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H-Aggregation Effects between #-Conjugated Chromophores in Cofacial Dimers and Trimers: Comparison of Theory and Single-Molecule Experiment Christoph Allolio, Thomas Stangl, Theresa Eder, Daniela Schmitz, Jan Vogelsang, Sigurd Höger, Dominik Horinek, and John M. Lupton J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b01188 • Publication Date (Web): 09 May 2018 Downloaded from http://pubs.acs.org on May 10, 2018

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The Journal of Physical Chemistry

H-Aggregation Effects between π-Conjugated Chromophores in Cofacial Dimers and Trimers: Comparison of Theory and SingleMolecule Experiment Christoph Allolio1,2,*), Thomas Stangl1, Theresa Eder1, Daniela Schmitz3, Jan Vogelsang1, Sigurd Höger3, Dominik Horinek2, and John M. Lupton1 1

Institut für Experimentelle und Angewandte Physik, Universität Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany and 2 Institut für Physikalische und Theoretische Chemie, Universität Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany 3 Kekulé-Institut für Organische Chemie und Biochemie der Universität Bonn,Gerhard-Domagk-Str.1, 53121 Bonn

Abstract Excited-state interchromophoric couplings in π-conjugated polymers present a daunting challenge to study as their spectroscopic signatures are difficult to separate from structuredependent intrachromophoric spectral characteristics. Using custom-designed molecular model systems in combination with single-molecule spectroscopy, a controlled coupling of the excited states between cofacially arranged π-conjugated oligomers is shown to be possible. Multiscale molecular dynamics simulations allow us to generate a representative ensemble of molecular structures of the model molecule embedded in a polymer matrix and examine the connection between structural fluctuations of the molecule with theoretically predicted and measured spectral signatures. The single molecules in the embedding matrix polymer can be assigned to specific conformational features with the help of computer-based “virtual spectroscopy”. By combining a quantum chemical with an analytical approach, we show that the coupling between the chromophores is well described by transition dipole coupling above an interchromophoric separation of ~4.5 Å. Even for aligned chromophores, however, twisting between repeat units of the -system and bending of the individual systems can lead to a decoupling of the chromophores to a degree far beyond what their equilibrium structures would suggest: tiny displacements of the molecular constituents can dramatically impact excited-state interactions. This observation has profound implications for the design of future tunable organic optoelectronic materials.

*) Corresponding author. Email: [email protected] Current Address: Institute of Chemistry and The Fritz Haber Research Center, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.

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Introduction Over the past years, devices based on organic optoelectronic materials have been greatly improved due to the development of an understanding of the interplay between chemical structure, microscopic molecular arrangement and macroscopic functionality.1 Nearly all organic optoelectronic materials consist of large -conjugated systems. Wide industrial adoption of these materials is often dependent on low-cost processable thin films formed from solution.1 As a result, actual devices contain high local concentrations of the optoelectronic material and are driven by a complex interplay of structural and electronic properties.3-5 In conjugated polymers (CPs), the nature of such aggregates makes it difficult to disentangle the various forms of interchromophoric coupling, such as H-aggregation,6 J-aggregation, excimeric states, formation of Frenkel excitons and -stacking,7-8 and separate them from onchain topological or chemical defects and bending of the chain inside the surrounding matrix.9-12 We refer to these chromophore interactions as H-like since a perfect H-aggregate would be non-emissive from the lowest state, which formally has zero oscillator strength. Indeed, conjugated chains are best thought of in the framework of admixtures of H-type and Jtype aggregation since chain packing improves intramolecular order, raising the intrachain transition dipole moment, while at the same time giving rise to H-type interactions. As all

interchromophoric coupling phenomena critically depend on distance they are not easily accessible through ensemble-based spectroscopy. In addition, CPs are well known to have a considerable degree of structural heterogeneity.1,13 Bulk measurements probe only an ensemble average, but the underlying structural distributions are unknown so that most of the relevant information is lost. Model systems based on poly(phenylene-ethynylenebutadiynylene) (PPEB) chromophores can be specifically engineered to exhibit well-defined spacings within a relatively narrow distribution14-15 or specifically designed intramolecular strain16. Single-molecule spectroscopy (SMS), reveals a remarkable amount of complexity hidden in even these simplified systems, as the spectroscopic properties of the isolated molecules vary widely and their distributions show distinct features.14-16 Molecular dynamics simulations enable us to generate representative conformations of the systems. Using “virtual spectroscopy”, we assign the characteristic features of the experimental distributions of spectroscopic observables – transition energy and lifetime – to specific molecular deformations. Using transition-orbital analysis we then explore the nature of the corresponding transitions. This combination allows us to disentangle the interplay of exciton coupling, bending, defects and fluorescence lifetime to an unprecedented extent. We report here the synthesis of a trimer array of chromophores as a new model system of interchromophoric interactions, and compare results to a closely related dimer system.14 The ACS Paragon Plus Environment

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spatial separation between the aligned molecules is expected to be ≈ 14 Å in the dimer and 7 Å in the trimer model-system.

