Discrete Ï-Stacks of Perylene Bisimide Dyes within Folda-Dimers

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Discrete #-Stacks of Perylene Bisimide Dyes within FoldaDimers: Insight into Long- and Short-range Exciton Coupling Christina Kaufmann, David Bialas, Matthias Stolte, and Frank Würthner J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b05490 • Publication Date (Web): 11 Jul 2018 Downloaded from http://pubs.acs.org on July 11, 2018

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Journal of the American Chemical Society

Discrete -Stacks of Perylene Bisimide Dyes within Folda-Dimers: Insight into Long- and Short-range Exciton Coupling Christina Kaufmann, David Bialas, Matthias Stolte, Frank Würthner* Institut für Organische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany and Center for Nanosystems Chemistry, Universität Würzburg, Theodor-Boveri-Weg, 97074 Würzburg, Germany E-mail: [email protected] Supporting Information Placeholder

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Abstract Four well-defined -stacks of perylene bisimide (PBI) dyes were obtained in solution by covalent linkage of two chromophores with spacer units of different length and sterical demand. Structural elucidation of the folda-dimers by in-depth nuclear magnetic resonance studies and geometry optimization at the level of density functional theory suggest different, but highly defined molecular arrangements of the two chromophores in the folded state enforced by the various spacer moieties. Remarkably, the dye stacks exhibit considerably different optical properties as investigated by UV/Vis absorption and fluorescence spectroscopy, despite only slightly different chromophore arrangements. The distinct absorption properties can be rationalized by an interplay of long- and short-range exciton coupling resulting in optical signatures ranging from conventional H-type to monomer like absorption features with low and appreciably high fluorescence quantum yields, respectively. To the best of our knowledge, we present the first experimental proof of a PBIbased “null-aggregate”, in which long- and short-range exciton coupling fully compensate each other, giving rise to monomer-like absorption features for a stack of two PBI chromophores. Hence, our insights pinpoint the importance of charge-transfer mediated short-range coupling that can significantly influence the properties of PBI -stacks.

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Introduction Due to their outstanding properties, the class of perylene bisimide (PBI) dyes has attracted lots of interest during the past decade. Easily tunable absorption and fluorescence properties,1,2 excellent photostability,3,4,5 and unique self-assembly features6 make them highly attractive for application in the field of organic electronics,7,8,9 photovoltaics10,11,12,13 and photonics.14,15,16,17 In general, the performances of these devices strongly depend on the optical properties of the active material, which are significantly influenced by interchromophoric interactions in the (poly-)crystalline phase.18,19 Therefore, it is of prime importance to understand the interaction between the dyes that affect the optical properties of the assemblies. A first approach towards a structure-properties relationship was achieved by Davydov20 and Kasha21,22,23 in the 1960s, who established the molecular exciton theory in solid state and solution, respectively. Within this model, the exciton coupling is described in terms of a long-range Coulomb interaction between the transition dipole moments (eg) of the chromophores (point-dipole-approximation), which allows a classification of dye assemblies into H- and J-aggregates in dependence of the geometrical arrangement of the dyes. Whereas a side-by-side arrangement of the chromophores results in a hypsochromic shift of the absorption band (H-aggregates),24,25,26 the head-to-tail orientation in J-aggregates leads to a bathochromic shift with respect to the monomer absorption band.27,28,29 Interestingly, PBI dyes can form both H- and J-aggregates,6 but the spectral changes upon aggregation are more complex because of the interplay of exciton and vibrational coupling.30,31,32 Thus, one can additionally observe changes of the vibronic spectral signature upon aggregation,33,34,6 arising from coupling of the electronic transition to vibrational modes of the perylene core. Albeit the optical properties of many PBI dye aggregates can be rationalized by assuming conventional long-range coupling between the chromophores along with vibrational 3



coupling,35,36,37,38 several examples are known where this picture fails.39,40,41 In a recent work, Spano et al. could demonstrate that charge-transfer mediated exciton coupling leads to enhanced Davydov splitting in PBI crystals.42 This short-range coupling arises from orbital overlap of adjacent chromophores and can be significant for closely -stacked chromophores43,44,45,46 as it is also the case for most PBI aggregates in solution.6 Also the large color range observed for PBI crystals, known as crystallochromy, can be attributed to an interplay of short- and long-range exciton coupling at the different chromophore arrangements.47,48,49 Notably, the interference between both couplings may lead to unexpected optical properties that can be beneficial for applications, which motivates for further investigation.50,51 However, in-depth studies require well-defined orientations of the chromophores as given in the crystalline state.52,53 Unfortunately, dye aggregates in crystals are usually not of limited size, which complicates theoretical studies, and investigation of the optical properties in the solid state can be quite challenging, e.g. due to reabsorption.54,55 Alternatively, well-defined dye assemblies can be realized in solution by covalent linkage of chromophores with appropriate spacer moieties leading to foldamers,56,57,58,59 cyclophanes60,61,62 or macrocycles,63,64 which enable the investigation of interchromophoric interactions in prearranged geometries of a finite number of dyes.65 Thus, in this work we have used the foldamer approach in order to study the optical properties of PBI -stacks comprising two chromophores in dependence of their arrangements. Bis-(perylene bisimide) dyes Bis-PBIs 13 were synthesized (Figure 1a), in which two PBI chromophores are covalently linked in the bay position by spacer moieties of different length and sterical demand. Structural elucidation based on 1Dand 2Dnuclear magnetic resonance (NMR) studies reveals a stacking of the two chromophores for all bis-PBI dyes in solution. The geometry-optimized structures obtained from density functional theory (DFT) calculation suggest only slightly different arrangements of the PBI units enforced by the different spacer moieties. Remarkably, the 4


