Enhanced Davydov Splitting in Crystals of a Perylene Diimide

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Enhanced Davydov Splitting in Crystals of a Perylene Diimide Derivative Ashli Austin, Nicholas J Hestand, Ian G McKendry, Chuwei Zhong, Xuanyu Zhu, Michael J. Zdilla, Frank C. Spano, and Jodi M. Szarko J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b00283 • Publication Date (Web): 14 Feb 2017 Downloaded from http://pubs.acs.org on February 22, 2017

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The Journal of Physical Chemistry Letters

Enhanced Davydov Splitting in Crystals of a

Perylene Diimide Derivative

Ashli Austin†, Nicholas J. Hestand§, Ian G. McKendry§‡, Chuwei Zhong§, Xuanyu Zhu†, Michael J. Zdilla§‡, Frank C. Spano§*, and Jodi M. Szarko†*

†Department of Chemistry, Lafayette College, Easton, Pennsylvania 18042, United States §Department of Chemistry and ‡Center for the Computational Design of Functional Layered Materials, Temple University, Philadelphia, Pennsylvania 19122, United States

AUTHOR INFORMATION Corresponding Authors *[email protected] ,*spano@temple.

ABSTRACT: We report the polarized absorption spectra of high quality, thin crystals of a perylene diimide (PDI) species with branched side chains (B2). The absorption spectrum shows

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exemplary polarization-dependent H-like and J-like aggregate behavior upon orthogonal excitation, with a sizable Davydov splitting (DS) of 1230 cm-1 and peak to peak splitting of 3040 cm-1. The experimental results are compared to theoretical calculations with remarkable agreement. The theoretical analysis of the polarized absorption spectra shows evidence of a high degree of intermolecular charge transfer, which, along with Coulombic coupling, conspire to create the unprecedented DS for this family of dye molecules. The large polarization dependence of the electronic spectra is attributed to the unique twisted crystal structure, in which a substantial rotational displacement exists between neighboring chromophores within a π-stack. These results highlight the strong sensitivity of the Davydov splitting to intermolecular geometry in PDI systems.

TOC GRAPHICS

KEYWORDS Polarization spectroscopy, charge transfer, Coulomb coupling, unit cell, pleochroism, organic electronics


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Over the past several years, organic optoelectronic materials have seen vast improvements in performance and device implementation.1-3 Progress in this field has been accelerated by combined efforts in the synthesis, characterization, and theoretical analysis of the structural and electronic properties of these electronically active systems.4-8 Specifically, the elucidation and manipulation of π-π stacking interactions has been crucial in driving this field forward as the nature of such intermolecular interactions has a profound influence on the macroscopic properties of the material. Perylene diimide (PDI) has been a particularly prolific conjugated benchmark system,9-11 in part due to the wide range of side chains that can be systematically varied to control the crystal packing arrangement and intermolecular interactions in the solid state.12 The packing of PDI crystals is typically a slipped stack13 or twisted “sandwich” stack14 structure. PDI crystals with one molecule per unit cell can show red or blue spectral shifts that have been attributed to J- or H-aggregates, respectively.11 Such classifications can be verified by appealing to vibronic spectral signatures, which are often more reliable than spectral shifts.4 Perlyene-based dyes display pronounced vibronic progressions in their solution (monomer) absorption spectra due to a strongly coupled symmetric ring stretching mode. The distribution of oscillator strength among the vibronic peaks is impacted by intermolecular interactions: generally, in J- (H-) aggregates, the oscillator strength of the lowest-energy vibronic peak increases (decreases) relative to the first sideband with increasing intermolecular coupling.4 In packing arrangements hosting two or more molecules per unit cell, the oscillator strength is divided among the orthogonally polarized lower and upper Davydov components (LDC and UDC, respectively), which generally exhibit red and blue spectral shifts relative to the monomer (see Figure1). When the Davydov splitting (DS) between the two components is sufficiently large – larger than the bandwidth derived from