Methods Experimental Details. The synthesis of the trichromophoric bicyclophane 1 is outlined schematically in Scheme 1 and elaborated in Scheme 2. The chromophoric units in the bichromophoric cyclophanes E as well as in the trichromophoric bicyclophanes E´ (horizontal lines, Scheme 1) are kept in a predefined distance by the covalent connection to the rigid clamp units (vertical lines, Scheme 1). In contrast to the bichromophoric cyclophanes E, which we described previously,14-15,17-18 the synthesis of the trichromophoric bicyclophanes requires a more elaborate protective group strategy. As shown schematically in Scheme 1, the synthesis of the bichromophoric cyclophanes E starts with a protected bisacetylenic precursor (A) with identical protecting groups. This precursor was statistically deprotected to form a mixture of completely deprotected and completely protected starting material, as well as the monoprotected bisacetylene B. Intermolecular Glaser coupling of B to C, subsequent deprotection and intramolecular Glaser coupling of D leads to the cyclophane E. The statistical deprotection of the protected trisacetylenic precursor with three identical protecting groups would, in principle, result in an only slightly more complex mixture containing completely deprotected, monoprotected, diprotected and completely protected products. However, since the three chromophores in the precursor are not at identical positions on the clamp unit, a statistical deprotection would lead to an inseparable mixture in which either the central or the outer acetylenes, or both, are protected or nonprotected. In order to overcome this problem a selective deprotection has to be involved in the synthesis of E´. The bicyclophane precursor A´ contains two different protecting groups in which the central acetylene is deprotected while the outer acetylenes remain protected. Subsequent intermolecular Glaser coupling of B forms C which contains, after deprotection, four equivalent acetylenes so that the problem of different isomers can be ruled out. Intramolecular acetylene dimerization then gives the bicyclophane E´. In order to realize this strategy, the clamp 219 was used in which the different halogens allow a selective cross coupling with the central (5) and outer chromophores (3). Different protecting groups at their acetylene ends allow a well-directed stepwise deprotection. Coupling of 2 with two equivalents of 3 and subsequent coupling with 5 leads to 6, in good yields, in which the central cyanopropyl dimethylsilyl (CPDMS) protecting group20 can be selectively removed while the more bulky



cyanopropyl diisopropylsilyl (CPDIPS) groups21 are not attacked. Intermolecular acetylene dimerization towards 8, deprotection of the outer chromophores and subsequent intramolecular coupling yield the trichromophoric bicyclophane 1 which was characterized by mass spectrometry as well as NMR and UV/Vis spectroscopy. Computational Details. Static Calculations Geometries were optimized on the RI22PBE023/def2-TZVP24 level of theory using the ORCA code in version 3.0.3.25 We used a TightSCF optimization criterion and the Grid5 preset. Optimized ground-state geometries were verified to be minima by the absence of negative eigenvalues in the internal coordinate Hessian matrix. Excited-state optimizations were obtained using the Tamm-Dancoff approximation (TDA) in the time-dependent Kohn-Sham equations26 and the same level of theory as for the ground-state calculations. Excited-state single points used the RIJCOSX27 approximation. The RI-SOS-CC2/def2-TZVP28-29 single point was computed using Turbomole v6.6.30 Molecular Dynamics. We used CP2K31 for QM/MM32. The trimer chromophore was solvated with 7821 Lennard-Jones (LJ) beads, using = 0.84 kcal/mol and = 4.7 Å from a preequilibrated simulation. Dielectric solvation effects of the experimental matrix were taken to be negligible as can be inferred from solution spectra in, e.g., toluene. Carbon, hydrogen, oxygen and nitrogen atoms were assigned LJ-Parameters for aromatic atoms from the CHARMM3633 force field. The simulation was conducted under periodic boundary conditions in a cubic box with 10 nm side length. We assigned masses of 6 and 2 atomic units to carbon and hydrogen, in order to increase simulation stability34 without slowing dynamics. The time step was 1 fs. The LJ cutoff was set to 1 nm. The “thermostat” of the simulation was set to 300 K by using a canonical sampling velocity rescaling35 with separate regions for the QM

and the MM part. The QM part consisted of the chromophore. To improve sampling, the alkyl sidechains were capped with methyl groups. Periodic boundary conditions for the Coulomb integrals were turned off. At the beginning of the simulation, the trimer was pre-equilibrated for 100 ps using self-consistent density functional tight-binding theory36 (DF-TB). The DFTB calculations used the parameters included in CP2K31 and the Grimme D3 dispersion corrections37, with optimized coefficients.38 From this starting point we then simulated the trimer as well as the dimer (after removing the trimer middle strand) for another 125 ps using AM139 with the same dispersion settings. The DF-TB simulation resulted in a strongly stacked geometry, while the AM1 simulation led to unfolding of the chromophore. In this way we sampled different modes of packing of the chromophores. We benchmarked π-π ACS Paragon Plus Environment

