Long-range corrected fragment molecular orbital density functional tight-binding method for excited states in large molecular systems.

Herein, we present a new method to efficiently calculate electronically excited states in large molecular assemblies, consisting of hundreds of molecules. For this purpose, we combine the long-range corrected tight-binding density functional fragment molecular orbital method (FMO-LC-DFTB) with an excitonic Hamiltonian, which is constructed in the basis of locally excited and charge-transfer configuration state functions calculated for embedded monomers and dimers and accounts explicitly for the electronic coupling between all types of excitons. We first evaluate both the accuracy and efficiency of our fragmentation approach for molecular dimers and aggregates by comparing it with the full LC-TD-DFTB method. The comparison of the calculated spectra of an anthracene cluster shows a very good agreement between our method and the LC-TD-DFTB reference. The effective computational scaling of our method has been explored for anthracene clusters and for perylene bisimide aggregates. We demonstrate the applicability of our method by the calculation of the excited state properties of pentacene crystal models consisting of up to 319 molecules. Furthermore, the participation ratio of the monomer fragments to the excited states is analyzed by the calculation of natural transition orbital participation numbers, which are verified by the hole and particle density for a chosen pentacene cluster. The use of our FMO-LC-TDDFTB method will allow for future studies of excitonic dynamics and charge transport to be performed on complex molecular systems consisting of thousands of atoms.

(De)localization dynamics of molecular excitons: comparison of mixed quantum-classical and fully quantum treatments.

Molecular excitons play a central role in processes of solar energy conversion, both natural and artificial. It is therefore no wonder that numerous experimental and theoretical investigations in the last decade, employing state-of-the-art spectroscopic techniques and computational methods, have been driven by the common aim to unravel exciton dynamics in multichromophoric systems. Theoretically, exciton (de)localization and transfer dynamics are most often modelled using either mixed quantum-classical approaches (e.g., trajectory surface hopping) or fully quantum mechanical treatments (either using model diabatic Hamiltonians or direct dynamics). Yet, the terms such as "exciton localization" or "exciton transfer" may bear different meanings in different works depending on the method in use (quantum-classical vs. fully quantum). Here, we relate different views on exciton (de)localization. For this purpose, we perform molecular surface hopping simulations on several tetracene dimers differing by a magnitude of exciton coupling and carry out quantum dynamical as well as surface hopping calculations on a relevant model system. The molecular surface hopping simulations are done using efficient long-range corrected time-dependent density functional tight binding electronic structure method, allowing us to gain insight into different regimes of exciton dynamics in the studied systems.

Transforming Dyes into Fluorophores: Exciton-Induced Emission with Chain-like Oligo-BODIPY Superstructures.

Herein we present a systematic study demonstrating to which extent exciton formation can amplify fluorescence based on a series of ethylene-bridged oligo-BODIPYs. A set of non- and weakly fluorescent BODIPY motifs was selected and transformed into discrete, chain-like oligomers by linkage via a flexible ethylene tether. The prepared superstructures constitute excitonically active entities with non-conjugated, Coulomb-coupled oscillators. The non-radiative deactivation channels of Internal Conversion (IC), also combined with an upstream reductive Photoelectron Transfer (rPET) and Intersystem Crossing (ISC) were addressed at the monomeric state and the evolution of fluorescence and (non-)radiative decay rates studied along the oligomeric series. We demonstrate that a "masked" fluorescence can be fully reactivated irrespective of the imposed conformational rigidity. This work challenges the paradigm that a collective fluorescence enhancement is limited to sterically induced motional restrictions.

Ultrafast Resonance Energy Transfer in Ethylene-Bridged BODIPY Heterooligomers: From Frenkel to Förster Coupling Limit.

