HJ-Aggregate Behavior of Crystalline 7,8,15,16-Tetraazaterrylene

Article pubs.acs.org/JPCC

HJ-Aggregate Behavior of Crystalline 7,8,15,16-Tetraazaterrylene: Introducing a New Design Paradigm for Organic Materials H. Yamagata,†,‡ D. S. Maxwell,‡ J. Fan,∥ K. R. Kittilstved,‡ A. L. Briseno,§ M. D. Barnes,‡ and F. C. Spano*,† †

Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States Department of Chemistry and §Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01002, United States ∥ Institute of Functional Nano & Soft Materials (FUNSOM), Soochow University, Suzhou 215123, China ‡

S Supporting Information *

ABSTRACT: Absorption and photoluminescence properties of terrylene derivative 7,8,15,16-tetraazaterrylene (TAT) in its solution and crystal phases have revealed rather unusual spectral characteristics that defy classification in terms of simple H- or J-aggregatecoupled systems. TAT readily forms crystalline aggregates by either self-assembly in solution or physical vapor deposition, based on π stacks aligned roughly along the crystallographic a axis. Using a Holstein-style Hamiltonian including both Frenkel and chargetransfer (CT) excitons, the crystal absorption and steady-state photoluminescence (PL) spectra/line shapes are shown to be determined by a competition between long-range Coulombic coupling, which induces H-aggregate behavior, and short-range charge-transfer-mediated coupling, which induces J-like behavior. Such “HJ” aggregates display J-aggregate signatures in the low-energy region of the absorption spectrum and H-aggregate signatures at higher energies, which are in excellent agreement with our experiments. The H/J competition also results in a sharp reduction in the exciton bandwidth and the appearance of an exciton band minima at k ≈ ±π/2, where k is the dimensionless wave vector along the stacking axis. The presence of a band minimum for nonzero values of k bestows hybrid HJ behavior in the PL spectrum. We present a new design paradigm for organic electronic materials on the basis of the constructive or destructive interference of short- and long-range coupling, postulating the existence of HH, JJ, JH, and HJ aggregates with unique transport and radiative properties.

I. INTRODUCTION

Excitations in many types of organic semiconductor aggregates and crystals can be viewed as Frenkel excitons, in which the excited electron and hole remain on the parent molecule.13 The electronic coupling responsible for exciton transport and delocalization is dictated by the molecular packing in the solid state. For a linear molecular aggregate such as a π stack, two different coupling types are readily distinguished from one another by virtue of the sign of the Coulombic coupling between neighboring molecules, JC.14−16 A negative value of JC, consistent with head-to-tail oriented molecules, defines J aggregates, whereas a positive value of JC, which often occurs in “face-toface” (or sandwich) complexes, defines H aggregates. Historically, the two coupling types have been identified primarily on the basis of their aggregation-induced absorption spectral shifts: J aggregates are red-shifted, whereas H aggregates are blueshifted.14−16 The assignment of aggregate type based solely on

The family of rylene dyes is attracting wide research interest as a promising material platform for small-molecule organic electronics,1−11 having applications as n-type conductors in fieldeffect transistors and as electron acceptors in OPV cells. Recently, Briseno and Wudl have introduced a new member of the terrylene family, 7,8,15,16-tetraazaterrylene (TAT),11,12 that has received attention as an efficient electron acceptor in OPV applications because it performs in a superior manner to terrylene as a result of TAT not being prone to excessive phase separation. TAT has been studied in nanostructured photovoltaic active layers, where high-density vertically oriented nanopillars can be readily grown on graphene or other substrates by physical vapor-deposition techniques.11 TAT is also highly emissive and crystallizes in a monoclinic unit cell, efficiently forming π stacks along the crystallographic a axis.12 Its known molecular-packing geometry, combined with single nanoscrystal spectroscopy,11 makes TAT single crystals an interesting testing ground for exciton-coupling models in organic semiconductors. © 2014 American Chemical Society

Received: September 5, 2014 Revised: November 7, 2014 Published: December 2, 2014 28842

dx.doi.org/10.1021/jp509011u | J. Phys. Chem. C 2014, 118, 28842−28854

The Journal of Physical Chemistry C

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The interference between short- and long-range coupling in organic materials is likely a universal phenomenon and, in principle, can occur in four ways, defining the aggregate types: JJ, HJ, JH, and HH (where the first letter pertains to the Coulombic coupling and the second letter pertains to the short-range coupling). This suggests a new paradigm for designing organic materials for optoelectronic applications. For example, a good OLED material is one with efficient charge transport and rapid (superradiant) exciton recombination. A JJ-type material that is optimized for strong short-range coupling would satisfy such requirements. A good solar cell absorber material must have rapid exciton transport and low recombination efficiencies, as in a strongly coupled HH-type material. The ability to control the J/ H competition is facilitated by the sensitivity of the short-range coupling to very small changes in the intermolecular orientation19,22,25,26 (i.e., the relative slip between molecules); this makes chemical tuning a viable method to tailor the sign and the magnitude of the short-range coupling. The Coulombic coupling (JC) also responds to changes in the intermolecular orientation but is far less sensitive.32,33 Perylene-based derivatives π stack in side-by-side sandwich complexes (JC > 0) as well as head-to-tail complexes (JC < 0),34,35 thereby providing the templates with which to tune the short-range coupling to achieve the four basic material types.