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interactions, torsional and thermal deformation energies of the DF-TB approach in the SI. We find them to be close to (TD-)DFT values, with only a small error of around 1 kJ/mol, but with a small systematically lower energy penalty for deformations. We strongly suspect that possible imbalances between π-stacking and bending energies will also be present in full DFT results.

Virtual Spectroscopy. To obtain a full ensemble of relaxed excited-state geometries trapped in a matrix further approximations had to be made. The first simplification is the use of state geometries.40-41 We show in the Supporting Information that the state reproduces the chromophore bonding pattern of the optimized TD-DFT state, so that the TD-DFT excitation energy on the DF-TB geometry does not differ by more than 0.04 eV from the optimized geometry. In the Supporting Information we also show that, for a single strand, thermalized energies correlate well between DF-TB and the full TD-DFT, which is much more computationally intensive. Furthermore, we assume that the molecules are trapped in a nearly fixed geometry due to the surrounding polymer matrix, so that strong changes in geometry due to the transition dipole coupling between chromophores do not occur. Note that these coupling interactions are neglected in the approximation. This conformational trapping is due to the surrounding polymer matrix, which introduces substantial inertia to the molecular dynamics. Note that this assumption is in agreement with experiment, where conformational changes, which would show up as changes in PL spectrum and lifetime, are not seen on timescales of several milliseconds. If they did occur, one would not be able to observe single-exponential PL decay features. Furthermore, we then approximate the full-TDDFT calculation with the recently developed simplified TD-DFT (sTDA) method by Grimme and co-workers.42 This method neglects the response of the XC-functional, and at long ranges replaces the exchange and Coulomb integrals by the corresponding interactions of partial charges. The sTDA method is completely in the spirit of a multipole coupling approximation, which we have shown to be accurate through static calculations in the main manuscript. Dimer and trimer snapshots were collected from the sampling part of the trajectory and were optimized for 100 steps using unrestricted DF-TB at a geometry. We used 114 snapshots of the trichromophore system from the AM1 trajectory as starting points. During the first ~30 ps we sampled at intervals of ~0.5 ps to better sample the packed mode, while later we sampled at approx. 1 − 2 ps. We used 96 snapshots from the bichromophore system, spaced at ~1 ps. From the QM part of the final geometries, we computed single points on the PBE0/6-311G*43 level of theory using Gaussian0944. The orbitals resulting from these single points were used ACS Paragon Plus Environment


for an approximate TD-DFT (sTDA)42 calculation with 25 % Hartree-Fock exchange. Results are red shifted in comparison to experiment. In addition, we computed full TDA-PBE0/6311G* single points on representative single points. NTOs were computed using the Gaussian 09 population analysis. We find them to be less red-shifted compared with (uncoupled) excitation energies with ∆Eexc around 2.4 eV, but they are still approx. 0.2 eV below the experimental value. In view of our benchmark results, this difference is most likely due to the method (the PBE0 result is red-shifted in comparison to the correlated results). The difference ∆∆Eexc between configurations is well conserved across methods.

Results and Discussion Morphology of the Chromophore Arrays. The molecular rulers reported here follow an established synthetic pathway and the complete synthesis and characterization of the new trimer model-system can be found in the Methods section as well as the Supporting Information.14 Their structural formula is given in Figure 1a. The molecules consist of two or three equally spaced PPEB oligomers. Simultaneous single-molecule fluorescence lifetime and spectral measurements were conducted by embedding the molecules in a non-fluorescent poly(methyl-methacrylate) (PMMA) matrix and investigating them with a confocal fluorescence microscope with a time-correlated single-photon counting (TCSPC) unit and a spectrometer equipped with a CCD camera (sample preparation and details of the microscope system can be found in ref. 15). The resulting Figure 1b correlates the peak position, i.e. the 0-0 electronic transition, of the photoluminescence (PL) spectrum and the PL lifetime "#$ , which were measured for 203 dimers (top panel) and 523 trimers (bottom panels). We find the 0-0 transition energy to be decreased and "%& to be increased in the more closely spaced trimer in comparison to the dimer. This change indicates the formation of excimer-like states.14,45-46 Crucially, a direct correlation exists between spectral red shift and increase in lifetime: the stronger the coupling, the greater the spectral shift and the stronger the retardation of the PL decay. The PL quantum yield was measured as described in Ref. 14 and found to be approximately 70 %, in agreement with the dimer structures. We stress that for the molecules considered in the lifetime-transition energy correlation, the quantum yield is likely higher, since the brightest molecules will preferentially show up in the single-molecule experiment. The PL lifetime should therefore be a good measure of the radiative lifetime of the transition. The inter-chromophore coupling is expected to occur mostly via Coulomb interactions of the transition dipoles, as is sketched in the inset of Figure 1b. Besides a shift of the mean PL peak


