- Email: [email protected]
Charge transfer mobility of naphthodithiophenediimide derivative: Normal-mode and bond length relaxation analysis
Chemical Physics Letters 645 (2016) 92–96
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Charge transfer mobility of naphthodithiophenediimide derivative: Normal-mode and bond length relaxation analysis Xiaoyan Liu, Yujuan Liu, Yujun Zheng ∗ School of Physics, Shandong University, Jinan 250100, China
a r t i c l e
i n f o
Article history: Received 24 September 2015 In final form 17 December 2015 Available online 24 December 2015
a b s t r a c t In this letter, the charge transfer mobility of naphthalenediimide (NDTI) derivative is investigated. By employing the normal-mode analysis and bond length relaxation analysis, the influences of chemical elements on reorganization energies and intermolecular electronic couplings are investigated in NDTI derivative. The results show that the introduction of atom O would decrease reorganization energy in hole-hopping process and increase electronic coupling. This analysis encourages the molecular and material design in organic semiconductors. © 2015 Elsevier B.V. All rights reserved.
1. Introduction In recent years there is a resurgence of interest in organic materials since the organic materials have many advantages, such as, low costs, ease of processing, flexibility, and easy chemical modifications [1,2]. However, the low charge transfer mobility is the main limiting factor for the applications of organic semiconductors. Many investigations have taken to improve its charge transfer mobility [3–9]. The drift mechanism of charge transfer mobility for organic materials is quite different from that for inorganic materials. It is known that the charge transfer mobility in inorganic materials is the charge drift from one atom to another atom. For organic materials, however, the charges drift from one molecule to another molecule, or from one part to another part of the same organic molecule. Han et al. investigated the quantitative structure–activity relationship of charge mobilities in -stacked systems, such as acene, acene derivatives and rubrene by firstprinciples simulation based on Marcus–Hush theory [7,10–12]. As we all know that the molecular potential energy and molecular packing modes have a great influences on the charge transfer mobility. And, the molecular structures affect not only the molecular potential energy, but also the molecular packing modes. 1,4,5,8-Naphthalenediimide (NDI) is one of the widely used organic semiconductors. N,N -dioctyl-Naphthodithiophenediimide (C8-NDTI) (its structure is schematically shown in Figure 1), one of NDI derivatives with two fused thiophenes, is attracted much attention since it has interesting optical and
∗ Corresponding author. E-mail address: [email protected] (Y. Zheng). http://dx.doi.org/10.1016/j.cplett.2015.12.038 0009-2614/© 2015 Elsevier B.V. All rights reserved.
electrical properties, and possesses a rather small HUMO–LUMO energy gap (∼ 2.1 eV) [13]. In this latter, the charge transfer mobility of C8-NDTI during both electron and hole transfer process is investigated. C8-NDTI possesses many special elements, such as, O, S and N, the influences of molecular elements on reorganization energies and intermolecular electronic couplings are discussed using the normal-mode analysis and bond length relaxation analysis. The analysis of the influences of molecular elements on the charge transfer mobility provides some new sights in the design of high charge transfer mobility. 2. Theoretical and computational method Our simulation model is based on first-principle quantum mechanics calculations combined with Marcus theory, using the hopping mechanism to describe the charge mobilities [14–16]. The charge hopping between neighboring molecules is supposed as the normal diffusion. Based on the Einstein relation, the mobility can be expressed as follows: =
e D, kB T
(1)
where e is the charge of electron, D is diffusion coefficient. The diffusion coefficient D can be written as follows: D=
1 2 d Wp, 2n
(2)
where n is the dimension of electronic diffusion, d is the molecular central distance. And, W is the hopping rate, p is the hopping probability, we let p = 1 in this letter.