spectral shifts, however, is subject to some ambiguity because spectral shifts may arise from other sources, for example, a gas-tocrystal red shift may obscure the exciton blue shift in weakly coupled H aggregates.17 Fortunately, the two coupling types can also be readily distinguished via aggregation-induced changes to the vibronic features present in the absorption and photoluminescence spectra.18 Dominant J-type coupling results in an enhancement of oscillator strength in the 0−0 origin transition relative to higher vibrationally excited side bands, whereas Htype coupling results in a diminished origin oscillator strength relative to higher side bands. The sign and magnitude of JC can therefore be readily determined quantitatively through the measurement of the relative intensities of the vibronic features.18 Recently, Yamagata et al.19 investigated short-range energy transfer induced by HOMO/HOMO (and LUMO/LUMO) wavefunction overlap between neighboring chromophores.20,21 In the limit that the diabatic charge transfer (CT) state is energetically separated from its parent Frenkel state (|ECT − EF| ≫ |te|, |th|), they showed that either J- or H-type aggregates with vibronic signatures identical to those caused by Coulombic coupling can be created, depending on the relative sign between the electron (te) and hole (th) transfer integrals as well as the ordering of the diabatic states. The CT-mediated short-range coupling, given by JSR = −2teth/(ECT − EF), induces H-aggregate photophysical behavior when JSR > 0, whereas J-aggregate behavior is induced when JSR < 0. The magnitudes and signs of te and th are extremely sensitive to small changes in the intermolecular orientation (i.e., slip-stacking) on a sub-angstrom length scale, as defined by the HOMO and LUMO nodal patterns. Such sensitivity has been shown by Kazmaier and Hoffmann22 to lead to the remarkable range of colors displayed by perylene dyes in the crystal phase (i.e., crystallochromy).23−26 The form of JSR suggests that the same sensitivity can also be exploited to control H- and J-aggregate behavior in molecular π stacks. The presence of both CT-induced short-range coupling and Coulombic long-range coupling in organic aggregates allows for interesting interference effects. For example, in polymer π stacks, it has been shown that Coulombic (H-type) interactions between chains compete with through-bond (J-type) interactions within chains (i.e., between adjacent repeated units), resulting in hybrid “HJ aggregate” photophysics.27−31 In this work, we show that H/J competition is also fundamental to small-molecule aggregates, wherein more precise evaluations of Coulombic and CT interactions are possible because of known crystal structures. Unlike in polymer studies where the H and J couplings were segregated (i.e., between different pairs of chromophores), in the present study we focus on integrated H and J couplings between the same pair of chromophores, specifically neighboring molecules within a π stack. On the basis of a combination of experimental data and modeling, we show that the characteristics of the crystal absorption and steady-state photoluminescence (PL) spectra of TAT nanopillars are determined by a competition between long-range Coulombic coupling, which induces H-aggregate behavior, and short-range CT coupling, which induces J-like behavior. The interference between the two results in J-aggregate signatures in the lowenergy region of the absorption spectrum and H-aggregate signatures at higher energies. The destructive nature of the coupling interference also has a profound effect on the shape of the lowest-energy exciton band from which emission originates, leading to a PL spectrum that displays hybrid H/J characteristics.

II. ABSORPTION AND PL SPECTRA The room-temperature absorption spectrum for a thin crystalline film of TAT grown on a fused-silica substrate is shown in Figure 1. The film was mounted on a closed-cycle optical cryostat, and

Figure 1. Spectra of 7,8,15,16-tetraazaterrylene (TAT) nanopillars on a silica substrate: blue curve, experimental absorption spectrum; red curve, PL spectrum; and dashed vertical line, the absorption (0−0) origin of TAT in solution. Left inset: molecular structure of TAT. Right inset: TAT spectra in a dilute chloroform solution (100 nM). All spectra were recorded at room temperature.

variable-temperature absorption spectra were recorded in a Fourier transform spectrometer equipped with a 75 W Xe lamp, a UV quartz beam splitter, and a photomultiplier tube for measuring absorption within the visible region. The crystal structure of TAT is depicted in Figure 2 and is based on the crystallographic data obtained in ref 12. TAT forms monoclinic crystals with two molecules per unit cell in the P21/c space group. The crystal displays herringbone-style packing in the bc plane and π stacks along the a axis. On fused-silica and graphene 28843



