Article pubs.acs.org/JPCC
Polarized Absorption in Crystalline Pentacene: Theory vs Experiment N. J. Hestand,† H. Yamagata,† Bolei Xu,† Dezheng Sun,‡ Yu Zhong,§ Avetik R. Harutyunyan,∥ Gugang Chen,∥ Hai-Lung Dai,† Yi Rao,*,† and F. C. Spano*,† †
Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States Department of Physics and §Department of Chemistry, Columbia University, New York, New York 10027, United States ∥ Honda Research Institute USA, Inc., Columbus, Ohio 43212, United States ‡
S Supporting Information *
ABSTRACT: The polarized absorption spectra of crystalline pentacene are obtained for excitation normal to the ab herringbone plane by measuring transmitted light in ultrathin crystals. The spectral line shapes for excitation polarized along b and orthogonal to b are analyzed theoretically using a Holstein-like Hamiltonian which includes both Frenkel and charge transfer (CT) excitons represented in a multiparticle basis set. The model agrees with prior estimates regarding the strong CT contribution (≈45%) of the exciton responsible for the b-polarized lower Davydov component. The polarization resolution allows one to also establish the nature of the upper Davydov component, which is found to contain far less CT content (≈15%), as well as the natures of the higher-energy vibronic excitons, which are found to consist of a complex mixture of Frenkel one- and two-particle states and CT excitons. Generally, the spectrum polarized along b displays J-aggregatelike vibronic signatures while the spectrum polarized orthogonal to b displays H-aggregate-like vibronic signatures. The assignment is entirely consistent with the calculated exciton band dispersions which agree well with the measured ones.
I. INTRODUCTION The oligoacene series continues to attract considerable attention for electronic applications such as field-effect transistors, due to their exceptionally high crystal-phase charge mobilities.1−5 More recently, tetracene and pentacene have come under intense scrutiny for their ability to promote rapid singlet exciton fission,6−17 potentially increasing the efficiency with which light can be converted to electricity in solar cell applications.12,13 Many groups have attempted to obtain a more fundamental understanding of the fission process and the potential role of intermediate charge transfer (CT) states, which necessarily involves a deep appreciation for the nature of the low-energy photoexcited states. In this regard, controversy has erupted over the CT exciton composition of the excited state responsible for the absorption origin (the lower Davydov component) in pentacene.18 Several theories predict a predominant CT admixture19−22 while others claim a substantial, but minority, component of 10−30%,18,23,24 an essentially even mixture of CT and Frenkel character,17,25 and even a negligible CT contribution.26 Experimental evidence for substantial Frenkel/CT exciton mixing near the absorption origin in pentacene has come mainly from measurements of the exciton band dispersion using electron energy loss spectroscopy by Knupfer and co-workers.27,28 Despite the heightened attention granted to pentacene photophysics, very few studies have reported its polarized absorption spectrum in the crystal phase.29−31 Although it is not difficult to grow pentacene single crystals with dimensions © 2015 American Chemical Society
greater than 1 mm by means of modern physical methods, a direct measurement of the absorption spectrum remains a challenge since at such thicknesses essentially all incident light is absorbed. In fact, the optimal thickness for obtaining the transmission UV−vis absorption spectrum is generally on the order of 200−400 nm, making it a formidable challenge to prepare high-quality, optically transparent single crystals of pentacene. In order to circumvent the strong absorbance of crystalline pentacene, light reflection or ellipsometry measurements have been employed.32−36 However, such methods allow only an indirect acquisition of the spectrum, as they require certain models for the extraction of the linear optical absorbance. In this paper, we present polarized absorption spectra of crystalline pentacene using direct transmission measurements. Thin single crystals of pentacene have been synthesized and irradiated normal to the ab herringbone plane which contains the most strongly coupled molecules. Because of the small area (19 000 cm−1), where extra peaks occur arising mostly from CT states. The dashed red and blue spectra in Figure 5 were obtained by multiplying the homogeneous line width by a factor of 5 for all transitions above 18 500 cm−1, where our calculations indicate a rapid increase in the density of states. The increased linewidth 22141
