Symmetry-Directed Control of Electronic Coupling for Singlet Fission

Letter pubs.acs.org/JPCL

Symmetry-Directed Control of Electronic Coupling for Singlet Fission in Covalent Bis−Acene Dimers Niels H. Damrauer* and Jamie L. Snyder Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309, United States S Supporting Information *

ABSTRACT: While singlet fission (SF) has developed in recent years within material settings, much less is known about its control in covalent dimers. Such platforms are of fundamental importance and may also find practical use in next-generation dye-sensitized solar cell applications or for seeding SF at interfaces following exciton transport. Here, facile theoretical tools based on Boys localization methods are used to predict diabatic coupling for SF via determination of one-electron orbital coupling matrix elements. The results expose important design rules that are rooted in point group symmetry. For Cssymmetric dimers, pathways for SF that are mediated by virtual charge transfer excited states destructively interfere with negative impact on the magnitude of diabatic coupling for SF. When dimers have C2 symmetry, constructive interference is enabled for certain readily achievable interchromophore orientations. Three sets of dimers exploiting these ideas are explored: a bis−tetracene pair and two sets of aza-substituted tetracene dimers. Remarkable control is shown. In one aza-substituted set, symmetry has no impact on SF reaction thermodynamics but leads to a 16-fold manipulation in SF diabatic coupling. This translates to a difference of nearly 300 in kSF with the faster of the two dimers (C2) being predicted to undergo the process on a nearly ultrafast 1.5 ps time scale. inglet fission (SF) has gained prominence as a thirdgeneration solar energy conversion strategy where higher energy photons may be converted to multiple lower-energy material excitations rather than a single excitation plus waste heat.1−5 Much of recent fundamental work has focused on material settings where the impact of singlet exciton delocalization, defect sites, and interfaces are mechanistically important.6−20 From an intellectual perspective but also a practical one having to do with future dye-sensitized solar cell strategies,1 it is important to interrogate SF mechanism in the base setting, that of a dimer. Initial efforts in the community exposed challenges for obtaining high yields,21,22 but recent observationsin acenes23−25 (and in work submitted by Bradforth and Thompson’s groups at USC), carotenoids (to be submitted by the Tauber group at UCSD), and even transient dimers26,27indicates significant promise. However, accessible design rules are not yet in place. Pentacene-based dimers may excel due to driving force as opposed to optimized coupling.23 For tetracene-based systems without the benefit of significant driving force, tools to better intuit the mechanism for SF coupling will help us to understand why, for example, some systems work well (e.g., in work submitted by Bradforth and Thompson’s groups at USC) while others do not.22 Further, such tools can be exploited in the development of next-generation dimer syntheses. We have been interested in geometrically well-defined dimers where tetracene-based chromophore units are juxtaposed in a partially cofacial arrangement.28,29 A prototypical system BT1 is shown in Figure S1 (with the C2ν molecule oriented with chromophores in the xz plane). Synthesis and photophysical

S

© XXXX American Chemical Society

study of systems of this nature (to be reported shortly) were initiated in an effort to understand how interchromophore vibrational motions may alter excited state couplings central to the control of SF rates.19 To interrogate dimers from the basis of theory, we have gravitated toward diabatic descriptions where the mechanism can be more readily intuited in terms of chromophore-localized reactant, intermediate, and product states and their couplings.3,30−35 For acene systems, the mechanism for SF that dominates in importance3,29,31,36 is one where the conversion of the reactant singlet exciton state (herein S0S1) to the multiexcitonic triplet pair state (herein 1TT) is mediated by virtual charge-transfer (CT) states characterized by both electron-transfer (ET) and hole-transfer (HT) pathways (see Figure S2). This means that intuition can be taken further because key interstate diabatic couplingsbetween the reactant S0S1 and the virtual CT states and between the virtual CT states and the product 1TTcan be very adequately described in terms of one-electron orbital couplings in a frontier orbital basis set. To obtain these matrix elements in covalent dimers (as opposed to noncovalent ones31), we have found that Boys orbital localization procedures are remarkably efficient and accurate.29 It is important to mention that other theoretical methods are being developed and applied, which take into account the multiconfigurational nature of the wave functions Received: September 30, 2015 Accepted: October 27, 2015

