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Does Inactive Alkyl Chain Enhance Triplet-Triplet Annihilation of 9,10-Diphenylanthracene Derivatives? Ryuma Sato, Hirotaka Kitoh-Nishioka, Kenji Kamada, Toshiko Mizokuro, Kenji Kobayashi, and Yasuteru Shigeta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01328 • Publication Date (Web): 13 Feb 2018 Downloaded from http://pubs.acs.org on February 20, 2018

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The Journal of Physical Chemistry

Does Inactive Alkyl Chain Enhance Triplet-Triplet Annihilation of 9,10-Diphenylanthracene Derivatives? Ryuma Sato,†,* Hirotaka Kitoh-Nishioka,†,‡ Kenji Kamada,§ Toshiko Mizokuro,ǁǁ Kenji Kobayashi,⊥ and Yasuteru Shigeta†,* †

Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan. ‡

Current address: JST-PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.

§

IFMRI, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31

Midorigaoka, Ikeda, Osaka 563-8577, Japan. ǁǁ

ESPRIT, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan. ⊥Department

of Chemistry, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka, Shizuoka, 422-8529, Japan.

AUTHOR INFORMATION Corresponding Author *Ryuma Sato and * Yasuteru Shigeta. *E-mail: [email protected] and [email protected]

ACS Paragon Plus Environment

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ORCID Hirotaka Kitoh-Nishioka: 0000-0002-6210-3641 Kenji Kamada: 0000-0002-7431-5254 Yasuteru Shigeta: 0000-0002-3219-6007

ABSTRACT It has been hypothesized that alkyl chains are inactive for electron transport processes through the chains. However, our theoretical study unveiled that loop-like alkyl chains can accelerate the electron transfer of triplet-triplet annihilation (TTA) through overlap of the pseudo π-orbital of the alkyl chain. The TTA reaction time (the inverse of the TTA rate) of the dimer models of 9,10-diphenylanthracene (DPA) or the alkyl-strapped derivatives (Cn-sDPAs) in solution was calculated by the sequential charge transfer processes of TTA with the Marcus theory. The for the Cn-sDPAs were much shorter compared to DPA even at long distances and

at various mutual orientations of the dimers. These shortened were due to the large electron coupling matrix elements through the pseudo π-orbital that was extended to the alkyl chains in the singly occupied orbitals. This finding supports the observed superior performance of TTA upconversion (TTA-UC) obtained with Cn-sDPAs.


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1. INTRODUCTION When a photon (for example, green light) is absorbed by a material, longer wavelength light (yellow or red) is generally emitted.1 Photon up-conversion (UC) is the opposite phenomenon, where shorter one (blue light) is emitted after the irradiation of (green) light. Since one photon with short wavelength is made from two photons with long wavelength, the energy of each photon is doubled, while the number of photons is halved.2,3 By installing the UC material on the surface of a solar cell, it can contribute to improvement in efficiency of solar cell, since it is possible to convert near infrared light, which does not contribute to any power generation, to visible light.4-8 Another application of the UC is photoactive cancer therapy, in which an UC light from biological window region (650 nm to 1000 nm) generates active oxygen nearby cancer tissue.9,10 There are several processes known as UC, such as simultaneous two-photon absorption and the multi-step two-photon absorption involving excited-state absorption and energy transfer with rare-earth elements. They require high intensity of light generated by laser, which is much higher than most incoherent light like sunlight (around the order of magnitude of 10 mW/cm2). Among several UC processes, triplet-triplet annihilation (TTA-UC) has recently attracted much attention both from experimental and theoretical researchers owing to the fact that it occurs with weak intensity light.4,11-32 In this process, two types of chromophores, a sensitizer and an emitter, are resolved in solvent. The former absorbs the light to generate triplet states after an intersystem crossing. The latter at first receives the energy from the sensitizer to become the triplet state (T1) emitter. After encounters of the T1 emitters, TTA occurs to yield a singlet ground state (S0) and a singlet excited state (S1) emitter. The S1 emitter emits the up-converted light whose photon energy is higher that of the incident light.4,7,11,12-23,26-28,30,31 One of the most widely investigated emitters for the fundamental research on the mechanism of TTA-UC