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translationally equivalent molecules within a given sublattice –, the LDC should take on the aforementioned vibronic characteristics of J-aggregates, while the UDC should display vibronic signatures to H-aggregates.15 Until now, no clear examples of this phenomenon have appeared in the literature because packing arrangements consistent with large DS signatures are infrequent. Here we discuss a benchmark PDI system with unprecedented optical and polarization properties. The crystallographic information for N,N’-Bis(3-pentyl)perylene-3,4,9,10-bis(dicarboximide) (B2) shows that it has the appropriate crystal structure to support Davydov splitting (Table S1).16 Specifically, the molecules π-stack in a unique twisted “sandwich” structure such that there is a substantial angle between the transition

dipole

moment

(TDM)

of

neighboring π-stacked molecules (Figure 2a). (There are eight molecules per unit cell for B2 crystals. However, the large intermolecular coupling Figure 1. Energy level diagram for a molecular dimer. When the transition dipole moments are not parallel, both the upper and lower states absorb light at orthogonal polarizations, giving rise to the upper and lower Davydov components observed spectroscopically.

between

nearest-neighbor

inequivalent molecules within a given π-stack dominates the DS, leading to the appearance of only two main Davydov components) By taking the sum and difference of the nearestneighbor TDMs, denoted by the blue arrows

in Figure 2, the TDMs of the two Davydov components result. As can be appreciated from Figure 2b, one of the Davydov components is oriented mainly along the short axis of the B2 crystal, while the other is oriented mainly along the long-axis of the B2 crystal. Polarized


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absorption

measurements

(see

below)

identify the LDC as mainly short-axis polarized while the UDC is long-axis polarized.

Furthermore,

the

close

interplanar distances between neighboring Figure 2. a) The crystal structure of nearestneighbor π-stacked B2 molecules with origins at the lattice points (0.5,0,0.5) and (0.5,0.5,0.5). The b-axis corresponds to the crystal’s long axis while the a- and c-axis project onto the crystal’s short axis. The projections of the transition dipole moments are shown as blue arrows. b) The sum and difference of the transition dipole moments. The sum, which corresponds to the LDC, is nearly parallel to the short crystal axis while the difference, which corresponds to the UDC, is nearly parallel to the long crystal axis. Both the sum and difference have nearly equal lengths, indicating similar oscillator strengths for the UDC and LDC. The remaining 3 pairs of inequivalent molecules within the unit cell are characterized by similar transition dipole moment projections.

π-stacked B2 molecules suggest large intermolecular

interactions

that

should

result in a sizable DS. Hence, B2 crystals serve as an ideal system to study the nature of the UDC and LDC. The image of isolated B2 crystals (Figure 3a)

shows

the

morphology

of

the

crystallites monitored in this work. The maximum absorbance ranges from 0.1-0.8, indicating a typical crystal thickness of 60500 nm. These thin, high quality crystals

are ideal for polarized absorption studies. Crystal images were also taken using polarized light at two incident polarization angles (Figure 3b and Figure 3c). A clear color change of reddishorange to purple is observed as the electric field vector of the light source rotates from alignment along the long axis to the short axis of the crystal. This phenomenon, called pleochrosim, is quantified via measurements of the wavelength dependent polarized absorbance at 590 nm and 500 nm for the two B2 crystals (Figures 3d and 3e) which are approximately orthogonal to each other. The dichroic ratios (D) at 500 nm and 590 nm were determined using ∥


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/∥ , where ∥ ( ) is the absorbance of the crystal with the electric field parallel (perpendicular) to the long axis. At 590 nm, the averaged dichroic ratio is D = −0.88 ±0.07 while at 500 nm, D = 0.15 ± 0.01. The high negative value for the dichroic ratio at 590 nm is consistent with the observed color change of the crystal as the polarization vector is rotated from the long crystal axis to the short crystal axis. Polarized absorption spectra of a single B2 crystal are shown in Figure 4a. When the incident light is polarized 90° relative to the long axis, the spectrum with the peak maximum, labeled a1, results. The a1 peak occurs at 16920 cm-1 (591 nm) and is red shifted from the 0-0 absorption peak of Figure 3. a) The unpolarized image of spatially separated B2 crystals. For all images, the black scale bar represents 40 μm. b,c) The polarized images of the same B2 crystals shown in a). The direction of the incident electric field is indicated on each figure. d,e) The polarization dependent absorbance of the area marked with a light blue triangle (d) or green pentagon (e) in image b). For the results shown in d) and e), the 0° polarization orientation is equal to the orientation of the red arrow shown in image b).

monomeric B2 in chlorobenzene (see Figure 4a) by 2160 cm-1 (67 nm). We therefore assign this spectrum to the LDC. In contrast, the spectrum at 0° incident excitation (long-axis polarized) is blue shifted relative to the solution spectrum.

