Article pubs.acs.org/JPCC
What Can Be Learned from Magnetic Field Effects on Singlet Fission: Role of Exchange Interaction in Excited Triplet Pairs Masanobu Wakasa,*,† Mana Kaise,† Tomoaki Yago,† Ryuzi Katoh,‡ Yusuke Wakikawa,§,∥ and Tadaaki Ikoma§ †
Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-ohkubo, Sakura-ku, Saitama-shi, Saitama 338-8570, Japan ‡ Department of Chemical Biology and Applied Chemistry, College of Engineering, Nihon University, Koriyama, Fukushima 963-8642, Japan § Graduate School of Science and Technology, Niigata University, 2-8050 Ikarashi, Nishi-ku, Niigata 950-2181, Japan S Supporting Information *
ABSTRACT: Magnetic field effects (MFEs) on singlet fission were studied by observing fluorescence from organic crystal of 1,6-diphenyl-1,3,5-hexatriene under magnetic fields of up to 5 T. We found anomalous MFE dips at magnetic fields higher than 2 T, in addition to the known MFEs which saturated around 1 T. The observed results were analyzed by using the stochastic Liouville equation (SLE) in which a distancedependent exchange interaction (J) in triplet pair, hopping of triplet, and geminate fusion in contacted triplet pair were incorporated. The SLE analysis revealed that the observed dips were caused by a MFE due to the level crossing mechanism and strongly suggested that the contacted triplet pair has a large J, which has been ignored in the previous model of MFEs on the singlet fission. Present results lead to the conclusion that the initial dissociation of the singlet exciton to the contacted triplet pair does not show the MFE and the triplet pair at a separated distance produced by hopping of the triplet plays an important role on the generation of the MFE on the singlet fission.
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tetracene,13 rubrene,11 and 1,6-diphenyl-1,3,5-hexatriene9 have been known to show clear MFEs on SF. As far as we know, however, no MFEs on SF have been reported for organic crystal of diphenylisobenzofuran possibly because of the tiny magnitude of MFEs, though the organic crystal has been recognized as efficient SF material.14 The standard Merrifield model cannot explain the above different responses of the SF processes to the magnetic field. Thus, the mechanism of the MFEs on SF is still veiled and consequently it is also unclear what information on the SF can be obtained from the MFEs. To solve the above problems, here, we carried out the study of MFEs on SF under high magnetic fields of up to 5 T using a superconducting magnet for the first time. So far, the MFEs on the SF have been studied by using the electromagnet and the range of the magnetic fields is generally limited within 1 T. The MFEs on SF with the wide range of magnetic fields were evaluated by monitoring the fluorescence intensity of organic crystals of 1,6-diphenyl-1,3,5-hexatriene (DPH, Scheme 1), which is one of the representative SF materials, showing clear MFEs.
INTRODUCTION Singlet fission (SF) is a process in which a singlet exciton on a molecule splits into two triplet excitons located in different molecules.1,2 The basis of the mechanism of SF together with triplet fusion (TF) has been established with theory involving electron spin interactions in the 1970s.3 In the 2000s, it was suggested that SF can be adopted organic solar cells to improve their quantum efficiencies.4,5 Since then the mechanism of SF has gained renewed interest and SF toward the efficient solar cell is currently one of the most active research fields in photochemistry and photophysics.2,6,7 Since the electron spins in the triplet exciton interact with magnetic field, SF and TF processes in some organic crystals show the remarkable magnetic field effects (MFEs) on their efficiencies.2,3,8−12 It is noted that the observation of MFEs was the only option to prove the existence of SF and TF processes. Most of the MFEs on SF and TF observed previously have been explained by the standard Merrifield model in which the dissociation of the singlet exciton to the triplet excitons is supposed to be affected by the magnetic field.3 In the model, the change of the singlet character in the triplet pairs is an origin of the MFEs on the SF efficiencies. However, analysis of the MFE based on the standard Merrifield model suffers from a lack of information on the absolute efficiencies of SF. For example, organic crystals of © 2015 American Chemical Society
Received: October 17, 2015 Revised: October 23, 2015 Published: October 27, 2015 25840
DOI: 10.1021/acs.jpcc.5b10176 J. Phys. Chem. C 2015, 119, 25840−25844
Article
The Journal of Physical Chemistry C