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Figure 2. (A) Nanopillar of crystalline TAT on a graphene or fused-silica substrate, (B) molecular arrangement within the bc herringbone plane, and (C) π stacking along the a axis.

substrates, TAT forms nanopillars11,12 where the TAT molecules are lying flat on the surface so that the a axis is canted against the surface normal by approximately 15°. The absorption spectrum in Figure 1 was obtained with the exciting light normal to the substrate surface. The room-temperature spectra of TAT grown on a fused-silica substrate and that of TAT grown on graphene11,12 were identical, and neither displayed a dependence on the polarization of the incident light. Hence, we could not detect any Davydov splitting (DS). Figure 1 also shows the room-temperature PL spectrum of the TAT crystal. Absorption and PL spectra of a dilute solution of TAT in chloroform (100 nM) are shown in the inset of Figure 1. The spectra are typical of most rylene dyes. The S0 → S1 electronic excitation is strongly coupled to an intramolecular symmetric stretching mode with a vibrational energy of ∼1200 cm−1, as revealed by the resonance Raman spectrum.11 Vibronic coupling gives rise to a progression of absorption features labeled as 0−v (v = 0, 1, 2, ...) where v is a vibrational quantum number in the S1 excited electronic state. The intensities are Poissonian with a Huang−Rhys (HR) factor characterizing the displacement of the excited harmonic well relative to the ground-state harmonic well near unity.12 The PL spectrum of solution-phase TAT is basically the mirror image of the absorption spectrum; note that the PL spectrum is qualitatively different from that reported in ref 11. On closer investigation, we have found that the PL spectrum of solution-phase TAT is highly sensitive to concentration: the PL spectrum reported in ref 11 was obtained using much higher TAT concentrations than those used in the present work. The ref 11 spectrum is likely influenced by dimers and larger clusters, as will be reported on in detail elsewhere. Figure 1 shows that upon crystallization the absorption spectrum significantly broadens and is dominated by a highenergy peak that is blue-shifted >2000 cm−1 from the solutionphase absorption origin,11,12 suggesting the presence of a strongly coupled H aggregate. However, strong H aggregation should also be accompanied by a marked decrease in the ratio of the oscillator strengths of the first two vibronic peaks,18 which is not the case for crystalline TAT. In fact, the 0−0/0−1 oscillator strength ratio, as determined by the spectral areas, slightly increases upon aggregation,36 signifying the presence of J aggregates.18 Moreover, there is also a significant portion of the spectrum that is red-shifted, which is also indicative of the presence of J aggregates. The general two-band line shape in Figure 1 is also found in the crystal-phase spectra of several other perylene derivatives;24−26,37−39 in some, the J-like low-energy

behavior is even more pronounced.26,38 The absorption spectrum line shape presents an interesting photophysical conundrum: how can a π stack of face-to-face-oriented chromophores (a classic Kasha H-aggregate)14−16 display Jaggregate photophysical signatures? By contrast, the PL spectrum is not grossly distorted upon crystallization; the main effects are an enhanced Stokes shift and a relative attenuation of the 0−0 peak. (The small peak at ∼18 000 cm−1 is most likely due to unaggregated monomers.) The PL spectrum resembles that associated with weakly coupled H aggregates in P3HT films,40 although self-absorption may also contribute to the attenuated 0−0 peak in Figure 1. If this is the case, then a 0−0 peak even larger than the 0−1 peak would exist in the absence of self-absorption and would be indicative of J-like behavior,18 further contributing to the perplexing photophysical behavior of TAT aggregates.

III. THEORETICAL MODEL AND EXPERIMENTAL OBSERVATIONS To capture accurately the vibronic coupling involving the 1200 cm−1 mode in TAT nanopillars, we employ a Holstein-style Hamiltonian that incorporates conventional Frenkel excitons as well as CT excitons. This model is similar to that employed by Spano and coworkers to study the important role played by charge transfer in the low-energy excitonic states of polyacene crystals,41 as originally recognized by Petelenz.42 Similar approaches incorporating both vibronic coupling and charge transfer in unraveling the photophysics of perylene-based aggregates and crystals were developed by Hennessy and Soos,43 Hoffmann et al.,44,45 and Gisslen and Sholtz.25,26 These authors also demonstrated the importance of Frenkel−CT mixing in understanding the details of the absorption spectrum line shape. In particular, Gisslen and Sholtz25,26 underscored the importance of the sign involved in the coupling between Frenkel and CT excitons. Because the main interactions between TAT molecules occur within a given π stack, we present in this section the Hamiltonian corresponding to a single π stack containing N molecules (Figure 2), relegating the fully 3D Hamiltonian to the Supporting Information. The latter includes the interactions between stacks necessary to account for DS. As discussed in the next section, the calculated DS of TAT nanopillars is small ( 0.