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importance of separated vibronic−vibrational excitations in the photophysics of pentacene. In marked contrast to the b-polarized spectrum, the first transition (A1) in the spectrum polarized mainly along the aaxisthe upper Davydov componentarises from an excited state which is dominated by one-particle Frenkel excitons, with a small CT admixture of less than 15%. The one-particle Frenkel excitations also play a majority role in the next higherenergy transition responsible for A2, although the CT admixture rises to almost 40%. Interestingly, the peak-to-peak separation between A1 and A2 is close to a vibrational quantum, showing that the excited states polarized ⊥b are more monomer-like than those polarized along b. The cluster of low-intensity transitions at 18 000 cm−1 (labeled A2′ in Figure 6) is responsible for the pronounced shoulder in the observed spectrum (see Figure 1b). Such states are dominated by CT excitons and two-particle Frenkel excitons. One of the most striking differences between the spectra polarized along b and orthogonal to b is the ratio of oscillator strengths involving the first two vibronic peakssee Figure 6. The measured B1/B2 ratio is ≈2.3, much larger than the 0−0/ 0−1 ratio of ≈1.2 in the monomer (solution) spectrum in Figure 1a. By contrast, the A1/A2 ratio is ≈0.75, significantly smaller than in the monomer spectrum. In past works involving Coulombically coupled Frenkel excitons we showed that a ratio increase (relative to the monomer) signifies J-aggregation, while a ratio decrease signifies H-aggregation.48 Hence, for pentacene, the b-polarized spectrum is J-like, while the ⊥b-polarized spectrum is H-like. Further clues into the J/H-aggregate nature of the polarized components can be obtained from the energy dispersions of the bands which contain the two Davydov components. We therefore evaluated the two lowest energy bands in crystalline pentacene within the reciprocal space stemming from the herringbone plane. In triclinic pentacene, the reciprocal lattice vectors Kb ≡ 2πa × c/(a × c·b) and Ka ≡ 2πb × c/(b × c·a) approximately point in the directions of b and a, respectively. For a herringbone layer containing N by N unit cells, the exciton wave vectors take on the values k = ka + kb with Kb = 0, ±Kb/N, ±2Kb/N, ..., Kb/2 and Ka = 0, ±Ka/N, ±2Ka/N, ..., Ka/ 2. Figure 7 shows the calculated energy bands; the point ka = kb = 0 on the red surface locates the energy of the optically allowed exciton polarized along b (and responsible for peak B1) while the corresponding point on the blue surface locates the optically allowed exciton polarized along the direction orthogonal to b (and responsible for peak A1). The energetic separation between the two surfaces at ka = kb = 0 is therefore the Davydov splitting. In Figure 7a only the Coulombic coupling is retained, by setting all electron and hole transfer integrals in the pentaceneparametrized Hamiltonian to zero, while in Figure 7b charge transfer is activated, corresponding to the complete Hamiltonian for pentacene used to evaluate the absorption spectra in Figure 5. In the presence of Coulomb coupling alone the DS is almost negligibleless than 100 cm−1and the polarizations of the two components are opposite to that observed experimentally. This was also found to be the case in tetracene.25 Activating Frenkel/CT mixing reverses the polarization assignments and dramatically increases the bandwidths. A large positive curvature develops in the lower band, mirrored by a large negative curvature induced in the upper band. The DS substantially increases to approximately 1000 cm−1, in excellent agreement with the measured value.29−31 The DS in
mimics enhanced population relaxation from the higher energy, primarily CT excitons. A further discrepancy between the experimental and calculated spectra is the ratio of the bpolarized to the ⊥b-polarized peak intensities (A1/B1), presumably due to our utilization of an isotropic dielectric constant. In order to further access the nature of the transitions responsible for the polarized spectra, Figure 5 also shows the polarized spectra calculated purely electronically (i.e., without vibronic coupling) by setting all HR factors to zero. The importance of vibronic coupling becomes immediately apparent. In particular, the DS more than doubles when vibronic coupling is neglected.