MFE on radical pairs, in which the so-called low field effects are generated by application of the weak magnetic field and coherent superposition of spin states in zero magnetic field.15−17 In addition to the low fields MFEs explained by the standard Merrifield model, we observed a new MFE on SF under the magnetic fields higher than 2 T. An inset in Figure 1 shows an expansion of the magnetic field dependence of fluorescence intensity in the presence of the magnetic fields higher than 2 T. Small but clear decreases (dips) in fluorescence intensities are found at the magnetic fields of 2.2, 2.9, and 4.4 T. Similar dips have been observed in MFEs on radical pairs and are attributed to the MFE due to the level crossing mechanism (LCM) in which the exchange interaction (J) plays an important role.18−21 When the paramagnetic species are correlated, the different spin states are energetically separated by the J gap. In the level crossing region, the J gap between the spin states is canceled by the Zeeman splitting between the spin states, allowing the efficient spin state mixing. The magnetic field for the level crossing between two spin states corresponds to the J gap between the spin states. Therefore, the observation of these dips in the high magnetic fields is strong proof that the large J actively operates in the pair of triplet excitons during the SF process. This point seems to contradict the standard Merrifield model3 where J in the triplet pair is completely neglected. When the large J is incorporated into the spin Hamiltonian in the standard Merrifield model, one cannot reproduce the reported MFEs on SF because the magnetic field cannot change the eigenstates of the spin states due to the large energy gap between the spin states. To realize the MFEs observed in the present study in detail, the results are analyzed by using the stochastic Liouville equation (SLE) in which the intramolecular spin interactions of D and E in the triplet exciton, the intermolecular interaction of J in the triplet pair and hopping of the triplet exciton, and the geminate fusion are incorporated. It should be noted that J decays exponentially with the distance in the triplet pair. The introduction of J implies that the triplet pairs are spincorrelated and the incorporation of the distance-dependent J allows coexistence of the different J conditions. The schematic view of a spin-correlated triplet pair (SCTP) model used in the SLE analysis is depicted in Figure 2. In our SCTP model, the first step of SF is a dissociation of the singlet exciton to a contacted triplet pair (initial SF). At the contacted triplet pair,
Scheme 1. Molecular Structure of DPH
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RESULTS AND DISCUSSION Figure 1 shows a magnetic field (B) dependence of relative fluorescence intensity (R(B)) observed for DPH microcrystals,
Figure 1. Magnetic field effects on the fluorescence of DPH crystal measured at 470 nm. Inset: An expansion of the data in the high magnetic fields.
where the data was normalized with fluorescence intensity (F) at the zero-magnetic field (R(B) = F(B)/F(0)). The intensity of fluorescence decreased with the application of the magnetic fields (0 < B ≤ 0.05 T), when the magnetic field is smaller or comparable with the electron spin−spin interactions (D and E) in the triplet exciton. The fluorescence intensity starts to increase with increasing the magnetic fields when the magnetic field is larger than the D and E values (0.05 T < B). The increase in fluorescence intensity is nearly saturated at the magnetic field of 1 T. Although the modification of the standard Merrifield model will be proposed later, here we attempt to rationalize the observed MFE with the simple Merrifield model. According to the Merrifield model,3 electrons spins in two triplet exctions couple, giving singlet, triplet, and quintet spin states. During SF process, the spin states must be conserved. Thus, the efficiency of SF is dependent on the degree of a singlet character in the two triplet excitons. In the absence of magnetic field, the electron spins are quantized along the molecular axis and each molecular axis (x, y, z) can work as a quantization axis for the electron spins. Thus, the electron spins have freedoms to cancel out spin angular momentum in the system. This increases the singlet character in the two triple excitons. In the presence of high magnetic fields, spin quantization axis is limited to the direction of magnetic field. As a result, the singlet character in the two triplet excitons decreases, causing inefficient SF from the singlet exciton and increase of fluorescence intensity. When a weak magnetic field is applied, major quantization axis is still the molecular axis. However, the electron spins precess slowly along the direction of the magnetic field, mixing the spin states in virtually zero magnetic field. In this situation, the singlet state is allowed to mix the several quintet states. This enhances the singlet character in the two triplet excitons, resulting in efficient SF and low fluorescence intensity. An analogous situation is found in