are not related by a point-symmetry operation. In such dimers, the TAT molecules are oriented in an edge-on “T” orientation. Because of the lack of symmetry, many couplings are activated between the MOs on one monomer with the MOs on the other, leading to unphysically large couplings. This symmetry problem is well known.57,58 More accurate values of the coupling integrals for orientation II and orientation III dimers are obtained using a cyclic TAT tetramer in which the C4 symmetry operation approximately holds (Figure 2). Accordingly, the magnitude of the hole-transfer integral is evaluated using |t h | =

tetramer tetramer E HOMO − E HOMO −3 4

Figure 5. Four frontier molecular orbitals of TAT dimers in order of increasing energy from bottom to top. The symmetries of the orbitals with respect to a translation operation (where periodic boundary conditions imply a simple exchange of the two molecules) are also indicated: (S) symmetric and (AS) antisymmetric. The ordering is consistent with negative values for both te and th, after taking into account eq 14.19 Because the TDM is directed along the long molecular axis, it is symmetric under translation. Therefore, the HOMO−LUMO transition is allowed, consistent with J aggregation.

among hA and hB shows that ⟨hA|ĥ|hB⟩ > 0; however, because th = −⟨hA|ĥ|lB⟩, we have th < 0. Hence, both te and th are negative for TAT stacks. IV.C. Effective Short-Range Coupling. Charge transfer between neighboring TAT molecules within a π stack leads to an effective short-range excitonic coupling. The latter can be understood as the transfer of an electron and a hole between neighboring molecules through a virtual CT state.20,21 The mechanism is valid strictly when the band of diabatic CT states is energetically well separated from the band of Frenkel excitons. Using second-order perturbation, we represent the short-range coupling by19 tt JSR ≈ −2 e h |ΔωCT| ≫ |te| , |th| ΔωCT (17)

(15)

with a similar expression for |te| obtained by replacing tetramer tetramer with Etetramer LUMO+3 and EHOMO−3 with ELUMO . In this manner, we find that te and th in orientations II and III are negligible compared to those in orientation I. Further refinement of the interactions in orientation I can be obtained by using a linear tetramer along the π-stacking direction. For this orientation, the hole charge transfer is determined from Etetramer HOMO

|t h | =

linear tetr. linear tetr. E HOMO − E HOMO −3 4 cos(π /5)

(16)

which is adapted for open boundary conditions. A similar tetr. linear tetr. expression for |te| is obtained by replacing Elinear HOMO with ELUMO+3 linear tetr. linear tetr. and EHOMO−3 with ELUMO . The calculated CT integrals are summarized in Table 1. We used three different computational methods: the semiempirical ZINDO method, density functional (DFT) model B3LYP, and model PW91 used by Zhao et al.2 The latter two DFT methods are coupled with the 6-31G(d) basis set. Table 1 shows that the CT integrals for orientations II and III are negligible, which is in agreement with the work of Zhao et al.2 Only the CT integrals along the stacking direction in orientation I attain substantial values; hence, in what follows we retain only the orientation I CT integrals (those between adjacent π-stacked molecules) based on B3LYP unless otherwise stated. As stated previously, the signs of te and th are of utmost importance in determining whether the effective short-range interaction is J- or H-like. For orientation I, the signs of te and th are determined from the ordering of the frontier MOs within a πstacked dimer by energy, using the translation operation to define the wavefunction phase (Figure 5). The dimer geometry is taken from the TAT crystal structure.12 The dimer MOs are essentially symmetric and antisymmetric combinations of the singlemolecule HOMOs (hA, hB) and LUMOs (lA, lB) The energy order in Figure 5 is consistent with te = ⟨lA|ĥ|lB⟩ < 0 because the dimer LUMO is symmetric under translation. The splitting

Hence, if the diabatic CT state is energetically above its parent Frenkel state (as is assumed for TAT), then eq 17 predicts Jaggregate behavior59 when teth > 0 and H-aggregate behavior when teth < 0. As shown in ref 19, all of the vibronic signatures are identical to those in conventional Coulomb-coupled J and H aggregates.18 In TAT π stacks, teth > 0 (Figure 5) such that the short-range coupling between neighboring chromophores induces J-like behavior. We emphasize that for TAT eq 17 only approximately accounts for the CT-mediated coupling. In all calculations to follow, we treat charge-transfer interactions exactly using the Hamiltonian in eq 4.

