All-DFTB Approach to the Parametrization of the System-Bath Hamiltonian Describing Exciton-Vibrational Dynamics of Molecular Assemblies.

Spectral density functions are central to the simulation of complex many body systems. Their determination requires making approximations not only to the dynamics but also to the underlying electronic structure theory. Here, blending different methods bears the danger of an inconsistent description. To solve this issue we propose an all-DFTB approach to determine spectral densities for the description of Frenkel excitons in molecular assemblies. The protocol is illustrated for a model of a PTCDI crystal, which involves the calculation of monomeric excitation energies and Coulomb couplings between monomer transitions, as well as their spectral distributions due to thermal fluctuations of the nuclei. Using dynamically defined normal modes, a mapping onto the standard harmonic oscillator spectral densities is achieved.

Spectral densities for Frenkel exciton dynamics in molecular crystals: A TD-DFTB approach.

Effects of thermal fluctuations on the electronic excitation energies and intermonomeric Coulomb couplings are investigated for a perylene-tetracarboxylic-diimide crystal. To this end, time dependent density functional theory based tight binding (TD-DFTB) in the linear response formulation is used in combination with electronic ground state classical molecular dynamics. As a result, a parametrized Frenkel exciton Hamiltonian is obtained, with the effect of exciton-vibrational coupling being described by spectral densities. Employing dynamically defined normal modes, these spectral densities are analyzed in great detail, thus providing insight into the effect of specific intramolecular motions on excitation energies and Coulomb couplings. This distinguishes the present method from approaches using fixed transition densities. The efficiency by which intramolecular contributions to the spectral density can be calculated is a clear advantage of this method as compared with standard TD-DFT.

Computing dispersive, polarizable, and electrostatic shifts of excitation energy in supramolecular systems: PTCDI crystal.

The gas-to-crystal-shift denotes the shift of electronic excitation energies, i.e., the difference between ground and excited state energies, for a molecule transferred from the gas to the bulk phase. The contributions to the gas-to-crystal-shift comprise electrostatic as well as inductive polarization and dispersive energy shifts of the molecular excitation energies due to interaction with environmental molecules. For the example of 3,4,9,10-perylene-tetracarboxylic-diimide (PTCDI) bulk, the contributions to the gas-to-crystal shift are investigated. In the present work, electrostatic interaction is calculated via Coulomb interaction of partial charges while inductive and dispersive interactions are obtained using respective sum over states expressions. The coupling of higher transition densities for the first 4500 excited states of PTCDI was computed using transition partial charges based on an atomistic model of PTCDI bulk obtained from molecular dynamics simulations. As a result it is concluded that for the investigated model system of a PTCDI crystal, the gas to crystal shift is dominated by dispersive interaction.

Structure Prediction of Self-Assembled Dye Aggregates from Cryogenic Transmission Electron Microscopy, Molecular Mechanics, and Theory of Optical Spectra.

Cryogenic transmission electron microscopy (cryo-TEM) studies suggest that TTBC molecules self-assemble in aqueous solution to form single-walled tubes with a diameter of about 35 Å. In order to reveal the arrangement and mutual orientations of the individual molecules in the tube, we combine information from crystal structure data of this dye with a calculation of linear absorbance and linear dichroism spectra and molecular dynamics simulations. We start with wrapping crystal planes in different directions to obtain tubes of suitable diameter. This set of tube models is evaluated by comparing the resulting optical spectra with experimental data. The tubes that can explain the spectra are investigated further by molecular dynamics simulations, including explicit solvent molecules. From the trajectories of the most stable tube models, the short-range ordering of the dye molecules is extracted and the optimization of the structure is iteratively completed. The final structural model is a tube of rings with 6-fold rotational symmetry, where neighboring rings are rotated by 30° and the transition dipole moments of the chromophores form an angle of 74° with respect to the symmetry axis of the tube. This model is in agreement with cryo-TEM images and can explain the optical spectra, consisting of a sharp red-shifted J-band that is polarized parallel to to the symmetry axis of the tube and a broad blue-shifted H-band polarized perpendicular to this axis. The general structure of the homogeneous spectrum of this hybrid HJ-aggregate is described by an analytical model that explains the difference in redistribution of oscillator strength inside the vibrational manifolds of the J- and H-bands and the relative intensities and excitation energies of those bands. In addition to the particular system investigated here, the present methodology can be expected to aid the structure prediction for a wide range of self-assembled dye aggregates.