Figure 2. Spin-correlated triplet pair (SCTP) model used for the SLE simulation. During the separation of the triplet pair and geminate fusion, the magnetic field effects are manifested in the fluorescence intensity. We assumed that the sign of J is negative. 25841
DOI: 10.1021/acs.jpcc.5b10176 J. Phys. Chem. C 2015, 119, 25840−25844
Article
The Journal of Physical Chemistry C the triplet pair has a large J value and magnetic fields do not affect the SF process yet because the magnitude of J is much larger than the D and E values and the Zeeman splitting induced by the applied magnetic fields. The spins in triplet pairs are strongly correlated and maintain a spin state of the precursor of the singlet exciton. After the generation of the contacted triplet pair, the triplet excitons hop to the neighboring molecule and the separated triplet pairs are generated. In the moderately separated triplet pair in which the magnitude of J matches the Zeeman splitting induced by the magnetic field, two of the spin states in the triplet pair are degenerated and the MFEs due to the LCM are generated. In the quasi-separated triplet pair in which the magnitude of J is much smaller than D and E values, J can be approximately neglected in the spin Hamiltonian while the spins in the triplet pair are still correlated weakly. The magnetic field dependence of the population of the spin states in the triplet pair is then described by the standard Merrifield model and the magnetic field can affect the spin states in the usual manner. By a hopping motion and the geminate fusion process in triplet pairs, a part of the separated triplet pairs returns to the singlet exciton, which emits fluorescence. Here the fusion process is spin-state selective and only triplet pair which has singlet character can generate the singlet exciton via geminate fusion. The other part of the separated triplet pairs escapes from the pair by hopping motions and loses spin correlation. In this model, the population changes of the spin states in the separated triplet pairs can be recognized as a variation in the intensity of fluorescence from the singlet exciton via hopping of the triplet exciton and the spin-state selective geminate fusion in the triplet pair. The scheme is analogous to the MFE mechanism in the radical pair systems, which have been extensively studied for the last 5 decades.18,22,23 The procedure of the SLE is the same with previous reports on radial pairs20 except the spin Hamiltonian. In the present study, the spin Hamiltonian (Ĥ (n)) for triplet pair n consists of the exchange interaction (Jn) between the two triplet excitons “a” and “b” and the dipole−dipole interaction within each triplet exciton:
Figure 3. Magnetic field effects on the yield of the excited singlet state calculated by using the stochastic Liouville equation (black line) together with the experimentally observed MFE (red line).
Figure 4. Magnetic field dependencies of the energy of singlet (S, red line), triplet (T, green line), and quintet (Q, blue line) states at the moderate separated triplet pair (pair2). We assumed that the sign of J is negative.
equal to the 3J and 6J values. In the experiment, we observe the three dips at the magnetic fields of 2.2, 2.9, and 4.4 T. Among these dips, the dips observed at the magnetic fields of 2.2 and 4.4 T show excellent agreement with the theoretical perditions. This good agreement confirms that the observed dips are caused by the LCM and contacted triplet pair has large J values. The dip observed at 2.9 T may be associated with the triplet pair generated in the different crystal phase24 or generated by the diffusion of the triplet in different directions. It may also be possible that level crossing between the triplet and quintet states affects the feature of the MFEs. Here we assumed that the dip observed at 2.9 T is caused by the triplet pair which has the same kinetic parameters but different J values. Assuming that the two different series of triplet pairs have the same population, the experimentally observed MFEs can be well reproduced as can be seen in Figure 3. Nevertheless, the SLE analysis strongly suggests that the contacted triplet pair has large J value and the MFEs are generated in the separated triplet pair. The parameters determined by the SLE analysis are listed in Table 1.