V. COMPARISON TO EXPERIMENTAL DATA Our analysis of the exciton coupling in TAT crystals shows that the dominant FE and CT interactions occur within the π stacks. Coulombic long-range coupling has a uniformly positive value within the stack and is therefore H-promoting, whereas the shortrange coupling in eq 17 has a negative value, promoting J-like behavior. To determine how the competition plays out in the photophysical response, we begin by considering a single π stack with N = 20 TAT molecules. Figure 6 shows the calculated absorption spectrum A(ω) = ∑ j Aj(ω) using eq 6. The summation is over the two polarization directions defining the molecular planes (bc′), consistent with the unpolarized 28848



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were unchanged from those used in the 1D calculation. The two models differ only in the Coulombic couplings, which are included for all pairs of TAT molecules and are therefore far more numerous in 3D. As stated in the previous section, the unscreened value of A in a 3D aggregate is 2466 cm−1, which is substantially smaller than the value of A in a single π stack (4180 cm−1). Hence, the dielectric screening that is required in a 3D crystal to reproduce the measured absorption spectrum is also smaller. By simply reducing the optical dielectric constant for a single π stack (ε = 4) by a factor of 2466/4180 (giving ε = 2.4), we obtained the 3D aggregate absorption spectrum shown in Figure 6, which also agrees very well with our experimental data. The calculated spectra for both models (Figure 6) reproduce the broad two-band nature of the measured spectrum as well as the 0−0/0−1 oscillator strength ratio near unity, which is practically unchanged from the solution spectrum. We have further determined that the Davydov splitting for 3D aggregates is only about 100 cm−1, which is consistent with the lack of any polarization dependence in the observed absorption spectrum. To investigate the individual impact of long-range (Coulombic) and short-range (wavefunction overlap) coupling on the absorption spectrum, we recalculated the absorption spectrum retaining only Coulombic couplings (Figure 7a, blue curve) and

Figure 6. Calculated absorption spectra for TAT aggregates: 1D, a single π stack directed along the a axis containing 20 TAT molecules; 3D, an aggregate consisting of 20 × 20 × 20 unit cells, with 2 TAT molecules per unit cell. Parameters common to both: ΔωCT = 1210 cm−1 (150 meV) and te and th taken from Table 1 (B3LYP) and scaled by q = 0.80, λ+2 = λ−2 = 0.5, and λ2 = 1.2. For 1D, the optical dielectric constant was set to ε = 4.0, whereas for the 3D aggregate it was set to ε = 2.4. The measured spectrum for TAT nanopillars on fused silica is also shown for comparison (Exp, black dots). Δ0−0 is adjusted so that calculated spectra are spectrally aligned with experiment. Spectral line widths are progressive (see the text following eq 9) with Γ = 425 cm−1 and ΔΓ = 100 cm−1.

excitation used in our measurements (section II). The Hamiltonian in eq 1 was parametrized as described in the previous section with only slight adjustments and subsequently diagonalized numerically to obtain all eigenstates and energies needed to evaluate A(ω). The Supporting Information illustrates how, on the basis of a systematic search through a phase space containing 104 points, we obtained the optimized parameters. The calculated spectra in Figure 6 assume a CT energy from eq 12 of ΔωCT = 1200 cm−1 (0.15 eV), a value similar to that used in modeling the absorption of crystalline tetracene.41 We show in the Supporting Information that good agreement with experimental results can also be obtained with a CT energy in the range of 400−2000 cm−1 and only slight changes to the other parameters. In addition, the B3LYP values of th and te used in Figure 6 were scaled by a factor of 0.8, and the effects of the dielectric medium were included by scaling the Coulombic couplings evaluated in section IV by 1/ε, where ε is the optical dielectric constant (assumed here to be isotropic). In perylene, which forms π stacks similar to those in TAT, the averaged dielectric constant is ε ≈ 3,39 which is somewhat smaller than the value used for the 1D stack (ε = 4) in Figure 6. The ionic HR factors, λ+2 and λ−2, were taken to be equal to 0.5, which is roughly half the neutral HR factor (λ2 = 1.2) derived from a solution-phase spectrum and is consistent with a softening of the macrocyclic stretching mode upon ionization. As illustrated in Figure 6, the calculated spectrum based on the Hamiltonian in eq 1 for a single TAT stack agrees very well with our experimental results. To investigate the 3D nanopillars, we employed the Hamiltonian in eq S.1 to repeat our absorption analysis of a crystal composed of 20 × 20 × 20 unit cells (with 2 TATs in each unit cell). The CT parameters, which are confined to the π stack,

Figure 7. (a) Blue curve, calculated absorption spectrum for a TAT π stack containing 20 chromophores excluding charge transfer (te = th = 0 and De = Dh = 0) but retaining the Coulombic coupling. The spectrum resembles a strongly coupled H aggregate. (b) Red curve, calculated spectrum for a TAT π stack excluding Coulombic coupling (Jσn;σ′n′ = 0) but retaining charge-transfer interactions. Here, the effective coupling induced by charge transfer bestows J-aggregate characteristics; most notably, an enhanced red-shifted 0−0 band. (a,b) Black curve, calculated spectrum including all interactions (short-range CT and Coulombic). 28849



