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Fluorescent triphenylamine derivative: Theoretical design based on reduced vibronic coupling
Chemical Physics Letters 615 (2014) 44–49
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Fluorescent triphenylamine derivative: Theoretical design based on reduced vibronic coupling Yuichiro Kameoka a , Masashi Uebe a , Akihiro Ito a,∗ , Tohru Sato a,b,∗∗ , Kazuyoshi Tanaka a a b
Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan Unit of Elements Strategy Initiative for Catalysts & Batteries, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan
a r t i c l e
i n f o
Article history: Received 28 August 2014 In final form 1 October 2014 Available online 13 October 2014
a b s t r a c t A triphenylamine derivative containing monocarborane was designed to exhibit fluorescence by considering vibronic couplings in the non-fluorescent parent compound. Off-diagonal vibronic coupling constants, which govern the rate constant of non-radiative transitions, were reduced. Based on analysis of vibronic coupling densities, this reduction was attributed to the fact that the highest occupied molecular orbital (HOMO), which is localized on the unsubstituted triphenylamine, became partly delocalized to monocarborane in the derivative, while the lowest unoccupied molecular orbital (LUMO) was strongly localized on triphenylamine. This suggests a design principle for the suppression of non-radiative decay in light-emitting materials. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Fluorescent molecules have been widely investigated for device application such as organic light-emitting diodes (OLEDs) [1–7] and fluorescent sensors [8–10]. To fabricate efficient and reliable devices, it is important to design fluorescent molecules with thermal and chemical stability [1], as well as high fluorescence quantum yield [11,12]. If there is a design principle to convert a nonfluorescent molecule to a fluorescent one, the variety and possible structures of fluorescent molecules can be extended. This would be also useful in other fields such as fluorescence labelling [13] and multifunctionalisation [14,15]. For example, bifunctional fluorescent molecules that are also paramagnetic [16] or capable of photoisomerisation [17] have been widely studied. Fluorescence competes with non-radiative decay, which involves internal conversion and vibrational relaxation. Internal conversion is caused by vibronic coupling (electron–phonon coupling). The rate constant of this process depends on the off-diagonal vibronic coupling constants (VCCs) between the initial and final states [18]. Large off-diagonal VCCs enhance non-radiative decay; therefore, it should be reduced in fluorescent molecules. VCCs can be analysed on the basis of electronic and vibrational structures by
∗ Corresponding author. ∗∗ Corresponding author at: Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan. E-mail addresses: [email protected] (A. Ito), [email protected] (T. Sato). http://dx.doi.org/10.1016/j.cplett.2014.10.004 0009-2614/© 2014 Elsevier B.V. All rights reserved.
expressing these in terms of density, i.e. the vibronic coupling density (VCD) [19,20]. Using the concept of VCD, we have succeeded in reducing VCCs and consequently, suppressing internal conversion in a fluorescent anthracene derivative [21,22]. The large increase in its fluorescence quantum yield has been experimentally confirmed [22]. However, anthracene itself is a fluorescent molecule. Although it is rather challenging to induce fluorescence in non-light-emitting molecules, it is possible using the VCD concept. The target molecule is triphenylamine (1) shown in Figure 1, and to the best of our knowledge, this compound, as well as its derivatives, does not exhibit fluorescence. We designed the triphenylamine derivative 2, shown in Figure 1, to which a monocarborane fragment is introduced. The derivatives of the monocarba-closo-dodecaborane (monocarborane) anion, CB11 H− , have attracted much attention 12 in material science because of their thermal and chemical stability, optical and magnetic properties, and extensibility [23,24]. In this Letter, we show that 2 can exhibit fluorescence through suppression of the internal conversion that normally occurs in 1. The cause of this suppression is elucidated through analysis of the VCDs, from which a design principle for fluorescent molecules is then proposed.
2. Theory The electronic wavefunction of the nth state is denoted by n (r, R), where r and R are the sets of the electronic and nuclear coordinates, respectively. Using the molecular Hamiltonian H and the
Y. Kameoka et al. / Chemical Physics Letters 615 (2014) 44–49
45
The integral of mn,˛ (ri ) is equal to Vmn,˛ :
Vmn,˛ =
mn,˛ (ri ) d3 ri .