X. Liu et al. / Chemical Physics Letters 645 (2016) 92–96
93
In this letter, dushin program [20] is employed to take the normal-mode analysis. In dushin, the vibrational modes are included in , and =
1
2
k Q2 ,
(8)
where k is the force constant, Q is the displacement between the neutral and charged molecules for normal mode (NM) . The geometry optimizations of C8-NDTI are carried out by Gaussian package with b3lyp/6-311g(d,p) basis [21] in this letter. The intermolecular electronic couplings are calculated employing the Amsterdam density functional (ADF) program in PW91/TZP basis [22,23]. 3. Results and discussion
Figure 1. The structure of N,N -dioctyl-NDTI.
3.1. Reorganization energy
The hopping rate can be evaluated using Marcus–Hush theory [17]: V2 W=
− e 4kB T , kB T
(3)
where V is the electronic coupling, corresponding to the frontier orbits (HOMO or LUMO) interaction, is the total reorganization energy which is the total of relaxation energies, T is temperature (we set T = 300 K here) and kB is Boltzmann constant. The reorganization energy is the total geometry relaxation energies when a charge is added and removed in a molecule [18]. It can be obtained by four-point method ∗ = 1 + 2 = (E0∗ − E0 ) + (E± − E± ),
(4)
where E0 and E± represent the energies of the neutral, cationic and anionic species in their lowest-energy geometries, respectively. E0∗ ∗ denote the energies of the neutral and charged species in and E± the geometries of the charged and neutral species, respectively. The charge transfer mobility, after considering Eqs. (1)–(3), can be written as follows: =
e 2
2
− (dV ) √ e 4kB T . (kB T )
3
(5)
From Eq. (5), it can be seen that the charge transfer mobility is concerned with three factors: the reorganization energy , the electronic coupling V and the intermolecular distance d. This represents that small reorganization energy, big electronic coupling and long intermolecular distances are good for getting high charge transfer mobility. However, long intermolecular distance d is not favor for big intermolecular electronic coupling. The intermolecular electronic coupling V is given by [19]:
J − 1 (e + e )S ˛ˇ 2 ˛ ˇ ˛ˇ V = , 2 1 − S˛ˇ
(6)
where S˛ˇ is the spatial overlap, J˛ˇ is charge transfer integral, e˛ and eˇ are energies at site ˛ and ˇ, respectively. They are defined as follows: S˛ˇ = ϕ˛ |ϕˇ , J˛ˇ = ϕ˛ |H|ϕˇ ,
(7)
e˛ = ϕ˛ |H|ϕ˛ , where H is the Kohn–Sham Hamiltonian, and ϕ˛(ˇ) is the monomer HOMOs (for hole transport) or LUMOs (for electron transport) with Lowdin’s symmetric transformation, which can be used as the orthogonal basis set for calculation [19].
The reorganization energy is usually composed of two parts: the inner reorganization energy and the outer reorganization energy. The outer reorganization energy is the influence of charge transfer on the molecular solids, which can be neglected for organic crystals. The inner reorganization energy is the molecular geometry relaxation during charge hopping process. In this letter, the inner reorganization energies are simulated by four-point potential method (Eq. (4)). Also, to take the normal-mode and bond length relaxation analysis, the reorganization energies are investigated via normal-mode analysis method. The geometry of C8-NDTI is optimized using b3lyp/6-311g(d,p) by Gaussian. The results of reorganization energies are listed in Table 1. From the table, it can be seen that the results from the two methods are nearly identical. The reorganization energy during hole-hopping process is significantly smaller than that of electron-hopping process. This means that C8-NDTI could be a good p-type semiconductor rather than n-type semiconductor in the view of values. 3.2. Electronic couplings Besides reorganization energy, the electronic coupling is another main factor determining charge hopping rate, which is connected with the molecular orbitals of the conjugated molecules. And the site energies (e˛ and eˇ ), spatial overlap (S˛ˇ ) and charge transfer integrals (J˛ˇ ) for one dimer are computed by employing the Amsterdam density (ADF) program with the PW91 exchangecorrelation functional and the TZP basis [22,23]. Based on Eq. (6), the electronic couplings of LUMO and HOMO are listed in Table 2. The electronic couplings of LUMO (for electron transport) (70.86 meV) Table 1 Reorganization energies and relaxation energies 1 and 2 of C8-NDTI.a Reorganization energies
Four-point method Normal-mode method a
Electron hopping
Hole hopping
1
2
1
2
0.141 0.140
0.141 0.142
0.282 0.282
0.075 0.077
0.072 0.070
0.147 0.147
The energies are in unit of eV.