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Figure 8. (a) Measured absorption spectrum for crystalline TAT at several temperatures. (b) Calculated absorption spectra for a TAT π stack containing 20 TAT molecules. The parameters are the same as reported in Figure 6. The various spectra differ only in their spectral line widths. The latter are reported as the percentage of the room-temperature value, Γ = 425 cm−1, with ΔΓ = 100 cm−1 held constant (see eq 9).

contribute to the 0−1 peak are slightly broader (and therefore less intense) than those that contribute to the 0−0 peak. The impact of H/J competition on the exciton dispersion (ωex(k)), corresponding to the lowest-energy band, is depicted in Figure 9. The dispersion curves for the three cases depicted in

only charge-transfer interactions (Figure 7b, red curve). The spectrum illustrated by the blue curve in Figure 7a is a classic Haggregate spectrum by virtue of its main absorption peak being blue-shifted by approximately 2000 cm−1 relative to the monomer absorption origin as well as a significantly reduced 0−0/0−1 peak ratio (as compared to the value of approximately unity displayed by the monomer spectrum in solution, Figure 1 inset). In marked contrast, the spectrum illustrated by the red curve in Figure 7b behaves like a classic J-aggregate spectrum. Its 0−0/0−1 ratio significantly exceeds the monomer value, and the main absorption peak is clearly the 0−0 peak that is red-shifted 1480 cm−1 from the monomer absorption origin (Figure 1 inset). When all short- and long-range couplings occur simultaneously, as in an actual TAT π stack, one obtains the black spectrum shown in Figure 7a,b, which is equivalent to the 1D spectrum in Figure 6. The main peak is still significantly blue-shifted, but the ratio between the 0−0 and 0−1 peaks is now roughly unity. The essentially unchanged 0−0/0−1 ratio occurring upon aggregation is indicative of a well-balanced competition between shortand long-range couplings. H/J competition in the absorption spectrum is more clearly seen at lower temperatures. Figure 8a shows the measured absorption spectra at temperatures in the range from 13 K to room temperature. The main impact of decreasing temperature is a significant reduction in the spectral line width, likely caused by reduced exciton (lattice) phonon scattering. To model the effect of decreasing temperature, we simply reduced the line width, Γ, which is reported in Figure 8b as a percentage of the room-temperature value of 425 cm−1. Because ΔΓ is based on the dispersion of vibronic energies, we left it unchanged. The calculated spectrum obtained using these conditions is in excellent agreement with the experimental data; in particular, the 0−0/0−1 ratio based on the peak intensities increases as the line width narrows in a manner practically identical to what is observed. It is important to note that changing Γ does not impact the oscillator strengths of the 0−0 and 0−1 lines because the Lorentzian spectra are area-normalized. The increase in the ratio evaluated using the 0−0 and 0−1 peak intensities (rather than area, as is required for oscillator strengths) is simply the result of employing the progressive line width: the transitions that

Figure 9. Exciton bands: black curve, calculated exciton energy relative to ω0−0 + Δ0−0 as a function of the dimensionless wave vector k along the π-stacking axis in a TAT π stack containing 20 chromophores. (The band energies correspond to the lowest-energy eigenstates of H in eq 1 using the parameters reported in Figure 6.) Blue curve, exciton band arising entirely from long-range Coulombic couplings (Figure 3 with ε = 4) calculated from H in eq 1 after setting te = th = 0 and De = Dh = 0. Red curve, exciton band arising entirely from CT interactions calculated from H in eq 1 after setting Jsn;s′n′ = 0. Black dashed curve, direct sum of blue and red curves.

Figure 7a,b are shown. The H-aggregate band (blue curve), representing fictitious TAT aggregates in which only the Coulombic couplings are retained, has negative curvature at k = 0 such that the corresponding exciton is highest in energy. Conversely, the J-aggregate band (red curve) that arises entirely from the short-range (charge-transfer) interactions maintains positive curvature with the k = 0 state residing at the bottom of the band. Interestingly, the bandwidths are very similar, indicating a well-balanced interference. The physically relevant case, in which all couplings are included, is represented by the 28850