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positions, the distribution scatters around 0.25 eV , which reflects the influence of the surrounding matrix and structural variations. Additionally, the intensity ratio between the 0-0 electronic transition and the 0-1 vibronic progression in dependence of the 0-0 peak position provides a fingerprint of the type of electronic coupling, i.e. J-type or H-type coupling. According to the theory put forward by Spano et al.47, we expect the 0-0/0-1 ratio to decrease with increasing 0-0 peak position for H-type coupling; and the 0-0/0-1 ratio to increase with increasing 0-0 peak position for J-type coupling, which arises as a consequence of planarization of the repeat units. Figure 1e and f displays this behavior for the dimer and trimer, respectively. We plot normalized single-molecule PL spectra on a false-color scale, with the x-axis representing the extracted 0-0 peak position and the y-axis representing the energy scale. To achieve a better signal to noise ratio, we averaged over 10 spectra with close peak energies and plot such averaged spectra of the dimer in panel e for all peak positions measured from 2.61 eV to 2.75 eV. For the trimer, we selected only spectra with peak energies ranging from 2.55 eV to 2.61 eV, because we expect H-type coupling to occur only in this energy region due to the increase in PL lifetime seen for these molecules. For the dimer the 0-1 peak intensity increases with respect to the 0-0 peak intensity for increasing 0-0 peak energies which is precisely the opposite effect than for the trimer. We conclude that dimer molecules with lower 0-0 peak energies are primarily due to increased J-type coupling, whereas trimer molecules with lower 0-0 peak energies are characterized by increased H-type coupling, consistent with the increased PL lifetime. Further information about the morphology of the chromophore arrays can be gained by SMS using excitation polarization fluorescence spectroscopy (ExPFS).48-50 In ExPFS the PL intensity of single light-absorbing and emitting objects, e.g. CPs,48 single molecules51 or perovskite crystals,52 is measured while rotating the angle of the linearly polarized excitation light in the xy-plane of the laboratory frame. The modulation depth, ', is obtained by fitting the intensity, ( , vs. polarization angle ) , to (*)+ ∝ 1 + './0[2*θ − 2+] , where 2 is the orientation of the net transition dipole moment of the molecule when the emission is maximized. This formulation of Malus’ law is equivalent to considering the ratio between the difference and sum of maximal PL intensities upon rotating the plane of polarization of the laser, M=(Imax-Imin)/(Imax+Imin). For the chromophore array, the observed value of ' is a measure of the polarization anisotropy. As can be seen in Figure 1c, the mean value of ' is centered around 0.8 in a narrow distribution measured from 677 trimer molecules, indicating that the chromophores are closely aligned. Specifically, the transition dipoles of the individual



chromophores are expected to correspond to the main axis of the π-system of the chromophore so that the orientation of the chromophore lies along the direction of the transition dipole. In the following we test whether the chromophores in the trimer system can behave as independent emitters or whether they are coupled by energy transfer and the resulting singlet-singlet annihilation. To do this, we consider the degree of multi-photon emission.53 The PL from single trimer molecules is separated by a 50/50 beam splitter onto two detectors and the intensity auto-correlation, 4*5+ *6"+, is calculated from the photon stream (shown in the inset of Figure 1c). Due to the pulsed excitation, with a repetition rate of 40 MHz, occurrences of multiple photon events are detected in steps of 25 ns. We find strong photon antibunching at zero delay between both detectors, suggesting that the trimer molecules behave as a single chromophore system. This behavior can arise either due to coherent coupling between the chromophores or due to incoherent excitation energy transfer. The system, therefore, fulfills a necessary prerequisite to study possible couplings between chromophores. We have found the same behavior in related dimer systems.14 To connect our measured spectroscopic results to individual morphologies of the molecules we employ virtual spectroscopy starting with the simulation of possible morphologies of the trimer molecule. Our computational study uses fully thermalized chromophores, i.e. conformations generated from molecular dynamics (MD) followed by local relaxation on the excited-state surface. SMS necessitates the immobilization of the molecules in a matrix, here PMMA, which is accounted for in the simulation by using a set of Lennard-Jones beads that resemble a nonpolar environment as a “virtual matrix” (see Computational Details). Although this situation is somewhat different from the real PMMA environment, our matrix satisfies the most important requirement of counteracting excessive π-stacking of the aromatic groups which would lead the dimer or trimer to collapse onto itself. Furthermore, our computational matrix is more fluid than the experimental one, since there is no entanglement of polymer chains considered which raises viscosity. This limitation does mean, however, that we can efficiently sample a wide range of realistic chromophore geometries. Note that a full optimization at 0 K in the gas phase would yield only a single datapoint, most probably with a tightly π-stacked chromophore.