Excited States of Xanthene Analogues: Photofragmentation and Calculations by CC2 and Time-Dependent Density Functional Theory.

Action spectroscopy has emerged as an analytical tool to probe excited states in the gas phase. Although comparison of gas-phase absorption properties with quantum-chemical calculations is, in principle, straightforward, popular methods often fail to describe many molecules of interest-such as xanthene analogues. We, therefore, face their nano- and picosecond laser-induced photofragmentation with excited-state computations by using the CC2 method and time-dependent density functional theory (TDDFT). Whereas the extracted absorption maxima agree with CC2 predictions, the TDDFT excitation energies are blueshifted. Lowering the amount of Hartree-Fock exchange in the DFT functional can reduce this shift but at the cost of changing the nature of the excited state. Additional bandwidth observed in the photofragmentation spectra is rationalized in terms of multiphoton processes. Observed fragmentation from higher-lying excited states conforms to intense excited-to-excited state transitions calculated with CC2. The CC2 method is thus suitable for the comparison with photofragmentation in xanthene analogues.

How Van der Waals Interactions Influence the Absorption Spectra of Pheophorbide a Complexes: A Mixed Quantum-Classical Study.

The computation of dispersive site energy shifts due to van der Waals interaction (London dispersion forces) was combined with mixed quantum-classical methodology to calculate the linear optical absorption spectra of large pheophorbide a (Pheo) dendrimers. The computed spectra agreed very well with the measurements considering three characteristic optical features occurring with increasing aggregate size: a strong line broadening, a redshift, and a low-energy shoulder. The improved mixed quantum-classical methodology is considered a powerful tool in investigating molecular aggregates.

Calculating Optical Absorption Spectra of Thin Polycrystalline Organic Films: Structural Disorder and Site-Dependent van der Waals Interaction.

We propose a new approach for calculating the change of the absorption spectrum of a molecule when moved from the gas phase to a crystalline morphology. The so-called gas-to-crystal shift Δ[Formula: see text] m is mainly caused by dispersion effects and depends sensitively on the molecule's specific position in the nanoscopic setting. Using an extended dipole approximation, we are able to divide Δ[Formula: see text] m = -QWm in two factors, where Q depends only on the molecular species and accounts for all nonresonant electronic transitions contributing to the dispersion while Wm is a geometry factor expressing the site dependence of the shift in a given molecular structure. The ability of our approach to predict absorption spectra is demonstrated using the example of polycrystalline films of 3,4,9,10-perylenetetracarboxylic diimide (PTCDI).

Site-dependence of van der Waals interaction explains exciton spectra of double-walled tubular J-aggregates.

The simulation of the optical properties of supramolecular aggregates requires the development of methods, which are able to treat a large number of coupled chromophores interacting with the environment. Since it is currently not possible to treat large systems by quantum chemistry, the Frenkel exciton model is a valuable alternative. In this work we show how the Frenkel exciton model can be extended in order to explain the excitonic spectra of a specific double-walled tubular dye aggregate explicitly taking into account dispersive energy shifts of ground and excited states due to van der Waals interaction with all surrounding molecules. The experimentally observed splitting is well explained by the site-dependent energy shift of molecules placed at the inner or outer side of the double-walled tube, respectively. Therefore we can conclude that inclusion of the site-dependent dispersive effect in the theoretical description of optical properties of nanoscaled dye aggregates is mandatory.

Frenkel to Wannier-Mott Exciton Transition: Calculation of FRET Rates for a Tubular Dye Aggregate Coupled to a CdSe Nanocrystal.

