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First-principles study of luminescence of fullerene-like clusters

Yang Xiao-Wei She Jie Zhou Si Zhao Ji-Jun

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First-principles study of luminescence of fullerene-like clusters

Yang Xiao-Wei, She Jie, Zhou Si, Zhao Ji-Jun
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  • Thermally activated delayed fluorescence (TADF), a unique molecular fluorescence mechanism, plays a key role in designing emitters of high efficiency. Carbon fullerenes such as C60 and C70 exhibit strong TADF with intensity even higher than that of the prompt fluorescence, owing to their long lifetimes of triplet state and modest singlet-triplet energy gaps. Thus, there arises the intriguing question whether other fullerene-like clusters can also have fluorescence and host the TADF effect. In this work, by time-dependent density functional theory (TD-DFT) calculations, we explore the excited-states of the experimentally reported boron nitride cage clusters B12N12, B24N24 and B36N36, as well as compound clusters B12P12, Al12N12 and Ga12N12 with the same geometry as B12N12. Using the HSE06 hybrid functional, the predicted energy gaps of these fullerene-like clusters are obtained to range from 2.83 eV to 6.54 eV. They mainly absorb ultraviolet light, and their fluorescence spectra are all in the visible range from 405.36 nm to 706.93 nm, including red, orange, blue, and violet emission colors. For the boron nitride cages, the energy gap of excited states increases with the cluster size increasing, accompanied by a blue shift of emission wavelength. For the clusters with B12N12 geometry and different elemental compositions, the excited energy gap decreases as the atomic radius increases, resulting in a red shift of emission wavelength. In addition, the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of these compound cage clusters are distributed separately on different elements, resulting in small overlap between HOMO and LUMO wavefunctions. Consequently, these fullerene-like clusters exhibit small singlet-triplet energy differences below 0.29 eV, which is beneficial for the intersystem crossing between the excited singlet state and triplet state, and hence promoting the TADF process. Our theoretical results unveil the fluorescence characteristics of cage clusters other than carbon fullerenes, and provide important guidance for precisely modulating their emission colors by controlling the cluster sizes and elemental compositions. These experimentally feasible fullerene-like compound clusters possess many merits as fluorophors such as outstanding stabilities, non-toxicity, large energy gap, visible-light fluorescence, and small singlet-triplet energy gap. Therefore, they are promising luminescent materials for applications in display, sensors, biological detection and labelling, therapy, and medicine.
      Corresponding author: Zhou Si, sizhou@dlut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11974068, 91961204).
    [1]

    Baleizao C, Berberan-Santos M N 2008 Ann. N. Y. Acad. Sci. 1130 224Google Scholar

    [2]

    Dos Santos P L, Etherington M K, Monkman A P 2018 J. Mater. Chem. C 6 4842Google Scholar

    [3]

    Parker C A, Hatchard C G 1961 Trans. Faraday Soc. 57 1894Google Scholar

    [4]

    Lam S K, Lo D 1997 Chem. Phys. Lett. 281 35Google Scholar

    [5]

    Wolf M W, Legg K D, Brown R E, Singer L A, Parks J H 1975 J. Am. Chem. Soc. 97 4490Google Scholar

    [6]

    Maciejewski A, Szymanski M 1986 J. Phys. Chem. 90 6314Google Scholar

    [7]

    Yusa S, Kamachi M, Morishima Y 1998 Photochem. Photobiol. 67 519Google Scholar

    [8]

    Nickel B, Klemp D 1993 Chem. Phys. 174 297Google Scholar

    [9]

    Nickel B, Klemp D 1993 Chem. Phys. 174 319Google Scholar

    [10]

    Uoyama H, Goushi K, Shizu K, Nomura H, Adachi C 2012 Nature 492 234Google Scholar

    [11]

    Sato K, Shizu K, Yoshimura K, Kawada A, Miyazaki H, Adachi C 2013 Phys. Rev. Lett. 110 247410

    [12]

    Tanaka H, Shizu K, Miyazaki H, Adachi C 2012 Chem. Commun. 48 11392Google Scholar

    [13]

    Lee J, Shizu K, Tanaka H, Nomura H, Yasuda T, Adachi C 2013 J. Mater. Chem. C 1 4599Google Scholar