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couplings are ignored due to the small magnitude of such integrals.30,31 This assumption has been tested for BT1 and holds.29 The end result is again an expression for coupling where a superposition of terms speaks to the interference (constructive or destructive) of ET (via tLL) and HT (via tHH) mediated pathways to SF. This expression will be used throughout this manuscript in the calculation of SF coupling. Breaking Planes in Bis−Tetracenes. As was implied in the Introduction, BT1 presents a key shortcoming for SF photophysics inasmuch as SF coupling vanishes at the structure of the ground state dimer. This can be readily understood as arising because of the so-called “nonhorizontal” coupling terms tHL and tLH and the fact that |hA⟩ and |hB⟩ are antisymmetric functions with respect to a reflection plane lengthwise through the molecule (xz plane in Figure S1) while |lA⟩ and |lB⟩ are symmetric. “Nonhorizontal” refers to the condition that the energy coupling involves a HOMO on one side of the dimer and a LUMO on the other. From this and the results of our vibronic coupling predictions,29 it stands to reason that structures conceptually similar to BT1 but where the plane of symmetry mentioned above is removed, may be interesting SF candidates. This point was recognized in our original work28 where the Longuet−Higgins−Roberts (LHR) approximation was applied.33,48 There, two additional molecules, BT1-trans and BT1-cis, which are shown in Figure 1, were proposed.

relevant for the states involved in SF and that these are also being applied to analyze interstate couplings.37−43 In our previous theoretical and computational interrogations of BT1,28,29 key issues central to this current manuscript emerged. First, in bis−tetracene dimers maintaining the C2ν point-group symmetry (e.g., BT1), diabatic coupling for SF (what will now be called SF coupling throughout) vanishes due to orbital symmetry properties. Second, when the molecule vibrates, SF coupling can emerge, but the motions must break the long-axis symmetry plane (xz in Figure S1); i.e., motions belonging to A2 and B2 irreducible representations.29 Third and most interestingly, quantum pathway interference effects are prominent. For B2 motions where a short-axis (yz) symmetry plane is preserved, the ET and HT pathways to mediated SF destructively interfere and SF coupling is lessened. For A2 motions where a C2 axis is preserved, these pathways constructively interfere, and coupling is enhanced.29 This current work draws on these ideas and asks whether symmetry-directed interference phenomena can serve as a design principle for dimers. Rules emerge that are applicable to a broad range of bis-acene systems. In specific aza-substituted bis-tetracene molecules, remarkable control is predicted. Between two related dimersone with Cs and the other with C2 symmetrythe SF reaction energetics are virtually identical and yet SF rate constants may be expected to differ by nearly a factor of 300 and with the faster species (of C2-symmetry) undergoing SF on an ultrafast time scale. Theoretical Approach. As noted, we have recently exploited facile Boys-localization methods (some details provided in the Supporting Information (SI)) to calculate one-electron orbital coupling matrix elements tAB = ⟨φA|F̂|φB⟩, where F̂ is the Fock operator and where φA and φB refer to frontier orbitals highest occupied molecular orbital (HOMO) or lowest unoccupied molecular orbital (LUMO)on the individual chromophores A or B of the dimer.29 An important consequence of this is being able to estimate SF coupling in covalent dimers according to eq 1.2,3,29,31,44 SF Coupling(S

Figure 1. Drawing and density functional theory (DFT)-optimized ground state geometry for BT1-trans and BT1-cis (ωB97X-D density functional, the 6-31G(d) basis set, and a polarizable continuum model of solvent parametrized for toluene28). The point group symmetries of these two molecules are C2 and Cs, respectively.