Table 2 The calculated electronic coupling Ve and Vh for transfer (in meV), the intermolecular ˚ the transport mobility e and h (in cm2 V−1 s−1 ) of center-of-mass distance d (in A), C8-NDTI. (The corresponding experimental result from Ref. [13] is in parentheses.) Parameters
C8-NDTI
Electronic couplings
Distance
Transfer mobility
Vh
Ve
d
h
e
56.13
70.86
3.56
0.407
0.127 (0.055)
94
X. Liu et al. / Chemical Physics Letters 645 (2016) 92–96
Figure 2. (a) Highest occupied molecular orbitals and (b) lowest unoccupied molecular orbitals of optimized C8-NDTI dimer.
Figure 4. Side view of C8-NDTI structure for clarity, octyl groups are omitted (a); the intermolecular center-of-mass distance for P pathway of the C8-NDTI (b).
bigger electronic negativity of atom O. That is, the electronic coupling during electron transfer process is much bigger than that during hole transfer process. Atoms N and S have little influence on the intermolecular van der Waals interactions. 3.3. Charge transfer mobility
Figure 3. Optimized structure of a dimer for C8-NDTI.
is larger than that of HOMO (for hole transport) (56.13 meV), which means C8-NDTI is more suitable to be used as n-type organic semiconductor in the view of HOMO/LUMO values. The HOMO and LUMO orbital distributions of C8-NDTI are shown in Figure 2, where we can see strong overlaps of -conjugating in HOMOs and LUMOs. Figure 3 shows the optimized structure of a dimer for C8-NDTI by employing the Materials Studio. We can note that there are 1.5 ring displacements along long molecular axis and a small displacements along short molecular axis. This kind of position is good for the overlap of LUMOs, which indicates the electronic coupling during electron hopping process is very strong. This kind of position is, however, not good for overlap of HOMOs. Therefore, the electronic coupling in the hole hopping process is much smaller than that of the electron hopping process. The contributions of the each element to the intermolecular interactions can also be analyzed by employing Crystal Explorer [24]. The relative contributions of H-all, C-all, O-all, S-all and Nall contacts to the Hirshfeld surface are listed in Table 3. From the Hirshfeld surface analysis, it is shown that atom O is very important in the intermolecular contacts, except for C and H atoms. And, there are more distributions of LUMO orbits on atom O for the Table 3 van der Waals interactions of C8-NDTI.a Contacts
H-all
C-all
O-all
S-all
N-all
%
74.7
14.2
7.7
2.5
0.9
a The values represent the contacts between the element and adjacent molecules account for the percentage of van der Waals interactions of the whole molecule.
