Ultrafast Exciton Self-Trapping upon Geometry Deformation in

Letter pubs.acs.org/JPCL

Ultrafast Exciton Self-Trapping upon Geometry Deformation in Perylene-Based Molecular Aggregates Alexander Schubert,† Volker Settels,† Wenlan Liu,† Frank Würthner,‡ Christoph Meier,§ Reinhold F. Fink,∥ Stefan Schindlbeck,⊥ Stefan Lochbrunner,⊥ Bernd Engels,*,† and Volker Engel*,† †

Universität Würzburg, Institut für Physikalische und Theoretische Chemie, Hubland Campus Nord, Emil-Fischer-Strasse 42, 97074 Würzburg, Germany ‡ Universität Würzburg, Institut für Organische Chemie, Am Hubland, 97074 Würzburg, Germany § Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université Paul Sabatier, 118 rte de Narbonne, 31062 Toulouse, France ∥ Universität Tübingen, Institut für Physikalische und Theoretische Chemie, Auf der Morgenstelle 18, 72076 Tübingen, Germany ⊥ Universität Rostock, Institut für Physik, Universitätsplatz 3, 18055 Rostock, Germany S Supporting Information *

ABSTRACT: Femtosecond time-resolved experiments demonstrate that the photoexcited state of perylene tetracarboxylic acid bisimide (PBI) aggregates in solution decays nonradiatively on a time-scale of 215 fs. High-level electronic structure calculations on dimers point toward the importance of an excited state intermolecular geometry distortion along a reaction coordinate that induces energy shifts and couplings between various electronic states. Time-dependent wave packet calculations incorporating a simple dissipation mechanism indicate that the fast energy quenching results from a doorway state with a charge-transfer character that is only transiently populated. The identified relaxation mechanism corresponds to a possible exciton trap in molecular materials. SECTION: Spectroscopy, Photochemistry, and Excited States

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are depicted in Figure 1 (left-hand side). The strong mutual couplings that highly depend on the nuclear geometry lead to

nefficient excitation energy transfer (EET) is one of the important reasons for the limited performance of thin film devices such as organic solar cells.1,2 To a major extent it is caused by exciton self-trapping processes that hamper the EET through energy loss often accompanied by geometrical distortions. These processes considerably shorten the travel distance of the exciton since they run on a similar time scale as EET.3 Despite their paramount importance, a consistent atomistic understanding of the underlying processes is still missing. Particularly, the role of charge transfer (CT) states is controversially discussed.4,5 This lack of information strongly hinders a complete understanding of the EET which, in turn, is necessary for the development of molecules with better suited properties.6 In this paper, we introduce a complete theoretical and experimental approach that provides such information and apply it to 3,4,9,10-perylene tetracarboxylic bisimide acid (PBI) H-aggregates in solution7 as representative for various organic semiconductors.8 Experimental studies indicate that the exciton localizes to dimers on a femtosecond time scale.9 This interpretation is supported by simulations that show that the spectrum of the aggregates can be well reproduced assuming dimers.11 On the basis of these findings, our theoretical approach uses molecular dimers consisting of two monomers M1 and M2 as smallest units. In the dimer model, self-trapping processes involve locally excited Frenkel configurations M1M*2 and M*1 M212 and the corresponding CT configurations (M−1 M+2 , M+1 M−2 ), which © 2013 American Chemical Society

Figure 1. Excitation scheme for localized Frenkel (M1M2*, M1*M2) and CT (M1± M2± ) excited states (left). Mutual couplings lead to nondegenerated mixed adiabatic states S1−S4 (right). The arrows indicate the absorption and emission processes (straight lines) and the S2 → S1 relaxation (dashed line).

four separated states (Sna, na = 1−4, right-hand panel of Figure 1) possessing mixed Frenkel and CT character.13 To compute the relevant potential energy curves (PEC) we use the spincomponent scaled second order coupled cluster method (SCSCC2/SVP), which provides an accuracy around 0.1 eV14 and reliable energy spacings of Frenkel and CT states. Received: January 11, 2013 Accepted: February 19, 2013 Published: February 19, 2013 792

dx.doi.org/10.1021/jz4000752 | J. Phys. Chem. Lett. 2013, 4, 792−796

The Journal of Physical Chemistry Letters

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procedure, the signal is decomposed into three components. The first component is a step function reflecting the bleach, which is switched on with the excitation and does not change thereafter. An exponentially decaying component with a negative amplitude and a time constant of 215 fs is the second contribution. It is attributed to stimulated emission since only bleach and emission lead to negative absorption changes, and the latter one is expected at the spectral position of the probe pulses according to Strickler−Berg symmetry. The decay indicates that the emission dissapears quickly after excitation. We note that this decay does not appear for nonaggregating PBIs.10 Furthermore, there is an oscillatory contribution with a period of 381 fs. As a key result, the data shows that the excited state is depopulated on an ultrafast time scale. To interpret these new results we use the SCS-CC2 method, which delivers reliable energy spacings of the involved Frenkel and CT states.14,18−23 The resulting potential energy curves (Va1−Va4) of the four lowest adiabatic excited states S1−S4 are displayed in Figure 3, upper left panel. At a vertical excitation

