Emergence of Coherence through Variation of Intermolecular

Letter pubs.acs.org/JPCL

Emergence of Coherence through Variation of Intermolecular Distances in a Series of Molecular Dimers Florian P. Diehl, Claudia Roos, Adile Duymaz, Bernd Lunkenheimer, Andreas Köhn, and Thomas Basché* Johannes Gutenberg-University, Institute of Physical Chemistry, Duesbergweg 10-14, D-55128 Mainz, Germany S Supporting Information *

ABSTRACT: Quantum coherences between electronically excited molecules are a signature of entanglement and play an important role for energy transport in molecular assemblies. Here we monitor and analyze for a homologous series of molecular dimers embedded in a solid host the emergence of coherence with decreasing intermolecular distance by single-molecule spectroscopy and quantum chemistry. Coherent signatures appear as an enhancement of the purely electronic transitions in the dimers which is reflected by changes of fluorescence spectra and lifetimes. Effects that destroy the coherence are the coupling to the surroundings and to vibrational excitations. Complementary information is provided by excitation spectra from which the electronic coupling strengths were extracted and found to be in good agreement with calculated values. By revealing various signatures of intermolecular coherence, our results pave the way for the rational design of molecular systems with entangled states. SECTION: Spectroscopy, Photochemistry, and Excited States − are well-defined. Employing frequency and time-resolved single molecule spectroscopy at low temperature and smoothly changing a single parameter − the intermolecular distance − various signatures of quantum coherence emerging with decreasing distance are reported and analyzed comprehensively within a vibronic coupling model.21−23 In the framework of this model and taking into account static disorder, we define the limits of strong and weak electronic coupling. In accordance with recent predictions,24 we find that in emission only the purely electronic 0,0-transition is coherently enhanced, while transitions into the vibrational states of the electronic ground state are not. Hence, the Franck−Condon factor of the 0,0transition largely determines the amount of coherent enhancement, as revealed in fluorescence emission spectra and lifetimes. Moreover, the number of lines observed in single-molecule excitation spectra divides the strong and weak coupling regimes. From the rates of excitation energy transfer (EET), deduced from the spectral line widths of energy donor chromophores, electronic coupling strengths are obtained and found to be in good agreement with results from quantum chemistry. Let us start by briefly describing the vibronic coupling model; full details are given in the Supporting Information. The model system consists of two chromophore sites, A and B. In the absence of coupling, the two electronic excited states, |ψA*B⟩ (chromophore A is in the excited electronic state) and |ψAB*⟩ (chromophore B is excited) can be assumed, which will be referred to as “diabatic basis” in the following. The potential

T

he interplay between the electronic coupling strength and dynamic and static disorder determines to which extent an electronic excitation is coherently shared among a collection of interacting molecules; that is, an entangled state is formed. Recently, ultrafast two-dimensional spectroscopy1 has provided signatures of quantum coherences on the time-scale of several hundred femtoseconds in photosynthetic antenna proteins and conjugated polymers at the bulk as well as single-molecule level.2−6 Coherent effects in electronically coupled molecules also show up on longer time scales, as evidenced by superradiant emission.7−9 To gain insight into the origin of coherence and the fundamentals of electronic coupling, simple molecular dimers are ideal model systems,10−13 while providing important implications for larger systems as natural and artificial light-harvesting complexes.14,15 The spectral information gained from bulk absorption and emission experiments, however, is often affected by inhomogeneous contributions from the interaction with the host material calling for singlemolecule studies. Indeed, single-molecule spectroscopy of molecular dimers and trimers has afforded novel insights into intermolecular couplings and superradiant emission16−20 and allowed for observing the two-photon transition of the entangled system at low temperature.16 So far, single-molecule investigations have been limited to dimers with fixed interchromophoric distances. Here we study a homologous series of oligo(p-phenylene) bridged PDI (perylene-3,4,9,10-tetracarboxdiimide) dimers (D0−D3) with intermolecular center-to-center distances from 1.3 to 2.6 nm (Figure 1). The bridges that connect the chromophores at the imide-nitrogens do not induce shifts of the electronic transitions, and the distance and orientation between the chromophores − crucial parameters for the coupling strengths © XXXX American Chemical Society

