Frenkel Exciton Theory Research Articles

Extracting the excitonic Hamiltonian of a chlorophyll dimer from broadband two-dimensional electronic spectroscopy.

We apply Frenkel exciton theory to model the entire Q-band of a tightly bound chlorophyll dimer inspired by the photosynthetic reaction center of photosystem II. The potential of broadband two-dimensional electronic spectroscopy experiment spanning the Qx and Qy regions to extract the parameters of the model dimer Hamiltonian is examined through theoretical simulations of the experiment. We find that the local nature of Qx excitation enables identification of molecular properties of the delocalized Qy excitons. Specifically, we demonstrate that the cross-peak region, where excitation energy is resonant with Qy while detection is at Qx, contains specific spectral signatures that can reveal the full real-space molecular Hamiltonian, a task that is impossible by considering the Qy transitions alone. System-bath coupling and site energy disorder in realistic systems may limit the resolution of these spectral signatures due to spectral congestion.

The light-harvesting complex 2 of Allochromatium vinosum: B800 absorption band splitting and exciton relaxation

Allochromatium (Alc.) vinosum has a double-peak structure of its absorption band around 800 nm. Previously, the excitonic origin of this feature has been demonstrated experimentally, but a detailed understanding still lacks a model Hamiltonian being able to reproduce absorption as well as exciton relaxation time scales. Here, we propose a system-bath model which accommodates these observables. It combines Frenkel exciton theory for a dimerized and energetically heterogeneous B800 pigment pool with a quantum master equation approach describing phase and energy relaxation according to an experimental spectral density. The analysis of this model shows that the LH2 of Alc. vinosum features an interesting interplay of two excitonic bands, which are originating from the different pigment pools.

Essential States Model for Merocyanine Dye Stacks: Bridging Electronic and Optical Absorption Properties

An extension of the essential states model is developed to investigate the absorption and electronic properties of a highly dipolar merocyanine dye and double and quadruple π-stacks formed upon the folding and self-assembly of appropriate spacer-tethered bis(merocyanine) dyes. Our analysis reveals that a simple two-state model is not sufficient to adequately describe the absorption features of a single chromophore. However, by including an additional bridge state, the absorption features are well described and reasonable values for the permanent and transition dipole moments are obtained. We show that the low-energy absorption band of the folded double stack results from vibronic coupling, whereas the additional absorption shoulder observed in the spectrum of the self-assembled quadruple stack is due to a transition to a lower excited state. Furthermore, the chromophores within both π-stacks exhibit an increase in the charge-transfer character in the ground state with respect to the single chromophore arising from polarizability effects, which are not accounted for in the conventional Frenkel exciton theory. These insights are of significant importance for the proper design of functional materials based on merocyanines and dipolar chromophores in general.

Design Principles for Two-Dimensional Molecular Aggregates Using Kasha’s Model: Tunable Photophysics in Near and Short-Wave Infrared

Technologies which utilize near-infrared (NIR) (700–1000 nm) and short-wave infrared (1000–2000 nm) electromagnetic radiation have applications in deep-tissue imaging, telecommunications, and satellite telemetry due to low scattering and decreased background signal in this spectral region. It is therefore necessary to develop materials that absorb light efficiently beyond 1000 nm. Transition dipole moment coupling (e.g., J-aggregation) allows for red-shifted excitonic states and provides a pathway to highly absorptive electronic states in the infrared. We present aggregates of two cyanine dyes whose absorption peaks red-shift dramatically upon aggregation in water from ∼800 to 1000 nm and 1050 nm, respectively, with sheet-like morphologies and high molar absorptivities (e ≈ 105 M–1 cm–1). We use Frenkel exciton theory to extend Kasha’s model for J- and H-aggregations and describe the excitonic states of two-dimensional aggregates whose slip is controlled by steric hindrance in the assembled structure. A c...