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When disorder is entirely absent, the spectrum calculated with T = 0 K (not shown) lacks a 0−0 emission peak; emission from excitons at the band minima in Figure 9 cannot terminate on the vibrationless ground state because the optical selection rule, Δk = 0, is violated.18,60 This is also true for conventional H aggregates. However, kbT at room temperature is larger than the barrier indicated in Figure 9 (ΔE ≈ 130 cm−1) allowing the k = 0 exciton to be populated; subsequent emission is responsible for the 0−0 peak in Figure 10a. (Note the side-band peaks are allowed for all values of k and do not require thermal activation.)18 Figure 10a further shows that the slight increase in the 0−0 emission peak energy (by ΔE) leads to a dilation in the spectral separation between the 0−0 and 0−1 peaks, which is in contrast to the contraction observed in the measured spectrum. The calculated PL spectrum shown in Figure 10b corresponds to a TAT π stack with diagonal disorder. The emission spectrum is averaged over 3000 configurations of disorder; within a given configuration, the transition energy offset of each TAT molecule is chosen randomly from a Gaussian distribution with a standard deviation of 420 cm−1. The calculated spectrum also includes an average over a Boltzmann distribution of emitters within each configuration assuming T = 300 K. The calculated spectral separation between the 0−0 and 0−1 peaks and the 0−0/0−1 intensity ratio are now in better agreement with our experimental observations. If self-absorption is contributing to the observed attenuation of the 0−0 peak, then removing self-absorption may result in a 0−0 peak that is significantly greater than the 0−1 peak. Conventional theory of H aggregates forbids the 0−0/0−1 ratio from being larger than the single-molecule value,18 which is approximately unity for TAT (Figure 1 inset). However, in the HJ-aggregate model championed here, the 0−0/0−1 ratio can exceed the molecular value because of the short-range J-like interactions. In Figure S.8, we show that when the CT energy is reduced to 50 meV the 0−0/0−1 ratio is double that shown in Figure 10b. The reduced CT energy leads to enhanced (J-like) short-range interactions and a reduction in the activation barrier ΔE. Figure S.8 also shows that a slight adjustment of the remaining parameters yields an acceptable reproduction of the measured absorption spectrum. The measured temperature dependence of the 0−0/0−1 PL ratio (if possible, with minimal self-absorption) should provide a more accurate estimate of ΔE. Such experiments are currently underway.

black curve. The H/J interference results in a sharp reduction in the exciton bandwidth (and hence exciton mobility) along with a relocation of the band minima to values of k near ±π/2. The double-well band dispersion is closely approximated by the sum of the H- and J-aggregate bands (dashed curve), further demonstrating the interfering nature of the exciton couplings. The shift to lower energies in the dashed curve versus the black curve arises from the differing impact of vibronic coupling in the three cases. The shape of the lowest-energy exciton band strongly affects the steady-state PL spectrum. Figure 1 shows that TAT aggregation is associated with a significant drop in the 0−0 emission intensity relative to that of 0−1. Although this is characteristic of H aggregates,18 we cannot discount some contribution from self-absorption, which reduces the blue side of the 0−0 peak near 17 000 cm−1 where aggregate absorption is significant (Figure 1). Self-absorption may also contribute to the observed reduction in the spectral separation between the 0−0 and 0−1 peaks to ∼1000 cm−1, which is less than a vibrational quantum (1200 cm−1). Figure 10 compares the measured PL spectrum with that calculated with T = 300 K and the parameters that best

VI. DISCUSSION AND CONCLUSIONS Crystalline TAT represents an interesting example of an HJ aggregate, with an absorption spectrum displaying hybrid H- and J-aggregate characteristics. The HJ-aggregate properties result from a competition between the mainly positive, long-range Coulombic couplings that induce H-like behavior and the negative, short-range CT-mediated couplings that induce J-like behavior. The resulting two-band absorption spectrum has features that are significantly blue-shifted (H-band) and redshifted (J-band), with a 0−0/0−1 oscillator strength ratio that is almost unchanged upon aggregation. Because the ratio is sensitive to the overall exciton bandwidth,18 its stability indicates an efficient destructive interference. The destructive nature of the interference also has a profound impact on the lowest-energy exciton band, which takes on a double-well shape with minima near k = ±π/2. The PL spectral line shape is H-like (in that 0−0 emission requires symmetry-breaking disorder and/or thermal excitation for activation) as well as J-like (because the 0−0/0−1

Figure 10. PL intensities: black curves, measured PL spectrum for TAT nanopillars; red and blue curves, calculated PL spectra for the 20 × 1 × 1 (1D) and 5 × 5 × 5 (3D) TAT aggregates parametrized as in Figure 6. (a) Gaussian homogeneous broadening is assumed with a standard deviation of 340 cm−1. (b) Gaussian inhomogeneous broadening is included through site-energy disorder. The on-site energies are chosen randomly from a Gaussian distribution with a standard deviation of σ = 420 cm−1. We averaged 3000 configurations to obtain the spectrum. In both cases, the calculated spectrum was normalized and aligned with the experimental spectrum at the 0−1 peak.