The peak maximum (b2) at 19960 cm-1 (501 nm) is about 900 cm-1 above the 0-0 peak in the B2 monomer spectrum. Hence, we assign the 0° spectrum to the UDC. Both Davydov components exhibit pronounced vibronic structure due to the 1400 cm-1 ring stretching mode, which is also present in the solution spectrum in Fig. 5a. Interestingly, the line shapes corresponding to the LDC and UDC behave just like J- and H-aggregates, respectively, with respect to the


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aforementioned vibronic signatures. In addition to the large spectral red shift, the a1/a2 ratio in the LDC is enhanced by about 10% compared to the corresponding quantity in the solution spectrum. The H-like attenuation of the b1/b2 ratio in the UDC compared to the monomer value is far more dramatic.4 By superimposing the polarized spectra taken at 10° intervals, two isobestic points are observed; one is at 21,500 cm-1 (465 nm) and the other is at 19200 cm-1 (520 nm). Furthermore, the dichroic ratio between the H-like and J-like components is near unity when the experimental spectra are fit using a linear analysis of the LDC and UDC components, indicating that the corresponding transition dipole moments project nearly equally onto the plane normal to excitation (see Figure 2), which is tentatively ascribed to the 201 or 301 exposed crystal planes. As a comparative system, the polarized absorption spectra of crystals made from N,N’Dipentyl-3,4,9,10-perylenedicarboximide (C5) are shown in Figure 4b. The optical properties of molecules similar to C5 have also been studied previously.1, 13 C5 and B2 have the same molar mass, but they differ by the geometry of their pendent aliphatic side chains, and, consequently, have vastly different crystal structures. B2 is monoclinic and belongs to the P21/c space group while C5 is triclinic and belongs to the 1 space group. Most importantly, C5 has a slipped stack morphology with only a single molecule per unit cell and, therefore, shows no Davydov splitting (see Table S2). The polarized absorption spectra of C5 show that the overall absorption spectral range is similar to B2, but does not contain two Davydov components. The dichroic ratio of the C5 crystal is 0.93 at 590 nm; the change in intensity of the absorption as a function of polarization angle illustrates that these are also high quality crystals.


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700 0.8

600

A

Wavelengt h (nm) 500 450

The 90° spectral offsets, along with the 400

presence of two isosbestic points in the B2

a1

a

b2

0.6

spectra,

a2

0.4

indicate

unambiguously

the

presence of two Davydov components with

0.2

b1

0.0 15000

90º 0º

20000 -1 Phot on Energy (cm )

Wavelength (nm) 600 500 450

700

a large (a1-b1) splitting of 1230 cm-1.17 To 25000

the best of our knowledge, this is the largest DS observed in perylene-, rubrene-,

400

or oilgoacene-based systems. The splitting

b 0.8

observed in other PDI derivatives is

0.6 A

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typically under 300 cm-1,18-19 mainly

0.4 0.2

-45º 45º

because the two unit cell molecules are in

0.0 15000

20000 -1 Photon Energy (cm )

25000

separate π-stacks in most PDI crystallites reported.

Figure 4. The polarized absorption spectrum of a) B2 and b) C5. Spectra are recorded at 10° increments. The crystal’s long axis is defined as 0°. Left insets: the molecular structure of a) B2 b) C5. Right insets: crystal morphology of a) B2 and b) C5.

Moreover,

the

peak-to-peak

splitting (a1-b2) is much larger at 3040 cm1

, so the pleochroic effect is further

enhanced in these crystals. In contrast, the

C5 crystals change from reddish-brown to colorless, which depicts an intensity change in the polarization rather than a spectral shift in the spectra from Davydov splitting. In the polarization dependent spectra shown in Figure 4b, no clear spectral shifts are observed. Pleochroic molecules have been established materials used in liquid crystal displays.20 More recently, donor-acceptor cocrystals have also shown a color change as a function of incident polarization angle.21 In B2, the pleochroic effect originates from a single molecular system.