(4)
Using electronic and vibrational structures as the bases, the offdiagonal VCD can provide some insight on the off-diagonal VCC, which governs the rate of internal conversion. 3. Computational method Figure 1. Structures of triphenylamine (1) and its derivative (2). The cage represents C(BH)11 .
mass-weighted normal coordinate Q˛ of mode ˛, the off-diagonal VCC between states m and n for mode ˛ is defined as
∂H(r, R) m (r, R0 ) n (r, R0 ) , ∂Q˛ R0
Vmn,˛ :=
(1)
where R0 is the reference nuclear configuration [25]. In the present case, the optimized geometry of the S1 state was chosen as R0 in discussing the internal conversion from the S1 to S0 state. The off-diagonal vibronic coupling density mn,˛ (ri ) between the Sm and Sn states for mode ˛ is defined as [20] mn,˛ (ri ) := mn (ri ) × v˛ (ri ),
(2)
where ri denotes the coordinates of the ith electron, mn (ri ) is the overlap density between the Sm and Sn states, and v˛ (ri ) is the derivative of the potential u(ri ) from all nuclei acting on a single electron given by
v˛ (ri ) :=
∂u(ri ) ∂Q˛
. R0
(3)
The geometries of 1 and 2 at the ground S0 state were optimized at the RB3LYP/6-31+G(d) level of theory, while those at the S1 excited state were optimized using time-dependent density functional theory (TD-DFT) with the same functional and basis set. Ten excited states were considered to obtain the adiabatic (AD) S1 state. Vibrational analysis of the ground S0 state was performed using the geometry of the AD S1 state. The Gaussian 09 package [26] was employed for these calculations. The level of theory is the same one used in a previous work by Oliva et al. [27] on carborane units connected by an unsaturated hydrocarbon. The authors confirmed the reliability of their DFT calculations by comparing data obtained from the CASSCF/CASPT2 method using the same basis set. Off-diagonal VCCs and VCDs between the S1 and S0 states were determined from normal modes in the S0 state obtained using the AD S1 state geometry. These calculations were performed using an in-house code. 4. Results and discussion The orbital diagrams of 1, 2, and the monocarborane anion are shown in Figure 2. The energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of 2 (3.943 eV) is closer to that of 1 (4.136 eV) than that of the monocarborane anion (6.623 eV). The orbital pattern of the LUMOs of 1 and 2 is the same, and apparently, that of the HOMO as
Figure 2. Frontier orbital diagrams of (a) monocarborane anion with degenerate orbitals, (b) 2, and (c) 1 at the B3LYP/6-31+G(d) level. The corresponding isovalues are 4 × 10−2 , 1 × 10−2 , and 2 × 10−2 a.u., respectively.
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Y. Kameoka et al. / Chemical Physics Letters 615 (2014) 44–49
Table 1 Calculated transition energies E for absorption (Abs.) and emission (Em.), wavelength , oscillator strength f, and contribution of HOMO–LUMO transition for 1 and 2. Molecule
E eV
nm
f
HOMO–LUMO %
1
Abs. Em.
3.4513 3.1094
359.24 398.74
0.0175 0.0158
98 98
2
Abs. Em.
3.2814 2.6878
377.83 461.28
0.0162 0.0086
98 99
well. This suggests that the HOMO and LUMO of 2 mainly originate from the triphenylamine fragment, although the HOMO is partly delocalized to the monocarborane fragment. The results of TD-DFT calculations for the S1 excited states of 1 and 2 are summarized in Table 1. The emission wavelengths of both compounds are in the range of visible light. The contribution of the HOMO–LUMO transition to the emitting states of 1 and 2 is almost 100%. The reorganisation energy within the Born–Oppenheimer approximation is E = 0.1759 and 0.2534 eV for 1 and 2, respectively. This indicates that vibrational relaxation occurred to a greater extent in 2 than in 1. On the other hand, the oscillator strength f of 2 is smaller than that of 1. As will be discussed later, the transition dipole moment, which is a factor of the oscillator strength, is related to the off-diagonal VCC; thus, there is a trade-off in controlling the off-diagonal VCC. The off-diagonal VCCs between the S1 and S0 states of 1 and 2 are shown in Figure 3(a) and (b), respectively. Off-diagonal vibronic couplings, which are responsible for non-radiative decay, were largely suppressed in 2. Consequently, the rate of non-radiative decay in 2 decreased upon introduction of monocarborane into 1. The maximum-coupling mode (i.e. normal mode with the maximum vibronic coupling) of 1 is mode 74 (1270 cm−1 ), which splits into modes 132 and 136 in 2 (1294 and 1332 cm−1 , respectively) as shown in Figure 5. Mode 77 of 1 (1310 cm−1 ), which is the second maximum-coupling mode, corresponds to mode 130 of 2 (1267 cm−1 ). The off-diagonal VCCs for these modes of 1 are suppressed in 2. The cause of the decrease in the VCC of the maximum-coupling mode of 1 will now be discussed by analysing the VCD. The off-diagonal VCDs between the S1 and S0 states for the maximum-coupling mode of 1 and the corresponding two modes of 2 are shown in Figure 4. The off-diagonal VCD 10,˛ is localized on the triphenylamine fragment of 1 and 2; however, that of the latter is suppressed in comparison with the former. This suppression of the VCD can be understood by considering the distributions of the potential derivatives and overlap densities (see Eq. (2)). The potential derivative v˛ for the maximum-coupling mode of 1 and the corresponding modes of 2 are shown in Figure 5. v˛ is
Figure 3. Off-diagonal vibronic coupling constants between the adiabatic S1 and S0 states for the normal modes of (a) 1 and (b) 2.
