Photoinduced Activity of Multichromophoric Biosystems.

Multichromophoric biosystems represent a broad family with very diverse members, ranging from light-harvesting pigment–protein complexes to nucleic acids. The former are designed to capture, harvest, efficiently transport, and transform energy from sunlight for photosynthesis, while the latter should dissipate the absorbed radiation as quickly as possible to prevent photodamages and corruption of the carried genetic information. Because of the unique electronic and structural characteristics, the modeling of their photoinduced activity is a real challenge. Numerous approaches have been devised building on the theoretical development achieved for single chromophores and on model Hamiltonians that capture the essential features of the system. Still, a question remains: is a general strategy for the accurate modeling of multichromophoric systems possible? By using a quantum chemical point of view, here we review the advancements developed so far highlighting differences and similarities with the single chromophore treatment. Finally, we outline the important limitations and challenges that still need to be tackled to reach a complete and accurate picture of their photoinduced properties and dynamics.

Real-Time Propagation TDDFT and Density Analysis for Exciton Coupling Calculations in Large Systems.

Photoactive systems are characterized by their capacity to absorb the energy of light and transform it. Usually, more than one chromophore is involved in the light absorption and excitation transport processes in complex systems. Linear-Response Time-Dependent Density Functional (LR-TDDFT) is commonly used to identify excitation energies and transition properties by solving the well-known Casida’s equation for single molecules. However, in practice, LR-TDDFT presents some disadvantages when dealing with multichromophore systems due to the increasing size of the electron–hole pairwise basis required for accurate evaluation of the absorption spectrum. In this work, we extend our local density decomposition method that enables us to disentangle individual contributions into the absorption spectrum to computation of exciton dynamic properties, such as exciton coupling parameters. We derive an analytical expression for the transition density from Real-Time Propagation TDDFT (P-TDDFT) based on Linear Response theorems. We demonstrate the validity of our method to determine transition dipole moments, transition densities, and exciton coupling for systems of increasing complexity. We start from the isolated benzaldehyde molecule, perform a distance analysis for π-stacked dimers, and finally map the exciton coupling for a 14 benzaldehyde cluster.

Theoretical Study on the Optical Properties of Multichromophoric Systems Based on an Exciton Approach: Modification Guidelines

AbstractRecent advances in experimental techniques have led to significant freedom in the design of supramolecular and polymeric systems. However, to develop efficient optical materials, appropriate design guidelines must be determined. Herein we propose a post‐modification strategy based on excitonic analysis to improve the emission and circularly polarized luminescence (CPL) of multichromophoric systems. The generation and annihilation mechanisms for the emission and CPL of an achiral crystal of 2,5‐diphenyl‐1,4‐distyrylbenzene (trans‐DPDSB), as an example, have been analyzed. The emission is predominantly attributed to a local transition within the single chromophore due to weak exciton coupling. The decomposed CPL components with the strong intensity originate from the interactions of exciton electric transition dipole moments between the chromophore and its adjacent monomers, which cancels each other out in enantiomeric pairs of the achiral system. Based on these findings, we propose a set of guidelines toward the improvement of photofunction. The Frenkel‐exciton decomposition analysis (FEDA), which reveals the contributions of components of the supramolecular system, provides new possibilities to exploit the potential of multichromophoric systems.

Semiconducting Polymer Dots with Modulated Photoblinking for High‐Order Super‐Resolution Optical Fluctuation Imaging

AbstractSuper‐resolution optical fluctuation imaging (SOFI) uses photoblinking to achieve fast, background free, 3D fluorescence nanoscopy. The on/off photoblinking characteristics are key factors for realizing high‐order SOFI. However, it remains a great challenge to tune the photoblinking of a fluorescent probe because most of the probes are typical single fluorophore systems with stochastic blinking nature. In this study, effective photoblinking modulation is demonstrated in a nanoscale multichromophoric system consisting of donor–acceptor semiconducting polymers. Numerical simulation is performed to quantitatively evaluate the impact of the number of acceptors on the photoblinking of the nanoparticle probe as well as the spatial resolution of the resulting SOFI nanoscopy. In tandem with simulation, a series of polymer dots (Pdots) are designed with varying donor–acceptor moieties that give rise to the modulated photoblinking behaviors, as evidenced by single‐particle fluorescence trajectories. The photoblinking behaviors are quantitatively compared in terms of autocorrelation function, dot retention fraction, and on/off time ratio. High‐performance photoblinking‐based nanoscopy is implemented by using the optimized Pdots, resolving subcellular structure at a spatial resolution of ≈95 nm. This study provides a useful approach to engineer the photoblinking properties of fluorescent nanoparticles for super‐resolution imaging applications.