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B2 has already shown promise as a material for use in photovoltaic and field effect transistor devices.22-23 It has also been shown that B2 retains some crystallinity in blended films.24 To analyze and manipulate the optoelectronic properties of this material, it is necessary to more fully comprehend the nature of spectral response. To understand the UDC and LDC spectral shapes and how they relate to the underlying exciton interactions, we employed a Holstein-style Hamiltonian that takes into account the strong coupling of the main (S0-S1) electronic transition in monomeric B2 to the symmetric ring stretching mode at approximately 1400 cm-1. The latter is the source of the pronounced vibronic progressions observed in the solution spectrum, which is modelled in Figure 5a with the parameters, all extracted from experiment, reported in the SI. To model the crystal, we considered a 100-stack crystallite with 10 molecules per stack within the context of the Frenkel/charge-transfer Holstein Hamiltonian, which includes all pair-wise Coulombic interactions as well as intermolecular charge-transfer (CT). This Hamiltonian is highly successful in describing the photophysics of PDI crystals.12, 18, 25 Our Hamiltonian was parameterized mainly through ab-initio calculations based on planar PDI molecules (without the B2 side-chains), as fully detailed in the SI. Briefly, the intermolecular interactions were evaluated based on a model crystal with molecular positions consistent with the B2 crystal structure after enforcing the approximate C2 symmetry about the (0.25,b,0.25)-axis within the unit cell. The Coulombic interactions were evaluated from atomic transition charge densities26-28 determined from time-dependent density functional theory (TD-DFT) calculations, and screened by a dielectric constant of ε=329 while the nearest-neighbor electron and hole transfer integrals, and , were extracted from DFT calculations of PDI dimers following previous methods.30-32 We also calculated the vibronic coupling parameters for the charge-transfer states using DFT as detailed previously.12 The only adjustable parameters were the energy of the nearest-neighbor


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CT state, which was positioned 1200 cm-1 above its parent Frenkel state,

an overall

solution-to-crystal spectral red shift of 500 cm-1, and an intrinsic linewidth of 550 cm-1 used in the Gaussian line shape function for all optical transitions. The CT energy is entirely consistent with values used to describe

similar

systems.12

Note

that

assuming C2 symmetry within the unit cell results in identical nearest-neighbor CT Figure 5. a) The calculated monomer absorption spectrum (solid) is compared to experimental spectrum (dotted) in a chlorobenzene solution. b) The calculated crystal spectrum for various polarization angles assuming excitation normal to the 301 plane (see SI for details).

energies and integrals for all π-stacks. This allowed us to minimize the number of adjustable parameters without significantly altering our main conclusions. When the

asymmetries are taken into account, our calculations predict additional (but much smaller) spectral splittings as discussed in the SI. Figure 5b shows the calculated crystal spectra as a function of polarization angle, to be compared with Figure 4a (see also Figure 6a). The excellent agreement between theory and experiment with respect to the polarization dependence, the DS, the dichroic ratio of the 0° and 90° spectra, and the finer vibronic features inspires confidence in the model and in its ability to accurately capture the underlying photophysics of this system. We note that the dichroic ratio of the 0° and 90° spectrum is strongly dependent on the crystal orientation relative to the incident light vector. Our simulations most accurately reproduce our measured spectra when the crystal


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is oriented such that the 301 or 201 faces are normal or nearly normal to the incident photon source although a range of n01 faces do an acceptable job (see Supporting Information). X-ray and electron diffraction results confirm that the b axis orientation is parallel to the long crystal axis in these systems, however we have not been able to index the crystal orientation on the glass slide because 1) the crystals are too small for XRD, and 2), the glass slide is incompatible with small area electron diffraction (SAED) analysis. The SAED results on drop cast crystals scraped away also confirm that the b axis is parallel to the long axis as evidenced by the systematic absence requirement of the P21/c space group in the b direction: k = 2n (Figure S12) However the a and b directions could not be indexed with certainty, although the SAED images are consistent with the n01 orientations implicated by theory and spectroscopy. Investigations are underway to definitively confirm this orientation. In order to appreciate the roles that the Coulomb and CT interactions play in defining the B2 absorption spectrum, we show in figures 6b and 6c simulations when either the charge-transfer integrals or Coulombic interactions are neglected, respectively. By comparing these simulations to experiment, we find that the large observed DS derives from both coupling sources. This is in contrast to the oligoacenes, which show a significantly smaller DS due almost entirely to Frenkel/CT mixing.33 The difference here is that the S0-S1 transition dipole moment in PDI is an order of magnitude larger than that corresponding to the (short-axis polarized) transition in tetracene or pentacene, leading to much stronger Coulombic coupling. In B2, the influence of the CT states is strongest in the J-like LDC; Figure 6c show that most of the 2000 cm-1 bathochromic shift arises from the coupling between the Frenkel and CT excitons. Frenkel/CT mixing is also responsible for the substantial oscillator strength in the spectral vicinity of the vibronic sidebands (a2-a4). Essentially, the higher-energy CT band borrows oscillator strength from the