Crucially, the MD sampling of full chromophore array structures qualitatively agrees with the key experimental observations both for the trimer and for the dimer: time-dependent densityfunctional theory (TD-DFT) calculations on the chromophore confirm that the transition


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dipole does indeed lie parallel to the - π-system, as is shown for an example of a localized excitation in Figure 2a. Furthermore, MD simulations also confirm the expected average chromophore separation of slightly less than 7 Å. This value is confirmed by the probability distribution of different spacings between chromophores in simulated trimer structures in Figure 2b. The distribution is bimodal due to the sampling of -stacked conformers (see Computational Details for a further discussion). Nevertheless, MD in the ground state confirms that the chromophores are aligned predominantly in parallel, as is seen by the low angle of orientation between them in the distribution plotted in black in Figure 2c. In the same figure we also show that despite some π-stacking, the bending angle of the chromophores is generally low (distribution shown in grey). These MD simulation results are encouraging since they qualitatively match the conformational information derived from SMS (Figure 1d) and the apparent variation in interchromophoric coupling strengths (Figure 1b) between single molecules. Virtual Spectroscopy. In Figure 3 the experimental single molecule PL results are compared directly to simulation results. We find the qualitative features of the experimental PL peak position vs. "%& distribution in the matrix to be well reproduced by the simulation. A broad distribution of PL energies is present in the simulated and experimental data set, with a clear correlation between spectral red shift and PL lifetime seen in the trichromophoric system in Figure 3b. The characteristic curvature of the scatter plot is well replicated. The distributions obtained from simulations appear somewhat broader than the experimental ones, which we attribute to the approximations made when simulating the matrix and the fact that the experimental PL lifetimes represent average values over the measurement time, which takes ~100 ms, while the calculations constitute single points on a partially relaxed geometry. The x-axes of the plots are scaled to take this difference into account. Due to the approximate electronic structure method adopted for calculating excitations (see Computational Details), the results are also systematically red shifted with respect to the experiment.54 Taking into account these systematic errors, we have obtained the simulation equivalent of an SMS experiment in a matrix. This will allow us to analyze and interpret the spectral features in detail.

Fixed Chromophore Arrays. In order to gain insight into the nature of the excitations and their coupling, we first examine static model systems. A Davydov transition dipole coupling model55 allows us to make a prediction of the magnitude of the energy splitting, as well as for ACS Paragon Plus Environment


the size of the hole and electron in comparison to the isolated chromophores (see Supporting Information). We note that the approach does not include charge-transfer (CT) excitations and bound excimers, so that their appearance in the experiment should result in serious differences to the Davydov predictions. In the case of a single chromophore, the excitation involves only the frontier orbitals, i.e. it is a pure (> 95 %) HOMO-LUMO → ∗ transition. We verified this finding using a correlated wavefunction reference (see Computational Details). For the coupled chromophores TD-DFT was used. Hybrid functionals work satisfactorily for excimeric interactions56, and our choice of the PBE023 functional generally is considered to be a good one for excitations of organic molecules.57 We find the excitation energies 6; of the chromophores with respect to the reference to be slightly lower with the PBE0 functional (by about 0.2 eV). We recomputed the coupling using CAM-B3LYP58 in order to check for CT excitations, but we obtained very similar behavior. The results for a parallel arrangement of half-size, i.e. three ring chromophores, one of which is optimized in the state, the other in the ? state, are given in Figure 4a. The chromophores are equal, but one of them is structurally relaxed because of the presence of the excitation. We find the overall excitation energies to be in quantitative agreement with the analytical model, with only slight deviations at small interchromophore separations. Furthermore, we can predict the localization of the exciton by computing the wavefunction coefficients from our model (see Supporting Information). A first guess would assume the excitation to be equally distributed among the chromophores. This situation is, however, far from accurate. Strikingly, a relatively small difference in excitation energy between the two chromophores, 66; , caused by a structural relaxation of ≈ 4.6 B (0.1 eV) of one of them, is sufficient to localize the excitation to a degree of 90 % on one of the two chromophores at 7 Å spacing. This localization reduces the observed red shift to about 30 % of the value for an equal pair of excitation energies (i.e. 66; = 0). As expected, we find a strong effect on the oscillator strength resulting from transition dipole cancellation, which is seen in the plot in Figure 4b. Having placed the optimized chromophore at equal distance to the two identical ? optimized chromophores, we expect the coupling and therefore the splitting Δ; in the trimer to be twice as large as for the dimer. Indeed, we find the computed splittings and lifetimes for the trimer to be about twice the result for the dimer, as shown in Figure 4a. To further verify that only dipole coupling is relevant, and not charge transfer or excimer formation, we also ACS Paragon Plus Environment