Received: November 20, 2013 Accepted: December 18, 2013

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dx.doi.org/10.1021/jz402512g | J. Phys. Chem. Lett. 2014, 5, 262−269

The Journal of Physical Chemistry Letters

Letter

The reorganization energy λ reflects the structural changes of the chromophore upon transition from the ground to the excited state and vice versa. The parameter Δ is introduced to model the detuning of the monomer electronic transitions due to static disorder. Dynamic disorder is not accounted for, which is justified by the experimental conditions (T = 1.2 K). The coupling potential V = ⟨ψA*B|Ĥ el|ψAB*⟩ is the matrix element of the electronic Hamiltonian with the two diabatic states |ψA*B⟩ and |ψAB*⟩. The strength of this coupling, in comparison with the other two parameters, is decisive for the type and strength of entanglement of the two subsystem excitations. The coupling potential can be eliminated by diagonalization of the Hamiltonian for each value of the reorganization coordinate, leading to adiabatic potential energy curves (see Figure 2). For sufficiently small values of V (relative to the reorganization energy λ), the lower adiabatic curve is a double minimum potential. To verify that this model fits to the investigated systems, we carried out quantum-chemical calculations. For the monomer, using hydrogen as residues at the imide groups, we predict a reorganization energy λ ≈ 2700 cm−1, while the electronic coupling V is well below 400 cm−1 in all cases (see later). This means that V ≪ λ/4, as assumed in Figure 2. This is confirmed by searches for local minima on the Born−Oppenheimer surface of the dimer S1 states. These result in symmetry-broken structures where one moiety assumes the same structure as the S1 state of the monomer while the other moiety assumes the S0 structure (see Supporting Information Table S1). A plot of the difference density shows that for these structures we have completely localized electronic states (cf. Supporting Information Figure S3). Hence, we have to stress that the formation of an entangled (and hence delocalized) electronic wave function does not play a role in all systems considered in this work. This is because V ≪ λ/4 holds, and the mixing of the electronic wave functions of the subsystems occurs only in a very small region along the reorganization coordinate (around Q = 0, see Figure 2a), while any small distortion along this coordinate leads to a localized electronic wave function.23,25 The total vibronic wave function is best described in the diabatic picture as a linear combination of

Figure 1. Molecular structures of compounds. The center-to-center distances between the PDI units were tuned by oligo(p-phenylene) linkers with varying length (n = 0−3). R denotes residues that provide solubility of the compounds (PDI: R = CH(C9H19)2, D0: R = CH(C6H13)2, D1−D3: R = CH(C9H19)2). The green arrows represent the orientations of the S1←S0 transition dipoles.

energy surfaces of the two states are shown in Figure 2a as a function of the reorganization coordinate Q, which connects the two equilibrium structures. The potentials are characterized by three parameters: The reorganization energy λ, the electronic coupling V, and the detuning Δ; see Figure 2.

Figure 2. Vibronic coupling model used in this study. (a) The two diabatic potential energy curves along the collective relaxation coordinate Q (blue: molecule A in excited electronic state, molecule B in ground state; green: vice versa) superposed by the adiabatic curves (red). The electronic coupling strength is denoted V, and the displacement of the two diabatic states is characterized by the vertical energy separation at the minimum λ, which equals the reorganization energy. (b) Schematic representation of the lowest nuclear vibrational wave functions χ(Q) in case of vanishing detuning (Δ = 0, upper panel) and localization of lowest nuclear vibrational wave functions in case of strong detuning (lower panel). 263



Letter * AA* where ωAA 0μ and F0μ are the vibronic transition frequencies on site A and their corresponding Franck−Condon factors (ωB0μ*B,