    [14]

    Liu L, Wei Q, Cheng Y, Ma H, Xiong S, Zhang X 2020 J. Mater. Chem. C 8 5839Google Scholar

    [15]

    Bachilo S M, Benedetto A F, Weisman R B, Nossal J R, Billups W E 2000 J. Phys. Chem. A 104 11265Google Scholar

    [16]

    Arbohast J W, Foote C S 1991 J. Am. Chem. Soc. 113 8886Google Scholar

    [17]

    Wasielewski M R, O'Neil M P, Lykke K R, Pellin M J, Gruen D M 1991 J. Am. Chem. Soc. 113 2774Google Scholar

    [18]

    Argentine S M, Kota K T, Francis A H 1995 J. Am. Chem. Soc. 117 11762Google Scholar

    [19]

    Berberan-Santos M N, Garcia J M M 1996 J. Am. Chem. Soc. 118 9391Google Scholar

    [20]

    Wang Y 1992 J. Phys. Chem. 96 764Google Scholar

    [21]

    Salazar F A, Fedorov A, Berberan-Santos M N 1997 Chem. Phys. Lett. 271 361Google Scholar

    [22]

    Anthony S M, Bachilo S M, Weisman R B 2003 J. Phys. Chem. A 107 10674Google Scholar

    [23]

    Li X 2007 Acta Phys. -Chim. Sin. 23 1792Google Scholar

    [24]

    Augusto V, Baleizão C, Berberan-Santos M N, Farinha J P S 2010 J. Mater. Chem. 20 1192Google Scholar

    [25]

    Zhao J, Du Q, Zhou S, Kumar V 2020 Chem. Rev. 120 9021Google Scholar

    [26]

    Zhao J, Ma L, Tian D, Xie R 2008 J. Comput. Theor. Nanosci. 5 7

    [27]

    Oku T, Nishiwaki A, Narita I 2004 Sci. Technol. Adv. Mater. 5 635

    [28]

    Oku T, Nishiwaki A, Narita I, Gonda M 2003 Chem. Phys. Lett. 380 620Google Scholar

    [29]

    Oku T, Nishiwaki A, Narita I 2004 Solid State Commun. 130 171Google Scholar

    [30]

    Oku T, Narita I, Nishiwaki A 2004 J. Phys. Chem. Solids 65 369Google Scholar

    [31]

    Oku T, Kuno Masaki, Narita I 2002 Diamond Relat. Mater. 11 940Google Scholar

    [32]

    Fowler P W, Heine T, Mitchell D, Schmidt R, Seifert G 1996 J. Chem. Soc. , Faraday Trans. 92 2197Google Scholar

    [33]

    Oku T, Hirano T, Kuno M, Kusunose T, Niihara K, Suganuma K 2000 Mater. Sci. Eng. B 74 206

    [34]

    Runge E, Gross E K U 1984 Phys. Rev. Lett. 52 997Google Scholar

    [35]

    Marques M A L, Gross E K U 2004 Annu. Rev. Phys. Chem. 55 427Google Scholar

    [36]

    Frisch M, Trucks G, Schlegel H, et al. 2016 Gaussian 16 (Revision A. 03) (Wallingford, CT: Gaussian. Inc.)

    [37]

    Hongzhiwei Technology, Device Studio, Version 2021 A, China. 2021. Available online: https://iresearch.net.cn/cloudSoftware (accessed on 21 January 2022)

    [38]

    Shuai Z 2020 Chin. J. Chem. 38 1223Google Scholar

    [39]

    Wu X, Liang X, Du Q, et al. 2018 J. Phys. Condens. Matter 30 354002Google Scholar

    [40]

    Wu X, Zhou S, Huang X, Chen M, Bruce King R, Zhao J 2018 J. Comput. Chem. 39 2268Google Scholar

    [41]

    Sai L, Wu X, Gao N, Zhao J, Bruce King R 2017 Nanoscale 9 13905Google Scholar

    [42]

    Wu X, Sai L, Zhou S, Zhou P, Chen M, Springborg M, Zhao J 2020 Phys. Chem. Chem. Phys. 22 12959Google Scholar

    [43]

    Watanabe K, Taniguchi T, Kanda H 2004 Nat. Mater. 3 404Google Scholar

    [44]