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computed the oscillator strength and excitation energies of the trimer with the central chromophore rotated by 90° at 7 Å and 14 Å. This condition should drastically change all overlap and quadrupole contributions. We find the oscillator strengths to be unaffected (for spacings down to 7 Å) and the excitation energy change to be small (0.03 eV at 7 Å spacing). We conclude that interchromophore coupling is well described by transition dipole coupling and the excitation in a polymer “crystal” such as the model dimer and trimer is of Frenkel exciton type.

Decomposition of the PL distribution. We replot the simulation results from Figure 3 in Figure 5 to examine a set of representative value combinations of PL peak position and oscillator strength more closely. The corresponding geometries of the molecules are shown in Figure 5b. For these geometries we performed full TD-DFT calculations and computed natural transition orbitals (NTOs). NTOs59 represent a unitary transformation of the electronic excitations into transitions between pairs of orthogonal orbitals. This approach allows us to compare the results of full TD-DFT calculations with the interpretation we developed from considering the single chromophore. We obtain a compact representation of the excitation which can be directly compared to the HOMO-LUMO transition of the optimized chromophore. The results are given in Figure 5b. We find that the shape of the orbitals generally indicates that the nature of the excitation is not changed by thermalization. This means that the orbitals represent the same → ∗ excitation observed for the isolated chromophore and model chromophore arrays. Only the electron NTO is shown, because except in cases of strong coupling, the hole-NTO does not differ substantially in spatial extent or position form the electron NTO. An example of a comparison of electron and hole NTO is shown in panel c). We specifically point out that charge transfer excitations were not found among these geometries. The structures and excitations plotted in Figure 5 show that for both systems, dimer and trimer, torsions, topological defects and excitations can be present on either of the chromophores. The examples given in Figure 5 succinctly demonstrate how the size of the exciton determines the PL energy. Defects and bending of the chromophore restrict the exciton size. It is, however, not trivial to predict the exact location of the excitation or its transition energy to the ground state from the molecular structure alone, as only small differences in bending and twisting impact its location. We find strongly bent chromophores to have a slightly lower overall transition dipole moment, as is to be expected, due to cancellation of parts of the transition dipole.16, 60This cancellation would be consistent with the observed increase of "%& at longer PL wavelengths. We note that our computed examples ACS Paragon Plus Environment


of systems with more blue-shifted transitions all have parts of the -system interrupted by torsional defects.

A typical case of strong interchromophore coupling is shown in Figure 5c. In this case we find the hole and the electron delocalized on both chromophores, as is predicted from the basic Davydov model of a superposition of wavefunctions for independent chromophores. Note also that, as expected from the basic model, the wavefunctions of the chromophores are sign inverted with respect to each other, thus lowering the total transition dipole and contributing to the Davydov splitting. However, we also want to point out another aspect of the interaction: the excitation creates an overlap of the -orbitals of the excited chromophores. In the ground state these orbitals are in an antibonding pattern with each other, while in the excited state, a favorable interaction is possible. The constructive overlap of the π* orbitals suggests the possible formation of an excimer via covalent ∗ − ∗ interactions. As the basic Davydov model is a zero-overlap approximation, this is an illustrative example of how transition dipole interaction is by no means incompatible with excimer formation, but may in fact enable it. We emphasize again that the greater part of the observed red-shift can be attributed to transition dipole coupling, however our static calculations also suggest another contribution at extremely close range.

The cases of strong red-shifts (i.e. low transition energies) generally involve small parts of the adjacent chromophores at very close distance, as can be seen by inspection of the examples IIII in Figure 5b). This observation seems at odds with the picture from static calculations and also with the intuitive understanding of the molecular structures as rulers with a fixed distance. However, we find that the excitation energies of the different chromophores on the trimer are rather different - in general by more than 0.3 eV and often by more than 0.6 eV. This difference creates a coupling situation rather different from the one of energetically similar chromophores. In Figure 6 we show how this difference in excitation energies of the two chromophores results in a greatly reduced coupling strength: shifting the two chromophores out of resonance necessitates much smaller separations between the chromophores to obtain a given red-shift and retardation in emission lifetime. The data in Fig. 6 is calculated from our transition dipole coupling model (see Supporting Information), which we know to be accurate at long to intermediate range. Furthermore, the second excitation is not necessarily centered on the adjacent chromophore, and might be shifted away from optimal interaction by a defect on the chain. Therefore, to obtain strong coupling as found in ACS Paragon Plus Environment