the local vibronic states of the two chromophores. Entanglement is therefore mediated by the vibrational part of the total vibronic wave function, as indicated in Figure 2b. This statement very likely holds for many systems considered in connection with energy-transfer processes, as these typically feature electronic couplings in the same range as the dimers considered in this work (see later). The main difference, in particular for biological systems, is a lower reorganization energy λ.26 The degree of entanglement is controlled by the value of the external perturbation Δ. For sufficiently small perturbations, we can confine the discussion to the interaction of the lowest vibronic state of each chromophore. We obtain two dimer wave functions, |D*0 ⟩ and |D*1 ⟩, with an energetic splitting given by Δ̃ = E*1 − E*0 = (Δ2 + 4Ṽ 2)1/2. Here the reduced coupling Ṽ = VF00 occurs with F00 as the Franck−Condon factor of the monomer 0,0-transition. When Δ increases, the states will localize gradually (Figure 2b, lower panel). A characteristic of entangled states is an interference (or coherent) contribution to observables like emission rates, leading to, for example, superradiance.8 Within the model put forward in Supporting Information Section 1.5, the interference contribution is expressed by a value * (with 0 ≤ * ≤ 1) as a function of the external perturbation Δ. A model distribution function P(*) is derived that predicts (for a given distribution of Δ and different reduced coupling strengths Ṽ , as realized in this study by dimers D0−D3 embedded in a PMMA host) the probability of finding dimers in either an entangled (* ≈ 1) or separable state (* ≈ 0), corresponding to delocalized or localized excitations. Below we will use P(*) to rationalize the observed trends in the single-molecule measurements. It is furthermore instructive to compare the width of the function *(Δ) for given Ṽ with the width of the probability distribution for Δ, which is usually assumed to be Gaussian with a standard deviation σ. From these distributions, we may derive a threshold value |Ṽ /σ|crit = ((ln 2)/6)1/2 ≈ 0.34; see Supporting Information Section 1.5 for details. For systems with a ratio |Ṽ /σ| above this threshold, *(Δ) is close to 1, even for significant external perturbations Δ. We will call this the strong-coupling case. For systems with |Ṽ /σ| below this threshold, *(Δ) drops to values close to 0, even for small Δ. This is the weak-coupling case. In the weak-coupling case, another effect will become important: For increasing Δ, the lower state will remain localized (Figure 2b, lower panel), but the higher state may become resonant to other vibrational levels of the second chromophore, in particular, as the density of vibrational states increases rapidly. This situation resembles that of an energy donor−acceptor compound, as investigated in a number of previous studies.17,20 Because recurrences will be increasingly suppressed due to the rising density of vibrational states in the acceptor state (augmented by coupling to phonons of the surrounding matrix), the coupling results in an incoherent EET process with a rate kEET.27−29 Given the approximations of the above model, this leads to the usual Golden Rule-type rate expression kEET = =

1 τEET

2π 2 |V | J ℏ

=

FB0μ*B refer to site B, accordingly). The vibronic terms are usually summarized as spectral overlap J. In Figure 3, single-molecule fluorescence emission spectra of PDI and the four dimers are shown. Independent of the

Figure 3. Single-molecule emission spectra of PDI and the dimers D0−D3. The gray shaded areas represent the full inhomogeneous distributions of the 0,0-transitions. The red shaded areas have been used to determine the intensities I0,1 (see text, λexc = 488 nm, T = 1.2 K, number of molecules studied: PDI: 156; D0: 291; D1: 369; D2: 339; D3: 251).

interchromophoric distance, all dimers possess the same vibronic structure as the PDI monomer. However, the intensity ratio between the 0,0-transition and the vibronic features marked in Figure 3 does change as is immediately seen by visual inspection of the data. Recently, it was shown by Spano24 − using a theoretical model similar to the one used by us − that for collinearly oriented transition dipoles (e.g., J-aggregates) the intensity of the purely electronic 0,0-transition (I0,0) is coherently enhanced relative to that of a transition into higher vibrational levels of the ground state (I0,1). In particular, the following relation was derived: I0,0 N = coh I0,1 S (2) where S is the Huang−Rhys factor of the coupled vibrational mode(s) and Ncoh is the exciton coherence number. This relation was shown to be valid for weak disorder and not too high temperatures, conditions which are met in our experiments. In the case of a dimer, Ncoh = 1 + ⟨*⟩, where * is the interference contribution previously introduced and the brackets denote a suitable averaging over the distribution function P(*). Note that the observation of an increased intensity ratio I0,0/I0,1 tells us that we have created an entangled dimer state that is due to the vibrational wave function only. A