A series of distinct BODIPY heterooligomers (dyads, triads, and tetrads) comprising a variable number of typical green BODIPY monomers and a terminal red-emitting styryl-equipped species acting as an energy sink was prepared and subjected to computational and photophysical investigations in solvent media. An ethylene tether between the single monomeric units provides a unique foldameric system, setting the stage for a systematic study of excitation energy transfer processes (EET) on the basis of nonconjugated oscillators. The influence of stabilizing ß-ethyl substituents on conformational space and the disorder of site energies and electronic couplings was addressed. In this way both the strong (Frenkel) and the weak (Förster) coupling limit could be accessed within a single system: the Frenkel limit within the strongly coupled homooligomeric green donor subunit and the Förster limit at the terminal heterosubstituted ethylene bridge. Femtosecond transient-absorption spectroscopy combined with mixed quantum-classical dynamic simulations demonstrate the limitations of the Förster resonance energy transfer (FRET) theory and provide a consistent framework to elucidate the trend of increasing relaxation lifetimes at higher homologues, revealing one of the fastest excitation energy transfer processes detected to date with a corresponding lifetime of 39 fs.

Ultrafast Energy Transfer Dynamics in a Squaraine Heterotriad.

A squaraine heterotriad consisting of three different covalently linked squaraine chromophores was synthesized, and its absorption spectra were interpreted in terms of Kasha's exciton coupling theory. Using the exciton couplings derived from model dyads (ca. 700 cm-1) as the input, we were able to predict the exciton state energies of the heterotriad. Transient absorption spectroscopy with femtosecond time resolution showed that excitation of the highest exciton state populates a state mainly localized at one terminal squaraine chromophore, and energy transfer to the lowest exciton state localized at the other terminal squaraine occurs within 30 fs. Field-induced surface hopping dynamics simulations support the assumption of ultrafast energy transfer. Moreover, they show the close relationship between internal conversion and energy transfer in the intermediate to weak coupling regime. The latter is a consequence of excitation localization caused by molecular vibrations.

Predicting fluorescence quantum yields for molecules in solution: A critical assessment of the harmonic approximation and the choice of the lineshape function.

For the rational design of new fluorophores, reliable predictions of fluorescence quantum yields from first principles would be of great help. However, efficient computational approaches for predicting transition rates usually assume that the vibrational structure is harmonic. While the harmonic approximation has been used successfully to predict vibrationally resolved spectra and radiative rates, its reliability for non-radiative rates is much more questionable. Since non-adiabatic transitions convert large amounts of electronic energy into vibrational energy, the highly excited final vibrational states deviate greatly from harmonic oscillator eigenfunctions. We employ a time-dependent formalism to compute radiative and non-radiative rates for transitions and study the dependence on model parameters. For several coumarin dyes, we compare different adiabatic and vertical harmonic models (AS, ASF, AH, VG, VGF, and VH), in order to dissect the importance of displacements, frequency changes, and Duschinsky rotations. In addition, we analyze the effect of different broadening functions (Gaussian, Lorentzian, or Voigt). Moreover, to assess the qualitative influence of anharmonicity on the internal conversion rate, we develop a simplified anharmonic model. We address the reliability of these models considering the potential errors introduced by the harmonic approximation and the phenomenological width of the broadening function.

Dynamic exciton localisation in a pyrene-BODIPY-pyrene dye conjugate.

The photophysics of a molecular triad consisting of a BODIPY dye and two pyrene chromophores attached in 2-position are investigated by steady state and fs-time resolved transient absorption spectroscopy as well as by field induced surface hopping (FISH) simulations. While the steady state measurements indicate moderate chromophore interactions within the triad, the time resolved measurements show upon pyrene excitation a delocalised excited state which localises onto the BODIPY chromophore with a time constant of 0.12 ps. This could either be interpreted as an internal conversion process within the excitonically coupled chromophores or as an energy transfer from the pyrenes to the BODIPY dye. The analysis of FISH-trajectories reveals an oscillatory behaviour where the excitation hops between the pyrene units and the BODIPY dye several times until finally they become localised on the BODIPY chromophore within 100 fs. This is accompanied by an ultrafast nonradiative relaxation within the excitonic manifold mediated by the nonadiabatic coupling. Averaging over an ensemble of trajectories allowed us to simulate the electronic state population dynamics and determine the time constants for the nonradiative transitions that mediate the ultrafast energy transfer and exciton localisation on BODIPY.

The mechanism of excimer formation: an experimental and theoretical study on the pyrene dimer.