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processes is 9,10-diphenylanthracene (DPA) due to its excellent emission property and availability.2,4,8,12,14-17,19,20,22,23,25,28-32 However, the TTA efficiency of DPA becomes lower coexisting with O2, which acts as a triplet quencher23,31 and also cause photobleaching of DPA by peroxide formation with singlet oxygen at the 9th and 10th positions of the anthracene. To overcome the deficiency of DPA on the photobleaching, several DPA derivatives were synthetized to avoid O2 from approaching the anthracence moiety.29 Among them, the DPA derivatives having loop-like bifunctional alkoxy linkers connecting the two phenyl groups of DPA, which are referred as alkyl-strapped DPAs (Cn-sDPAs, where n is the number of the carbons in each strap, Figure 1) developed by one of us show excellent UC quantum yield (UCQY) compared to the unsubstituted DPA when they were used as emitter both in liquid and solid12 environments although the substitution might interfere with the TTA process via elongating intermolecular distance due to steric hindrance of the bulky straps. Particularly, the crystalline C7-sDPA in air exhibited almost same quantum efficiency compared to that in Ar atompsphere, and still has higher efficiency than the crystalline DPA.32 This indicates that the durability towards O2 does not explain the difference in the efficiency. The TTA energy matching conditions, excitation energies, and other photochemical properties of C7-sDPA were nearly identical with Cn-sDPAs with varying strap lengths and with DPA alone (see Table 1 and Supporting Information Table S1 and Table S2 for detailed analyses). Therefore, it remains unclear why the efficiency of the TTA process of Cn-sDPAs, which have inactive alkyl chains in ordinary charge/energy transfer processes, is higher than that of DPA.


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Figure 1. Chemical structures of DPA and Cn-sDPA.

Figure 2. Model dimer structures. The black dots indicate the center of mass positions of the anthracene moieties. The distance between two center of mass positions, d, has been varied between 9.77-17.19 Å and the molecular orientation angle, θ, has been varied between 0-90 degrees in 15 degree increments.

In our previous study33 we theoretically estimated the TTA reaction time [i.e. the inverse of the rate constant of the TTA processes ( 1/ )] and the diffusion coefficient for DPA in solution; the TTA reaction time was calculated using the model structures as shown Figure 2, where the monomer structure was fixed to the optimized structure of T1 and the distance between the center of mass positions of the anthracene moieties (d) and the angle between the two normal vectors ( ) were fixed for given values. We found that is fast (< 10 ns) within an intermolecular distance of d 10 Å, while it becomes very slow (> 1000 µs) at longer distances

(> 12 Å). Moreover, the molecular orientation of two DPAs with the fast TTA is limited only at


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90 degrees. The diffusion-limited reaction time with an effective reaction radius of d 10 Å was 37 µs. This value was estimated based upon a diffusion coefficient of DPA in the dimethyl sulfoxide (DMSO) solvent of 1.77 10–10 m2 s–1 obtained by molecular dynamics (MD) simulation. This indicated that the TTA of DPA mainly occurs when two DPAs become close and form a suitable conformation for TTA. In this study, the same theoretical approaches developed in the previous paper33 were applied to the TTA process of Cn-sDPAs in solution in order to understand the enhancement of the UC-QY of Cn-sDPAs.

Figure 3. Electron transfer process of triplet-triplet annihilation via the charge separation state.

Here, we assume that a TTA process consists of two sequential one-electron transfer reactions via a charge separation (CS) state (see Figure 3). Elucidation of the TTA rate via the indirect one-electron pathway can be obtained using the steady state approximation:33,34

, , 1 , ,

where kX,Y is the electron transfer rate constant (kET) from an initial state X (T1T1 or CS) to a final state Y (T1T1, S1S0 or CS) and is estimated by the Marcus formula for non-adiabatic electron transfer:33-35


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∆' 1 2 | | exp $− ( 2 4 ℏ 4 T