Our approach differs from theoretical methods that treat nuclear dynamics classically and use semiempirical electronic structure theory for the electronic degrees-of-freedom to enable the necessary large number of calculations.15 Such approaches, which provide valuable insights for many systems, are not applicable in our case since the energy gaps between Frenkel and CT states are not sufficiently accurate and dispersion effects are not taken into account. The dimer model in combination with a time-dependent Hartree−Fock (TD-HF) approach could assign the absorption band of PBI-aggregates at around 480 nm to the population of the second electronic state (S2) possessing predominantly Frenkel character. It furthermore indicated that the strongly red-shifted, broad emission band results from photoemission from the lowest Frenkel state (S1) (see Figure 1).5 The broadness of the emission band originates from the potential energy surface topology of the S1 state. Its lifetime is long since the S1 state adopts a nearly vanishing transition dipole moment for the transition to the ground state. Thus, the S1 state serves as a trapping state for the excitonic energy, and its population limits the exciton transfer efficiency. These investigations essentially explained the spectra, but they were inappropriate to elucidate the involvement of CT states due to well-known shortcomings of TD-HF.13,16 They could furthermore not provide an understanding of the S2 → S1 transition, which is of tremendous importance for an understanding of the photophysical properties of perylene-based systems. To shed light on this important aspect, we perform additional femtosecond transient absorption measurements. An aggregating PBI-derivative17 dissolved in methylcyclohexane is excited near its absorption maximum at 480 nm by 30 fs pulses with an energy of about 50 nJ focused to a spot diameter of 150 μm. Ten times weaker probe pulses with a duration of 40 fs are applied at 520 nm, which is in the red wing of the upper absorption band of the aggregate (for details, see Supporting Information10). The measured absorption change is displayed as a function of the delay time after excitation in the upper part of Figure 2. Also shown is the signal obtained from the pure solvent to indicate the time resolution. Using a fitting

Figure 3. Adiabatic (Vana(q), upper left panel) and diabatic ((Vdnd(q), upper right panel) excited state potentials as a function of q. The values of q = 0 and q = 1 correspond to the equilibrium geometries of the ground neutral and CT state, respectively. Lower left panel: charge transfer character of the different adiabatic states. Lower right panel: Diabatic potential coupling elements.

geometry (q = 0), the relative positions of the two predominantly Frenkel states, S1 and S2, deviate only 0.08 eV from experiment.11 The CT state S3 is predicted to be so close in energy (about 0.04 eV) that crossings with the Frenkel state along the way to its equilibrium geometry cannot be excluded. To investigate this possibility, we computed the PECs along a reaction coordinate that linearly relates the initial ground state, M1M2, geometry with coordinates R⃗ i to the M+1 M−2 equilibrium geometry with coordinates R⃗ f as R⃗ = R⃗ i + q(R⃗ f − R⃗ i), where R⃗ collectively denotes the coordinates of all nuclei. The M+1 M−2 equilibrium geometry was estimated by combining the computed geometries of charged monomers M ± . As intermolecular coordinates we used the ground state values since their relaxation takes place on a longer time scale. The corresponding adiabatic potentials are depicted in Figure 3 (upper left panel), which also gives the electronic characters of the states (lower left panel). Computed oscillator strengths ( f 0,1 = 0.04, f 0,2 = 1.02, f 0,3 = 0.07, and f 0,4 = 0.01), indicate that photon excitation from the ground state into the main

Figure 2. Time-dependent absorption change ΔOD at 520 nm (open circles), signal of the pure solvent (upper fine line), and model function fitted to the data (thick solid line). The three lower lines show the contributions to the model function. They are shifted to lower ΔOD values for better visibility. 793