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chromophore stacks exhibit very distinct optical properties as explored by UV/Vis absorption and fluorescence spectroscopy. The variations of the absorption properties can be rationalized by an interplay of long- and short-range coupling, which leads to completely unexpected optical signatures underlying the importance of charge-transfer mediated coupling50 for -stacked PBI chromophores.

Results and Discussion Synthesis Bis-PBIs 1–3 and Ref-PBI were synthesized according to the synthetic route depicted in Figure 1a. Literature known monobrominated precursor 1,66 bearing long branched alkyl chains to ensure high solubility in various organic solvents, turned out to be a suitable building block for the facile introduction of different linker moieties in a one-pot synthesis. Thus, Bis-PBIs 1–3 could be easily obtained in 21–30% yields via nucleophilic aromatic substitution reaction67 of precursor 1 with the respective dihydroxy spacer units 2a–d.68,69,70 In an analogous manner, reference compound Ref-PBI could be synthesized from compound 1 and phenol in 39% yield (Figure 1a and Scheme S1). The target compounds were first purified by column chromatography followed by recycling gel permeation chromatography (GPC). For characterization of the newly synthesized compounds see the Supporting Information.

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Figure 1. (a) Synthesis of covalently linked Bis-PBIs 1–3 and chemical structure of reference compound Ref-PBI. (b) Schematic representation of the folding process into a discrete -stack of two chromophores with defined molecular arrangement exemplified for Bis-PBI 2.

Optical Properties UV/Vis absorption studies were performed for Ref-PBI and Bis-PBIs 1–3 in 1,1,2,2tetrachloroethane (TCE) at room temperature. No spectral changes can be observed at different concentrations (c0 = 103106 M; Figure S1), which allows us to exclude intermolecular aggregation of the investigated dyes under these experimental conditions. Ref-PBI shows an absorption spectrum characteristic for monomeric PBI dyes, with a main absorption band at 537 nm corresponding to the S0–S1 transition and a molar extinction coefficient (εmax) of 50100 M1 cm1 (Figure 2a and Table 1).5,71

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Figure

2.

Absorption

(blue

solid

lines,

c0 = 105 M),

7

normalized

fluorescence

(red

solid

lines,

7

c0 = 10 M) and excitation spectra (green dashed lines, c0 = 10 M) of (a) Ref-PBI, (b) Bis-PBI 1, (c) Bis-PBI 2 and (d) Bis-PBI 3(S) in TCE at room temperature. The wavelengths for excitation (ex) and detection (em) to obtain the fluorescence and excitation spectra, respectively, are highlighted by arrows in the graphs. Insets: Samples of Ref-PBI and Bis-PBIs 1–3(S) under UV light ( = 365 nm) and fluorescence quantum yields (Fl).

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Furthermore, additional absorption bands at 503 nm and 463 nm can be observed, which represent vibronic progressions of the main absorption band resulting from a coupling of the electronic transition to CC-stretching modes of the perylene core with an average frequency of ~1400 cm1.30,72 The ratio of the intensities of the 00 and the 01 absorption bands (A00/A01) amounts to 1.45 (Table 1). Changes of this ratio are commonly used to monitor the aggregation process of PBI dyes73,74 and enable to determine the exciton coupling energy.32 The weak absorption in the range of 350–450 nm can be assigned to the S0–S2 transition of the PBI chromophore.71 In comparison to Ref-PBI, the spectrum of Bis-PBI 1 shows a blue-shifted absorption maximum at 511 nm with an extinction coefficient of 61000 M1 cm1 and a reversal of the intensities of the 00 and 01 absorption bands, with a drastically decreased ratio of A00/A01 = 0.69 (Figure 2b and Table 1). This indicates the presence of co-facially -stacked PBI chromophores30,32,75,76 with pronounced H-type coupling. The reversal of the band intensities arises from an interplay of exciton and vibrational coupling in the so-called intermediate coupling regime.30,72,32 Thus, a folding of Bis-PBI 1 into a stack of two PBI chromophores seems reasonable (Figure 1b), as no concentrationdependent changes could be observed. Quite differently, for Bis-PBI 2 a bathochromic shift of the absorption maximum to 551 nm with εmax = 76700 M1 cm1 and only a minor decrease of the ratio A00/A01 = 1.30 can be observed (Figure 2c and Table 1). The minor decrease of the intensity ratio indicates only weak H-type coupling between the PBI chromophores.32 Thus, on first glance the absorption properties of Bis-PBI 2 do not suggest a -stacking of the PBI chromophores, which should result in a prominent decrease of the ratio of the intensities of the 00 and 01 bands.