Comparative Computational Study of Electronic Excitations of Neutral and Charged Small Oligothiophenes and Their Extrapolations Based on Simple Models.

This work reports electronic excitation energies of neutral and charged oligothiophenes (OTn) with repeat unit n = 2–6 computed by routinely used semiempirical and time-dependent density functional theory (TD-DFT) methods. More specifically, for OTn, OTn+, and OTn–, we calculated vertical transition energies for electronic absorption spectroscopy employing the Zerner’s version of intermediate neglect differential overlap method for structures optimized by the PM6 semiempirical method and the TD-DFT method with three different functionals, B3LYP, BVP86, and M06-2X, for structures optimized by the ground-state DFT method employing the same functionals. We also calculated vertical transition energies for the emission spectroscopy from the lowest singlet excited states by employing the TD-DFT method for the structures optimized for the lowest singlet excited states. In addition to computational results in vacuum, solution phase data calculated at the level of polarizable continuum model are reported and compared with available experimental data. Most of the data are fitted reasonably well by two simple model functions, one based on a Frenkel exciton theory and the other based on the model of independent electrons in a box with sinusoidal modulation of potential. Despite similar levels of fitting performance, the two models produce distinctively different asymptotic values of excitation energies. Comparison of these with available experimental and computational data suggests that the values based on the exciton model, while seemingly overestimating, are closer to true values than those based on the other model. This assessment is confirmed by additional calculations for a larger oligomer. The fitting parameters offer new means to understand the relationship between electronic excitations of OTs and their sizes and suggest the feasibility of constructing simple coarse-grained exciton-bath models applicable for aggregates of OTs.

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer.

The electronic excited states of molecular aggregates and their photophysical signatures have long fascinated spectroscopists and theoreticians alike since the advent of Frenkel exciton theory almost 90 years ago. The influence of molecular packing on basic optical probes like absorption and photoluminescence was originally worked out by Kasha for aggregates dominated by Coulombic intermolecular interactions, eventually leading to the classification of J- and H-aggregates. This review outlines advances made in understanding the relationship between aggregate structure and photophysics when vibronic coupling and intermolecular charge transfer are incorporated. An assortment of packing geometries is considered from the humble molecular dimer to more exotic structures including linear and bent aggregates, two-dimensional herringbone and "HJ" aggregates, and chiral aggregates. The interplay between long-range Coulomb coupling and short-range charge-transfer-mediated coupling strongly depends on the aggregate architecture leading to a wide array of photophysical behaviors.

Origin of DNA-Induced Circular Dichroism in a Minor-Groove Binder.

Induced circular dichroism (ICD) of DNA-binding ligands is well known to be strongly influenced by the specific mode of binding, but the relative importance of the possible mechanisms has remained undetermined. With a combination of molecular dynamics simulations, CD response calculations, and experiments on an AT-sequence, we show that the ICD of minor-groove-bound 4',6-diamidino-2-phenylindole (DAPI) originates from an intricate interplay between the chiral imprint of DNA, off-resonant excitonic coupling to nucleobases, charge-transfer, and resonant excitonic coupling between DAPIs. The significant contributions from charge-transfer and the chiral imprint to the ICD demonstrate the inadequacy of a standard Frenkel exciton theory of the DAPI-DNA interactions.

Single Molecule Spectroscopy of Monomeric LHCII: Experiment and Theory.

We derive approximate equations of motion for excited state dynamics of a multilevel open quantum system weakly interacting with light to describe fluorescence-detected single molecule spectra. Based on the Frenkel exciton theory, we construct a model for the chlorophyll part of the LHCII complex of higher plants and its interaction with previously proposed excitation quencher in the form of the lutein molecule Lut 1. The resulting description is valid over a broad range of timescales relevant for single molecule spectroscopy, i.e. from ps to minutes. Validity of these equations is demonstrated by comparing simulations of ensemble and single-molecule spectra of monomeric LHCII with experiments. Using a conformational change of the LHCII protein as a switching mechanism, the intensity and spectral time traces of individual LHCII complexes are simulated, and the experimental statistical distributions are reproduced. Based on our model, it is shown that with reasonable assumptions about its interaction with chlorophylls, Lut 1 can act as an efficient fluorescence quencher in LHCII.