Ĥ (n) = −2Jn Sa S b + gμB B ·(Sa + S b) ⎛ S2 S 2⎞ + D⎜Saz 2 − a + S bz 2 − b ⎟ 3 3 ⎠ ⎝ + E(Sax 2 − Say 2 + S bx 2 − S by 2)
The notations have their usual meanings. The detailed SLE analysis is described in the Supporting Information. It should be noted that the initial SF process does not show the MFE in the SLE. Since no significant changes were found in the calculated results when the numbers of N > 5 were used, the SLE simulation with N = 5 is depicted in Figure 3 together with the experimental results. The experimental results including the dips in the high magnetic fields were well reproduced by our SLE model. The energy diagram of the magnetic field dependence of the spin states in the triplet pair is depicted in Figure 4. The diagram shows that level crossing involving the singlet state are found at three different magnetic fields where the magnetic field is equal to 2J, 3J, and 6J. In the level crossing region with the 2J value, the spin states are not mixed because of the absence of the mixing term in the spin Hamiltonian. Thus, the only two dips are expected at the magnetic fields where the magnetic field is
Table 1. Optimized Recombination and Hopping-Rate Constants (kf and kH), Site Number (N) for the Geminate Pair, and Magnitude of Exchange Interactions (J) in the Triplet Pairs from the Analysis Based on the SLE Calculation Using the One-Dimensional Lattice Model J/cm−1 kf/s
−1
5 × 109
−1
kh/s
6 × 1010
N
pair1
pair2
pair3−5
5
−50
−0.69 (−0.90)a
0
a
Value in parentheses shows the auxiliary J value used to reproduce the dip observed at 2.9 T.
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DOI: 10.1021/acs.jpcc.5b10176 J. Phys. Chem. C 2015, 119, 25840−25844
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The difference between the standard Merrifield model and our model is when the MFEs are generated. In the Merrifield model,3 J is neglected and the MFEs are generated during the initial SF process. In our model, on the other hand, the large J in the contacted triplet pair locks the spin states; therefore, the magnetic field cannot change the spin states at the contacted triplet pair which is produced by the initial SF process. The MFEs on the fluorescence intensity are generated after the separation and the geminate fusion in the triplet pair. The MFEs are influenced by the magnitude of J in the triplet pair and the rates of the initial SF, hopping, and geminate fusion. The present study demonstrated that the detailed analysis on the MFEs can provide the valuable dynamical information on the SF processes. It is also possible to link the MFEs and the efficiencies of the SF by using our model. When efficient SF and no MFE are observed for an organic crystal, it can be explained by blocking of the geminate fusion in our model. In such a way, one can discuss the absolute efficiency of SF from the MFE analysis.
CONCLUSION The MFEs due to the LCM were observed in the SF process in the organic crystals of DPH under the high magnetic field of up to 5 T. The results were analyzed by using the SLE in which the distant dependent J in a triplet pair was incorporated for the first time. We propose the new mechanism of the MFEs on the SF. In the proposed mechanism, the origin of the MFEs on the SF is the interchanging of the spin state at a separated triplet pair and not the variation of the initial SF rate. The MFEs contain dynamical information on the SF involving the initial SF, hopping of the triplet exciton, and geminate fusion. Thus, the analysis on the MFE can provide the valuable information on SF processes in organic materials. ASSOCIATED CONTENT
S Supporting Information *
Details of experimental and SLE analyses. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b10176.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address ∥
Advanced Instrumental Analysis Center, Shizuoka Institute of Science and Technology, 2200-2 Toyosawa, Fukuroi, Shizuoka 437-8555, Japan. (Y.W.) Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported in part by a Grant-in-Aid for Scientific Research on Innovative Area of “All Nippon Artificial Photosynthesis for Living Earth” (Area No. 2406) (No. 25107509) and of “Stimuli-responsive Chemical Species for the Creation of Functional Molecules” (Area No. 2408) (No. 15H00917) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. 25843
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DOI: 10.1021/acs.jpcc.5b10176 J. Phys. Chem. C 2015, 119, 25840−25844