2π 2 * B*B AA * B*B |V | ∑ F0AA μ F0ν δ(ω0μ − ω0ν ) ℏ μν (1) 264



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Table 1. Photophysical Parameters and Electronic Couplings of PDI and the Dimers D0−D3a ⟨I0,0/I0,1⟩ PDI D0 D1 D2 D3

0.89 1.38 1.20 1.08 0.94

± ± ± ± ±

0.11 0.33 0.34 0.25 0.21

Ncoh 1.5 1.3 1.2 1.1

± ± ± ±

0.4 0.4 0.3 0.2

⟨τR⟩/ns

⟨τEET⟩/ps

⟨Vexp⟩/cm−1

Vcalc/cm−1

⟨Ṽ ⟩/cm−1

|⟨Ṽ ⟩/σ|

± ± ± ± ±

0.3 ± 0.2 0.8 ± 0.4 1.9 ± 0.8

[−235] −117 ± 43 −57 ± 15 −34 ± 6

−293 −137 −72 −41

−77 −38 −19 −11

0.50 0.25 0.12 0.07

3.9 2.7 3.0 3.4 3.4

0.2 0.5 0.4 0.5 0.4

⟨I0,0/I0,1⟩: average ratios of intensities of 0,0- and 0,1-vibronic transitions (see Figure 3); Ncoh: coherence numbers, calculated according to eq 2 with Huang−Rhys factor S = 1.12 determined from I0,1/I0,0 for PDI; ⟨τR⟩: average values of radiative lifetimes; ⟨τEET⟩: average values of energy transfer time constants; ⟨Vexp⟩: average values of electronic coupling strengths derived from τEET (see eq 1), the value for D0 is an estimate based on the calculations (see text); Vcalc: calculated electronic coupling strengths; ⟨Ṽ ⟩: reduced electronic coupling strengths (⟨Ṽ ⟩ = ⟨Vexp⟩F00), for D0 the theoretical coupling strength reduced by 20% was used instead of Vexp; |⟨Ṽ ⟩/σ|: ratio of reduced coupling strength and site disorder σ. The error margins given correspond to the standard deviation of the (sampling) distributions. a

fully entangled electronic exited state, as assumed in the Kasha model,30 would cause an enhancement of the entire emission band, but with I0,0/I0,1 unchanged in comparison with the monomer. To evaluate I0,1 from the experimental spectra, we do not consider a single vibronic transition but integrate the intensity of the vibronic transitions marked in red in Figure 3, which is justified because the same set of transitions appears in the monomer and dimer spectra. It is seen in Table 1 that the intensity ratio I0,0/I0,1 is largest for D0 and decreases until for D3 it reaches a value close to that of the monomer. Values for Ncoh (Table 1) were calculated according to eq 2 using a Huang−Rhys factor of 1.12, which was determined from the ratio I0,1/I0,0 in the monomer spectrum. With decreasing intermolecular distance, the coupling grows and leads to different probability distributions for the coherent contribution P(*) (see Supporting Information Section 1.5). The model predicts a high probability for finding delocalized states for D0, while for the other dimers largely localized states with * close to zero become more likely. The observation that only the 0,0-transition is enhanced by coherent contributions is also reflected by the lifetimes of the dimer states. Distributions of single-molecule fluorescence lifetimes of the monomer and the dimers are presented in Figure 4, and the corresponding average values ⟨τR⟩ are presented in Table 1. Here we assume that the fluorescence lifetimes equal the radiative lifetimes because the fluorescence quantum yields of monomer and dimers are close to unity.31 As discussed for the emission spectra (see above and Supporting Information Section 1.7), only the 0,0-transition rate is enhanced, while all other transition rates remain unchanged relative to the monomer. Therefore, even for strong coupling the radiative lifetime of a dimer will not drop by a factor of two as predicted by simple exciton models neglecting vibronic coupling.30 Dimers D3 and D2 exhibit identical decay times, longer than those of D0 but shorter than that of the monomer. We note that part of this shortening is attributed to an increase in the total transition dipole moments by the oligo(pphenylene)-bridges,32 which scales with the number of phenylene units. This is corroborated by results from model compounds given in Supporting Information Table S4. With decreasing interchromophoric distance, τR is further reduced (Table 1) for D0 by a factor of 1.4 compared with the monomer. The fluorescence emission spectral and lifetime data clearly have proven the emergence of coherence when the interchromophoric distance in the dimers is decreased. These measurements, however, do not provide the electronic coupling