Molecular Packing in Organic Solar Cell Materials: Insights from the Emission Line Shapes of P3HT/PCBM Polymer Blend Nanoparticles

Semiconducting polymer devices have seen tremendous progress in development of material and device designs, while device efficiencies have made substantial gains. Still, the effect of material morphology on the optoelectronic properties of semiconducting polymers is not completely understood even though these materials make up the active device layer. In this study we use computational methods to simulate different poly(3-hexylthiophene) (P3HT) morphologies, predict their emission spectra, and compare them to experimentally observed emission spectra for P3HT nanoparticles. We use published X-ray diffraction data on P3HT polymorphs to build the molecular models of nanodomains that differ in the side-chain packing. The atomic and electronic structures of both nanodomains are studied with the force field, Hartree–Fock, CIS, and density functional theory methods. The results confirm the coexistence of type I and II nanodomains, where the shift of the backbones in the same stack is determined by the differences in side-chain packing. Upon excitation, the polymer chains in type II domain are free to slide to their optimal arrangement in the stack, whereas in type I domain this sliding is hindered by the steric repulsion of the side chains and the chains are essentially constrained to keep the ground state geometry. These nanodomains, therefore, differ in their emission spectra: type I emission has a single 0–0 vibronic band, while type II demonstrates pronounced vibronic progression. In agreement with Frenkel exciton theory, splitting of the excited state depends on the longitudinal shift of the π-systems. However, we find that due to the constraints arising from P3HT being confined in nanosized particles, the type I nanodomain increasingly appears as an additional emitter that exhibits J-aggregate character. As a result, a pronounced vibronic structure appears as PCBM blending ratios increase, as opposed to the changes in emission profile due to a different degree of disorder present in weakly coupled H-aggregates. These findings are distinct from those made for bulk P3HT materials.

Spectroscopy of BODIPY in solid phase: crystal and nanoparticles

We compare the absorption and fluorescence spectra of single crystals and suspensions of nanoparticles with the prediction of the Frenkel theory. The single crystals of a novel synthesized fluorescent BODIPY derivative dye, adamantyl mesityl BODIPY (4,4-difluoro-3,5-di-(adamantyl)-8-mesityl-4-bora-3a,4a-diaza-s-indacene), have been prepared. Their birefringence and dichroism have been studied. The X-ray crystallography shows a monoclinic crystal with all transition moments parallel to one common plane. The refractive indices along the two neutral axes have been measured for a wavelength from 530 to 700 nm, with a difference, Δn equal to 0.11. The Frenkel exciton theory was used here to describe the coupling of the electronic excited states in the crystals. The coupling estimated by the dipolar approximation was compared with the excited state splitting calculated by TDDFT in dimers. A perfect crystal absorption spectrum is predicted. The spectral broadening that occurs at room temperature is also taken into account. The absorption spectrum of the monocrystal is reproduced without adjustable parameters. But we had to take into account the presence of optical leaks in our microspectrophotometer before comparing experiment and theory. The controlled size nanoparticles (NPs) produced by our 3D hydrodynamic focusing microfluidic system exhibit molecule like absorption. We could reproduce their absorption and fluorescence spectra assuming a strong disorder in the Frenkel model. We conclude that the nanoparticles are amorphous.