IV. NATURE OF THE TRANSITIONS The nature of the various transitions observed in the polarized absorption spectra of crystalline pentacene can be appreciated from Figure 6, which shows the dominant transitions
Figure 6. Calculated stick spectrum for excitation polarized along b (top) and normal to b (bottom) in crystalline pentacene.
represented in a bar spectrum, where the bar height is proportional to the oscillator strength of each transition. The relative CT contribution is indicated by the red shaded region of each bar, while the Frenkel contribution is divided between one-particle (black) and two-particle (blue) components. As is immediately apparent, the excited state responsible for the dominant b-polarized B1 transitionthe lower Davydov componenthas a large CT admixture, approximately 45%, in agreement with our earlier estimates.17,25 The Frenkel component is largely due to one-particle states. The higher energy transitions responsible for peaks B2 and B3 have a more complex composition. In particular, the main transition within the B2 cluster arises from an excited state with dominant CT admixtureroughly 65%with the smaller Frenkel contribution due almost entirely to two-particle states. Such states also contribute strongly to the main B3 transition, highlighting the 22142
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Figure 8. Calculated energy dispersion parallel to the Ka (blue line) and Kb (red line) reciprocal lattice directions compared with the experimentally measured dispersions from ref 28 using EELS. The experimental data is shown as the error bars of the measurement. Note that in ref 28 the a and b crystallographic axis labels are interchanged relative to our definitions. Hence, a* in ref 28. corresponds to our Kb, while b* corresponds to our Ka.
V. NATURE OF THE EXCITON DISPERSION In this section we examine the origin of the band curvatures of the two lowest energy surfaces in crystalline pentacene. The band curvatures ultimately derive from the mixing between Frenkel and CT excitons as demonstrated in Figure 7, with practically no role played by Coulomb coupling. The essential physics responsible for the band shapes of Figures 7 and 8 is present in a much simpler model consisting of a onedimensional (1D) crystal with two molecules per unit cell, in which only the nearest-neighbor electron and hole transfer is included while Coulomb coupling and vibronic coupling are entirely neglected; see Figure 9. The 1D crystal has translational symmetry as well as a 2-fold screw axis along the aggregate axis (“b”) which interchanges the two sublattices. In the following analysis, the basis set is limited to Frenkel and nearest-neighbor CT excitons. The energy of a diabatic CT excitation is taken to be ω0−0 + ECT, where ω0−0 is the molecular S0 → S1 transition energy (recall ℏ is set to unity) . In the simple model outlined above, the diabatic Frenkel and CT exciton bands are flat and dispersionless. There are two Frenkel bands (red and blue dashed lines in Figure 9); one symmetric (red) and the other antisymmetric (blue) with respect to the screw rotation. The four CT bands, which are higher in energy by ECT, are not shown in Figure 9. The transition to the k = 0 state in the symmetric FE band is allowed and b-polarized, while the transition to the k = 0 state in the antisymmetric FE band is allowed and a-polarized. Activating te and th allows mixing to occur between the Frenkel and CT excitons of like symmetry, resulting in the bands shown by the solid curves in Figure 9. The excition with wave vector k in the symmetric (antisymmetric) band has energy given by
Figure 7. Calculated energy dispersion for the two lowest energy excitons in pentacene for directions within the Herringbone plane. In (a) Frenkel/CT exciton mixing is excluded by setting all CT integrals to zero. In (b) Frenkel/CT mixing is included. All other parameters are the same as in Figure 5.