In the above equation, TDA is the electronic coupling matrix element between a donor (D) and an acceptor (A), and ∆' and are the difference in the Gibbs free energy between the initial and

final states, and the reorganization energy, respectively. The Planck constant divided by 2, Boltzmann constant, and temperature are represented by ℏ , and T, respectively. The electronic structure calculations were utilized to estimate TDA, ∆' , and . Moreover, MD

simulations were applied to investigate the diffusion constant and the distribution of the intermolecular distance between two DPA derivatives. The differences in kTTA and the diffusionlimited reaction times of Cn-sDPAs compared to DPA derived in the previous study are discussed. 2. METHODS In the followings, the numerical methods are described. Several methodologies were combined to obtain TDA, ∆', and , which are necessary to evaluate the TTA rate constants as shown in eqs. 1 and 2. Ideally, an ensemble average is needed to calculate the vast numbers of all possible configurations of the emitters in solution but it requires enormous effort. The model structures were constructed using the Winmostar software36 (see Supporting Information SI1). The model structures of the Cn-sDPA dimers were used to evaluate the TTA reaction time ( in an implicit solvent model. The tilt and role angles of the two anthracene moieties were fixed for simplicity. The TDA values were calculated by the FMO method37-39 followed by the LCMO approach40 with the FMO2-LC-UBLYP/6-31G(d) level of theory obtained using GAMESS [ver. Dec 5, 2014]41 and the homemade module for FMO-LCMO (see Supporting Information SI2). In


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order to determine the driving force (∆') and the reorganization energy from the Marcus

equation, the following approximations were applied: 1) ∆' obtained as the energy difference between the neutral and charge separated states and 2) the CS consisted of a reduced monomer pair and oxidized monomers. The energy of the CS state (ECS) was calculated using the Wellerlike relation.42-45 The intramolecular reorganization energies ( )* +,-) were calculated by a four-point approximation where the energy of a state Y in an optimized geometry of a state X ./0 was estimated (X, Y = S0, S1, T1, cation, and anion).46-48 The outer-sphere reorganization

energies were calculated by the Born-Hush approach. For both ∆' and calculations, the PCM(U)B3LYP-D3/6-31G(d) and PCM-TD-B3LYP-D3/6-31G(d) levels of theory were employed using the Gaussian 09 software package49 (see Supporting Information SI3). For MD simulations of the diffusion coefficients and the diffusion-limited rate constants, the AMBER14 program package50 was used. The calculation details can be found in the Supporting Information SI4. 3. RESULTS AND DISCUSSION 3.1 Energy Matching Condition of TTA reaction for DPA and Cn-sDPAs We first investigated the energy difference between the triplet state and the singlet excited state to confirm an energy matching condition for TTA, since TTA occurs when twice the triplet energy (2∆. 1 ) is higher than the singlet energy (∆. 2 ), i.e. ∆∆. 2∆. 1 −

∆. 1 ≥ 0. The energy of the ground state (S0), the lowest singlet excited state (S1), and the

triplet state (T1) were calculated at each optimized geometry in dimethyl sulfoxide (DMSO) with the PCM-CAM-(U)B3LYP-D3/6-311+G(d,p)//PCM-(U)B3LYP-D3/6-31G(d) and PCM-TDCAM-B3LYP-D3/6-311+G(d,p)//PCM-TD-B3LYP-D3/6-31G(d) levels of theories. It is clearly shown that the energy matching condition, ∆∆. ≥ 0, holds for C6-, C7-, and C8-sDPA, where


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∆∆. are 0.187, 0.168, and 0.239 eV, respectively (see Table 1). According to these results, TTA surely occurs in the all Cn-sDPAs and the wavelengths of emission are almost the same in spite of the difference in the accessory alkyl chain group (alkyl-strap moiety) as reported previously.34 In comparison with these derivatives, an energy loss of C7-sDPA is the lowest among them, while that of C8-sDPA is the highest, indicating that C7-sDPA is the most efficient in view of the energy conversion. Table 1. Singlet excitation energy ( ∆. 2 ), triplet excitation energy ( ∆. 1 ), and the differential energy for the energy matching (2∆. 1 − ∆. 15 ) for Cn-sDPAs and DPA in eV. Energy [eV]

DPA[33]