    Lambrecht W R L, Segall B 1993 Phys. Rev. B 47 9289Google Scholar

    [45]

    Zhu Q, Guo X, Zhang J 2019 J. Comput. Chem. 40 1578Google Scholar

    [46]

    Peng Q, Fan D, Duan R, Yi Y, Niu Y, Wang D, Shuai Z 2017 J. Phys. Chem. C 121 13448Google Scholar

    [47]

    Vincenzo S, Pagliai M, Ciabini L, Cardini G 2001 J. Phys. Chem. A 105 11192Google Scholar

    [48]

    Kumar K S, Patnaik A 2010 J. Comput. Chem. 31 1182

    [49]

    Chen X K, Tsuchiya Y, Ishikawa Y, Zhong C, Adachi C, Brédas J L 2017 Adv. Mater. 29 1702767Google Scholar

    [50]

    Taffet E J, Olivier Y, Lam F, Beljonne D, Scholes G D 2018 J. Phys. Chem. Lett. 9 1620Google Scholar

    [51]

    Saigo M, Miyata K, Tanaka S, Nakanotani H, Adachi C, Onda K 2019 J. Phys. Chem. Lett. 10 2475Google Scholar

    [52]

    Kasha M 1950 Discuss. Faraday Soc. 9 14Google Scholar

    [53]

    Yuan F, Yuan T, Sui L, Wang Z, Xi Z, Li Y, Li X, Fan L, Tan Z, Chen A, Jin M, Yang S 2018 Nat. Commun. 9 1Google Scholar

    [54]

    Palit D K, Sapre A V, Mittal J P, Rao C N R 1992 Chem. Phys. Lett. 195 1Google Scholar

    [55]

    Sun Y P, Wang P, Hamilton N B 1993 J. Am. Chem. Soc. 115 6378Google Scholar

    [56]

    Khandelwal P, Poddar P 2017 J. Mater. Chem. B 5 9055Google Scholar

    [57]

    Marcus R A 1956 J. Chem. Phys. 24 966Google Scholar

    [58]

    Marcus R A Sutin N 1985 Biochim. Biophys. Acta 811 265Google Scholar

    [59]

    Marcus R A 1993 Rev. Mod. Phys. 65 599Google Scholar

    [60]

    Samanta P K, Kim D, Coropceanu V, Brédas J L 2017 J. Am. Chem. Soc. 139 4042

    [61]

    Gao X, Bai S, Fazzi D, Niehaus T, Barbatti M, Thiel W 2017 J. Chem. Theory Comput. 13 515Google Scholar

    [62]

    Liu Y, Lin M, Zhao Y 2017 J. Phys. Chem. A 121 1145

    [63]

    Turro, N J 1991 Modern Molecular Photochemistry (Sausalito, CA: University Science Books) p29

    [64]

    Lu T, Chen F 2012 J. Comput. Chem. 33 580Google Scholar

    [65]

    Liu Z, Lu T, Chen Q 2020 Carbon 165 461Google Scholar

    [66]

    Grabowski Z R, Rotkiewicz K 2003 Chem. Rev. 103 3899Google Scholar

  • 图 1  6种类富勒烯团簇的基态结构, 其中B, N, P, Al, Ga原子的颜色分别用浅粉色、蓝色、浅紫色、紫粉色和棕色表示

    Figure 1.  Ground-state structures of six fullerene-like clusters. The B, N, P, Al, and Ga atoms are shown in pink, blue, purple, magenta, and brown colors, respectively.

    图 2  类富勒烯团簇的电子态密度. 填充和未填充区域分别代表占据态和未占据态, 数字给出HOMO-LUMO能隙, 插图为前线轨道分布, 等值面设为0.04 a.u.

    Figure 2.  Density of states (DOS) of fullerene-like clusters in their ground states. The occupied states are shadowed. The HOMO-LUMO gap is given for each cluster. The insets display the HOMO and LUMO wavefunctions, with an isosurface value of 0.04 a.u.

    图 3  类富勒烯团簇的(a)吸收光谱和(b)发射光谱

    Figure 3.  (a) Absorption spectra and (b) emission spectra of fullerene-like clusters.