pentacene is considerably greater than the value measured for tetracene (≈600 cm−1)60 due to the enhanced Frenkel/CT mixing. The calculated band dispersions in Figure 7b agree well with the measured momentum-dependent exciton energies obtained using EELS by Roth et al.,28 as demonstrated in Figure 8. The positive curvature of the lower band is characteristic of Jaggregates, since the point ka = kb = 0 defines the band minimum, and is the source of the J-like behavior observed in the b-polarized spectrum (enhanced B1/B2 ratio vs the monomer). Conversely, the negative curvature of the upper band, which is characteristic of H-aggregates, is responsible for the H-like behavior (attenuated A1/A2 ratio) for the spectrum polarized orthogonal to b. Note that although B1 is strongly red-shifted relative to the monomer (see Figure 1), consistent with its J-like behavior, the peak A1 is also red-shifted, in contrast to the blue shift expected for H-like behavior. This unusual feature is due to the manner in which the negative curvature of the upper surface develops in pentacene. In conventional Coulomb-coupled H-aggregates, the negative curvature arises because the energy of the k = 0 exciton is shifted positively relative to all other excitons. However, for pentacene as well as CT-mediated H-aggregates61 the negative curvature is instead the result of a strong negative shif t in the energies of the high wave vector excitons. This will be explored in greater detail in section V.
ES(AS)(k) = ω0 − 0 + ΔS(AS)(k)
(4a)
where the k-dependent energy shifts are given by 22143
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th have the same sign, as in pentacene, the lower band is symmetric and the lower Davydov component is b-polarized. By contrast, opposite signs for te and th result in the lower band being antisymmetric, and the lower Davydov component being a-polarized. Hence, the polarization of the two Davydov components depends critically on the relative sign between te and th. We have confirmed the sign sensitivity in the polarization ordering of the Davydov components for the pentacene-parametrized Hamiltonian in section III: imposing opposite signs for te(l) and th(l) for l = ±(1/2,1/2) and for l = ±(1/2,−1/2) interchanges the polarizations of the two Davydov components. The resulting spectra are shown in Figure S.5 in the Supporting Information.
VI. DISCUSSION/CONCLUSION We have resolved the polarization dependence of the absorption spectrum in crystalline pentacene with excitation normal to the 001 herringbone plane, and subsequently analyzed the spectral line shapes using a theory based on vibronically coupled Frenkel and CT excitons. Overall, the calculated line shapes normal to and along the crystallographic b-axis are in very good agreement with experiment. Our combined experimental/theoretical approach yielded detailed information on the nature of several of the low-lying optical excitations. The high CT content (about 45%) for the exciton responsible for the b-polarized lower Davydov component (or B1) is consistent with previous analyses based on the unpolarized absorption spectrum.17,25 The polarization resolution of the current work allowed us to also probe the nature of the exciton responsible for the mainly a-polarized upper Davydov component (A1). In marked contrast to the B1 exciton, the exciton responsible for A1 has only a small CT admixture, ≈15% . The measured DS of ≈1000 cm−1 is accurately captured by the theory and is almost entirely due to Frenkel/CT exciton mixing, consistent with our earlier analysis.25 Coulomb coupling plays a very minor role (see Figure 7a), as is also the case for tetracene,25 since the oscillator strength of the short-axis polarized S0 → S1 transition is very weak.43 The theory also quantitatively accounts for the spectral positions and oscillator strengths of several of the higher-energy a- and b-polarized excitations arising, in part, from vibronic coupling involving the ubiquitous totally symmetric ringstretching mode at approximately 1400 cm−1. Such states are comprised of a complex mixture of one- and two-particle Frenkel excitons as well as CT excitons. Unlike in anthracene and tetracene, the b-polarized progression in pentacene (B1, B2, B3) is highly irregular and grossly distorted from the regular progression observed for the unaggregated monomer in solution (see Figure 1). The enhanced distortion and greater DS exhibited by pentacene is due to greater Frenkel/CT mixing. The latter is due to the relative ease for dissociating local Frenkel excitons into ion pair states in pentacene vs tetracene and anthracene. Generally, this is due to the diminishing value of Ip − EA (Ip = ionization potential, EA = electron affinity) expected with increasing oligoacene length. As estimated early on using electroabsorption spectroscopy, the lowest CT exciton in pentacene is approximately 0.29 eV higher in energy than the lowest (mainly) Frenkel exciton, considerably smaller than the corresponding values for anthracene (0.43 eV) and tetracene (0.35 eV).58,63 Indeed, Figure 6a shows a cluster of predominantly CT states approximately 0.25 eV above the lower Davydov component, consistent with the assignments
Figure 9. (top) One-dimensional crystal lattice with two molecules per unit cell. Arrows indicate the short-axis polarized transition dipole moments. The directions shown correspond to the b-polarized transition. (bottom) Dispersion curves for the diabatic Frenkel bands and for the lowest two excitons after Frenkel/CT exciton mixing. The higher-energy diabatic CT exciton bands with energy ECT = 800 cm−1 is not shown. The case shown corresponds to te and th having the same sign, with te = th = 200 cm−1.