localized on the triphenylamine fragment for both 1 and 2. It has a -type distribution originating from the in-plane displacement of the benzene rings. For each benzene ring, the distribution of v˛ is similar for 1 and 2. On the other hand, the overlap density consists of the product of HOMO and LUMO densities because the S1 excited states are mainly due to the HOMO–LUMO transition. The HOMO and LUMO of the AD S1 states of 1 and 2 are shown in Figure 6. The HOMO of 2 (b1) is partly delocalized to the monocarborane fragment, while the LUMO (b2) is strongly localized on the triphenylamine fragment. Therefore, the overlap density of 2 is small because the LUMO coefficient of the monocarborane fragment is small. In contrast to 2, the HOMO and LUMO of 1 (a1 and a2, respectively) are
Figure 4. Off-diagonal vibronic coupling density between the adiabatic S1 and S0 states for vibrational mode (a) 74 of 1, and (b) 132 and (c) 136 of 2. The isovalue is 5 × 10−6 a.u.
Y. Kameoka et al. / Chemical Physics Letters 615 (2014) 44–49
47
Figure 5. Derivative of the electronic-nuclear potential for vibrational mode (a) 74 of 1, and (b) 132 and (c) 136 of 2. The isovalue is 5 × 10−3 a.u.
almost equally distributed among the three benzene rings. However, in 2, the LUMO is largely distributed to one benzene ring, while the HOMO is strongly localized on the two other rings. This can also contribute to the suppression of the overlap density of 2. The overlap densities between the S1 and S0 states of 1 and 2 are shown in Figure 7. As expected from the distributions of the HOMO and LUMO, the 10 of 2 (Figure 7(b)) is small in comparison with that of 1 (Figure 7(a)). Because 10,˛ is the product of the potential derivative and overlap density, and the distribution of the former is similar in 1 and 2, the suppression of the VCD for the maximumcoupling mode of 1 can be attributed to the reduction of the overlap density. Details of the VCD analysis for the second maximum-coupling mode of 1 and corresponding mode of 2 are given in Supplementary Data. The findings were the same as in the case of the maximumcoupling mode. The off-diagonal VCDs were localized on the triphenylamine fragment of 1 and 2, and that of 2 was suppressed in comparison with 1. On the other hand, 1 and 2 have similar
distributions of the potential derivative on the triphenylamine fragment. Therefore, the suppression of the off-diagonal VCC in 2 is attributed to the reduction of the overlap density on this fragment. Based on the discussion above, we propose a design principle to suppress non-radiative decay in molecules: if an excited state, which is expected to be the emitting state, originates from the excitation between a pair of MOs (HOMO and LUMO in the present case), one of the MOs should be delocalized over the fragments and the other should be localized on one of the fragments. This leads to a small overlap density in the overlap region, which consequently results in small off-diagonal VCCs. Thus, non-radiative decay in the molecule will be suppressed. There is, however, a trade-off in suppressing the off-diagonal VCC: the decrease in overlap density also decreases the transition dipole moment. The transition dipole moment is expressed as [20]
mn =
−exmn (x) d3 x.
Figure 6. Molecular orbitals of the adiabatic S1 state of 1 (a1, HOMO; a2, LUMO) and 2 (b1, HOMO; b2, LUMO). The isovalue is 2 × 10−2 a.u.
(5)
48
Y. Kameoka et al. / Chemical Physics Letters 615 (2014) 44–49
Figure 7. Overlap density between the adiabatic S1 and S0 states of (a) 1 and (b) 2. The isovalue is 1 × 10−3 a.u.