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Table 1. UV/Vis and fluorescence spectroscopic data of Bis-PBIs 13(S) and Ref-PBI measured in TCE at room temperature.

Ref-PBI

Bis-PBI 1

Bis-PBI 2

Bis-PBI 3(S)

abs(A00) a / nm

537

549

551

555

abs(A01) a / nm

503

511

513

515

max(A00) a / M1cm1

50100

42300

76700

101500

max(A01) a / M1cm1

34500

61000

59200

65500

1/2a / cm1

1260



930

840

[A00 / A01]a / 1

1.45

0.69

1.30

1.55

emb / nm

561

641

635

573

Stokesb / cm1

800

3970

2400

570

Flb / %

83

12

34

44

Fl,1b,c / ns (amplitude)

4.4 (100%)

3.9 (10%)

4.1 (1%)

3.9 (11%)

Fl,2b,c / ns (amplitude)

-

16.7 (90%)

10.9 (99%)

8.4 (89%)



a

c0 = 105 M. c0 = 107 M, OD < 0.05. c Fl were determined by tail fit analysis of data obtained from time-correlated single photon counting measurements with ps laser diode at 505 nm using the magic angle setup. b

This also holds true for Bis-PBI 3(S), for which we observe a slightly larger bathochromic shift (555 nm) of the absorption bands and even a small increase of the ratio of the band intensities to A00/A01 = 1.55 indicating very weak J-type coupling (Figure 2d and Table 1).32 In addition, a narrowing of the absorption bands is present (1/2 = 840 cm1) along with an increase of εmax to 101500 M1 cm1, that is characteristic for J-type aggregates.77,78,29 As expected for a pair of two enantiomers, Bis-PBIs 3(R) and 3(S) exhibit the same absorption properties (Figure S2) and thus, we will mainly focus on the optical features of Bis-PBI 3(S) in the following parts.

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Hence, while the absorption properties of Bis-PBI 1 indicate a -stacked arrangement of the PBI chromophores with pronounced H-type coupling, the absorption spectra of Bis-PBI 2 and BisPBI 3(S) reveal weak H- or J-type coupling, respectively. Therefore, one might expect clearly different orientations of the chromophores for all bis-PBI folda-dimers, leading to the distinct absorption features. As expected, circular dichroism (CD) spectroscopy reveals no CD signal for Ref-PBI (Figure S5), since the atropo-enantiomers arising from the slight twist of the naphthalene units of the PBI core can easily convert into each other at room temperature.79 Also for Bis-PBIs 12 no CD signal can be observed. In contrast, the spectra of Bis-PBI 3(R) and Bis-PBI 3(S) each show pronounced (bisignated) Cotton effects with mirror image behaviour as expected for two enantiomers arising from the hindered rotation around the 1,1’-binaphthyl axis. Notably, Cotton effects are not only present in the UV region where the spacer moiety absorbs, but also in the visible absorption range of the PBI´s S0–S1 (450–650 nm) and S0–S2 (350–450 nm) transitions. The corresponding zerocrossings are located at the absorption maxima of the respective bis-PBIs revealing chiral exciton coupling between the two chromophores, which indicates close proximity of the PBI moieties in a fixed chiral arrangement36 with locked twist of the naphthalene units of the two PBI cores80. To gain further insight into the electronic coupling of the herein investigated PBI dimers, steady state fluorescence spectroscopy was performed under high diluted conditions in TCE (c0 = 107 M, Figure 2) to avoid reabsorption effects.54 Ref-PBI shows a fluorescence spectrum characteristic for PBI monomers with an emission maximum (λem) at 561 nm and well-resolved vibronic fine structure and mirror-image relationship to the absorption band (Figure 2a and Table 1). Furthermore, a small Stokes shift of 800 cm1 and a high fluorescence quantum yield of 83% was determined, which is typical for monomeric perylene bisimide chromophores.81,6,2