    图 4  (a)类富勒烯团簇的基态($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}0} $)、激发单重态($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}1} $)和三重态的HOMO-LUMO能隙($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{T}1} $); (b)发射波长与$ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}1} $的关系图

    Figure 4.  (a) Histogram of HOMO-LUMO gaps of the ground state ($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}0} $), excited singlet state ($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}1} $) and triplet state for the fullerene-like clusters ($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{T}1} $); (b) relationship between emission wavelength and $ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}1} $.

    图 5  类富勒烯团簇S1态的空穴(黄色)和电子(粉色)密度分布. 数字给出空穴和电子波函数的重叠值, 等值面设为0.04 a.u.

    Figure 5.  Electron (magenta) and hole (yellow) density distributions for the excited singlet state of fullerene-like clusters. The overlap between hole and electron wavefunctions are given for each cluster, with an isosurface value of 0.04 a.u.

    表 1  6种类富勒烯团簇的基态性质, 包括对称性(Sym.)、直径(D)、平均键长(d)、最小频率(νmin)、原子间电荷转移(CT)、键级(BO)、HOMO-LUMO能隙($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}0} $)以及吸收波长(λabs)

    Table 1.  Ground-state properties of six fullerene-like clusters, including the symmetry (Sym.), diameter (D), average bond lengths (d), minimum frequency (νmin), Mulliken charge transfer (CT), average wiberg bond order (BO), HOMO-LUMO gap ($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}0} $), and absorption wavelength (λabs).

    Fullerene-like clustersSym.Ddνmin/
    cm–1
    CT
    /e
    BO$ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}0} $/eVλabs
    /nm
    B12N12Th4.801.46323.191.450.876.54189.60
    B24N24S86.681.44155.051.140.886.11202.94
    B36N36Td8.441.46169.511.290.876.20200.00
    B12P12Th6.351.91147.750.161.913.30375.75
    Al12N12Th5.961.82154.331.931.833.62342.54
    Ga12N12Th6.171.88104.801.760.622.83438.16
    DownLoad: CSV

    表 2  6种类富勒烯团簇的激发态性质, 包括S1态的发射波长(λex)、HOMO-LUMO能隙($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}1} $)、激发能(ES1)、S1态和T1态的能量差(∆EST)、自旋-轨道耦合常数(V)、以及重组能(λS, λT)

    Table 2.  Excited-state properties of six fullerene-like clusters, including emission wavelength (λex), HOMO-LUMO gap ($ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}1} $), and emission energy of S1 state (ES1), energy difference between the S1 and T1 state (∆EST), spin-orbit coupling constant (V), and recombination energy of S1 state and T1 state (λS, λT).

    Fullerene-like clustersλex/nm$ {E}_{\mathrm{H}\mathrm{L}}^{\mathrm{S}1} $/eVES1/eVEST/eVV/cm–1λS/eVλT/eV
    B12N12488.383.022.540.250.707.0×10–33.0×10–4
    B24N24405.363.693.060.250.011.3×10–21.2×10–2
    B36N36462.403.322.680.270.268.0×10–31.0×10–2
    B12P12706.932.081.750.290.072.3×10–20.14
    Al12N12455.833.002.720.270.296.8×10–20.15
    Ga12N12644.472.191.920.149.861.9×10–23.0×10–3
    DownLoad: CSV
  • [1]

    Baleizao C, Berberan-Santos M N 2008 Ann. N. Y. Acad. Sci. 1130 224Google Scholar

    [2]

    Dos Santos P L, Etherington M K, Monkman A P 2018 J. Mater. Chem. C 6 4842Google Scholar

    [3]

    Parker C A, Hatchard C G 1961 Trans. Faraday Soc. 57 1894Google Scholar

    [4]

    Lam S K, Lo D 1997 Chem. Phys. Lett. 281 35Google Scholar

    [5]

    Wolf M W, Legg K D, Brown R E, Singer L A, Parks J H 1975 J. Am. Chem. Soc. 97 4490Google Scholar

    [6]

    Maciejewski A, Szymanski M 1986 J. Phys. Chem. 90 6314Google Scholar

    [7]

    Yusa S, Kamachi M, Morishima Y 1998 Photochem. Photobiol. 67 519Google Scholar

    [8]