Characterization of the coherent dynamics of bacteriochlorophyll a in solution

Disclosing the physical origin of quantum beatings in the early dynamics of biological light-harvesting pigment-protein complexes is one of the major challenges in the ultrafast spectroscopy community. 2D electronic spectroscopy (2DES) is a powerful tool for this purpose, but the complexity of the beating behavior in multichromophoric systems complicates the interpretation. For this reason, the availability of control datasets providing a full characterization of the response of isolated chromophores is highly desirable to untangle the features of intermolecular interactions from the properties of individual pigments. Here, a thorough 2DES characterization of the frequencies and dephasing times of intramolecular vibrational coherences of bacteriochlorophyll a in solution is provided. Several beating modes in the ground and excited state have been found and their dephasing times have been determined. The obtained results represent an essential interpretation key of the beating dynamics of pigment-protein complexes binding bacteriochlorophyll a.

Simulating Fluorescence-Detected Two-Dimensional Electronic Spectroscopy of Multichromophoric Systems.

We present a theory for modeling fluorescence-detected two-dimensional electronic spectroscopy of multichromophoric systems. The theory is tested by comparison of the predicted spectra of the light-harvesting complex LH2 with experimental data. A qualitative explanation of the strong cross-peaks as compared to conventional two-dimensional electronic spectra is given. The strong cross-peaks are attributed to the clean ground-state signal that is revealed when the annihilation of exciton pairs created on the same LH2 complex cancels oppositely signed signals from the doubly excited state. This annihilation process occurs much faster than the nonradiative relaxation. Furthermore, the line shape difference is attributed to slow dynamics, exciton delocalization within the bands, and intraband exciton–exciton annihilation. This is in line with existing theories presented for model systems. We further propose the use of time-resolved fluorescence-detected two-dimensional spectroscopy to study state-resolved exciton–exciton annihilation.

Stepwise Two-Photon-Induced Electron Transfer from Higher Excited States of Noncovalently Bound Porphyrin-CdS/ZnS Core/Shell Nanocrystals.

There has been an increasing amount of interest in stepwise two-photon-absorption (2PA)-induced photochemical reactions because of their extremely lower power thresholds compared to that of the simultaneous process and drastic reaction enhancements in some cases. However, stepwise 2PA-induced photochemical reactions were reported only in single chromophores and covalently bound bichromophores and there are few reports on these reactions in noncovalently bound systems because of weak electronic interactions among chromophores. This study demonstrated the stepwise 2PA-induced electron transfer from higher excited states in noncovalently bound protoporphyrin IX·CdS/ZnS core/shell nanocrystals (NCs). The electron transfer from higher excited states of porphyrin to CdS NCs successfully overcomes the activation barrier associated with the wide bandgap ZnS shell, indicating that a high reduction potential can be obtained with the stepwise 2PA process. The concept presented in this study can be applied to various noncovalently bound multichromophore systems to explore nonlinear photoresponses.

Multireference exciplex binding energies: Basis set convergence and error

AbstractIn multichromophore systems, characterization of electronic structure requires characterization of exciplexes, electron‐hole pairs delocalized over multiple molecules. Computing exciplex binding energy requires an accurate description of both the noncovalent interactions between the chromophores and their excited electronic states. The critical role of basis set selection for accurate description of noncovalent interactions is well known, but for some of the most accurate excited‐state methods, basis set dependence is incompletely understood. In this work, the impact of basis set size and diffuseness on CASSCF/NEVPT2 binding energies is determined for three systems in their lowest singlet excited states: the benzene excimer, the cis‐butadiene‐benzene exciplex, and the benzene‐naphthalene exciplex. We demonstrate that excellent CBS binding energies may be obtained using the moderately‐sized jun‐cc‐pV(D + d)Z and jun‐cc‐pV(T + d)Z basis sets and a simple N−3 model. Repeating this procedure with the N = 3, 4 basis sets from the most diffuse basis set family applied to each system yields a binding energy of 56.6 ± 1.2 kJ/mol for the benzene excimer and binding energies of 11.1 ± 0.5 kJ/mol and 19.2 ± 1.7 kJ/mol for the cis‐butadiene‐benzene exciplex and the benzene‐naphthalene exciplex, respectively.