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In contrast, the well-resolved fine structure is lost in the fluorescence spectrum of Bis-PBI 1 and a broad, unstructured emission band at 641 nm with a considerably large Stokes shift of 3970 cm1 is present (Figure 2b and Table 1). Further, the fluorescence quantum yield is drastically decreased to 12%, which is indicative for the formation of an excimer.82,83 The excimer state is commonly observed for -stacked PBI dyes and arises from structural rearrangement of the chromophores in the excited state.82 Additionally, the emission spectrum of Bis-PBI 1 exhibits a small shoulder at ~570 nm, probably due to traces of remaining monomer fluorescence from a small amount of unfolded species, which can be observed for the other bis-PBIs as well (vide infra).84 Surprisingly, despite of its monomer-like absorption features Bis-PBI 2 likewise shows a typical excimer emission band at 635 nm, however with a reduced Stokes shift of 2400 cm1 and a significantly higher fluorescence quantum yield of 34% (Figure 2c, Table 1). Thus, also the fluorescence spectrum of Bis-PBI 2 suggests a -stacking of the chromophores, which is surprising due to the weak H-type coupling observed in the absorption spectrum of Bis-PBI 2. In contrast, monomer-like signatures can be observed in the emission spectrum of Bis-PBI 3(S) (λem = 573 nm) with a well-resolved vibronic fine structure and a small Stokes shift of 570 cm1 (Figure 2d, Table 1). This is in accordance with the UV/Vis absorption spectrum indicating very weak J-type exciton coupling between the two PBI chromophores. However, the fluorescence spectrum of Bis-PBI 3(S) is slightly broadened compared to Ref-PBI and a decreased fluorescence quantum yield of 44% was determined, which is rather unusual for conventional J-type PBI aggregates with a large longitudinal displacement of the chromophores.85 The measured excitation spectra for all bis-PBI dyes are in accordance with the corresponding absorption profiles revealing species selective emission from the corresponding folded state (Figure 2, green dotted lines).

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Further information on the excited state properties of the PBI dyes was gained by fluorescence lifetime measurements (Figure S6). Ref-PBI exhibits a fluorescence lifetime of 4.4 ns in the chosen solvent TCE at room temperature (Table 1), in agreement with previously reported values for monomeric PBI chromophores.86,87,88 On the contrary, for the samples of Bis-PBIs 13(S) two fluorescence lifetimes were determined (Table 1). The shorter lifetime of ∼4 ns with significantly lower amplitude is comparable to the value of Ref-PBI and thus, can be attributed to emission from unfolded and presumably more emissive species. In the case of Bis-PBIs 1and2, the second lifetime of 16.7 and 10.9 ns, respectively, is distinctly longer as expected for PBI excimers due to the more forbidden radiative transition to the ground state potential surface (Table 1).6 The second fluorescence lifetime of 8.4 ns determined for Bis-PBI 3(S) is also increased, despite the monomerlike emission spectrum, indicating considerable interaction between the chromophores. Hence, the spectroscopic investigations by UV/Vis, CD and fluorescence spectroscopy reveal distinct variations of the optical properties of the presumably folded bis-PBIs, which can only be rationalized by different structural arrangements of the two chromophores.

NMR spectroscopy Structural information on supramolecular aggregates can be gleaned by NMR spectroscopy. Therefore, we have performed NMR studies for Ref-PBI and Bis-PBIs 13(S) in 1,1,2,2tetrachloroethane-d2 (TCE-d2) to investigate the structural arrangement of the dyes. First, diffusionordered spectroscopy (DOSY) was applied to all compounds and comparable hydronamic radii of 11.011.3 Å were determined (Figure S11) that are reasonably larger than the one of Ref-PBI (8.4 Å). According to our UV/Vis studies, temperature has no significant influence on the folding process of the bis-PBI dyes (Figure S3). Thus, the 1H NMR spectra shown in Figure 3a were 12


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recorded at 370 K as all three folda-dimers show remarkably sharp and well resolved proton signals under these conditions. This is rather unusual for -stacked PBI chromophores, for which broad and undefined proton signals are usually observed.35,89 Ref-PBI exhibits a typical monomer spectrum of a phenoxy bay-substituted PBI chromophore (Figure 3a).71 The signals were assigned to the individual protons based on 2D homonuclear correlation spectroscopy (COSY), rotating frame nuclear Overhauser effect spectroscopy (ROESY) and in addition with heteronuclear single quantum correlation (HSQC) and heteronuclear multiple-bond correlation (HMBC) NMR measurements. Remarkably, the proton marked in black (9.60 ppm) shows a significant downfield shift in comparison to the other protons of the PBI chromophore. This downfield shift can be explained as a CHO hydrogen bonding interaction of the aromatic bay proton to the oxygen atom of the phenoxy-substituent, which is in close proximity.71 Hence, the chemical shift of this proton can give insight into the conformation of the oxygen-substituent and its electron lone pairs. In contrast, the proton marked in red (8.35 ppm) exhibits an upfield shift due to the ring current of the phenoxy substituent leading to a magnetic shielding.71 The NMR spectra of Bis-PBIs 13(S) also show only one set of sharp signals revealing a welldefined arrangement of the chromophores with high symmetry (Figure 3a). The pronounced upfield shift of the PBI protons in comparison with Ref-PBI indicate a stacking of the chromophores, which results in a shielding of the protons by the adjacent -surface.90,91