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Frenkel band. Figure 6b shows that it is not possible to adequately reproduce the LDC component using Coulombic coupling alone. In contrast, the UDC is entirely H-like and can be reasonably well reproduced when only Coulomb coupling is considered (Figure 6b) suggesting that the spectral signatures of the UDC are driven primarily by Coulombic coupling. The full calculation of the UDC (Figure

6a)

captures

both

the

drastic

reduction in the first vibronic band (b1) relative to the second band (b2) and the large Figure 6. a) The calculated 0° and 90° spectra are compared directly to experiment (dotted lines). b) The calculated spectra neglecting charge-transfer interactions ( 0) are compared to experiment. c) The calculated spectra neglecting Coulomb coupling are compared to experiment.

blue shift of the main peak b2. In conclusion, we have shown that B2 crystals display a large Davydov splitting, unprecedented within the rylene family,

driven by a combination of long-range Coulomb coupling and short-range CT-mediated coupling. The applications for these crystals are numerous. The orthogonal orientation of the transitions allows for the possibility of recording electronic properties, such as mobility, in the LDC and UDC simultaneously. The contributions of UDC and LDC have also been a recent topic of discussion regarding the efficiency of singlet fission where intermolecular CT plays a crucial role.34-36 We believe that B2 may provide an ideal system for understanding singlet fission and, in general, the elaborate interplay between CT and Coulomb coupling in driving the


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photophysical response of organic molecular crystals. Additionally, the polarization control afforded by B2 and related perlyenes may play a key role in elucidating the relationship between transport (charge and energy) and photophysical properties, as both strongly depend on the generally anisotropic nature of intermolecular coupling. Ultimately, such information may allow for an unprecedented level of control in the design of the next generation of optoelectronic materials.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. Experimental details, polarization spectroscopy setup, x-ray and SAED characterization, and theoretical analysis details are included. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Notes Any additional relevant notes should be placed here. The authors declare no competing financial interests. ACKNOWLEDGMENT A.A was funded by the Bolton Fund at Lafayette College. X.Z. was funded by the EXCEL Program at Lafayette College. F.C.S is supported by the NSF, grant No. DMR-1505437. Bill Miles is acknowledged for helpful discussions.


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References (1) Briseno, A. L.; Mannsfeld, S. C. B.; Reese, C.; Hancock, J. M.; Xiong, Y.; Jenekhe, S. A.; Bao, Z.; Xia, Y. Perylenediimide Nanowires and Their Use in Fabricating Field-Effect Transistors and Complementary Inverters. Nano Lett. 2007, 7, 2847-2853. (2) Hoeben, F.; Herz, L.; Daniel, C.; Jonkheijm, P.; Schenning, A.; Silva, C.; Meskers, S.; Beljonne, D.; Phillips, R.; Friend, R.; Meijer, E. Efficient Energy Transfer in Mixed Columnar Stacks of Hydrogen-Bonded Oligo(P-Phenylene Vinylene)S in Solution. Angew. Chem. Int. Ed. 2004, 43, 1976-1979. (3) Zhang, F.; Inganas, O.; Zhou, Y.; Vandewal, K. Development of Polymer–Fullerene Solar Cells. Natl. Sci. Rev. 2016, 3, 222-239. (4) Spano, F. C. The Spectral Signatures of Frenkel Polarons in H- and J-Aggregates. Acc. Chem. Res. 2010, 43, 429-439. (5) Würthner, F. Perylene Bisimide Dyes as Versatile Building Blocks for Functional Supramolecular Architectures. Chem. Comm. 2004, 2004, 1564-1579. (6) Polkehn, M.; Tamura, H.; Eisenbrandt, P.; Haacke, S.; Mery, S.; Burghardt, I. Molecular Packing Determines Charge Separation in a Liquid Crystalline Bisthiophene-Perylene Diimide Donor-Acceptor Material. J. Phys. Chem. Lett. 2016, 7, 1327-1334. (7) Son, M.; Park, K. H.; Shao, C. Z.; Wurthner, F.; Kim, D. Spectroscopic Demonstration of Exciton Dynamics and Excimer Formation in a Sterically Controlled Perylene Bisimide Dimer Aggregate. J. Phys. Chem. Lett. 2014, 5, 3601-3607.