Surface Hopping within an Exciton Picture. An Electrostatic Embedding Scheme.

We report the development and the implementation of an exciton approach that allows ab initio nonadiabatic dynamics simulations of electronic excitation energy transfer in multichromophoric systems. For the dynamics, a trajectory-based strategy is used within the surface hopping formulation. The approach features a consistent hybrid formulation that allows the construction of potential energy surfaces and gradients by combining quantum mechanics and molecular mechanics within an electrostatic embedding scheme. As an application, the study of a molecular dyad consisting of a covalently bound BODIPY moiety and a tetrathiophene group is presented using time-dependent density functional theory (TDDFT). The results obtained with the exciton model are compared to previously performed full TDDFT dynamics of the same system. Our results show excellent agreement with the full TDDFT results, indicating that the couplings that lead to excitation energy transfer (EET) are dominated by Coulomb interaction terms and that charge-transfer states are not necessary to properly describe the nonadiabatic dynamics of the system. The exciton model also reveals ultrafast coherent oscillations of the excitation between the two units in the dyad, which occur during the first 50 fs.

- stacking vs. C-H/ interaction: Excimer formation and charge resonance stabilization in van der Waals clusters of 9,9'-dimethylfluorene.

Studies of exciton and hole stabilization in multichromophoric systems underpin our understanding of electron transfer and transport in materials and biomolecules. The simplest model systems are dimeric, and recently we compared the gas-phase spectroscopy and dynamics of van der Waals dimers of fluorene, 9-methylfluorene (MF), and 9,9'-dimethylfluorene (F1) to assess how sterically controlled facial encumbrance modulates the dynamics of excimer formation and charge resonance stabilization (CRS). Dimers of fluorene and MF show only excimer emission upon electronic excitation, and significant CRS as evidenced in a reduced ionization potential for the dimer relative the monomer. By contrast, the dimer of F1 shows no excimeric emission, rather structured emission from the locally excited state of a tilted (non π-stacked) dimer, evidencing the importance of C-H/π interactions and increased steric constraints that restrict a cofacial approach. In this work, we report our full results on van der Waals clusters of F1, using a combination of theory and experiments that include laser-induced fluorescence, mass-selected two-color resonant two-photon ionization spectroscopy, and two-color appearance potential measurements. We use the latter to derive the binding energies of the F1 dimer in ground, excited, and cation radical states. Our results are compared with van der Waals and covalently linked clusters of fluorene to assess both the relative strength of π-stacking and C-H/π interactions in polyaromatic assemblies and the role of π-stacking in excimer formation and CRS.

Electronic energy transfer in biomacromolecules

Electronic energy transfer is widely used as a molecular ruler to interrogate the structure of biomacromolecules, and performs a key task in photosynthesis by transferring collected energy through specialized pigment–protein complexes. Förster theory, introduced over 70 years ago, allows linking transfer rates to simple structural and spectroscopic properties of the energy‐transferring molecules. In biosystems, however, significant deviations from Förster behavior often arise due to breakdown of the ideal dipole approximation, dielectric screening effects due to the biological environment, or departure from the weak‐coupling regime. In this review, we provide a concise overview of advances in simulations of energy transfer in biomacromolecules that allow overcoming the main limitations of Förster theory. We first discuss advances in quantum chemical methods to compute electronic couplings, their extension to multiscale formulations to include screening effects, and strategies to treat the interplay between coupling fluctuations and energy transfer dynamics. We then examine the spectral overlap term, and how this quantity can be estimated from simulations of the spectral density of exciton–phonon coupling. Finally, we discuss rate theories that can describe energy transfers in situations where strong coupling leads to delocalized excitions, a common situation found in closely packed multichromophoric systems such as photosynthetic complexes and nucleic acids.This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics Theoretical and Physical Chemistry > Spectroscopy

Wavelength-Dependent Exciton-Vibrational Coupling in the Water-Soluble Chlorophyll Binding Protein Revealed by Multilevel Theory of Difference Fluorescence Line-Narrowing.