As in Eq. (5), mn is equal to the integral of the product of the overlap density and position vector. Therefore, a large and widespread distribution of the overlap density yields a large transition dipole moment, while a small overlap density results in the suppression of non-radiative decay. Indeed, in the present case, the oscillator strength of 2 was reduced in comparison with 1, as a manifestation of this trade-off. Although the overlap density of 2 decreased, it still has a widespread distribution on the triphenylamine fragment (Figure 7(b)). This can be an effective strategy to avoid a significant decrease in the transition dipole moment and to suppress the off-diagonal VCCs by reducing the overlap density. 5. Conclusion We designed the triphenylamine derivative 2, which exhibits fluorescence unlike the non-light-emitting triphenylamine (1). The off-diagonal vibronic coupling constants (VCCs) of 2, which govern the rate constant of non-radiative decay, were reduced in comparison with 1. Based on the concept of VCD, the cause of this reduction is the partial delocalisation of the HOMO to monocarborane, concurrent with the localisation of the LUMO on triphenylamine. Compound 2 has already been synthesized and observed to exhibit fluorescence. This experimental study will be reported in the future. It should be noted that 1 itself is not fluorescent, and the emitting state of 2 is due to the transition between the HOMO and LUMO, which are localized on the triphenylamine fragment. In other words, the chromophore of 2 is the triphenylamine fragment. From Eqs. (2) and (4), a general principle for the suppression of non-radiative decay is as follows: the suppression of overlap density results in the reduction of the off-diagonal vibronic coupling constants, and therefore, the reduction of the rate constant of non-radiative decay. Based on the present analysis and above principle, we propose a molecular design principle for the suppression of non-radiative decay in light-emitting materials: if an excited state, which is expected to be the emitting state, originates from the excitation between a pair of MOs, one of the MOs should be delocalized over the fragments and the other should be localized on one of the fragments. Employing this principle, we can expect to extend the variety and possible structures of fluorescent molecules and increase the efficiency of light-emitting molecules. Quite recently the photoluminescence quantum yield (PLQY) of a triphenylamine derivative (PLQY = 6%) has been reported [28]. They have also reported that a tribiphenylamine derivative yielded a high PLQY (PLQY = 37%). However, according to our preliminary calculations for the tribiphenylamine derivative, the chromophore
of the molecule is not triphenylamine. We also investigated the reason for the high PLQY of the tribiphenylamine derivative. We found the mechanism is different from what we have discussed here. We will publish the result in the near future. Acknowledgements Numerical calculations were partly performed at the Supercomputer Laboratory of Kyoto University and the Research Center for Computational Science in Okazaki, Japan. This work was partly supported by a Grant-in-Aid for Scientific Research (B) (No. 24310090) from the Japan Society for the Promotion of Science (JSPS) and Grant-in-Aid for Scientific Research on Innovative Areas “New Polymeric Materials Based on Element-Blocks (No. 2401)” (Nos. 24102014 and 25102516) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. Appendix A. Supplementary Data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. cplett.2014.10.004. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
J.R. Sheats, et al., Science 273 (1996) 884. U. Mitschke, P. Bäuerle, J. Mater. Chem. 10 (2000) 1471. R.H. Friend, et al., Nature 397 (1999) 121. W. Helfrich, W.G. Schneider, Phys. Rev. Lett. 14 (1965) 229. C.W. Tang, S.A. VanSlyke, Appl. Phys. Lett. 51 (1987) 913. M.A. Baldo, S. Lamansky, P.E. Burrows, M.E. Thompson, S.R. Forrest, Appl. Phys. Lett. 75 (1999) 4. A. Endo, M. Ogasawara, A. Takahashi, D. Yokoyama, Y. Kato, C. Adachi, Adv. Mater. 21 (2009) 4802. A.P. de Silva, H.Q.N. Gunaratne, T. Gunnlaugsson, A.J.M. Huxley, C.P. McCoy, J.T. Rademacher, T.E. Rice, Chem. Rev. 97 (1997) 1515. S.W. Thomas III, G.D. Joly, T.M. Swager, Chem. Rev. 107 (2007) 1339. L. Basabe-Desmonts, D.N. Reinhoudt, M. Crego-Calama, Chem. Soc. Rev. 36 (2007) 993. C.-H. Zhao, A. Wakamiya, Y. Inukai, S. Yamaguchi, J. Am. Chem. Soc. 128 (2006) 15934. M. Shimizu, Y. Takeda, M. Higashi, T. Hiyama, Angew. Chem. Int. Ed. 48 (2009) 3653. B. Valeur, M.N. Berberan-Santos, Molecular Fluorescence: Principles and Applications, 2nd edn., Wiley-VCH, Weinheim, 2012. E. Coronado, J.R. Galán-Mascarós, C.J. Gómez-García, V. Laukhin, Nature 408 (2000) 447. D. Maspoch, D. Ruiz-Molina, J. Veciana, Chem. Soc. Rev. 36 (2007) 770. A. Louie, Chem. Rev. 110 (2010) 3146. K. Matsuda, M. Irie, J. Photochem. Photobiol. C 5 (2004) 169. M. Uejima, T. Sato, D. Yokoyama, K. Tanaka, J.-W. Park, Phys. Chem. Chem. Phys. 16 (2014) 14244. T. Sato, K. Tokunaga, K. Tanaka, J. Phys. Chem. A 112 (2008) 758.