1 0S1→ TT)

1

=

|⟨ TT| Hel|1̂ AC⟩⟨1AC| Hel|̂ S0S1⟩ + ⟨1TT| Hel|1̂ CA⟩⟨1CA| Hel|̂ S0S1⟩| ΔECT

≈ | 3/2 (t HLt LL − t LHt HH)| /ΔECT

In Figure 2 are shown localized orbitals |hA⟩, |lA⟩, |hB⟩, and |lB⟩ for both of the molecules (set 1) as well as the calculated Fock matrices. There are several notable qualities to the data. First, for both molecules, a coupling asymmetry is found wherein |tHH| is significantly larger than |tLL|. This is the opposite of what is found for BT129 and for the aza-dimers that will be discussed later. The explanation lies in the nodal patterns of the respective orbitals that are involved in these “horizontal” interchromophore couplings (vide infra). This issue will become particularly important for the aza-dimers discussed next. Second, the nonhorizontal |tHL| and |tLH| terms are larger by more that a factor of 3 for BT1-cis relative to BT1-trans. We had qualitatively predicted this trend using (1) orbital coefficient arguments based the pairing theorem28,49 and (2) application of the LHR approximation.33,48 Arguably the most important point derived from Figure 2 has to do with constructive versus destructive interference of mediated pathways to SF. With the orbital phase convention used in the figure, tHH and tLL exhibit a common sign for both molecules.50 From eq 1 this means that SF coupling will decrease in magnitude when tHL and tLH have a common sign,

(1)

There are several approximations here that have been justified elsewhere. First, direct coupling (see Figure S2) between the reactant S0S1 and the singlet-coupled multiexciton product 1TT is insignificant and ignored.3,29,31,33,36 As such, SF coupling occurs via mediation by virtual charge transfer states 1 AC or 1CA (Anion or Cation on either chromophore), whose energy lies at ΔECT above the reactant S0S1. This condition is common in acene systems.24,28,29,32,40,41,45 Note that a sum of two terms is needed. In the first (involving 1AC), an ETmediated pathway to product is being invoked. In the second (involving 1CA), an HT mediated pathway is operational. The sum of the two pathways comprises the interference, constructive or destructive, needed in the determination of SF coupling (see Figure S2). In the second part of this expression, where one-electron matrix elements tAB have been substituted, the diabatic states relevant for SF are approximated with HOMO and LUMO basis functions on each of the chromophores A and B: |hA⟩, |lA⟩, |hB⟩, and |lB⟩.2,21,30,31,33−35,40,41,46,47 Further, two-electron Coulomb repulsion terms in the description of diabatic state 4457

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interference will always prevail (see SI for examples), provided, as expected, that nearest neighbor interchromophore interactions dominate in the respective determination of tHH and tLL. It is also noted that the overall notion of using symmetry to control SF coupling would broadly apply to acene (anthracene, pentacene, etc.) or substituted-acene dimers because nodal patterns of |h⟩ and |l⟩ generally match those of tetracene. Using eq 1 and previously reported28 values of ΔECT, SF coupling is calculated to be 2.0 meV for BT1-cis and 1.1 meV for BT1-trans (Table S1). It is emphasized that these values are of the same magnitude as the coupling seen for a noncovalent Tc dimer model of crystalline Tc (where SF has quantitative yield) in a high-level model Hamiltonian calculation by Shiozaki and co-workers32 (5.4 meV)51 and in our own estimation of using the Boys methodology (7.3 meV).29 For BT1-cis, where the mediated pathways destructively interfere, the larger relative coupling (compared to BT1-trans) is achieved with significant help from the relatively large |tHL| or |tLH| terms, the significant asymmetry in |tHH| versus |tLL|, and a lower relative value of ΔECT (see Table S1). For the C2symmetric BT1-trans, where all coupling terms are comparatively smaller and where ΔECT is larger, a respectable SF coupling value of 1.1 meV is achieved due to the constructive interference of mediated SF pathways. It is possible to take quantification one step further, using a Marcus-like nonadiabatic rate constant expression (eq 2) derived from second-order perturbation theory31 to estimate kSF.31,45