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Figure 3. (a) Selected area of the 1H NMR (400 MHz) spectra of Ref-PBI and Bis-PBIs 13(S) in TCE-d2 at 370 K (c0 = 2 x 103 M) with PBI protons marked as indicated in the molecular structure displayed in panel (c). The protons marked with an asterisk represent protons of the spacer moieties. (b) Superposition of COSY (blue) and ROESY (red: positive signal / cyan: negative signal) spectra of Bis-PBI 3(S) at 373 K in TCE-d2 (c0 = 1.4 x 103 M, 600 MHz). (c) Molecular structure of the PBI chromophore with marked protons and space-filling model of a PBI -stack comprising two chromophores. The purple double-headed arrows indicate close spatial proximity between the protons according to the cross-peaks observed in the ROESY spectrum of Bis-PBI 3(S). Only the interaction for one side of the -stack is shown and the spacer moiety is omitted for clarity.

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Whereas the 1H NMR spectra of Bis-PBI 2 and Bis-PBI 3(S) look rather similar, larger deviations can be observed for Bis-PBI 1. Especially the protons highlighted in black (8.63 ppm) and green (7.82 ppm) show a drastic upfield shift, which is less pronounced for Bis-PBIs 2 and 3(S). Hence, a similar conformation of the oxygen-substituent for Bis-PBIs 2 and 3(S) seems reasonable, while a distinctly different arrangement of the bay-substituent can be assumed for Bis-PBI 1. To unambiguously confirm the -stacking of the PBI chromophores, we have performed 2D ROESY measurements, that allow to determine protons in close spatial proximity. We observe for all bis-PBI dyes a cross-peak between the protons marked in red (so-called headland position) and black (bay position, Figure 3b and Figure S810). This cross-peak is not present in the ROESY spectrum of Ref-PBI (Figure S7), so that we can rule out that the signal arises from spatial proximity of these protons within one chromophore. Since the cross-peak is furthermore not observed in the COSY spectrum of the bis-PBIs (Figure 3b and Figure S810), it does not represent a COSY artefact. For Bis-PBIs 1 and 3(S) we can additionally observe a cross-peak between the headland protons marked in green and red (Figure S8 and Figure 3b), which is also not observed for Ref-PBI (Figure S7). All these findings support a tight -stacked arrangement of the PBI chromophores in which the protons are in close proximity (Figure 3c and Figure S810).

Geometry Optimizations The results obtained by NMR spectroscopy reveal for all bis-PBIs a -stacked geometry of the chromophores, which is not at all obvious from the UV/Vis data. To gain deeper insight into the structural arrangement of the chromophores, geometry optimizations at the density functional theory (DFT) level were performed. We employed the def2-SVP basis set92 and the B97D3

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functional including Grimme’s dispersion correction93 being necessary to adequately describe the structures of PBI aggregates.94,38 The geometry-optimized structures are depicted in Figure 4 (for each bis-PBI we calculated the structure of the S-enantiomer regarding the axial chirality of the spacer moiety). Accordingly, all three bis-PBIs exhibit a -stacked arrangement of the chromophores with an interchromophoric distance of 3.33.5 Å and C2 symmetry. Bis-PBI 1 shows the largest distance (3.5 Å) due to the p-terphenyl-spacer moiety, which does not enable a closer contact between the two PBI chromophores. The chromophores in Bis-PBIs 2and 3(S) both have a distance of about 3.3 Å because of the same length of the biphenyl and 1,1’-binaphthyl spacer units. For all bis-PBIs a torsional displacement between the chromophores can be observed with increasing angle from Bis-PBI 1 (14°), Bis-PBI 2 (22°) to Bis-PBI 3(S) (25°) accompanied by a displacement of the dyes’ centers by 1.0 Å (Bis-PBI 1), 1.9 Å (Bis-PBI 2) and 2.1 Å (BisPBI 3(S)). According to Fink et al., the optimal ground state geometry of a -stack comprising two non-substituted PBI chromophores exhibits a -distance of 3.4 Å and a rotational angle of 29° without transversal and longitudinal shift of the chromophores.94 Hence, our employed spacer moieties force the two PBI chromophores to stack in an unusual manner. The two naphthalene moieties of the PBI chromophores exhibit a twist of 12° (p-terphenyl), 11° (biphenyl) and 10° (1,1’binaphthyl) arising from the sterical hindrance of the bay-substituents. The twist can be also observed for the geometry-optimized structure of Ref-PBI, however less pronounced (5°) due to the lower steric hindrance of the phenoxy group in the bay position (Figure S13b).