C6-sDPA

C7-sDPA

C8-sDPA

∆.S1 -S0 .S1 − .S0

2.498

2.525

2.574

2.515

1.386

1.356

1.371

1.377

0.274

0.187

0.168

0.239

∆.T1 -S0 .T1 − .S0

∆∆. 2.T1 -S0 − .S1

3.2 TTA Reaction Time for DPA and Cn-sDPAs We estimated the TTA reaction time () for the Cn-sDPA dimer model structures (see Supporting Information Figure S1) using eqs. 1 and 2, the FMO-linear combination of molecular orbital (FMO-LCMO) method, a four-point approximation, and the Born-Hush approach (see numerical method described later). Figure 4 shows the plots of the resultant TTA reaction time against the center of mass distance between two monomers for several mutual orientations. The reaction time increased exponentially with respect to the distance, because the observed TTA process is governed by the sequential charge transfer (SCT) mechanism. The for C6-, C7-, and

C8-sDPA were within 1 µs when the distance was approximately 12 Å, while the for DPA was longer than 1000 µs. Thus, the of the Cn-sDPAs were nearly 1000 times shorter than that of


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DPA even if the center of mass distances are long enough (e.g. 12 Å).33 The other characteristic feature of Cn-sDPAs is that the intermediate angles of the molecular orientation between 0 and 90 degrees tend to have shorter unlike DPA; short were observed at 30 and 45 degrees for C6-sDPA, 45 and 60 degrees for C7-sDPA, and 45, 60, and 75 degrees for C8-sDPA. Meanwhile, DPA has short only at 0 and/or 90 degrees depending on the distance.

* In this paper, we have shown that the calculation method for the ECS of DPA changed in the presence or absence of ∆.6+78 (see Supporting Information SI3). Figure 4. TTA reaction times, 1/ [ps], for DPA33 and Cn-sDPAs.

3.2 Molecular Orbitals and Overlap Integral for DPA and Cn-sDPAs


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In order to understand the different properties of Cn-sDPAs and DPA, we analyzed their singly occupied molecular orbitals (SOMOs) since the overlap (i.e. exchange integral) of two SOMOs is a dominant TDA factor in the SCT mechanism. As illustrated in Figure 5, the SOMOs of C7-sDPA delocalize not only over the anthracene moiety, but also over the alkyl strap moiety forming a pseudo π-orbital. In contrast, the SOMOs of DPA were completely localized in the anthracene moiety (see Supporting Information Figure S2 for all SOMOs including other CnsDPAs). This pseudo π-orbital consists of both π-orbital of the anthracene moiety and the 9orbitals of the alkyl strap moieties. These results indicate that the pseudo π-orbital induces the long-range electron transport, because the overlap between the pseudo π-orbital in the SOMOs becomes large when the molecular orientation is 15-60 degrees (see Supporting Information Figure S3). These results also demonstrate that the alkyl strap moiety plays a significant role in the enhancement of TTA due to the delocalization of the SOMOs (i.e. the pseudo π-orbital) even though it has been theorized to be inert in the TTA process. Furthermore, we depicted the overlap integral, SDA, obtained by FMO calculation for DPA and Cn-sDPAs in Figure S4. Magnitude of SDA for Cn-sDPAs was often larger than that for DPA between 30 and 60 degrees.


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Figure 5. Localized monomer SOMOs of DPAs (a) and C7-sDPAs (b) obtained by FMO2-LCUBLYP/6-31G(d), where d =10.93 Å and θ = 0 degrees. Two SOMOs are superimposed on the one panel. Here red and green (blue and orange) represent positive (negative) sigh of the SOMOs. The isovalue = 0.001. 3.3 Diffusion Coefficient for DPA and Cn-sDPAs In order to understand how often two emitters encounter one another in solution, we utilized MD simulation to estimate the diffusion coefficient and the distribution of the center of mass distance for the Cn-sDPA dimers. The obtained diffusion coefficients, Ddiff, for C6-, C7-, and C8-sDPA were 0.8510–10, 0.8810–10, and 1.4910–10 m2s–1, respectively. Based upon Ddiff, we estimated the diffusion-limited rate constants (kdif = 8π NA Ddiff deff), and we assumed an effective distance of the TTA reaction to be deff = 10 Å as adopted from the previous investigation with DPA. The corresponding diffusion-limited reaction times for C6-, C7-, and C8-sDPA were 77.5, 72.5, and 44.2 µs, respectively, which are the same order of magnitude as DPA. Although the reaction times of C6- and C7-sDPA are longer than the reaction time of C8sDPA, the distribution of the center of mass distance below 15 Å (the electron transfer limit) for C6-, C7-, and C8-sDPA was 6.35, 12.67, and 3.78%, respectively. Therefore, two C7-sDPAs