Figure 2. Localized frontier orbitals orbitals |hA⟩, |lA⟩, |hB⟩, and |lB⟩ and Fock matrices (values in meV) for set 1: BT1-trans (left) and BT1-cis (right). Important “nonhorizontal” one-electron couplings that were zero in BT1 (C2ν symmetry) are shown in red. The viewpoint of these molecules is one in which the methylene group of the bicyclic bridge is headed into the paper.

and it will increase when tHL and tLH have the opposite sign. The former case that is relevant for BT1-cis corresponds to destructive interference between HT and ET mediated pathways to 1TT. SF coupling in this molecule, then, relies on the fact that |tHH| ≠ |tLL|. In the latter case that is relevant for BT1-trans, the HT- and ET-mediated pathways constructively interfere. It is worth emphasizing the clear analogy to what was observed for vibrations in BT1:29 A2 motions that preserve the C2 symmetry element enable constructive interference of pathways, while B2 motions that preserve the reflection plane switch on destructive interference. The generality of these effects has been considered (see details in S.I.). With a common set of frontier orbital basis functions used for related C2 and Cs dimers based on a prechosen (but ultimately arbitrary) phase convention outlined in the SI, it can be seen that it is always the case that tHL = −tLH for C2 systems and tHL = tLH for Cs systems. The reason is tied to the fact that |lA⟩ is symmetric to |lB⟩ after either a C2 ̂ or a σ̂ symmetry operation, whereas |hA⟩ is antisymmetric to |hB⟩ following C2 ̂ but symmetric to |hB⟩ following σ̂ . Constructive interference of pathways for C2 dimers and destructive interference for Cs dimers then demands that tHH and tLL have a common sign. This condition is easy to satisfy and is the case for all of the dimers explored herein. It is possible to switch C2 dimers to destructive interference for SF if the two chromophores are arranged such that tHH and tLL have opposite sign. There are many approaches to interchromophore connectivity (outside of the ones discussed herein) where this will be the case, including, we believe, ones recently explored for pentacene dimers.23 This is shown schematically in Figure S4(i) and discussed in the relevant SI text. Interestingly, for some nonrigid dimers, conformational motions, even when C2 symmetry is maintained throughout, could result in switching between constructive and destructive interference of pathways. Critically for Cs dimers, destructive

k SF ≈

⎛ −(ΔE + λ)2 ⎞ SF ⎟ V 2 × exp⎜ 2 4λkBT ⎝ ⎠ 4π ℏ λkBT 2π

(2)

The quantity ΔESF (E(2 × T1) − E(S1)) has been calculated by us28 to be negative and similar for both BT1-cis and BT1trans with respective values of −117 meV and −119 meV (see Table S2). For the reorganization energy λ, one can draw from recent work analyzing rate constants for SF in a large number (10) of aceneoid systems using a Bixon-Jortner expression that combines both adiabatic and nonadiabatic electron transfer theory.45 Therein, λ is fixed at 130 meV and justified as a typical value. With this, kSF at 298 K is calculated to be 1.9 × 1011 s−1 (τSF = 5.2 ps) for BT1-cis and 5.4 × 1010 s−1 (τSF = 19 ps) for BT1-trans (Table S4). Both values would be expected to compete very favorably with other radiative and nonradiative pathways open to the S1 excited state. The observed excitedstate lifetime τobs for Tc in 298 K toluene is 4.2 ns;52 thus, simple calculations of SF yield (ϕSF = kSF/(kSF + kobs)) indicate unity even for BT1-trans. It should be pointed out that these rate constants are sensitive to λ, and it is possible that for future toluene solution experiments, a value of 130 meV is too low of an estimation by way of ignoring contributions due to solvent. However, it is also the case that solvent reorganization (λsolvent) is not expected to be large given the nonpolar character of toluene. Using a Marcus two-sphere model for λsolvent applicable to electron transfer problems,53 which will thus overestimate λsolvent relevant to the energy transfer problem being studied herein, we calculate a value of order 150 meV. SF time constants with λ(total) = 300 meV have been calculated for comparison purposes (Table S4), and we find of 23.2 and 80.9 ps for BT1-cis and BT1-trans, respectively. While certainly slower, calculated SF yields are still close to unity (0.98 for the slower BT1-trans). 4458