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Figure 4. Top view (left) and side view (right) onto the geometry-optimized structures of (a) Bis-PBI 1, (b) Bis-PBI 2 and (c) Bis-PBI 3(S) obtained by DFT (B97D3/def2-SVP) calculations. For all bis-PBI dyes the structure of the Senantiomer regarding the axial chirality of the spacer moiety was calculated. Purple double arrows indicate close spatial proximity between the protons depicted in red, black and green according to the cross peaks observed in the ROESY NMR spectra. For clarification only the coupling on one side of the chromophore is displayed.

17



The geometry-optimized structures are in agreement with our results obtained by NMR studies. The C2 symmetry leads to only one set of signals for the chromophores since the respective protons are chemically equivalent. In addition, whereas for Bis-PBIs 23(S) the oxygen of the bay substituents of the PBI chromophores have similar conformation (Figure 4b,c right), the arrangement is distinctly different in the case of Bis-PBI 1 (Figure 4a, right). Therefore, the hydrogen bonding of the proton marked in black is less pronounced for Bis-PBI 1 resulting in an increased upfield shift of the signal in the 1H NMR spectrum (Figure 3a). The cross-peaks observed in the ROESY NMR spectra between the red and black marked protons as well as between the red and green marked protons (for Bis-PBIs 1 and 3(S)) can be rationalized by the close proximity of the protons within the -stacks (Figure 4). Further, the likeness of the 1H NMR spectrum of Bis-PBIs 2 and 3(S) suggests a very similar arrangement of the chromophores as evident from the geometry-optimized structures. The excimer emission observed for Bis-PBIs 12 is also in accordance with a -stacked arrangement of the chromophores. It is well known that the excimer state of PBI aggregates is reached by structural reorganization leading to a geometry with a torsion angle between the chromophores of almost zero.95, 83 However, this arrangement is not possible for the more rigid Bis-PBI 3(S) with a large rotational barrier around the 1,1’-binaphthyl axis.96 Therefore, the typical excimer emission band is not observed for Bis-PBI 3(S) but a rather sharp and well-resolved emission spectrum with a small Stokes shift being quite unusual for -stacked PBI dyes.6

Theoretical Investigation Whereas our results obtained from fluorescence and NMR studies provide strong evidence for a stacking of the PBI chromophores in the folded state, UV/Vis spectra apparently do not support the presence of a folded -stacked arrangement. As shown for a large number of self-assembled 18


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and folded PBI aggregates,56,33,34,6 close cofacial -stacking should lead to a drastic decrease of the ratio A00/A01 in the UV/Vis spectra, which is not observed for Bis-PBIs 2 and 3(S) (Figure 2). The spectral changes upon aggregation of PBI dyes are commonly described in terms of excitonvibrational coupling, where the electronic transition couples to the vibrational modes of the chromophores.30,32 The exciton coupling is mainly assigned to long-range Coulomb coupling between the transition dipole moments of the chromophores leading to H- or J-type coupling with positive or negative exciton coupling energy, respectively. We used the transition charge method97 to determine the Coulomb coupling for Bis-PBIs 13(S). Hereby, the transition dipole moments of the chromophores are replaced by point atomic charges and the exciton coupling energy equals the Coulomb interaction between the transition charges of the different chromophores:97

J=

(a)

Here, qi

(1) (2)

1 4πε0

∑i ∑j

qi ∙qj

(1) (2) |ri  rj |

(1)

. (a)

represents the transition charge on atom i of chromophore a, ri

corresponds to the

position vector of the respective transition charge and ε0 is the vacuum permittivity. This method gives reliable results for interchromophoric distances shorter than the size of the chromophores,98 whereas the dipole-dipole approximation usually dramatically overestimates the exciton coupling energy.99 We used time-dependent DFT (TDDFT) calculations with the long-range corrected functional B97100 and def2-SVP92 as basis set to calculate the transition density for Ref-PBI (for further information see the Supporting Information). The density was fitted to atomic partial charges and the exciton coupling energies were then calculated by Equation 1 using the structures obtained from geometry optimizations (Figure 4). The results are shown in Table 2. Accordingly, all bis-PBI dyes studied in this work exhibit pronounced H-type coupling (JCoul > 0) in the range of 19



Page 20 of 33

545678 cm1. Such coupling should lead to the reversal of the intensities of the 00 and 01 absorption bands as observed for Bis-PBI 1 with respect to Ref-PBI (Figure 2), which arises from the interplay of exciton and vibrational coupling.30,32 However, for Bis-PBIs 2 and 3(S) we do not observe a significant decrease of the ratio A00/A01 contradicting the presence of pronounced Htype coupling according to the calculated exciton coupling energies. Spano et al. have developed a method to determine the exciton coupling energy based on the intensities of the 00 and 01 absorption bands of aggregates that show exciton-vibrational coupling.32,36,40 We have applied this model for Bis-PBIs 13(S) and compared the values with the ones obtained by the transition charge method (Table 2, for details see the Supporting Information).