    Nickel B, Klemp D 1993 Chem. Phys. 174 297Google Scholar

    [9]

    Nickel B, Klemp D 1993 Chem. Phys. 174 319Google Scholar

    [10]

    Uoyama H, Goushi K, Shizu K, Nomura H, Adachi C 2012 Nature 492 234Google Scholar

    [11]

    Sato K, Shizu K, Yoshimura K, Kawada A, Miyazaki H, Adachi C 2013 Phys. Rev. Lett. 110 247410

    [12]

    Tanaka H, Shizu K, Miyazaki H, Adachi C 2012 Chem. Commun. 48 11392Google Scholar

    [13]

    Lee J, Shizu K, Tanaka H, Nomura H, Yasuda T, Adachi C 2013 J. Mater. Chem. C 1 4599Google Scholar

    [14]

    Liu L, Wei Q, Cheng Y, Ma H, Xiong S, Zhang X 2020 J. Mater. Chem. C 8 5839Google Scholar

    [15]

    Bachilo S M, Benedetto A F, Weisman R B, Nossal J R, Billups W E 2000 J. Phys. Chem. A 104 11265Google Scholar

    [16]

    Arbohast J W, Foote C S 1991 J. Am. Chem. Soc. 113 8886Google Scholar

    [17]

    Wasielewski M R, O'Neil M P, Lykke K R, Pellin M J, Gruen D M 1991 J. Am. Chem. Soc. 113 2774Google Scholar

    [18]

    Argentine S M, Kota K T, Francis A H 1995 J. Am. Chem. Soc. 117 11762Google Scholar

    [19]

    Berberan-Santos M N, Garcia J M M 1996 J. Am. Chem. Soc. 118 9391Google Scholar

    [20]

    Wang Y 1992 J. Phys. Chem. 96 764Google Scholar

    [21]

    Salazar F A, Fedorov A, Berberan-Santos M N 1997 Chem. Phys. Lett. 271 361Google Scholar

    [22]

    Anthony S M, Bachilo S M, Weisman R B 2003 J. Phys. Chem. A 107 10674Google Scholar

    [23]

    Li X 2007 Acta Phys. -Chim. Sin. 23 1792Google Scholar

    [24]

    Augusto V, Baleizão C, Berberan-Santos M N, Farinha J P S 2010 J. Mater. Chem. 20 1192Google Scholar

    [25]

    Zhao J, Du Q, Zhou S, Kumar V 2020 Chem. Rev. 120 9021Google Scholar

    [26]

    Zhao J, Ma L, Tian D, Xie R 2008 J. Comput. Theor. Nanosci. 5 7

    [27]

    Oku T, Nishiwaki A, Narita I 2004 Sci. Technol. Adv. Mater. 5 635

    [28]

    Oku T, Nishiwaki A, Narita I, Gonda M 2003 Chem. Phys. Lett. 380 620Google Scholar

    [29]

    Oku T, Nishiwaki A, Narita I 2004 Solid State Commun. 130 171Google Scholar

    [30]

    Oku T, Narita I, Nishiwaki A 2004 J. Phys. Chem. Solids 65 369Google Scholar

    [31]

    Oku T, Kuno Masaki, Narita I 2002 Diamond Relat. Mater. 11 940Google Scholar

    [32]

    Fowler P W, Heine T, Mitchell D, Schmidt R, Seifert G 1996 J. Chem. Soc. , Faraday Trans. 92 2197Google Scholar

    [33]

    Oku T, Hirano T, Kuno M, Kusunose T, Niihara K, Suganuma K 2000 Mater. Sci. Eng. B 74 206

    [34]

    Runge E, Gross E K U 1984 Phys. Rev. Lett. 52 997Google Scholar

    [35]

    Marques M A L, Gross E K U 2004 Annu. Rev. Phys. Chem. 55 427Google Scholar

    [36]

    Frisch M, Trucks G, Schlegel H, et al. 2016 Gaussian 16 (Revision A. 03) (Wallingford, CT: Gaussian. Inc.)