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experiment, we sampled geometries of π-stacked structure, which resulted from the choice of the method as described in the Computational Details and Supporting Information. We found strong coupling was absent in geometries without some degree of π-stacking. This finding is independent of the method used to compute excitations, since it could be replicated with full TDA-DFT. All of this evidence indicates that a significant amount of -stacking, and, possibly, excimer formation does indeed occur in the excited state. We do, however, take note that there is a general red shift of the spectrum of the trichromophore system with respect to the dimer in experiment and even in theory. It is possible that the chromophore decoupling is slightly overestimated in our simulation and additionally the scattering in transition energies of the single-chromophore excitation itself is larger. There might also be a mechanical stabilization of the trichromophore system involved in the case of enhanced interchromophore coupling, because strong bending of one chromophore in one direction will induce deformation of the remaining chromophores: all three chromophores are implicitly mechanically coupled. The success of our simple approximations, however, indicates that for our chromophore structure an analytical theory of coupling mechanisms in conjugated polymers should be possible, if the dependence of the excitation energy on the intrachromophore bending and torsional deformation of the oligomer is fully characterized. Future designs of molecular arrays for sophisticated optoelectronic applications will have to either take structural fluctuations into account from the start or ensure sufficient rigidity of the systems to avoid distortion-induced decoupling. This may be achieved by choosing an appropriate support or devising additional structural constraints within the molecule.

Conclusions

We have combined organic chemistry, SMS, and quantum chemistry to successfully unravel the coupling between adjacent cofacial chromophores. We have introduced new modelsystems where chromophores are clamped at a fixed spatial distance through the introduction of linkers. The distances between the chromophores were chosen so as to obtain dipole-dipole coupling in one case and no coupling in the second case. SMS unravels the heterogeneous distribution of τPL and PL peak-emission energies of the chromophore arrays, which provide a direct measure of the interchromophore coupling. Using QM/MM molecular dynamics and TD-DFT we reproduced the main features of this conformational distribution in a “virtual matrix”, i.e. effectively in the condensed phase, from first principles calculations. We then assigned spectral features to specific molecular structures. The underlying excitations are of ACS Paragon Plus Environment


→ ∗ nature. Their coupling via transition dipoles is responsible for the observed PL

lifetime increase, a signature of intramolecular interchromophore H-aggregation. We also find some indication of ∗ − ∗ interactions at very close range. The oligomer exhibits sufficient flexibility to give rise to a broad range of bending and torsional deformations, which in general lead to a blue shift in the spectrum, counteracting to a certain extent the red-shift due to H-aggregation. In addition, deformations and defects of the oligomer decrease the strength of the interchromophoric coherent coupling with respect to the energetically minimized structures, necessitating closer interchromophore spacings to achieve the observed excimerlike emission signatures. The results offer a glimpse of the complexity of intermolecular interactions in flexible extended π-systems and highlight how intramolecular dynamics, even in the solid state, can strongly modify spectral characteristics over time. While analytical approaches to understanding such intermolecular interactions, in particular H-aggregation, in large systems such as conjugated polymers are helpful for developing a qualitative picture of molecular assembly, only microscopic spectroscopy combined with microscopic theory can reveal the contributions of all possible degrees of freedom.

Supporting Information

The Supporting Information contains additional details of the synthesis and the full characterization of the synthesized compound as well as the analytical model for the Davydov coupling, a comparison of DF-TB and PBE0 optimized geometries and a correlation of the unrestricted DF-TB and TD-DFT energies obtained from a single chromophore trajectory as well as a benchmark of the π-stacking interactions and torsional deformation energies combined with further computational details.

Acknowledgements

The authors are indebted to the Volkswagen Foundation for continued support of the collaboration as well as to the European Research Council for support through the Starting Grant MolMesON (305020) and the DFG through grant No. VO 1714/6-1. SH thanks the DFG for funding through grant No. HO 1448/17-1. References (1) Ostroverkhova, O. Organic Optoelectronic Materials: Mechanisms and Applications. Chem. Rev. 2016, 116, 13279–13412. ACS Paragon Plus Environment

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Scheme 1. Schematic representation of the synthetic approach to the bichromophoric cyclophane E and the trichromophoric bicyclophane E'. Protected bisacetylenic precursor A, triacetylene A', monodeprotected precursors B and B', intermediates after intermolecular Glaser coupling C and C', fully deprotected intermediates D and D' before intramolecular Glaser coupling to the final products.