reproduced the absorption spectrum in Figure 6. In Figure 10a, the calculated spectrum is shown for TAT aggregates without disorder, evaluated using a Gaussian homogeneous line-shape function; disorder is included in Figure 10b. Details of the PL calculations are found in the Supporting Information; steadystate emission is assumed to proceed from a Boltzmann distribution of excitons dispersed according to the double-well band in Figure 9. 28851



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that also forms π stacks.38 Interestingly, the absorption spectrum is very similar to the TAT absorption spectrum reported here, suggesting an HJ aggregate. The possibility of an ideal aggregate type for singlet exciton fission will be explored in a future work.

ratio can significantly exceed the molecular value for sufficiently large |JSR|). It is interesting that the physical basis of the H/J competition described herein is different from that recently reported in conjugated polymer π stacks.27−31 In the latter, the H and J interactions are segregated, with J-like coupling along the polymer chain and H-like coupling between chains. In TAT π stacks, the H and J interactions compete within the same pair of chromophores, leading to more dramatic H/J manifestations in absorption and PL spectra. In TAT π stacks, the interference between short- and longrange broadening is directly evident in the exciton dispersion, ωex(k). When measured relative to the local Frenkel exciton transition energy, ω0−0 + Δ0−0, ωex(k) approximately obeys ωex (k) = ωexLR (k) + ωexSR (k)

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ASSOCIATED CONTENT

S Supporting Information *

Full Hamiltonian for a 3D TAT crystal, further information about the parametrization of the TAT molecules, the optimization of aggregate parameters, a comparison of B3LYP DFT- and PW91 DFT-calculated electron- and hole-transfer integrals, a description of how the PL spectrum is calculated, and an exploration of the absorption and PL spectra for other diabatic CT energies. This material is available free of charge via the Internet at http://pubs.acs.org.

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(18)

ωLR ex

where corresponds to the dispersion in a π stack with only long-range Coulombic coupling and ωSR ex corresponds to the dispersion in a π stack with only short-range (CT-induced) coupling. In TAT, the long- and short-range bands have similar widths (∼350 cm−1) but opposite curvatures characteristic of H and J aggregates, respectively. The resulting interference leads to a sharp reduction in the exciton bandwidth by a factor of 2 to 3, as depicted in Figure 9. The compromised bandwidth may be relevant to recent accounts of enhanced exciton trapping in certain perylene derivatives.61,62 It is quite interesting that crystalline TAT, which hosts π stacks of practically cofacially eclipsed TAT molecules, does not show excimer emission, as is quite common in similarly stacked perylene chromophores.63−65 In TAT π stacks, the diabatic CT exciton band may be spectrally more distant from the (diabatic) Frenkel band than in perylene π stacks, thereby preventing the significant Frenkel/CT mixing required for excimer formation. We are currently investigating this idea further. The hypersensitivity of the electron- and hole-transfer integrals to small changes in intermolecular orientation, for example, small slips of one molecule relative to its neighbor,19,22,25 translates to a similar sensitivity in the short-range coupling because JSR in eq 17 depends on the product teth. Hence, in TAT it should be possible to chemically tune the sign of JSR in order to engineer a conversion from an HJ aggregate to an HH aggregate where both long- and short-range couplings are positive. In the simplest case, where teth changes sign (but not magnitude), our calculations predict a 4-fold increase in the exciton bandwidth. Such HH aggregates with strong short- and long-range couplings should make ideal absorbers in solar cells, where enhanced exciton mobilities and reduced radiative decay rates are desired. One can also envision JH and JJ aggregates, based on perylene π stacks, with negative Coulombic coupling (i.e., head-to-tail orientations).34,35 The negative short- and longrange exciton couplings in JJ aggregates result in a constructively enhanced exciton bandwidth in which the k = 0 exciton remains at the bottom of the band. Hence, JJ aggregates with strong shortrange and long-range coupling should make excellent lightemitting diodes, which require rapid charge transport (via large short-range coupling) and high radiative efficiencies. The prospect of a null HJ or JH aggregate17 with compensating short- and long-range coupling is also intriguing. The important process of singlet fission66−69 is likely enhanced by mixing between the initially excited Frenkel exciton and lowenergy CT states, and it should therefore be susceptible to the interference effects discussed here. Recently, a high fission yield has been measured in the crystalline form of a perylene derivative

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS F.C.S. is supported by the National Science Foundation (grant no. DMR-1203811). M.D.B. and D.M. acknowledge support from the Department of Energy (grant no. DE-FG0205ER15695). H.Y. acknowledges support from PHaSE EFRC (grant DE-SC0001087). A.L.B. acknowledges support from the Office of Naval Research (N0001471410053). We thank Y. Zhang and T. Mirabito for providing graphene/TAT substrates.

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HJ-Aggregate Behavior of Crystalline 7,8,15,16-Tetraazaterrylene

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