Table 2. Calculated exciton coupling energies and hole/electron transfer integrals for Bis-PBIs 13(S).

Bis-PBI 1

Bis-PBI 2

Bis-PBI 3(S) 

a

1

b

1

J / cm

713

152

7 

J / cm

643

77

10

JCoulc / cm1

678

554

545

te / cm1

66

697

658

th / cm1

428

547

675

JCTd / cm1

35

477

555

a

Estimated from the intensity ratio of the A00 and A01 absorption bands in the UV/Vis spectra. Determined based on Equation 3. c Calculated by the transition charge method. d Determined based on Equation 2. b

Whereas the exciton coupling energy for Bis-PBI 1 (713 cm1) obtained by the method of Spano et al. is in very good agreement with the one obtained by the transition charge method (678 cm1),

20


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large deviations are observed in the case of Bis-PBIs 2 and 3(S). For Bis-PBI 2, an exciton coupling energy of JCoul = 554 cm1 was estimated based on the transition charge method, while our analysis based on the absorption spectrum reveals significantly weaker coupling (J = 77 cm1). The same is true for Bis-PBI 3(S), for which the transition charge method gives an exciton coupling energy of JCoul = 545 cm1 and thus, pronounced H-type coupling should be observed. However, the results according to Spano’s method predict negligible J-type coupling (J = 7 cm1). Thus, whereas the absorption spectrum of Bis-PBI 1 can be rationalized by exciton-vibrational coupling between the PBI chromophores, assuming that the exciton coupling can be mainly described by (long-range) Coulomb interaction between the transition charges, this description fails for Bis-PBIs 2 and 3(S). Therefore, additional contributions have to be taken into account to understand the absorption spectra of these PBI dye stacks. For short interchromophoric distances as present in -stacks, charge-mediated short-range coupling can be significant and thus, influence the absorption properties of aggregates.43,50,46,51 This short-range coupling arises from HOMOHOMO

and

LUMOLUMO

overlap

enabling

charge-transfer

between

the

molecules.43,101 Under the assumption that the charge-transfer state and the local Frenkel exciton state are well separated (perturbative limit), the exciton coupling energy for the short-range coupling can be calculated by:43,50 JCT = 2

te th , ECT  ES1

(2)

where te and th represent the electron and hole transfer integrals, respectively, and ECT  ES1 is the energy difference between the charge transfer and the local Frenkel exciton state. The overall coupling can be then described as the sum of the (long-range) Coulomb coupling and the chargetransfer mediated short-range coupling:43,50

21



J = JCoul + JCT.

Page 22 of 33

(3)

The interference effect between long- and short-range coupling can be constructive or destructive depending on the sign of the coupling energies. We calculated the transfer integrals for Bis-PBIs 13(S) employing the unique fragment approach102 as implemented in the Amsterdam Density Functional program package.103, 104, 105 The TZP basis set106 and the PW91 functional107 was used, which gives reliable results for PBI dyes.108 Accordingly, all three bis-PBI dyes exhibit J-type short-range coupling according to Equation 2, since the electron and hole transfer integrals are both positive (Table 2) and ECT  ES1 > 0. Hence, the overall coupling should be weakened due to the charge-transfer mediated coupling. Bis-PBIs 2 and 3(S) show a significant HOMOHOMO and LUMOLUMO overlap as evident from the large values of the hole and electron transfer integrals. In contrast, while also Bis-PBI 1 exhibits a considerable HOMOHOMO overlap (th = 428 cm1), the LUMOLUMO overlap is remarkably small (te = 66 cm1). This is reflected in the different energy splitting of the frontier molecular orbitals of the bis-PBI dyes (Figure 5). Therefore, we may assume a significantly weaker J-type short-range coupling for Bis-PBI 1. To determine the short-range coupling energy (JCT) for the PBI stacks, the energy difference ECT  ES1 between the charge transfer state and the local Frenkel exciton state is required (Equation 2). Unfortunately, it is difficult to calculate reliable values for this energy difference.109 Assuming that the charge transfer state is 1600 cm1 above the local Frenkel state, which is in good agreement with the results obtained for PBI crystals,42 we obtain the short-range coupling energies shown in Table 2.

22


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Figure 5. Schematic energy diagram of the relative positions of the frontier molecular orbitals of Bis-PBI 1, Ref-PBI and Bis-PBI 3(S) along with a schematic representation of their folded structure in solution. The orbital energies were obtained from single point calculations (PW91/TZP) on the geometry-optimized structures.