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[26] M.J. Frisch, et al., Gaussian 09, Revision C. 01, Gaussian Inc., Wallingford, CT, 2009. [27] J.M. Oliva, L. Serrano-Andrés, Z. Havlas, J. Michl, J. Mol. Struct.: THEOCHEM 912 (2009) 13. [28] C. Quinton, V. Alain-Rizzo, C. Dumas-Verdes, F. Miomandre, G. Clavier, P. Audebert, RSC Adv. 4 (2014) 34332.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Fluorescent triphenylamine derivative: Theoretical design based on reduced vibronic coupling Yuichiro Kameoka a , Masashi Uebe a , Akihiro Ito a,∗ , Tohru Sato a,b,∗∗ , Kazuyoshi Tanaka a a b
Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan Unit of Elements Strategy Initiative for Catalysts & Batteries, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan
a r t i c l e
i n f o
Article history: Received 28 August 2014 In final form 1 October 2014 Available online 13 October 2014
a b s t r a c t A triphenylamine derivative containing monocarborane was designed to exhibit fluorescence by considering vibronic couplings in the non-fluorescent parent compound. Off-diagonal vibronic coupling constants, which govern the rate constant of non-radiative transitions, were reduced. Based on analysis of vibronic coupling densities, this reduction was attributed to the fact that the highest occupied molecular orbital (HOMO), which is localized on the unsubstituted triphenylamine, became partly delocalized to monocarborane in the derivative, while the lowest unoccupied molecular orbital (LUMO) was strongly localized on triphenylamine. This suggests a design principle for the suppression of non-radiative decay in light-emitting materials. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Fluorescent molecules have been widely investigated for device application such as organic light-emitting diodes (OLEDs) [1–7] and fluorescent sensors [8–10]. To fabricate efficient and reliable devices, it is important to design fluorescent molecules with thermal and chemical stability [1], as well as high fluorescence quantum yield [11,12]. If there is a design principle to convert a nonfluorescent molecule to a fluorescent one, the variety and possible structures of fluorescent molecules can be extended. This would be also useful in other fields such as fluorescence labelling [13] and multifunctionalisation [14,15]. For example, bifunctional fluorescent molecules that are also paramagnetic [16] or capable of photoisomerisation [17] have been widely studied. Fluorescence competes with non-radiative decay, which involves internal conversion and vibrational relaxation. Internal conversion is caused by vibronic coupling (electron–phonon coupling). The rate constant of this process depends on the off-diagonal vibronic coupling constants (VCCs) between the initial and final states [18]. Large off-diagonal VCCs enhance non-radiative decay; therefore, it should be reduced in fluorescent molecules. VCCs can be analysed on the basis of electronic and vibrational structures by
∗ Corresponding author. ∗∗ Corresponding author at: Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan. E-mail addresses: [email protected] (A. Ito), [email protected] (T. Sato). http://dx.doi.org/10.1016/j.cplett.2014.10.004 0009-2614/© 2014 Elsevier B.V. All rights reserved.