    [37]

    Hongzhiwei Technology, Device Studio, Version 2021 A, China. 2021. Available online: https://iresearch.net.cn/cloudSoftware (accessed on 21 January 2022)

    [38]

    Shuai Z 2020 Chin. J. Chem. 38 1223Google Scholar

    [39]

    Wu X, Liang X, Du Q, et al. 2018 J. Phys. Condens. Matter 30 354002Google Scholar

    [40]

    Wu X, Zhou S, Huang X, Chen M, Bruce King R, Zhao J 2018 J. Comput. Chem. 39 2268Google Scholar

    [41]

    Sai L, Wu X, Gao N, Zhao J, Bruce King R 2017 Nanoscale 9 13905Google Scholar

    [42]

    Wu X, Sai L, Zhou S, Zhou P, Chen M, Springborg M, Zhao J 2020 Phys. Chem. Chem. Phys. 22 12959Google Scholar

    [43]

    Watanabe K, Taniguchi T, Kanda H 2004 Nat. Mater. 3 404Google Scholar

    [44]

    Lambrecht W R L, Segall B 1993 Phys. Rev. B 47 9289Google Scholar

    [45]

    Zhu Q, Guo X, Zhang J 2019 J. Comput. Chem. 40 1578Google Scholar

    [46]

    Peng Q, Fan D, Duan R, Yi Y, Niu Y, Wang D, Shuai Z 2017 J. Phys. Chem. C 121 13448Google Scholar

    [47]

    Vincenzo S, Pagliai M, Ciabini L, Cardini G 2001 J. Phys. Chem. A 105 11192Google Scholar

    [48]

    Kumar K S, Patnaik A 2010 J. Comput. Chem. 31 1182

    [49]

    Chen X K, Tsuchiya Y, Ishikawa Y, Zhong C, Adachi C, Brédas J L 2017 Adv. Mater. 29 1702767Google Scholar

    [50]

    Taffet E J, Olivier Y, Lam F, Beljonne D, Scholes G D 2018 J. Phys. Chem. Lett. 9 1620Google Scholar

    [51]

    Saigo M, Miyata K, Tanaka S, Nakanotani H, Adachi C, Onda K 2019 J. Phys. Chem. Lett. 10 2475Google Scholar

    [52]

    Kasha M 1950 Discuss. Faraday Soc. 9 14Google Scholar

    [53]

    Yuan F, Yuan T, Sui L, Wang Z, Xi Z, Li Y, Li X, Fan L, Tan Z, Chen A, Jin M, Yang S 2018 Nat. Commun. 9 1Google Scholar

    [54]

    Palit D K, Sapre A V, Mittal J P, Rao C N R 1992 Chem. Phys. Lett. 195 1Google Scholar

    [55]

    Sun Y P, Wang P, Hamilton N B 1993 J. Am. Chem. Soc. 115 6378Google Scholar

    [56]

    Khandelwal P, Poddar P 2017 J. Mater. Chem. B 5 9055Google Scholar

    [57]

    Marcus R A 1956 J. Chem. Phys. 24 966Google Scholar

    [58]

    Marcus R A Sutin N 1985 Biochim. Biophys. Acta 811 265Google Scholar

    [59]

    Marcus R A 1993 Rev. Mod. Phys. 65 599Google Scholar

    [60]

    Samanta P K, Kim D, Coropceanu V, Brédas J L 2017 J. Am. Chem. Soc. 139 4042

    [61]

    Gao X, Bai S, Fazzi D, Niehaus T, Barbatti M, Thiel W 2017 J. Chem. Theory Comput. 13 515Google Scholar

    [62]

    Liu Y, Lin M, Zhao Y 2017 J. Phys. Chem. A 121 1145

    [63]

    Turro, N J 1991 Modern Molecular Photochemistry (Sausalito, CA: University Science Books) p29

    [64]

    Lu T, Chen F 2012 J. Comput. Chem. 33 580Google Scholar

    [65]

    Liu Z, Lu T, Chen Q 2020 Carbon 165 461Google Scholar

    [66]

    Grabowski Z R, Rotkiewicz K 2003 Chem. Rev. 103 3899Google Scholar

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  • supplement 123601-20212426补充材料.pdf supplement
Metrics
  • Abstract views:  3464
  • PDF Downloads:  129
  • Cited By: 0
Publishing process
  • Received Date:  29 December 2021
  • Accepted Date:  22 January 2022
  • Available Online:  28 February 2022
  • Published Online:  20 June 2022

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