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The Journal of Physical Chemistry Letters Breaking Symmetry with Heteroatoms. The observations above lead us to explore more subtle ways of breaking symmetry in bis-acene analogues of BT1. Synthetic expediency (not discussed here) leads us toward two sets of molecules (both with C2 and Cs members) shown in the respective headers of Figures 3 and 4 (called sets 2 and 3). These systems have a

situation occurs, but now it is for the coupling of the localized HOMO orbitals. (see Figure 2). This of course means that for each of the aza-dimers, the ET-mediated pathway to SF dominates, while for BT1-cis and BT1-trans, the HT-mediated pathway is most important (see Table S1). A second point emphasized is that while the impact of azasubstitution on orbital shape compared to BT1 is subtle (see Figures 3 and 4 in comparison to Figure 2 in our previous work29), important coupling effects arise for sets 2 and 3. For example, quantification via the Fock matrices indicates that one-electron coupling values tHL and tLH, which were rigorously zero in the C2ν-symmetric BT1, are now nonzero (red values in Figures 3 and 4) due to the symmetry breaking imposed by the aza-substitution. We are particularly interested in the symmetry-controlled pathway interference effects that parallel what was seen for BT1-cis and BT1-trans. In both set 2 and set 3, the “horizontal” coupling terms tHH and tLL show a common sign given that both chromophores in each dimer are juxtaposed directly across from each other via the norbornyl bridge (see further discussion in the SI). This means (vide supra) that SF will occur via constructive interference of ET and HT pathways in C2-symmetric species, where tHL and tLH have the opposite sign (aza-BT1-2-C2 and aza-BT1-3-C2) and via destructive interference of these pathways in Cs-symmetric species, where tHL and tLH have a common sign (aza-BT1-2-Cs and aza-BT1-3-Cs). In an important contrast to set 1 (BT1-cis and BT1-trans), dimers in both set 2 and set 3 have larger nonhorizontal coupling magnitudes |tHL| and |tLH| when they are C2-symmetric versus Cs-symmetric; i.e., when SF coupling benefits from constructive interference of pathways. For example, |tHL| = |tLH| = 1.2 meV in aza-BT1-2-Cs, whereas in aza-BT1-2-C2, |tHL| = |tLH| = 4.1 meV. The trend is even more pronounced in set 3, where |tHL| = |tLH| = 5 meV in aza-BT1-3-Cs and a remarkable 27 meV in aza-BT1-3-C2. This effect is also symmetry controlled and appears to originate with how aza-substitution at the periphery of molecule polarizes the respective frontier orbitals at the vicinity of the bridge. In order to calculate diabatic couplings and ultimately estimate rate constants, state energetics are needed (see SI and Table S2). Dimers in set 2 have both vertical and localized S1 energies that are comparable to BT1. Singlets within set 3 are slightly stabilized, but the amount (of order of 20 meV) is unremarkable. CT state energies have also been calculated (Table S3). It is found, as expected, that the oxidized states of aza dimers are destabilized relative to what is found in BT1 (of order 180 meV for set 2 and 250 meV for set 3). This is anticipated to be of practical value when we ultimately work with these compounds in synthesis and photophysical settings where O2 may be present. At the same time, the reduced states of these heteroatom substituted dimers are stabilized by comparable amounts. These energy shifts for the oxidized versus reduced forms counteract each other and, in the end, CT energies calculated for all aza dimers are within 10 meV of that seen in BT1. With values for ΔECT in hand, diabatic couplings for SF can be calculated (Table S1). For set 2, values of 0.12 and 1.5 meV are obtained for aza-BT1-2-Cs and aza-BT1-2-C2, respectively. Because the horizontal coupling elements remain essentially fixed across this set, this >12-fold increase is driven by the constructive interference of pathways to SF as well as the larger nonhorizontal coupling terms for the C2 species. Based on oneelectron couplings and coupling products listed in Table S1,