One of the most powerful line-narrowing techniques used to unravel the homogeneous lineshapes of inhomogeneously broadened systems is difference fluorescence line-narrowing spectroscopy. When this spectroscopy was applied to multichromophoric systems so far, the spectra were analyzed by an effective two-level system approach, composed of the electronic ground state and the lowest exciton state. An effective Huang-Rhys factor was assigned for the coupling of this state to the vibrations. Here, we extend this approach by including a multilevel line shape theory, which takes into account the excitonic coupling between pigments and thereby the effect of the delocalization of the excited states explicitly. In this way, it becomes possible to extract the spectral density of the local exciton-vibrational coupling. The theory is applied to the recombinant water-soluble chlorophyll binding protein reconstituted with chlorophyll a or b and reveals a significant decrease of the Huang-Rhys factor of the local exciton-vibrational coupling with decreasing transition energy of the chlorophylls. This decrease could be due to the increase in steric interactions reducing the flexibility of the environment and red-shifting the site energy of the pigments.

Solid-State Photon Upconversion Materials: Structural Integrity and Triplet-Singlet Dual Energy Migration.

Triplet-triplet annihilation-based photon upconversion (TTA-UC) is a process wherein longer-wavelength light (lower-energy photons) is converted into shorter-wavelength light (higher-energy photons) under low excitation intensity in multichromophore systems. There have been many reports on highly efficient TTA-UC in solution; however, significant challenges remain in the development of solid-state upconverters in order to explore real-world applications. In this Perspective, we discuss the advantages and challenges of different approaches for TTA-UC in solvent-free solid systems. We consider that the energy migration-based TTA-UC has the potential to achieve ideal materials with high UC efficiency at weak solar irradiance. While the UC performance of such systems is still limited at this moment, we introduce recently developed important concepts to improve it, including kinetic/thermodynamic donor dispersion in acceptor assemblies, defectless crystals, and triplet-singlet dual energy migration. Future integration of these concepts into a single material would realize the ideal TTA-UC system.

Direct observation of exciton\u2013exciton interactions

Natural light harvesting as well as optoelectronic and photovoltaic devices depend on efficient transport of energy following photoexcitation. Using common spectroscopic methods, however, it is challenging to discriminate one-exciton dynamics from multi-exciton interactions that arise when more than one excitation is present in the system. Here we introduce a coherent two-dimensional spectroscopic method that provides a signal only in case that the presence of one exciton influences the behavior of another one. Exemplarily, we monitor exciton diffusion by annihilation in a perylene bisimide-based J-aggregate. We determine quantitatively the exciton diffusion constant from exciton–exciton-interaction 2D spectra and reconstruct the annihilation-free dynamics for large pump powers. The latter enables for ultrafast spectroscopy at much higher intensities than conventionally possible and thus improves signal-to-noise ratios for multichromophore systems; the former recovers spatio–temporal dynamics for a broad range of phenomena in which exciton interactions are present.

Towards Accurate Simulation of Two-Dimensional Electronic Spectroscopy.

We introduce the basic concepts of two-dimensional electronic spectroscopy (2DES) and a general theoretical framework adopted to calculate, from first principles, the nonlinear response of multi-chromophoric systems in realistic environments. Specifically, we focus on UV-active chromophores representing the building blocks of biological systems, from proteins to nucleic acids, describing our progress in developing computational tools and protocols for accurate simulation of their 2DUV spectra. The roadmap for accurate 2DUV spectroscopy simulations is illustrated starting with benchmarking of the excited-state manifold of the chromophoric units in a vacuum, which can be used for building exciton Hamiltonians for large-scale applications or as a reference for first-principles simulations with reduced computational cost, enabling treatment of minimal (still realistic) multi-chromophoric model systems. By adopting a static approximation that neglects dynamic processes such as spectral diffusion and population transfer, we show how 2DUV is able to characterize the ground-state conformational space of dinucleosides and small peptides comprising dimeric chromophoric units (in their native environment) by tracking inter-chromophoric electronic couplings. Recovering the excited-state coherent vibrational dynamics and population transfers, we observe a remarkable agreement between the predicted 2DUV spectra of the pyrene molecule and the experimental results. These results further led to theoretical studies of the excited-state dynamics in a solvated dinucleoside system, showing that spectroscopic fingerprints of long-lived excited-state minima along the complex photoinduced decay pathways of DNA/RNA model systems can be simulated at a reasonable computational cost. Our results exemplify the impact of accurate simulation of 2DES spectra in revealing complex physicochemical properties of fundamental biological systems and should trigger further theoretical developments as well as new experiments.

Electronic Couplings in (Bio-) Chemical Processes.