Figure 4. Fluorescence lifetime distributions of PDI and the dimers D0−D3. Gaussians and linear combinations of two Gaussians (D1) fitted to the data are shown. (Host matrix: PMMA, T = 1.2 K, number of molecules studied: PDI: 90; D0: 156; D1: 166; D2: 62; D3: 148).

strengths, which can be extracted from single-molecule fluorescence excitation spectra, as shown in Figure 5 for PDI and the four dimers. For D3, mostly two zero-phonon lines (ZPLs) are observed corresponding to the purely electronic transitions of the two chromophores. With decreasing interchromophoric distance, the percentage of single-molecule spectra with two observable ZPLs drops, reaching zero for D0 (D3: 85%, D2: 65%, D1: 25%, D0: 0%). The occurrence of only a single ZPL for D0 is a signature of strong coupling (see also Supporting Information Section 1.6) because for a collinear geometry the transition to the lower energy delocalized dimer state is allowed while the transition to the upper delocalized dimer state is forbidden. Moreover, the red shifts of both excitation and emission spectra of D0 (Figures 3 and 5) are further indications for strong coupling. For the twoZPL cases (Figure 5), which represent weak coupling (vide infra), the higher energy ZPLs (donor ZPLs) are significantly broadened, which we attribute to fast population decay by EET to the lower energy transition chromophores (acceptors). 265



Letter

screening by the surrounding medium.33 Good agreement between experiment and theory is found (Table 1), whereby the theoretical values are larger by ∼20%. Taking this systematic deviation into account, we estimate the electronic coupling of D0 to −235 cm−1. This agrees with the findings for a similar dimer.12 Being in possession of the coupling strengths, we can compare the reduced couplings Ṽ = VF00 to the spread of site energies (or static disorder) characterized by the parameter σ. This parameter is derived from the distribution of 0,0-transition = 155 cm−1, see Figure energies of the PDI monomer (σPMMA PDI ̃ 3). The following values of |V/σ| are obtained: D0: 0.50, D1: 0.25, D2: 0.12, D3: 0.07. Using the threshold value of 0.34, as previously suggested, we can classify D2 and D3 as weakcoupling cases, while D0 is a strong-coupling case. Hence, when going from D3 to D0, a transition from weak to strong coupling occurs, with D1 being a borderline case. A closer inspection of the lifetime distribution of D1 (Figure 4) reveals that it is bimodal. This interpretation is supported by the bimodal distributions found for the * probability distribution (see Supporting Information Section 1.5). The maxima of the lifetime distribution of D1 are located around those of D0 and D2 and D3, respectively. Remarkably, the transition from weak to strong coupling does not occur continuously but proceeds via a bimodal distribution for a critical size of the coupling parameter |Ṽ /σ|. Finally, we note that for the limiting cases there is a correlation between the number of ZPLs in the excitation spectra and the fluorescence lifetimes. For the strong coupling case D0, only a single ZPL has been found for all molecules, and the monomodal lifetime distribution yields an average value of 2.7 ns. For the weak coupling case D3, mostly two ZPLs appear, and the monomodal lifetime distribution yields an average value of 3.4 ns. In summary, by varying the intermolecular distance in the series of dimers, D0−D3, we have experimentally followed and theoretically analyzed how the competition between electronic coupling strength and static disorder controls the appearance of detectable quantum-mechanical coherences. The coupling strengths realized in our experiments cover the typical range found in biological energy transfer systems, while the reorganization energies observed by us are somewhat larger than observed for biological chromophores.26 The strongcoupling case is realized by D0. The measured enhanced ratio of emission intensities I0,0/I0,1 and the ratio of monomer to dimer lifetimes (which is smaller than two) clearly indicate that the coherences have to be addressed as superposition of the vibrational part of the vibronic states of the dimer. The notion of an entangled (delocalized) electronic wave function is not appropriate. Moreover, transitions involving excited vibrational levels do not preserve the coherence. For decreasing electronic coupling, coherent signatures are increasingly wiped out by static disorder introduced by the polymer host. Concomitantly, transitions to the upper dimer state become observable in the excitation spectra. These bands are significantly broadened, which can be consistently attributed to an incoherent EET process. In addition, our single-molecule experiments reveal that the lifetime distributions do not change uniformly but show a broad bimodal distribution in case of D1, in accordance with theoretical modeling. The results presented here clearly have shown that the degree of entanglement between the chromophores16,34 can be controlled by their spatial separation. It also critically depends