expressing these in terms of density, i.e. the vibronic coupling density (VCD) [19,20]. Using the concept of VCD, we have succeeded in reducing VCCs and consequently, suppressing internal conversion in a fluorescent anthracene derivative [21,22]. The large increase in its fluorescence quantum yield has been experimentally confirmed [22]. However, anthracene itself is a fluorescent molecule. Although it is rather challenging to induce fluorescence in non-light-emitting molecules, it is possible using the VCD concept. The target molecule is triphenylamine (1) shown in Figure 1, and to the best of our knowledge, this compound, as well as its derivatives, does not exhibit fluorescence. We designed the triphenylamine derivative 2, shown in Figure 1, to which a monocarborane fragment is introduced. The derivatives of the monocarba-closo-dodecaborane (monocarborane) anion, CB11 H− , have attracted much attention 12 in material science because of their thermal and chemical stability, optical and magnetic properties, and extensibility [23,24]. In this Letter, we show that 2 can exhibit fluorescence through suppression of the internal conversion that normally occurs in 1. The cause of this suppression is elucidated through analysis of the VCDs, from which a design principle for fluorescent molecules is then proposed.
2. Theory The electronic wavefunction of the nth state is denoted by n (r, R), where r and R are the sets of the electronic and nuclear coordinates, respectively. Using the molecular Hamiltonian H and the
Y. Kameoka et al. / Chemical Physics Letters 615 (2014) 44–49
45
The integral of mn,˛ (ri ) is equal to Vmn,˛ :
Vmn,˛ =
mn,˛ (ri ) d3 ri .
(4)
Using electronic and vibrational structures as the bases, the offdiagonal VCD can provide some insight on the off-diagonal VCC, which governs the rate of internal conversion. 3. Computational method Figure 1. Structures of triphenylamine (1) and its derivative (2). The cage represents C(BH)11 .
mass-weighted normal coordinate Q˛ of mode ˛, the off-diagonal VCC between states m and n for mode ˛ is defined as
∂H(r, R) m (r, R0 ) n (r, R0 ) , ∂Q˛ R0
Vmn,˛ :=
(1)
where R0 is the reference nuclear configuration [25]. In the present case, the optimized geometry of the S1 state was chosen as R0 in discussing the internal conversion from the S1 to S0 state. The off-diagonal vibronic coupling density mn,˛ (ri ) between the Sm and Sn states for mode ˛ is defined as [20] mn,˛ (ri ) := mn (ri ) × v˛ (ri ),
(2)
where ri denotes the coordinates of the ith electron, mn (ri ) is the overlap density between the Sm and Sn states, and v˛ (ri ) is the derivative of the potential u(ri ) from all nuclei acting on a single electron given by
v˛ (ri ) :=
∂u(ri ) ∂Q˛
. R0
(3)
The geometries of 1 and 2 at the ground S0 state were optimized at the RB3LYP/6-31+G(d) level of theory, while those at the S1 excited state were optimized using time-dependent density functional theory (TD-DFT) with the same functional and basis set. Ten excited states were considered to obtain the adiabatic (AD) S1 state. Vibrational analysis of the ground S0 state was performed using the geometry of the AD S1 state. The Gaussian 09 package [26] was employed for these calculations. The level of theory is the same one used in a previous work by Oliva et al. [27] on carborane units connected by an unsaturated hydrocarbon. The authors confirmed the reliability of their DFT calculations by comparing data obtained from the CASSCF/CASPT2 method using the same basis set. Off-diagonal VCCs and VCDs between the S1 and S0 states were determined from normal modes in the S0 state obtained using the AD S1 state geometry. These calculations were performed using an in-house code. 4. Results and discussion The orbital diagrams of 1, 2, and the monocarborane anion are shown in Figure 2. The energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of 2 (3.943 eV) is closer to that of 1 (4.136 eV) than that of the monocarborane anion (6.623 eV). The orbital pattern of the LUMOs of 1 and 2 is the same, and apparently, that of the HOMO as
Figure 2. Frontier orbital diagrams of (a) monocarborane anion with degenerate orbitals, (b) 2, and (c) 1 at the B3LYP/6-31+G(d) level. The corresponding isovalues are 4 × 10−2 , 1 × 10−2 , and 2 × 10−2 a.u., respectively.
46
Y. Kameoka et al. / Chemical Physics Letters 615 (2014) 44–49
Table 1 Calculated transition energies E for absorption (Abs.) and emission (Em.), wavelength , oscillator strength f, and contribution of HOMO–LUMO transition for 1 and 2. Molecule
E eV
nm
f
HOMO–LUMO %
1
Abs. Em.
3.4513 3.1094
359.24 398.74
0.0175 0.0158
98 98
2
Abs. Em.