Calculations of the exciton coupling elements between the DNA bases using the transition density cube method

Excited states of the double-stranded DNA model (A)12.(T)12 were calculated in the framework of the Frenkel exciton theory. The off-diagonal elements of the exciton matrix were calculated using the transition densities and ideal dipole approximation associated with the lowest energy pipi* excitations of the individual nucleobases as obtained from time-dependent density functional theory calculations. The values of the coupling calculated with the transition density cubes (TDC) and ideal dipole approximation (IDA) methods were found to be significantly different for the small interchromophore distances. It was shown that the IDA overestimates the coupling significantly. The effects of structural fluctuations of the DNA chain on the magnitude of dipolar coupling were also found to be very significant. The difference between the maximum and minimum values was as large as 1000 and 300 cm(-1) for the IDA and TDC methods, respectively. To account for these effects, the properties of the excited states were averaged over a large number of conformations obtained from the molecular dynamics simulations. Our calculations using the TDC method indicate that the absorption of the UV light creates exciton states carrying the majority of the oscillator strength that are delocalized over at least six DNA bases. Upon relaxation, the excitation states localize over at least four contiguous bases.

Heterogeneous Exciton Dynamics Revealed by Two-Dimensional Optical Spectroscopy

We show that optical two-dimensional (2D) spectroscopy can recover ultrafast heterogeneous dynamics of closely spaced delocalized exciton states from a molecular exciton manifold characterized by a single absorption band. The complete experimental third-order nonlinear optical response from room-temperature J-aggregates in liquid phase is reproduced for the first time with self-consistent Frenkel exciton theory combined with modified Redfield theory. We show that exciton relaxation between the exciton states and nuclear-motion-induced exchange-narrowed energy fluctuations of individual delocalized exciton states can be distinguished because these two processes lead to a distinctively different evolution of the absolute 2D spectrum. Our technique also allows recovery of the variation of the exciton relaxation rates as well as the degree of exciton delocalization across the absorption band.

Exciton Effects in the Dimer and Higher Aggregates of a Simple Merocyanine Dye. A CS INDO CI Based Theoretical Study

A simple streptomerocyanine with five methine carbons (Mc) has been used as a suitable model system to investigate theoretically the optical properties in organized assemblies of merocyanine dyes. The subject was treated by a methodology making use of a semiempirical quantum chemistry description of the isolated chromophore within the Frenkel exciton theory. Both an extended CS INDO CIPSI and easier CS INDO SCI (with different parametrizations of electron repulsion integrals) schemes were applied in order to establish the role played by the quality of the wave functions. The exciton states were built on the 1(ππ*) (HOMO-LUMO) excited-state responsible for the “color” band of Mc. Exciton effects were first analyzed for two stable dimer structures, having H- and J-type character, located by use of a semiempirical intermolecular potential and the simulated annealing method. Then, attention was shifted from dimers to higher-order model aggregates built in such a way as to obtain typical H (columnar) and J (staircase) arrangements. Exciton-state properties (energies and transition dipole moments) were studied as a function of the aggregation number N (up to N = 50). The results are discussed with reference to the approximations used to calculate the excitonic matrix as well as to the effects of changing from CIPSI to simple SCI schemes.

Frenkel excitons in disordered chromophore complexes: Theory of optical absorption of Langmuir–Blodgett layers including pheophorbide-a

Absorption spectra of dye molecules embedded in a Langmuir–Blodgett layer are simulated within a Frenkel-exciton theory. The spectra are determined in using a time-dependent formulation based on the exciton density matrix. Disorder with respect to the positions and the excitation energy of the dye molecules is accounted for within a numerical Monte Carlo treatment. The approach is used to interpret recent measurements on behenic acid layers including pheophorbide-a in a monomeric as well as dimeric form. The concrete type of aggregation and the degree of diagonal disorder can be clarified. Multilayer systems are also discussed.