Figure 5. Single-molecule fluorescence excitation spectra of PDI and the dimers D0−D3. PDI and D0 exhibit only one purely electronic zero-phonon line (ZPL). In contrast, the dimers D1−D3 feature a second, clearly broadened purely electronic ZPL at higher energies (Host matrix: PMMA, T = 1.2 K, number of molecules studied: PDI: 66; D0: 175; D1: 204; D2: 203; D3: 184).

Moreover, the widths of the donor ZPLs increase from D3 to D1, as exemplified in Figure 5. In the following, we analyze dimer spectra, which exhibit two ZPLs. It has been shown that energy-transfer times can be extracted from the line width ΔνD of the donor chromophores20 by the following relation: 1 τEET = 2π ΔνD (3) Broad distributions of EET times are found (Supporting Information Figure S8) because even for a fixed interchromophoric distance static disorder inevitably leads to a distribution of spectral overlaps.20 The average EET times are 1.9 (D3), 0.8 (D2), and 0.3 ps (D1); see Table 1. By using eq 1, the full electronic couplings Vexp can be extracted from the EET rates. The spectral overlap J is calculated from the normalized experimental line-shape functions of donor emission f D(ν̃) and acceptor absorption aA(ν̃) J=

∫0

∞

fD (ν)̃ aA (ν)̃ dν ̃

(4)

This expression was evaluated for each single dimer by using representative low-temperature emission and simulated absorption spectra, shifted according to the actual spectral positions of donor and acceptor in the corresponding excitation spectra.20 The distributions of electronic couplings Vexp are presented in Supporting Information Figure S8 and the corresponding average values in Table 1. We note that V < 0 by convention, as all dimers represent J-coupling cases. For D0, electronic couplings could not be extracted because only excitation spectra with one ZPL were observed. In addition, quantum-chemical calculations of the electronic coupling were performed, including the effect of dielectric 266



Letter

determination of the EET times, we had to verify that other contributions to the donor line widths as optical dephasing or fast spectral diffusion were negligible. For the PDI monomer (in PMMA), an average line width of 4 ± 1 GHz was found, which is close to the experimental resolution and clearly smaller than the widths (25−900 GHz) extracted experimentally by fitting Lorentzian profiles to the donor transitions in the dimers. In addition, by varying the excitation intensities over more than one order of magnitude (5−100 W/cm2), we verified that the measured line shapes were not powerbroadened. Fluorescence lifetimes were determined by TCSPC (λexc = 488 nm, I ≈ 2 to 3 kW/cm2, νrep = 20 MHz, τp = 6 ps) similar to the ensemble method (vide supra). In contrast, all photons transmitted by a 500 nm long pass filter were used for the weighted least-squares tail fitting analysis of the decay curves. Computational Methods. All quantum-chemical calculations were carried out using the TURBOMOLE suite of programs (V6.5, development version; see also www.turbomole.de). The PDI monomer ground-state structure was determined by the MP2 method and SVP-type basis sets.43 For calculations of the excited-state structure, we used ADC(2).44,45 Both MP2 and ADC(2) employ the RI approximation with the appropriate fitting basis sets.46 MP2 and ADC(2) structure optimizations with SVP basis sets were also performed for the N,N′-linked dimer (D0). For the other members of the homologous series (D1−D3), we restricted the computational level for structure optimizations in the excited states to configuration interaction with singly excited determinants (CIS), employing the SVP basis. Electronic couplings were obtained from the electronic Davydov splitting calculated with ADC(2)/SVP at the MP2/ SVP ground-state structures. The screening effects of the environment were approximated by a continuum solvation model (conductor-like screening model COSMO, 47 as described in ref 33).