Scheme 2. Synthetic route to the trimer structure. a) PdCl2(PPh3)2, CuI, PPh3, THF, piperidine, RT, overnight, 71 %; b) Pd2dba3, CuI, tBu3P, piperidine, 70 °C, overnight, 89 %; c) K2CO3, THF, MeOH, RT, 4 h, 69 %; d) PdCl2(PPh3)2, CuI, I2, THF, piperidine, RT, overnight, 87 %; e) 1 M TBAF in THF, RT, 1 h, 80 %; f) PdCl2(PPh3)2, CuI, I2, THF, diisopropylamine, 50 °C, 96 h, 28 %.


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Figure 1. (a) Structures of the dimer (left) and trimer (right) model system. Two or three oligomer chromophores (blue) are organized using two clamping units (gray) to give trimers with an interchromophoric spacing of 7 Å or dimers with 14 Å spacing. (b) The PL spectrum and lifetime report on the interaction strength of these H-aggregate structures. Scatter plots of PL lifetime, "%& , vs. PL peak energy of the electronic transition, ;?G? , for 203 single dimer (top) and 523 trimer molecules (bottom). The inset depicts the energetic splitting of the excited state, E, due to coherent coupling of neighboring transition dipole moments. (c) Schematic representation of the measurement procedure for the determination of the overall ACS Paragon Plus Environment


absorption dipole alignment by excitation polarization fluorescence spectroscopy (ExPFS). The ExPFS modulation depth, M, is determined from the degree of linear polarization in the excitation and is defined in the inset. (d) ' histogram for 677 trimer molecules, showing almost perfect linearly polarized absorption of the single molecules. Inset: intensity crosscorrelation, 4*5+ *Δ"+, of the single-molecule fluorescence for 25 single trimers. The ratio of the central peak, HI , to the lateral peaks, H& , is stated in the panel, and indicates near perfect photon antibunching, implying effective coupling between the three chromophores. (e, f) Normalized spectra plotted on a false-color intensity scale of the dimers (e) and trimers (f) sorted by increasing 0-0 peak positions. 10 spectra with consecutive 0-0 peak positions are averaged to increase the signal to noise.


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Figure 2. (a) Snapshot of the molecular structure and natural transition orbitals of the trichromophore model-system in a “virtual matrix” of Lennard-Jones beads, designed to emulate the effect of the PMMA matrix in the single-molecule experiments. The white arrow indicates the overall transition dipole moment. (b) Histogram of the interchromophore distance values obtained from the mid-chain carbon atoms of adjacent chromophores in the equilibrated trimer structures. (c) Histogram of the chain-chain bending angle, i.e. the angle between the orientation vectors formed by the two terminal carbon atoms on the chromophores (black bars). The chain bending angle (grey bars), i.e. the angle between the orientation vector and the vector connecting a terminal carbon to a mid-chain carbon atom shows a similar distribution.



Figure 3. Comparison of experimental and theoretical single-molecule 0-0 transition energies and PL lifetime, the "%& values. The experimental data are shown in grey and red, the results of the simulations in blue for the dimer of 14 Å separation (a) and the trimer array of 7 Å interchromophore separation (b). The experimental data is referenced to the bottom and left axes, the theoretical values to the top and right axes. The different axes reflect the fact that the computational results are red-shifted with respect to the experimental results. Oscillator strength is dimensionless.


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Figure 4. Coupling of arrays of simplified chromophores as described in the Supporting Information as a function of distance, in terms of the fluorescence energy (a) and the oscillator strength (b). In (a), simulated → ? transistions are compared with a Davydov transition dipole coupling model for the dimer. The trimer transitions are compared with dimer transitions by multiplying the simulated dimer red-shift with respect to infinitely separated chromophores by two. The excitation and partial optimizations were carried out on the (TDA-)PBE0/defTZVP level of theory.



Figure 5. (a) Computational “single-molecule spectroscopy” of the distributions of the oscillator strength vs. transition energy for the dimer (top) and trimer (bottom). (b) Natural transition orbitals (NTOs), i.e. the electron part of the exciton, of the lowest excited state in the dimer (I-III) and the trimer 1-6. (c) The hole and electron NTOs are given for geometry 1 and are found to be virtually identical. The orbital cutoffs are 0.05 atomic units.


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Figure 6. PL red-shift in the trimer computed from our transition dipole coupling model between two of the chromophores at a dipole strength of J5 = 70 atomic units, given as a function of the distance between chromophores and the difference in uncoupled excitation energy of the chromophores. As the chromophores move out of resonance, the coupling and corresponding red-shift decreases for a given spacing. The plot is computed following the Davydov coupling model (see Supporting Information), and the dipole strength is close to the value obtained for uncoupled chromophores in the full DFT snapshots.



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