3.2814 2.6878
377.83 461.28
0.0162 0.0086
98 99
well. This suggests that the HOMO and LUMO of 2 mainly originate from the triphenylamine fragment, although the HOMO is partly delocalized to the monocarborane fragment. The results of TD-DFT calculations for the S1 excited states of 1 and 2 are summarized in Table 1. The emission wavelengths of both compounds are in the range of visible light. The contribution of the HOMO–LUMO transition to the emitting states of 1 and 2 is almost 100%. The reorganisation energy within the Born–Oppenheimer approximation is E = 0.1759 and 0.2534 eV for 1 and 2, respectively. This indicates that vibrational relaxation occurred to a greater extent in 2 than in 1. On the other hand, the oscillator strength f of 2 is smaller than that of 1. As will be discussed later, the transition dipole moment, which is a factor of the oscillator strength, is related to the off-diagonal VCC; thus, there is a trade-off in controlling the off-diagonal VCC. The off-diagonal VCCs between the S1 and S0 states of 1 and 2 are shown in Figure 3(a) and (b), respectively. Off-diagonal vibronic couplings, which are responsible for non-radiative decay, were largely suppressed in 2. Consequently, the rate of non-radiative decay in 2 decreased upon introduction of monocarborane into 1. The maximum-coupling mode (i.e. normal mode with the maximum vibronic coupling) of 1 is mode 74 (1270 cm−1 ), which splits into modes 132 and 136 in 2 (1294 and 1332 cm−1 , respectively) as shown in Figure 5. Mode 77 of 1 (1310 cm−1 ), which is the second maximum-coupling mode, corresponds to mode 130 of 2 (1267 cm−1 ). The off-diagonal VCCs for these modes of 1 are suppressed in 2. The cause of the decrease in the VCC of the maximum-coupling mode of 1 will now be discussed by analysing the VCD. The off-diagonal VCDs between the S1 and S0 states for the maximum-coupling mode of 1 and the corresponding two modes of 2 are shown in Figure 4. The off-diagonal VCD 10,˛ is localized on the triphenylamine fragment of 1 and 2; however, that of the latter is suppressed in comparison with the former. This suppression of the VCD can be understood by considering the distributions of the potential derivatives and overlap densities (see Eq. (2)). The potential derivative v˛ for the maximum-coupling mode of 1 and the corresponding modes of 2 are shown in Figure 5. v˛ is
Figure 3. Off-diagonal vibronic coupling constants between the adiabatic S1 and S0 states for the normal modes of (a) 1 and (b) 2.
localized on the triphenylamine fragment for both 1 and 2. It has a -type distribution originating from the in-plane displacement of the benzene rings. For each benzene ring, the distribution of v˛ is similar for 1 and 2. On the other hand, the overlap density consists of the product of HOMO and LUMO densities because the S1 excited states are mainly due to the HOMO–LUMO transition. The HOMO and LUMO of the AD S1 states of 1 and 2 are shown in Figure 6. The HOMO of 2 (b1) is partly delocalized to the monocarborane fragment, while the LUMO (b2) is strongly localized on the triphenylamine fragment. Therefore, the overlap density of 2 is small because the LUMO coefficient of the monocarborane fragment is small. In contrast to 2, the HOMO and LUMO of 1 (a1 and a2, respectively) are
Figure 4. Off-diagonal vibronic coupling density between the adiabatic S1 and S0 states for vibrational mode (a) 74 of 1, and (b) 132 and (c) 136 of 2. The isovalue is 5 × 10−6 a.u.
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Figure 5. Derivative of the electronic-nuclear potential for vibrational mode (a) 74 of 1, and (b) 132 and (c) 136 of 2. The isovalue is 5 × 10−3 a.u.