on the energetic detuning between the dimer states. More ordered molecular environments as found in crystalline16,35 or Sphol’skii matrices36 would lead to much smaller detunings while the intermolecular distances are preserved. Besides realizing more easily the strong coupling case even for D3, such environments would lead to more stable ZPLs. Under such conditions, the optical response of the dimers can be controlled by strong and multiple laser fields, which allows exploring the prospects of quantum-state engineering and manipulation of molecular qubits.37,38 While vibronic coupling and short decoherence times ultimately limited by the fluorescence lifetime appear as major drawbacks for such applications, molecules with smaller Huang−Rhys factors are available and single organic molecular electron spins with a lifetime of seconds have been detected at room temperature.39

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EXPERIMENTAL SECTION Perylenediimide Dimers. The PDI monomer and the oligo(pphenylene) bridged PDI dimers (Figure 1) were synthesized according to the literature.30,40,41 Bulky side groups R at the imide nitrogen atoms inhibit π-stacking and solubilize the dyes for synthesis without affecting their spectroscopic properties. (PDI: R = CH(C9H19)2, D0: R = CH(C6H13)2, D1−D3: R = CH(C9H19)2). Bulk Spectroscopy. Steady-state absorption and fluorescence spectra (Supporting Information Figure S7) were measured on an Omega 20 spectrometer (Bruins Instruments) and a FluoroMax-2 fluorometer (Jobin Yvon), respectively. Absorption spectra were corrected for the pure PMMA film absorbance, and fluorescence spectra (λexc = 488 nm) were corrected for the monochromator and detector sensitivity. Time-resolved fluorescence spectroscopy was performed on a FluoroLog-3 fluorometer (Jobin Yvon) using pulsed light (λexc = 488 nm, νrep = 20 MHz, τp = 6 ps) from a fiber laser (Fianium SC400-PP-AOTF) for excitation. The overall time resolution of the setup was quantified by the fwhm (full width at halfmaximum) of the instrumental response function (IRF) to ∼110 ps at λem = 488 nm. Single-Molecule Spectroscopy. Thin-film samples (thickness ∼100 nm) were prepared by spin-coating 30 μL of dye/ chloroform (2 × 10−8 mol/L) and PMMA/toluene (20 g/L) mixtures (ratio 1:200) onto thoroughly cleaned class cover slides at 4000 rpm for 120 s. The fluorescence imaging and spectroscopy of single molecules at T = 1.2 K was conducted using a home-built laser scanning confocal microscope that has been described in detail elsewhere.42 Here sample and microscope objective were mounted in an optical cryostat and immersed in superfluid liquid helium. Fluorescence images and emission spectra were taken using an argon ion laser for excitation (λexc = 488 nm, I ≈ 2 to 3 kW/cm2). All emission light transmitted by a 488 nm long pass filter was collected and analyzed by an APD (MPD PD-50) and spectrograph (Acton Spectra Pro 500i, 150 grooves/mm grating, resolution: 20 cm−1) equipped with a thermoelectric cooled camera (Andor Technology Newton EM-CCD DU970-BV), simultaneously. Fluorescence excitation spectra were recorded by a tunable ring dye laser (Coherent 899-01) operated in broadband mode (bandwidth: 2 to 3 GHz) using Coumarin 334 as laser dye. While scanning the dye laser across the molecular absorption profile (505−550 nm, BP525/50), the red-shifted emission transmitted by a 568 nm long pass filter is detected by an APD (MPD PD-50). Dependent on the particular scan range, excitation intensities of 1−150 W/cm2 were applied. For the

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ASSOCIATED CONTENT

S Supporting Information *

Detailed description of the vibronic coupling model, details of the quantum-chemical calculations, bulk absorption and emission spectra, bulk fluorescence lifetimes of model compounds, and distribution of EET times and corresponding electronic couplings. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: + 49 (0) 6131 39 22707. Fax: + 49 (0) 6131 39 23953. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

We thank Michaela Wagner for help in synthesis of the dimers investigated in this study. Financial support from the Deutsche Forschungsgemeinschaft (SFB625 and Heisenberg fellowship to A.K., KO 2337/3-1) and the Fonds der Chemischen Industrie is gratefully acknowledged. A.K. and B.L. acknowledge financial support from Bundesministerium für Bildung und Forschung, contract no. 13N10722 (part of MESOMERIE project). 267



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