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(8) Zhan, X. W.; Facchetti, A.; Barlow, S.; Marks, T. J.; Ratner, M. A.; Wasielewski, M. R.; Marder, S. R. Rylene and Related Diimides for Organic Electronics. Adv. Mater. 2011, 23, 268284. (9) Sung, J.; Nowak-Król, A.; Schlosser, F.; Fimmel, B.; Kim, W.; Kim, D.; Würthner, F. Direct Observation of Excimer-Mediated Intramolecular Electron Transfer in a CofaciallyStacked Perylene Bisimide Pair. J. Am. Chem. Soc. 2016, 138, 9029-9032. (10) Wasielewski, M. R. Self-Assembly Strategies for Integrating Light Harvesting and Charge Separation in Artificial Photosynthetic Systems. Acc. Chem. Res. 2009, 42, 1910-1921. (11) Wurthner, F.; Saha-Moller, C. R.; Fimmel, B.; Ogi, S.; Leowanawat, P.; Schmidt, D. Perylene Bisimide Dye Assemblies as Archetype Functional Supramolecular Materials. Chem. Rev. 2016, 116, 962-1052. (12) Gisslén, L.; Scholz, R. Crystallochromy of Perylene Pigments: Influence of an Enlarged Polyaromatic Core Region. Phys. Rev. B 2011, 83, 155311. (13) Struijk, C. W.; Sieval, A. B.; Dakhorst, J. E. J.; van Dijk, M.; Kimkes, P.; Koehorst, R. B. M.; Donker, H.; Schaafsma, T. J.; Picken, S. J.; van de Craats, A. M.; Warman, J. M.; Zuilhof, H.; Sudhölter, E. J. R. Liquid Crystalline Perylene Diimides: Architecture and Charge Carrier Mobilities. J. Am. Chem. Soc. 2000, 122, 11057-11066. (14) Ghosh, S.; Li, X.; Stepanenko, V.; Würthner, F. Control of H and J

Type Π Stacking

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(15) Kistler, K. A.; Pochas, C. M.; Yamagata, H.; Matsika, S.; Spano, F. C. Absorption, Circular Dichroism, and Photoluminescence in Perylene Diimide Bichromophores: PolarizationDependent H- and J-Aggregate Behavior. J. Phys. Chem. B 2012, 116, 77-86. (16) Maniukiewicz, W.; Bojarska, J.; Olczak, A.; Dobruchowska, E.; Wiatrowski, M. 2,9-Di-3Pentylanthra[1,9-Def:6,5,10- D&Apos;E&Apos;F&Apos;]Diisoquinoline-1,3,8,10-Tetrone Acta Cryst 2010, E66, 2570-2571. (17) Beljonne, D.; Yamagata, H.; Bredas, J. L.; Spano, F. C.; Olivier, Y. Charge-Transfer Excitations Steer the Davydov Splitting and Mediate Singlet Exciton Fission in Pentacene. Phys. Rev. Lett. 2013, 110, 226402. (18) Hoffmann, M.; Schmidt, K.; Fritz, T.; Hasche, T.; Agranovich, V.; Leo, K. The Lowest Energy Frenkel and Charge-Transfer Excitons in Quasi-One-Dimensional Structures: Application to Meptcdi and Ptcda Crystals. Chem. Phys. 2000, 258, 73-96. (19) Mizuguchi, J.; Tojo, K. Electronic Structure of Perylene Pigments as Viewed from the Crystal Structure and Excitonic Interactions. J. Phys. Chem. B 2002, 106, 767-772. (20) Long, T. M.; Swager, T. M. Using “Internal Free Volume” to Increase Chromophore Alignment. J. Am. Chem. Soc. 2002, 124, 3826-3827. (21) Blackburn, A. K.; Sue, A. C. H.; Shveyd, A. K.; Cao, D.; Tayi, A.; Narayanan, A.; Rolczynski, B. S.; Szarko, J. M.; Bozdemir, O. A.; Wakabayashi, R.; Lehrman, J. A.; Kahr, B.; Chen, L. X.; Nassar, M. S.; Stupp, S. I.; Stoddart, J. F. Lock-Arm Supramolecular Ordering: A Molecular Construction Set for Cocrystallizing Organic Charge Transfer Complexes. J. Am. Chem. Soc. 2014, 136, 17224-17235.