The understanding of excimer formation in organic materials is of fundamental importance, since excimers profoundly influence their functional performance in applications such as light-harvesting, photovoltaics or organic electronics. We present a joint experimental and theoretical study of the ultrafast dynamics of excimer formation in the pyrene dimer in a supersonic jet, which is the archetype of an excimer forming system. We perform simulations of the nonadiabatic photodynamics in the frame of TDDFT that reveal two distinct excimer formation pathways in the gas-phase dimer. The first pathway involves local excited state relaxation close to the initial Franck-Condon geometry that is characterized by a strong excitation of the stacking coordinate exhibiting damped oscillations with a period of 350 fs that persist for several picoseconds. The second excimer forming pathway involves large amplitude oscillations along the parallel shift coordinate with a period of ≈900 fs that after intramolecular vibrational energy redistribution leads to the formation of a perfectly stacked dimer. The electronic relaxation within the excitonic manifold is mediated by the presence of intermolecular conical intersections formed between fully delocalized excitonic states. Such conical intersections may generally arise in stacked π-conjugated aggregates due to the interplay between the long-range and short-range electronic coupling. The simulations are supported by picosecond photoionization experiments in a supersonic jet that provide a time-constant for the excimer formation of around 6-7 ps, in good agreement with theory. Finally, in order to explore how the crystal environment influences the excimer formation dynamics we perform large scale QM/MM nonadiabatic dynamics simulations on a pyrene crystal in the framework of the long-range corrected tight-binding TDDFT. In contrast to the isolated dimer, the excimer formation in the crystal follows a single reaction pathway in which the initially excited parallel slip motion is strongly damped by the interaction with the surrounding molecules leading to the slow excimer stabilization on a picosecond time scale.

Excimer formation dynamics in the isolated tetracene dimer.

The understanding of excimer formation and its interplay with the singlet-correlated triplet pair state 1(TT) is of high significance for the development of efficient organic electronics. Here, we study the photoinduced dynamics of the tetracene dimer in the gas phase by time-resolved photoionisation and photoion imaging experiments as well as nonadiabatic dynamics simulations in order to obtain mechanistic insight into the excimer formation dynamics. The experiments are performed using a picosecond laser system for excitation into the S2 state and reveal a biexponential time dependence. The time constants, obtained as a function of excess energy, lie in the range between ≈10 ps and 100 ps and are assigned to the relaxation of the excimer on the S1 surface and to its deactivation to the ground state. Simulations of the quantum-classical photodynamics are carried out in the frame of the semi-empirical CISD and TD-lc-DFTB methods. Both theoretical approaches reveal a dominating relaxation pathway that is characterised by the formation of a perfectly stacked excimer. TD-lc-DFTB simulations have also uncovered a second relaxation channel into a less stable dimer conformation in the S1 state. Both methods have consistently shown that the electronic and geometric relaxation to the excimer state is completed in less than 10 ps. The inclusion of doubly excited states in the CISD dynamics and their diabatisation further allowed to observe a transient population of the 1(TT) state, which, however, gets depopulated on a timescale of 8 ps, leading finally to the trapping in the excimer minimum.

The origin of the solvent dependence of fluorescence quantum yields in dipolar merocyanine dyes.

Fluorophores with high quantum yields are desired for a variety of applications. Optimization of promising chromophores requires an understanding of the non-radiative decay channels that compete with the emission of photons. We synthesized a new derivative of the famous laser dye 4-dicyanomethylen-2-methyl-6-p-dimethylaminostyryl-4H-pyran (DCM), i.e., merocyanine 4-(dicyanomethylene)-2-tert-butyl-6-[3-(3-butyl-benzothiazol-2-ylidene)1-propenyl]-4H-pyran (DCBT). We measured fluorescence lifetimes and quantum yields in a variety of solvents and found a trend opposite to the energy gap law. This motivated a theoretical investigation into the possible non-radiative decay channels. We propose that a barrier to a conical intersection exists that is very sensitive to the solvent polarity. The conical intersection is characterized by a twisted geometry which allows a subsequent photoisomerization. Transient absorption measurements confirmed the formation of a photoisomer in unpolar solvents, while the measurements of fluorescence quantum yields at low temperature demonstrated the existence of an activation energy barrier.