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approach each other more frequently than C6- and C8-sDPA, and, in addition to the result of TTA reaction time, this result will predict that UC-QY of C7-sDPA is higher than that of others. 4. CONCLUSIONS In order to understand the enhancement of TTA efficiency mediated by Cn-sDPAs in comparison to DPA, we determined the TTA reaction times () and the diffusion coefficients (Ddiff) of the alkyl-strapped DPA derivatives (Cn-sDPAs) in solution utilizing quantum mechanical calculations and MD simulations. Even though the energy matching conditions were virtually the same for all molecules including DPA (see Table 1), the of the Cn-sDPAs were much shorter than that of DPA even when the center of mass distance was long. Moreover, the of the Cn-sDPAs were significantly shorter compared to DPA at the various molecular orientations due to the delocalization of the SOMOs in the Cn-sDPAs. Our MD results indicated that the diffusion-limited reaction times of the Cn-sDPAs were within the same order of magnitude as DPA, but the probability of the center of mass distance below 15 Å of C7-sDPA was highest among Cn-sDPAs. Based upon the large TDA values and high distribution within the SCT mechanism in solution, the UC-QY of C7-sDPA is probably higher than that of DPA, C6-, and C8-sDPA. It should be emphasized that the fast TTA reaction occurring within the broad ranges of the center of mass distance and of the molecular orientation (by augmentation of the loop-like alkyl straps) originated from the formation of the pseudo π-orbital. This pseudo π-orbital was derived from the hybridization between the π-orbital in the anthracene moiety and the 9-orbital in the alkyl strap moieties. In contrast, we also estimated the for the dimer models of linear alkyl

chains substituted to DPA and confirmed that values were longer than that of DPA (see Supporting Information Figures S5 and S6). The different behavior between the loop-like and


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linear alkyl chains likely originated from the differences in both rigidity and proximity to the anthracene core and in formation of pseudo π-orbital. The loop-like alkyl chains are located just above the anthracene moiety, which causes the interaction of the 9-orbital of the former can interact with π-orbital of the latter resulting in the delocalization of π-orbital toward vertical direction with respect to the anthracene moiety, leading formation in the pseudo π-orbital. Based upon this fast TTA reaction through the pseudo π-orbital of the alkyl strap moieties, the close distribution of dimers in solution found for C7-sDPA can explain the experimentally observed fact that the C7-sDPA has superior TTA quantum efficiency. It has been hypothesized that the alkyl chain is electronically inert and utilized as insulation linker between the emitters or between the emitter and the sensitizer to keep them close to each other (i.e., to prevent the selfquenching and/or the self-assembling).52-54 However, this study clarified that the loop-like alkyl can be utilized not only a protecting group but also as an electron-transfer mediator. The present theoretical analyses clearly reveal a new principle of molecular design for efficient TTA by effectively expanding the π-orbital through the loop-like alkyl chain.

ASSOCIATED CONTENT Dimer model structures, obtained molecular orbitals, FMO method and FMO-LCMO method, energy of the charge separated state and reorganization energy, molecular dynamics simulation, and the TTA reaction time for the linear alkyl chains DPA are available in Supporting Information.


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] *E-mail: [email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was supported by Grants-in-Aid for Scientific Research of the Innovative Areas “Photosynergetics” (No. JP26107004) from MEXT, Japan and support for cooperative work by the Institute of Molecular Science (IMS). The computations were performed at the Research Center for Computational Science (RCCS) at IMS, the Institute of Solid State Physics (ISSP) at the University of Tokyo, and the Center for Computational Sciences (CCS) at University of Tsukuba.

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