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absorption band (higher energy excitonic state) results in the population of state S2 at q = 0. Here, the two lowest states are mainly Frenkel states, while the S3 state has predominantly CT character. As anticipated, along the way to the M1+M 2− equilibrium geometry, an avoided crossing between the states S2 and S3 around q = 0.4 can be identified. As a consequence, the S2 state acquires CT-character, whereas the S3 state becomes mostly Frenkel-type. Here, a nonadiabatic transition can be imagined that transfers the exciton to the lower state. It is worthwhile to mention that, in going from one to the other geometry (i.e., from q = 0 to q = 1), the atomic positions are not changed dramatically where a deviation in position is about 0.01 Å, in the average. To describe the corresponding nuclear dynamics, we integrate the time-dependent Schrödinger equation numerically24 incorporating a potential energy matrix with the diabatic potential curves Vdnd(q) and their coupling elements Vndmd(q) displayed in Figure 3, right panel, in combination with an appropriate effective mass.10,25 The diabatic potentials Vdnd(q)26 approximately conserve the electronic character as a function of the nuclear coordinates. Vd1, Vd2 correspond to the Frenkel states, and Vd3, Vd4 correspond to the CT states. The coupling elements Vndmd(q) (which are responsible for transitions between states of different character) are chosen as Gaussians of various widths, and only the couplings V14 = V41, V24 = V42 and V34 = V43 are taken as nonzero. Note, that the resulting diabatic states and their couplings completely result from quantum chemical calculations, i.e., they contain no empirical fit parameters. To simulate the femtosecond excitation process, we choose as an initial function the vibrational function of the electronic ground state derived from the ground-state adiabatic potential Va0(q) (not shown in Figure 3). Dissipation is included phenomenologically by introduction of a damping of the excited state wave function components. In this way, energy disperses irreversibly into the bath (see Supporting Information). As seen in the probability densities given in Figure 4 (upper panels) the initially prepared wave packet moves periodically in the photoexcited Frenkel state (nd = 2), until the density is transferred via the doorway CT state (nd = 4) to the lowest Frenkel state (nd = 1), where it is accumulated in the vicinity of its equilibrium position. The populations of these states given in Figure 4 (lower panel) support this interpretation: The intermediate CT-state (nd = 4) is populated only to a small amount since the population is directly transferred to the lower state (nd = 1). This transfer can be traced back to the broad coupling region between the two lowest diabatic states (nd = 1 and 4). It explains why, for PBI-aggregates, the typical anionic or cationic bands27 are not seen in transient spectra. Accordingly, the model calculations show that the upper state is depopulated within 200 fs, which agrees quite nicely with the measured value. Taking additional modes into account, our computation can also interpret the oscillatory contribution with a period of 381 fs (see Supporting Information). The competing processes determining the fate of the exciton are summarized in Figure 5. The transition (1→2) gives the experimentally indicated very fast localization of the exciton to dimers. Afterward, the exciton transfer from the initially populated Frenkel state (2) to the lower lying Frenkel state (6) is induced, which is possible due to the mediation of a transiently populated CT-state (5). According to our experimental and theoretical findings, this transfer (2→5→6)

Figure 4. Upper and middle panel: time-dependent probability densities |(ψdnd(q,t)|2 of the diabatic states (nd = 1,2). Lower panel: population dynamics in the diabatic electronic states (nd).

can take place within about 200 fs. This time scale is comparable to or shorter than the one of EET (2→4), which can be as fast as 50−200 fs28 but is in many cases slower. Therefore, each exciton will hop at most a few times before it moves to (6), where it is irreversibly stabilized by about 0.35 eV. This means that, even if the energy transfer is extremely fast, relaxation takes place because after a few jumps the transition to the lower electronic state on another dimeric unit occurs with high probability. In situation (6), the exciton has reached the S1 state, but it is not yet relaxed to its minimum (7). This relaxation (6→7) proceeds on the PEC of the intermolecular torsional motion.29 We computed the torsional wave packet dynamics using the potentials, which are given in ref 5. Because of the large moment of inertia and the flat potential, this motion (which ends up in a face-to-face orientation) takes place on a picosecond time scale. Due to the accompanied destabilization of the ground state, the excitation energy decreases by a total amount of 0.73 eV. This explains the red shift of the measured emission spectrum.5 The interplay between energy loss and geometrical deformation causes an immobilization of the exciton, which prevents further EET, i.e., the exciton is very efficiently self-trapped. This finding is in agreement with our measurements of polarization anisotropy, which gave no indication of exciton migration (see Supporting Information10). Furthermore, in the experiments, no evidence for exciton−exciton annihilation or singlet fission were detected. The latter is in agreement with recent computations about the energy position of the relevant triplet states,8 which employed the same computational methods as used in this study. The strong similarities in the electronic structures of perylene based compounds8 indicate that the self-trapping processes described above have a strong impact on the photophysics of all perylene-based dyes. The resulting inefficient EET might be an important reason for disappointing efficiencies of correspond794



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Figure 5. Processes determining the fate of electronic excitations in PBI-aggregates. The color changes from blue to red indicate an accompanying loss of excitation energy.

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ing devices.30 The model indicated by our combined approach predicts that improved EET can only be obtained for morphologies that either exhibit larger energy gaps between Frenkel and CT states or in which the lower Frenkel state is initially populated (e.g., J-aggregates). The latter is in line with recent experiments.28

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ASSOCIATED CONTENT

S Supporting Information *

Further details about absorption spectra, transient absorption of nonaggregating PBI, ab initio computations, monomer geometries, the kinetic and potential energy operators, the applied diabatization scheme, the dissipation model, and vibrational quantum beats can be found in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (B.E.); [email protected] (V.E.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by the DFG (GRK 1221, FOR 1809, SFB 652), the VW-Stiftung, and the DAAD (PROCOPE) program is gratefully acknowledged. 795



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Ultrafast Exciton Self-Trapping upon Geometry Deformation in

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