almost equally distributed among the three benzene rings. However, in 2, the LUMO is largely distributed to one benzene ring, while the HOMO is strongly localized on the two other rings. This can also contribute to the suppression of the overlap density of 2. The overlap densities between the S1 and S0 states of 1 and 2 are shown in Figure 7. As expected from the distributions of the HOMO and LUMO, the 10 of 2 (Figure 7(b)) is small in comparison with that of 1 (Figure 7(a)). Because 10,˛ is the product of the potential derivative and overlap density, and the distribution of the former is similar in 1 and 2, the suppression of the VCD for the maximumcoupling mode of 1 can be attributed to the reduction of the overlap density. Details of the VCD analysis for the second maximum-coupling mode of 1 and corresponding mode of 2 are given in Supplementary Data. The findings were the same as in the case of the maximumcoupling mode. The off-diagonal VCDs were localized on the triphenylamine fragment of 1 and 2, and that of 2 was suppressed in comparison with 1. On the other hand, 1 and 2 have similar
distributions of the potential derivative on the triphenylamine fragment. Therefore, the suppression of the off-diagonal VCC in 2 is attributed to the reduction of the overlap density on this fragment. Based on the discussion above, we propose a design principle to suppress non-radiative decay in molecules: if an excited state, which is expected to be the emitting state, originates from the excitation between a pair of MOs (HOMO and LUMO in the present case), one of the MOs should be delocalized over the fragments and the other should be localized on one of the fragments. This leads to a small overlap density in the overlap region, which consequently results in small off-diagonal VCCs. Thus, non-radiative decay in the molecule will be suppressed. There is, however, a trade-off in suppressing the off-diagonal VCC: the decrease in overlap density also decreases the transition dipole moment. The transition dipole moment is expressed as [20]
mn =
−exmn (x) d3 x.
Figure 6. Molecular orbitals of the adiabatic S1 state of 1 (a1, HOMO; a2, LUMO) and 2 (b1, HOMO; b2, LUMO). The isovalue is 2 × 10−2 a.u.
(5)
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Y. Kameoka et al. / Chemical Physics Letters 615 (2014) 44–49
Figure 7. Overlap density between the adiabatic S1 and S0 states of (a) 1 and (b) 2. The isovalue is 1 × 10−3 a.u.
As in Eq. (5), mn is equal to the integral of the product of the overlap density and position vector. Therefore, a large and widespread distribution of the overlap density yields a large transition dipole moment, while a small overlap density results in the suppression of non-radiative decay. Indeed, in the present case, the oscillator strength of 2 was reduced in comparison with 1, as a manifestation of this trade-off. Although the overlap density of 2 decreased, it still has a widespread distribution on the triphenylamine fragment (Figure 7(b)). This can be an effective strategy to avoid a significant decrease in the transition dipole moment and to suppress the off-diagonal VCCs by reducing the overlap density. 5. Conclusion We designed the triphenylamine derivative 2, which exhibits fluorescence unlike the non-light-emitting triphenylamine (1). The off-diagonal vibronic coupling constants (VCCs) of 2, which govern the rate constant of non-radiative decay, were reduced in comparison with 1. Based on the concept of VCD, the cause of this reduction is the partial delocalisation of the HOMO to monocarborane, concurrent with the localisation of the LUMO on triphenylamine. Compound 2 has already been synthesized and observed to exhibit fluorescence. This experimental study will be reported in the future. It should be noted that 1 itself is not fluorescent, and the emitting state of 2 is due to the transition between the HOMO and LUMO, which are localized on the triphenylamine fragment. In other words, the chromophore of 2 is the triphenylamine fragment. From Eqs. (2) and (4), a general principle for the suppression of non-radiative decay is as follows: the suppression of overlap density results in the reduction of the off-diagonal vibronic coupling constants, and therefore, the reduction of the rate constant of non-radiative decay. Based on the present analysis and above principle, we propose a molecular design principle for the suppression of non-radiative decay in light-emitting materials: if an excited state, which is expected to be the emitting state, originates from the excitation between a pair of MOs, one of the MOs should be delocalized over the fragments and the other should be localized on one of the fragments. Employing this principle, we can expect to extend the variety and possible structures of fluorescent molecules and increase the efficiency of light-emitting molecules. Quite recently the photoluminescence quantum yield (PLQY) of a triphenylamine derivative (PLQY = 6%) has been reported [28]. They have also reported that a tribiphenylamine derivative yielded a high PLQY (PLQY = 37%). However, according to our preliminary calculations for the tribiphenylamine derivative, the chromophore
of the molecule is not triphenylamine. We also investigated the reason for the high PLQY of the tribiphenylamine derivative. We found the mechanism is different from what we have discussed here. We will publish the result in the near future. Acknowledgements Numerical calculations were partly performed at the Supercomputer Laboratory of Kyoto University and the Research Center for Computational Science in Okazaki, Japan. This work was partly supported by a Grant-in-Aid for Scientific Research (B) (No. 24310090) from the Japan Society for the Promotion of Science (JSPS) and Grant-in-Aid for Scientific Research on Innovative Areas “New Polymeric Materials Based on Element-Blocks (No. 2401)” (Nos. 24102014 and 25102516) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. Appendix A. Supplementary Data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. cplett.2014.10.004. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
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