ECT 2
ΔS(k) =
−
2(te 2 + th 2) + 4teth cos(k /2) + ECT 2 /4 (4b)
ΔAS(k) =
ECT 2 −
2(te 2 + th 2) − 4teth cos(k /2) + ECT 2 /4 (4c)
Here, the signs of te and th are consistent with the phase convention in which the HOMO (LUMO) on one sublattice is obtained from the HOMO (LUMO) on the other sublattice by the 2-fold screw rotation. Figure 9 shows that Frenkel/CT mixing results in a lower band with positive curvature and an upper band with negative curvature, similar to the case of pentacene in Figures 7 and 8. Interestingly, the upper band develops negative curvature, as defines H-aggregates, because the downward energy shift increases with exciton wave vector. In this simple model, where te and th were taken to be equal, the k = 0 exciton in the upper (antisymmetric) band undergoes no energy shift at all, as can be shown directly from eq 4c. However, if we were to make te and th unequal in magnitude, the k = 0 exciton in the upper band would undergo a red shift since ΔAS(k=0) < 0. This mechanism of creating the H-like band61 is therefore entirely different than the conventional mechanism of Kasha which is predicated entirely on Coulomb coupling.62 In the simple 1D aggregate of Figure 9, which band is symmetric or antisymmetric depends on the relative sign of te and th. One can readily appreciate from eqs 4a−4c that if te and 22144
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the danger in assigning H- and J-like behavior based solely on spectral shifts. In the present case, the red shift of A1 is due to the peculiar nature of CT-mediated H-aggregates,61 as discussed in section V. We have found that in pentacene, and oligoacenes in general, the polarizations of the lower and upper Davydov components depend sensitively on the relative signs of the electron and hole transfer integrals connecting molecules in the two (inequivalent) sublattices. This is most easily appreciated for the simple 1D crystal in Figure 9 using eqs 4a−4c. When teth > 0, the lower Davydov component is b-polarized and the upper Davydov component is polarized perpendicular to b. Reversing the sign of teth interchanges the polarizations of the two components. The relationship between the band polarizations and the sign of teth assumes a phase convention for the HOMOs and LUMOs in the two sublattices based on a symmetry operation which exchanges the two sublattices but leaves the b-polarized transition dipole moment unchanged, such as the 2-fold screw rotation in Figure 9. In triclinic pentacene the two molecules in the unit cell are not related by a symmetry operation. However, one can still perform a 2-fold screw rotation along b to determine the MO phases and therefore the relative signs of te and th as described in ref 25 (see also the Supporting Information). In triclinic pentacene, Table 1 shows that te and th in the (1/2,1/2) direction have the same sign, as is also the case in the (1/2,−1/2) direction. Hence, the lower Davydov component must be b-polarized, as is found in experiment. When Coulomb coupling is dominant (which is not the case for pentacene), the sign of the coupling dictates the polarization assignments of the Davydov components. This has been discussed previously for chiral PDI bichromophores which are arranged in a way which resembles the molecular orientations present in a single unit cell of an oligoacene herringbone aggregate.69 The anisotropic properties of the low-lying excitations in crystalline pentacene should have immediate impact on singlet fission. In ref 17 it was shown that a similarly parametrized Frenkel/CT exciton Hamiltonian as the one employed here supports significant coupling between CT states and the multiexciton (“TT”) states, without disturbing the unpolarized absorption spectral line shape. With the more accurate parametrization obtained by reproducing both polarization components in hand, further investigation of singlet fission in pentacene is warranted, and will form the basis of future investigations.