Accordingly, Bis-PBI 1 shows weak J-type short-range coupling (JCT = 35 cm1) so that the overall coupling is mainly due to long-range Coulomb coupling, which is of H-type nature. In contrast, Bis-PBIs 2 and 3(S) show strong J-type short-range coupling, being of similar magnitude as the H-type long-range coupling. This leads to a negligible overall coupling according to Equation 3. Therefore, only small changes of the intensity ratio of the 00 and 01 absorption bands are observed in the UV/Vis spectra of Bis-PBIs 2 and 3(S), whereas Bis-PBI 1 shows the typical signature of an H-type aggregate with significantly reduced ratio A00/A01 (Figure 2, Table 1). For Bis-PBI 3(S) the short-range coupling even slightly exceeds the long-range coupling resulting in a small increase of A00/A01. It has to be noted that the perturbative approach represents an approximation since the requirement of pronounced energetic separation between the 23



local Frenkel exciton state and charge transfer state is not fully given.109,40 However, our analysis reveals strong competition between short- and long-range coupling explaining the distinct spectral signatures of the PBI -stacks. As evident from the calculated exciton coupling energies (Table 2), the long-range Coulomb coupling shows only minor changes within the series of Bis-PBIs 13(S). The interaction of the transition charges is less sensitive towards structural rearrangements than the charge-transfer mediated short-range coupling, which depends on the HOMOHOMO and LUMOLUMO overlap of the chromophores.50 Since the HOMO and LUMO distribution of Ref-PBI exhibits a significant number of nodal planes (Figure S13c) the orbital overlap of the chromophores is hypersensitive to the geometry of the -stack.48,110 Therefore, subtle changes of the chromophores’ arrangements may lead to unexpected optical properties of dye stacks as demonstrated for BisPBIs 13(S). In addition, the orbital overlap decreases exponentially with increasing distance, whereas the Coulomb coupling between the transition charges only shows a reciprocal dependence (Equation 1). Hence, the smaller --distance in Bis-PBIs 2and3(S) leads to a further increase of the charger-transfer mediated short-range coupling. Moreover, we attribute the lack of observable splitting in the absorption spectra, which could be expected for rotational displacement of the two chromophores, to the much weaker oscillator strength for the lower Davydov component.111 According to the nomenclature proposed by Spano et al.,50 we can classify the -stack of Bis-PBI 1 as a Hj aggregate, while Bis-PBIs 2 and 3(S) represent HJ aggregates. Here, the first letter stands for the long-range Coulomb coupling and the second letter for the short-range coupling, respectively, and a small/capital letter describes weak/strong coupling. Remarkably, theoretical investigations performed by the same group predicted the existence of so-called “nullaggregates”, in which the interference between short- and long-range coupling leads to a complete

24


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vanishing of the overall coupling.40 These types of aggregates are supposed to show a vibronic signature similar to the one observed for the monomer species but with a small bathochromic shift. As this is indeed the case for Bis-PBI 3(S) (Figure 2d), we could prove this hypothesis for PBI dyes and provide the first experimental proof for the existence of PBI-based “null-aggregates”. Interestingly, the exciton mobility within “null-aggregates” is expected to be supressed as theoretically investigated for 7,8,15,16-tetraazaterrylene crystals.112 Hence, the interplay of longand short-range coupling can have significant influence on the (photo-)physical properties of dye aggregates being of high importance for applications. Further, the fact that monomer-like UV/Vis absorption spectra can be observed also for closely stacked dyes with large transition dipole moments, as given for PBIs, should raise our awareness that there are cases in which UV/Vis spectroscopy does not allow to distinguish between stacked (folded) and non-stacked structures.

Conclusion In conclusion, we have synthesized four new well-defined bis-PBI folda-dimers, in which two chromophores are covalently linked in the bay position by different spacer moieties. All of these molecules undergo folding in solution resulting in discrete -stacks of two PBI chromophores as elucidated by in-depth UV/Vis, CD, fluorescence and NMR spectroscopic studies. The geometryoptimized structures obtained from DFT calculations reveal slightly different chromophore arrangements in the folded state. However, the dye stacks exhibit distinctly different absorption properties resulting from a competition between long- and short-range exciton coupling. Theoretical investigation reveal that the latter arises from HOMOHOMO and LUMOLUMO overlap of the chromophores, which is very sensitive to the structural arrangement of the dyes. Hence, small changes of the geometry can have considerable influence on the optical properties of 25



the -stack as demonstrated in this work. These insights are of significant importance for the fundamental understanding of dye aggregates, the application of UV/Vis spectroscopy for the assignment of folded or self-assembled -stacked species, as well as for the design of organic materials for applications in e.g. photovoltaics and photonics. Furthermore, the fluorescence properties (quantum yield and lifetime) show significant changes within this series, which will be the focus of our investigations devoted to the in-depth understanding of the excited states. Acknowledgments This work has been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the research unit FOR 1809.

Supporting Information. Experimental details, including synthesis, NMR, UV‐vis, CD, fluorescence spectroscopy as well as quantum chemical calculations are available free of charge via the Internet at http://pubs.acs.org.

26


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