During the last two decades, 2D optical techniques have been extended to the visible range, targeting electronic transitions. Since the report of the very first 2D electronic measurement (Hybl et al. in J Chem Phys 115:6606-6622, [2001]), two-dimensional electronic spectroscopy (2DES) has allowed fundamentally new insights into the structure and dynamics of condensed-phase systems (Ginsberg et al. in Acc Chem Res 42:1352-1363, 2009; Jonas in Annu Rev Phys Chem 54:425-463, 2003), producing experiments that measure correlations among electronic states of an absorbing species within complex systems. 2DES is used to investigate photo-physical phenomena involving electronic or vibrational couplings in multi-chromophoric systems [energy transfer in photosynthesis is one great example of how 2DES can disentangle various energy transfer pathways (Brixner et al. in Nature 625-628, 2005; Engel et al. in Nature 446:782-786, 2007; Collini et al. in Nature 463:644-647, 2010)], but also ultrafast photochemical processes in which the tracked molecules change permanently or are heterogeneous (Ruetzel et al. in Proc Natl Acad Sci 111:4764-4769, 2014; Consani et al. in Science 339:1586-1589, 2013). We divide this chapter according to some of the major areas that have been established thanks to 2DES in the following fields: heterogeneity of systems, excitation energy transfer mechanisms, photo-induced coherent oscillations associated with electronic and vibrational couplings, and complex chemical reactions (Fig.1). Fig.1 Main fields impacted by two-dimensional electronic spectroscopy (2DES) in condensed phase. The major discoveries of each field will be described in different paragraphs.

The highly excited-state manifold of guanine: calibration for nonlinear electronic spectroscopy simulations

A computational protocol based on the complete and restricted active space self-consistent field (CASSCF/RASSCF) methods and their second-order perturbation theory extensions (CASPT2/RASPT2) is employed to benchmark the highly excited-state manifold of the DNA/RNA canonical purine nucleobase guanine in vacuo. Several RASPT2 schemes are tested, displaying a steady convergence of electronic transition energies and dipole moments upon active space enlargement toward the reference values. The outcome allows calibrating and optimizing computational efforts by considering cheaper and more approximate RAS schemes that could enable the characterization of the excited-state manifolds of multi-chromophoric systems, such as DNA/RNA nucleobase dimers or multimers. Simulations of two-dimensional electronic spectra show similar trends to those observed on the other purine nucleobase adenine, deviating from this and other pyrimidine nucleobases in featuring its main excited-state absorption signal, embodied by sizable double HOMO to LUMO excitation contributions, in the UV probing window.

Theoretical study of chromophores for biological sensing: Understanding the mechanism of rhodol based multi-chromophoric systems

Development of two-photon fluorescent probes can aid in visualizing the cellular environment. Multi-chromophore systems display complex manifolds of electronic transitions, enabling their use for optical sensing applications. Time-Dependent Density Functional Theory (TDDFT) methods allow for accurate predictions of the optical properties. These properties are related to the electronic transitions in the molecules, which include two-photon absorption cross-sections. Here we use TDDFT to understand the mechanism of aza-crown based fluorescent probes for metals sensing applications. Our findings suggest changes in local excitation in the rhodol chromophore between unbound form and when bound to the metal analyte. These changes are caused by a charge transfer from the aza-crown group and pyrazol units toward the rhodol unit. Understanding this mechanism leads to an optimized design with higher two-photon excited fluorescence to be used in medical applications.

Theory of Anisotropic Circular Dichroism of Excitonically Coupled Systems: Application to the Baseplate of Green Sulfur Bacteria.

A simple exciton theory for the description of anisotropic circular dichroism (ACD) spectra of multichromophoric systems is presented that is expected to be of general use for the analysis of structure-function relationships of molecular aggregates such as photosynthetic light-harvesting antennae. The theory is applied to the baseplate of green sulfur bacteria. It is demonstrated that only the combined analysis of ACD and circular dichroism (CD) spectra for the present baseplate bacteriochlorophyll (BChl) a dimer allows for an unambiguous determination of the parameters of the exciton Hamiltonian from experimental data. The analysis of experimental absorption and linear dichroism spectra suggests that either the NMR structure has to be refined or in addition to the dimers seen in the NMR structure and in the CD and ACD spectra, BChl a monomers are present in the baseplate carotenosome sample. A refined dimer structure is presented, explaining all four optical spectra.