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(22) Kim, S. S.; Bae, S.; Jo, W. H. A Perylene Diimide-Based Non-Fullerene Acceptor as an Electron Transporting Material for Inverted Perovskite Solar Cells RSC Adv. 2016, 6, 1992319927. (23) Wiatrowski, M.; Dobruchowska, E.; Maniukiewicz, W.; Pietsch, U.; Kowalski, J.; Szamel, Z.; Ulanski, J. Self-Assembly of Perylenediimide Based Semiconductor on Polymer Substrate. Thin Solid Films 2010, 518, 2266-2270. (24) Weintraub, M. T.; Xhakaj, E.; Austin, A. The Effects of Donor: Acceptor Intermolecular Mixing and Acceptor Crystallization on the Composition Ratio of Blended, Spin Coated Organic Thin Films. J. Mater. Chem. C 2016, 4, 7756-7765. (25) Hestand, N. J.; Spano, F. C. Interference between Coulombic and Ct-Mediated Couplings in Molecular Aggregates: H- to J-Aggregate Transformation in Perylene-Based π-Stacks. J. Chem. Phys. 2015, 143, 244707. (26) Beljonne, D.; Cornil, J.; Silbey, R.; Millie, P.; Bredas, J. L. Interchain Interactions in Conjugated Materials: The Exciton Model Versus the Supermolecular Approach. J. Chem. Phys. 2000, 112, 4749-4758. (27) Chang, J. C. Monopole Effects on Electronic Excitation Interactions between Large Molecules .1. Application to Energy-Transfer in Chlorophylls. J. Chem. Phys. 1977, 67, 39013909. (28) Kistler, K. A.; Spano, F. C.; Matsika, S. A Benchmark of Excitonic Couplings Derived from Atomic Transition Charges. J. Phys. Chem. B 2013, 117, 2032-2044.


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(29) El-Nahhas, M. M.; Abdel-Khalek, H.; Salem, E. Structural and Optical Properties of Nanocrystalline 3,4,9,10-Perylene-Tetracarboxylic-Diimide Thin Film. Adv. Cond. Matter Phys. 2012. (30) Mikolajczyk, M. M.; Czyznikowska, Z.; Czelen, P.; Bielecka, U.; Zalesny, R.; Toman, P.; Bartkowiak, W. Quantum Chemical Study of Hole Transfer Coupling in Nucleic Acid Base Complexes Containing 7-Deazaadenine. Chem. Phys. Lett. 2012, 537, 94-100. (31) Senthilkumar, K.; Grozema, F. C.; Bickelhaupt, F. M.; Siebbeles, L. D. A. Charge Transport in Columnar Stacked Triphenylenes: Effects of Conformational Fluctuations on Charge Transfer Integrals and Site Energies. J. Chem. Phys. 2003, 119, 9809-9817. (32) Valeev, E. F.; Coropceanu, V.; da Silva, D. A.; Salman, S.; Bredas, J. L. Effect of Electronic Polarization on Charge-Transport Parameters in Molecular Organic Semiconductors. J. Am. Chem. Soc. 2006, 128, 9882-9886. (33) Hestand, N. J.; Yamagata, H.; Xu, B.; Sun, D.; Zhong, Y.; Harutyunyan, A. R.; Chen, G.; Dai, H.-L.; Rao, Y.; Spano, F. C. Polarized Absorption in Crystalline Pentacene: Theory Vs Experiment. J. Phys. Chem. C 2015, 119, 22137-22147. (34) Eaton, S. W.; Shoer, L. E.; Karlen, S. D.; Dyar, S. M.; Margulies, E. A.; Veldkamp, B. S.; Ramanan, C.; Hartzler, D. A.; Savikhin, S.; Marks, T. J.; Wasielewski, M. R. Singlet Exciton Fission in Polycrystalline Thin Films of a Slip-Stacked Perylenediimide. J. Am. Chem. Soc. 2013, 135, 14701-14712. (35) Smith, M. B.; Michl, J. Recent Advances in Singlet Fission. Annu. Rev. Phys. Chem. 2013, 64, 361-386.


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(36) Renaud, N.; Sherratt, P. A.; Ratner, M. A. Mapping the Relation between Stacking Geometries and Singlet Fission Yield in a Class of Organic Crystals. J. Phys. Chem. Lett. 2013, 4, 1065-1069.


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Enhanced Davydov Splitting in Crystals of a Perylene Diimide

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