The coupling is investigated of Frenkel-like exciton states formed in a tubular dye aggregate (TDA) to Wannier-Mott-like excitations of a semiconductor nanocrystal (NC). A double well TDA of the cyanine dye C8S3 with a length of 63.4 nm and a diameter of 14.7 nm is considered. The TDA interacts with a spherical Cd819Te630 NC of 4.5 nm diameter. Electronic excitations of the latter are described in a tight-binding model of the electrons and holes combined with a configuration interaction scheme to consider their mutual Coulomb coupling. To achieve a proper description of TDA excitons, a recently determined structure has been used, the energy transfer coupling has been defined as a screened interaction of atomic centered transition charges, and the site energies of the dye molecules have been the subject of a polarization correction. Even if both nanoparticles are in direct contact, the energy transfer coupling between the exciton levels of the TDA and of the NC stays below 1 meV. It results in FRET-type energy transfer with rates somewhat larger than 10(9)/s. They coincide rather well with recent preliminary experiments.

Concerted charge and energy transfer processes in a highly flexible fullerene-dye system: a mixed quantum-classical study.

Photoinduced excitation energy transfer and accompanying charge separation are elucidated for a supramolecular system of a single fullerene covalently linked to six pyropheophorbide-a dye molecules. Molecular dynamics simulations are performed to gain an atomistic picture of the architecture and the surrounding solvent. Excitation energy transfer among the dye molecules and electron transfer from the excited dyes to the fullerene are described by a mixed quantum-classical version of the Förster rate and the semiclassical Marcus rate, respectively. The mean characteristic time of energy redistribution lies in the range of 10 ps, while electron transfer proceeds within 150 ps. In between, on a 20 to 50 ps time-scale, conformational changes take place in the system. This temporal hierarchy of processes guarantees efficient charge separation, if the structure is exposed to a solvent. The fast energy transfer can adopt the dye excitation to the actual conformation. In this sense, the probability to achieve charge separation is large enough since any dominance of unfavorable conformations that exhibit a large dye-fullerene distance is circumvented. And the slow electron transfer may realize an averaging with respect to different conformations. To confirm the reliability of our computations, ensemble measurements on the charge separation dynamics are simulated and a very good agreement with the experimental data is obtained.

Mixed quantum-classical description of excitation energy transfer in supramolecular complexes: screening of the excitonic coupling.

A mixed quantum-classical description of excitation energy transfer (EET) in large chromophore complexes with significant conformational flexibility is improved by considering screening and local-field effects. To account for the environmentally induced modification of the excitonic coupling J(mn)(ε>1) between chromophore m and n, the Poisson-transition-charges-from-electrostatic-potential (Poisson-TrEsp) method is utilized. A parameterization scheme for the such derived screening/local field factors is introduced, which allows for their incorporation to a mixed quantum-classical description. The method is applied to the supramolecular complex P16 formed by sixteen pheophorbide-a molecules covalently linked to a butanediamine dendrimer and dissolved in ethanol. Data calculated using the novel parameterized screening method are compared to those obtained by alternative screening approaches. Averaging the screening factors in different ways may reproduce ensemble experiments on EET well, while the description of single molecule properties requires the consideration of individual screening factors.

A mixed quantum-classical description of excitation energy transfer in supramolecular complexes: Förster theory and beyond.

Electronic excitation energy transfer (EET) is described theoretically for the chromophore complex P(4) formed by a butanediamine dendrimer to which four pheophorbide-a molecules are covalently linked. To achieve a description with atomic resolution, and to account for the effect of an ethanol solvent, a mixed quantum-classical methodology is utilized. Room-temperature molecular dynamics simulations are used to describe the nuclear dynamics, and EET is accounted for in utilizing a mixed quantum-classical formulation of the transition rates. Therefore, the full quantum expression of the EET rates is given and the change to a mixed quantum-classical version is briefly explained. The description results in the calculation of transition rates which coincide rather satisfactory with available experimental data on P(4). It is also shown that different assumptions of classical Förster theory are not valid for P(4). The temporal behavior of EET deduced from the rate equations is confronted with that following from the solution of the time-dependent Schrödinger equation entering the mixed quantum-classical description of EET. From this we can conclude that EET in flexible chromophore complexes such as P(4) can be rather satisfactory estimated by single transition rates. A correct description, however, is only achievable by using a sufficiently large set of rates that correspond to the various possible equilibrium configurations of the complex.