Figure 3. Localized frontier orbitals orbitals |hA⟩, |lA⟩, |hB⟩, and |lB⟩ and Fock matrices (values in meV) for for set 2: aza-BT1-2-C2 (left) and aza-BT1-2-Cs (right). Important “nonhorizontal” one-electron couplings that were zero in BT1 (C2ν symmetry) are shown in red.

Figure 4. Localized frontier orbitals orbitals |hA⟩, |lA⟩, |hB⟩, and |lB⟩ and Fock matrices (values in meV) for set 3: aza-BT1-3-C2 (left) and azaBT1-3-Cs (right). Important “nonhorizontal” one-electron couplings that were zero in BT1 (C2ν symmetry) are shown in red.

practical advantage inasmuch as their eventual synthesis can exploit a precursor that our group has used in the making of BT1. Aza-substitution may also impart added stability toward oxidation54−56 (vide infra). A first point to address is that, in contrast to BT1-cis and BT1-trans, the aza dimers exhibit a coupling asymmetry (Figures 3 and 4) wherein, |tHH| < |tLL|; i.e., similar to what was encountered for the parent dimer BT1.29 The nature of this asymmetry for all of the molecules discussed in this manuscript can now be rationalized. In sets 2 and 3, and in BT1, the larger relative value of |tLL| is primarily driven by spatial overlap of a single orbital lobe per LUMO (∼ spanning two carbons), located at the point of connection to the bicyclic bridge (Figures 3 and 4). For BT1-cis and BT1-trans, a comparable 4459

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both effects are significant, but the interference of pathways is most important (true for both sets). For set 3, SF couplings are calculated to be 0.59 and 9.90 meV for aza-BT1-3-Cs and azaBT1-3-C2, respectively, indicating an even larger (>16-fold) symmetry-driven increase within the set. The 9.90 meV for azaBT1-3-C2 is particularly large, representing a 35% increase relative to the 7.3 meV that we have calculated for a noncovalent dimer from the tetracene crystal structure (vide supra).29 As was elaborated earlier, the calculated values for ΔESF and diabatic coupling (Tables S2 and S1) can be used to approximate rate constants for SF according to the Marcus expression in eq 2. Again using a reorganization energy of λ = 130 meV (vide supra), SF (298 K) is predicted to occur in 12 ns for aza-BT1-2-Cs, and to then decrease by more than 2 orders of magnitude to 84 ps for aza-BT1-2-C2 (a factor of 143 decrease). The relative difference in time constants is even more dramatic in set 3. There, SF is predicted to occur in azaBT1-3-Cs in 430 ps and to drop to a nearly ultrafast 1.5 ps for aza-BT1-3-C2 where nonhorizontal couplings are larger and where constructive interference-mediated pathways are in place (a factor of 282 decrease). In summary we have explored symmetry-directed design rules for optimizing diabatic coupling for SF in covalent dimers where the mechanism involves mediation via virtual charge transfer states. These rules may be expected to be of significant value for elaborating bis-acene systems where SF driving force is small or even uphill. When a dimer has the common Cs symmetry, the charge-transfer mediated pathways involving electron transfer versus hole transfer destructively interfere and finite SF coupling in these cases relies on the fact that horizontal interchromophore frontier orbital couplings tLL and tHH are unequal. To optimize diabatic coupling for SF, C2symmetric dimers may be envisioned, but care must be taken in how the two chromophores are linked. If done properly, nonhorizontal interchromophore orbital couplings tLH and tHL can be maximized, while at the same time ensuring that electron-transfer and hole-transfer mediated pathways to SF constructively interfere. With such design elements, remarkable control of SF rate constants is possible. In one set of dimers explored herein (set 3), C2 versus Cs symmetry should have no effect on SF reaction thermodynamics, and yet SF rate constants should vary by nearly a factor of 300.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support from the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Science, U.S. Department of Energy, through Grant DE-FG0207ER15890. This work utilized the Carver supercomputer of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231. We thank Dr. Ethan Alguire and Professor Joseph Subotnik of the University of Pennsylvania for preliminary help in calculating one-electron coupling matrix elements and for providing access to their code implementing the Boys localization procedure.