made in ref 58. The correspondingly larger Frenkel/CT exciton mixing in pentacene is accommodated in the current model by allowing for extended charge-separated states with electron− hole separations out to 20 Å.17 Notably, in ref 25 only nearestneighbor CT states were incorporated, necessitating an unphysically small energy for ionizing a local Frenkel exciton into the (1/2,1/2) charge-separated pair. Interestingly, several groups have accounted for the satellite bands (B2,B3) in the b-polarized spectrum by considering only electronic excitations (Frenkel and CT) via the Bethe−Salpeter equation, and have attained satisfactory agreement with experiment.19−22 This has also been shown for TIPSpentacene.64 Hence, one may question the importance of vibronic coupling in accounting for B2 and B3. Figure 5a demonstrates that after removing vibronic coupling the bands are significantly attenuated but retain roughly the same spectral positions as observed in experiment, in rough agreement with refs 19−22. This is not the case, however, for the component polarized perpendicular to b. Without vibronic coupling the spectrum in Figure 5b no longer resembles the experimental spectrum; the majority of the ⊥b oscillator strength is retained by the lowest energy excitation (A1), which is so strongly blueshifted that the DS is roughly double the measured value. The greater impact of vibronic coupling on the ⊥b spectrum is consistent with the greater Frenkel character of the A1 and A2 peaks. Hence, vibronic coupling is necessary for achieving quantitative agreement with experiment. The higher energy B2, B3, ... and A2, A2′, ... transitions are a complex mixture of vibronic satellites and excitons of mixed Frenkel and CT character, in agreement with the assessment of Roth et al.28 As shown in earlier works41,42,61 strong Frenkel/CT mixing can mimic Coulomb coupling in creating H- and J-like exciton bands defined by the ordering of the excitons: in J-like exciton bands the lowest state has wave vector k = 0 consistent with a positive band curvature, while in H-like bands the highest exciton has k = 0 and the band curvature is negative. The greatly enhanced ratio of the B1 to B2 oscillator strengths observed in the b-polarized spectrum of pentacene, more than a factor of 2 larger than the 0−0/0−1 ratio for the monomer in solution, as well as the large red shift of B1, are spectral signatures of J-aggregation48 and arise from the positive curvature of the lowest-energy exciton band. The calculated curvature is indeed positive and the overall band dispersion is in excellent agreement with that measured by Roth et al. using EELS28 (see Figure 8). Furthermore, a large positive curvature of the lowest energy band also predicts J-like characteristics for the photoluminescence (PL) spectrum,48,52 namely a large 0− 0/0−1 ratio which decreases with temperature, as is the case for tetracene.65−67 In this regard, Anger et al. has shown that PL arising from the lower Davydov exciton in pentacene is characterized by a large 0−0/0−1 ratio (>10) which decreases precipitously with temperature.68 In stark contrast, the (mainly) a-polarized spectrum in pentacene maintains a progression in which the A1/A2 ratio is suppressed relative to the 0−0/0−1 ratio for a monomer in solution, as is characteristic of an H-aggregate.48 This arises from the negative curvature of the band containing the mainly apolarized upper Davydov component (see Figure 7b), which agrees well with the EELS measurements of Roth et al.28 We point out that although the lower Davydov component (B1) is red-shifted from the 0−0 peak in solution, as expected for Jaggregates, the upper Davydov component (A1) also remains slightly red-shifted, despite its H-like nature. This underscores
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b07163. More complete descriptions of the experiment and pentacene samples; additional information about the parametrization of the pentacene Hamiltonian; details regarding the absorption spectrum calculations and phase convention used in choosing the signs of the electron and hole transfer integrals (PDF)
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest. 22145
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ACKNOWLEDGMENTS F.C.S. is supported by the National Science Foundation, Grant DMR-1505437. Y.R. thanks Dr. Colin Nuckolls for his support in the preparation of pentacene samples and Yajing Wu for her assistance in the experimental setup. The experimental work was supported by the Honda Research Institute, USA.
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