Disordered Exciton Analysis of Linear and Nonlinear Absorption Spectra of Antenna Bacteriochlorophyll Aggregates: LH2−Only Mutant Chromatophores of Rhodobacter sphaeroides at 8 K under Spectrally Selective Excitation

The objective of this work is two-fold. First, the effects of static diagonal disorder on the linear and nonlinear absorption spectra of excitons in circular molecular aggregates are studied by computer modeling. Second, it is demonstrated that this simplified model successfully reproduces the main features of both the ground-state absorption and initial pump−probe absorption difference spectra of LH2 antenna proteins from photosynthetic bacteria measured upon spectrally selective population of excitons at low temperature. Of the usual first-order approximations in the Frenkel exciton theory, our model exploits only two: the two-state and the zero electron−vibrational coupling approximations. In our model, the molecules of the aggregate are allowed to have different site energies. The coupling between all aggregate molecules is taken into account. An important difference between our study and previous work is that the exciton state selective spectra are calculated corresponding to the recently performed ...

Photoluminescence under selective excitation of thiophene oligomers: relationship to microcrystalline structure

The photoluminescence of thin films of various sexithiophene oligomers has been studied by using excitations near the absorption edge. This emission shows at least two overlapping spectra with very different features. The position of the 0-0 line of the low-energy emission is clearly dependent on the nature and microcrystallinity of the oligomer under study, in contrast with the high-energy one. An identification of the crystalline and molecular levels involved is suggested by using Frenkel exciton theory in the limiting cases of strong and weak intermolecular coupling. Spectral effects due to the reduced size of the grains are discussed.

Femtosecond time-resolved optical response of phthalocyanine Langmuir–Blodgett film

The mechanism of 2,9,16,23-tetra-heptadecylamido-substituted vanadyl phthalocyanine Langmuir–Blodgett film was studied with femtosecond laser pulses. After the excitation into the first electronic excited band, an ultrafast decay due to phonon-exciton coupling greatly affected by temperature was observed. Following this process, exciton-exciton annihilation leads to the recovery of the ground state with a decay time of about 10 ps. The Frenkel exciton theory was employed to give a complete interpretation of the dynamics. An even slower relaxation was also observed.

Theory of the radical-electron configurations and optical excitations in short-chain polydiacetylene oligomers.

The chain-length-dependent radical-electron structure of short polydiacetylene chains is calculated using a configuration model. The butatriene-to-acetylene transition and a change from diradicals to dicarbenes as a function of chain length is described. By introduction of coupled electronic two-level systems a one-dimensional Frenkel exciton theory is applied for an explanation of the chain-length-dependent uv-absorption spectra. The theoretical results are in good agreement with the experimental observations.

A model of the primary process in photosynthesis

AbstractThe arrangement of membrane‐bound pigments, proteins, and lipids in the thylakoids of higher plants is described, and the role of the membrane in preventing the back‐reaction is discussed. The photosynthetic bacterium halobacterium halobium is also described. A simplified quantum‐mechanical picture of the primary process in photosynthesis is presented, and the mechanism of electron‐hole separation in this picture is compared with the corresponding mechanism in a silicon solar cell. An appendix discusses the application of Frenkel exciton theory to the antenna effect.

Effects of the internal field in the spectra of molecular crystals and the theory of excitons

It is shown that a very large set of optical properties of molecular crystals (pure crystals, crystals containing impurities, and crystalline solutions) in the region of the lowest singlet electronic (or vibrational) excited states, where the mutual interaction of the molecules does not violate their neutrality, can be treated without bringing in exciton concepts, but by generalizing to anisotropic media the methods of molecular optics that had been developed before Frenkel's ideas on the exciton had appeared. This treatment is based on using the method of the acting field, which goes back to Lorentz, and also on the results of Born and Ewald et al., which permit one to calculate the electric field acting on some particular molecule in the crystal, and in particular, with account taken of the higher multipoles of the polarizability of the molecules. It is shown that this approach permits one to calculate the dielectric constant of the crystal with account taken of spatial dispersion, to treat the polarization and splitting of light-absorption bands in crystals, and polarization of impurity absorption bands, as well as an entire series of other problems that were previously studied in less general form only within the framework of the Frenkel exciton theory. The limits of applicability of the presented approach are also discussed.