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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.jpclett.5b02186. General figures including a representation of BT1 and a cartoon showing SF coupling pathways in a frontier orbital basis set. Data tables for determination of SF couplings, state energies, and SF rate constants. Summaries of methods used for calculating orbital coupling matrix elements, for calculating state energies, and for calculating CT state energies. A discussion of the generality of symmetry effects on SF coupling in dimers. Cartesian coordinates for the computationally expensive S1‑Locstates of the aza-BT1 dimers. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 4460

DOI: 10.1021/acs.jpclett.5b02186 J. Phys. Chem. Lett. 2015, 6, 4456−4462

Letter

The Journal of Physical Chemistry Letters

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(17) Musser, A. J.; Maiuri, M.; Brida, D.; Cerullo, G.; Friend, R. H.; Clark, J. The Nature of Singlet Exciton Fission in Carotenoid Aggregates. J. Am. Chem. Soc. 2015, 137, 5130−5139. (18) Musser, A. J.; Liebel, M.; Schnedermann, C.; Wende, T.; Kehoe, T. B.; Rao, A.; Kukura, P. Evidence for Conical Intersection Dynamics Mediating Ultrafast Singlet Exciton Fission. Nat. Phys. 2015, 11, 352− 357. (19) Grumstrup, E. M.; Johnson, J. C.; Damrauer, N. H. Enhanced Triplet Formation in Polycrystalline Tetracene Films by Femtosecond Optical-Pulse Shaping. Phys. Rev. Lett. 2010, 105, 257403. (20) Arias, D. H.; Ryerson, J. L.; Cook, J. D.; Damrauer, N. H.; Johnson, J. C. Polymorphism Influences Singlet Fission Rates in Tetracene Thin Films. Chem. Sci. 2015, in press. (21) Johnson, J. C.; Akdag, A.; Zamadar, M.; Chen, X.; Schwerin, A. F.; Paci, I.; Smith, M. B.; Havlas, Z.; Miller, J. R.; Ratner, M. A.; Nozik, A. J.; Michl, J. Toward Designed Singlet Fission: Solution Photophysics of Two Indirectly Coupled Covalent Dimers of 1,3Diphenylisobenzofuran. J. Phys. Chem. B 2013, 117, 4680. (22) Müller, A. M.; Avlasevich, Y. S.; Schoeller, W. W.; Müllen, K.; Bardeen, C. J. Exciton Fission and Fusion in Bis(Tetracene) Molecules with Different Covalent Linker Structures. J. Am. Chem. Soc. 2007, 129, 14240−14250. (23) Sanders, S. N.; Kumarasamy, E.; Pun, A. B.; Trinh, M. T.; Choi, B.; Xia, J. L.; Taffet, E. J.; Low, J. Z.; Miller, J. R.; Roy, X.; Zhu, X. Y.; Steigerwald, M. L.; Sfeir, M. Y.; Campos, L. M. Quantitative Intramolecular Singlet Fission in Bipentacenes. J. Am. Chem. Soc. 2015, 137, 8965−8972. (24) Zirzlmeier, J.; Lehnherr, D.; Coto, P. B.; Chernick, E. T.; Casillas, R.; Basel, B. S.; Thoss, M.; Tykwinski, R. R.; Guldi, D. M. Singlet Fission in Pentacene Dimers. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 5325−5330. (25) Lukman, S.; Musser, A. J.; Chen, K.; Athanasopoulos, S.; Yong, C. K.; Zeng, Z. B.; Ye, Q.; Chi, C. Y.; Hodgkiss, J. M.; Wu, J. S.; Friend, R. H.; Greenham, N. C. Tuneable Singlet Exciton Fission and Triplet-Triplet Annihilation in an Orthogonal Pentacene Dimer. Adv. Funct. Mater. 2015, 25, 5452−5461. (26) Walker, B. J.; Musser, A. J.; Beljonne, D.; Friend, R. H. Singlet Exciton Fission in Solution. Nat. Chem. 2013, 5, 1019−1024. (27) Stern, H. L.; Musser, A. J.; Gelinas, S.; Parkinson, P.; Herz, L. M.; Bruzek, M. J.; Anthony, J.; Friend, R. H.; Walker, B. J. Identification of a Triplet Pair Intermediate in Singlet Exciton Fission in Solution. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 7656−7661. (28) Vallett, P. J.; Snyder, J. L.; Damrauer, N. H. Tunable Electronic Coupling and Driving Force in Structurally Well-Defined Tetracene Dimers for Molecular Singlet Fission: A Computational Exploration Using Density Functional Theory. J. Phys. Chem. A 2013, 117, 10824− 10838. (29) Alguire, E. C.; Subotnik, J. E.; Damrauer, N. H. Exploring NonCondon Effects in a Covalent Tetracene Dimer: How Important Are Vibrations in Determining the Electronic Coupling for Singlet Fission? J. Phys. Chem. A 2015, 119, 299−311. (30) Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R. Microscopic Theory of Singlet Exciton Fission. I. General Formulation. J. Chem. Phys. 2013, 138, 114102. (31) Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R. Microscopic Theory of Singlet Exciton Fission. II. Application to Pentacene Dimers and the Role of Superexchange. J. Chem. Phys. 2013, 138, 114103. (32) Parker, S. M.; Seideman, T.; Ratner, M. A.; Shiozaki, T. Model Hamiltonian Analysis of Singlet Fission from First Principles. J. Phys. Chem. C 2014, 118, 12700−12705. (33) Greyson, E. C.; Vura-Weis, J.; Michl, J.; Ratner, M. A. Maximizing Singlet Fission in Organic Dimers: Theoretical Investigation of Triplet Yield in the Regime of Localized Excitation and Fast Coherent Electron Transfer. J. Phys. Chem. B 2010, 114, 14168− 14177. (34) Beljonne, D.; Yamagata, H.; Bredas, J. L.; Spano, F. C.; Olivier, Y. Charge-Transfer Excitations Steer the Davydov Splitting and 4461

DOI: 10.1021/acs.jpclett.5b02186 J. Phys. Chem. Lett. 2015, 6, 4456−4462

Letter

The Journal of Physical Chemistry Letters (54) Wu, Y. S.; Liu, K.; Liu, H. Y.; Zhang, Y.; Zhang, H. L.; Yao, J. N.; Fu, H. B. Impact of Intermolecular Distance on Singlet Fission in a Series of TIPS Pentacene Compounds. J. Phys. Chem. Lett. 2014, 5, 3451−3455. (55) Herz, J.; Buckup, T.; Paulus, F.; Engelhart, J.; Bunz, U. H. F.; Motzkus, M. Acceleration of Singlet Fission in an Aza-Derivative of TIPS-Pentacene. J. Phys. Chem. Lett. 2014, 5, 2425−2430. (56) Chen, Y.; Shen, L.; Li, X. Effects of Heteroatoms of Tetracene and Pentacene Derivatives on Their Stability and Singlet Fission. J. Phys. Chem. A 2014, 118, 5700−5708.

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DOI: 10.1021/acs.jpclett.5b02186 J. Phys. Chem. Lett. 2015, 6, 4456−4462