A obvious characteristic in the molecular structure of C8-NDTI is the high planarity of the NDTI core (see Figure 4). From Eq. (5), we can see that the charge transfer mobility is partly dependent on the distance (d) between two molecular centroids in one dimer by using the Materials Studio. Our numerical simulation ˚ it is indicated in shows that the distance of the C8-NDTI is 3.56A, Figure 4. The charge transfer mobility can be obtained by using Eq. (5). The results of the hole and electron transport mobility of C8NDTI are listed in Table 2. For comparison, the experimental result of electron mobility by Fukutomi et al. [13] is also listed in the table, it is 0.055 cm2 V−1 s−1 . As noted in Ref. [13], the experimental results are depending on the substrate surface treatment and the substrate temperature during film deposition, the electron mobility extracted from the saturation regime was somewhat varied [13]. Our theoretical results in this letter are taken under the ideal conditions at room temperature. Our theoretical results provide the reliable results and assist to better understand the intramolecular and intermolecular charge transport behaviors. As shown in Table 2, the charge transfer mobility for hole transfer process is quite bigger than that of electron transfer process. As noted by Marcus–Hush theory, the small reorganization energies and high electronic couplings are good for getting high charge transfer mobility. For C8-NDTI, the electronic coupling is much strong during electron transfer process, and the reorganization energy is also bigger, the charge transfer mobility of electron transfer is much smaller than that during hole transfer process. This depends on the molecular compositions and bond natures. The concrete analysis is shown in the following section. 4. Normal-mode and bond length relaxation analysis To further understand the difference of the reorganization energies between hole/electron hopping process, we first
X. Liu et al. / Chemical Physics Letters 645 (2016) 92–96
95
Figure 5. The relaxation energies () spectra of C8-NDTI for hole and electron transfer process. Panels (a) and (b) are the relaxation energies for neutral and charged states during electron transfer process; panels (c) and (d) are the relaxation energies for neutral and charged state during hole transfer process.
discuss the influences of elements on reorganization energies in this section. The reorganization energy spectra are taken using DUSHIN [20], it is shown in Figure 5. For anionic state, the contributions of normal modes to reorganization energy are mainly coming from high frequency modes of 1500–1800 cm−1 . These modes correspond to the bond length stretching vibrations. For cationic state, however, the contributions of normal modes to reorganization energy are rather small for high frequency modes. For electron hopping process, the reorganization energy 1 and 2 are nearly identical. The main contributions of normal modes for 1 are 1593 cm−1 , 1759 cm−1 , 1435 cm−1 and 287 cm−1 , they correspond to C C stretching vibrations in molecular backbone, C O stretching vibrations, the stretching vibrations of hydrogen bond O H and the bending vibrations of molecular backbone, respectively. For 2 , the modes 1708 cm−1 , 1596 cm−1 , 613 cm−1 and 281 cm−1 contribute the most of the relaxation energies. Among these modes, 1708 cm−1 , which corresponds to the stretching vibrations of C O bond, makes the biggest contributions. The other three normal modes are the stretching vibrations of C C in molecular backbone, the stretching vibrations of hydrogen bond O H and the bending vibrations of molecular backbone, respectively. For hole hopping process, however, the main contributions of normal modes to 1 are 1560 cm−1 , 706 cm−1 , 1387 cm−1 and 1759 cm−1 . The four normal modes are composed of the stretching vibrations of C C in molecular backbone, S C stretching vibrations, the stretching vibrations of hydrogen bond O H and the stretching vibrations of C O bond, respectively. The stretching vibrations of C C bond at 1560 cm−1 contributes to the most of reorganization energies. As for 2 during hole hopping process, the main contributions of normal modes are 1441 cm−1 , 1477 cm−1 , 1374 cm−1 and 393 cm−1 . The normal modes of 1441 cm−1 , 1477 cm−1 and 1374 cm−1 are the vibrations of hydrogen bond O H.
Figure 6. The bond numbers in C8-NDTI for C O, C S and C N.
By the above analysis of reorganization energies, it can be seen that the bond length stretching vibrations contribute to the most of the reorganization energies. As shown in Figure 6, the bonds of C X (X stands for atoms of O, S and N) are numbered. The changes of C X bond lengths in anionic and cationic state are displayed in Figure 7. The changes of their lengths are calculated via subtracting the bond length of the neutral state from the bond length of charged states.
Figure 7. The bond lengths of C O, C S and C N in C8-NDTI.
96
X. Liu et al. / Chemical Physics Letters 645 (2016) 92–96
As shown in Figure 7, the changes of bond lengths in stretching vibrations of C X present big differences during electron and hole hopping process. For C N bonds (4, 5 and 6 as shown in the figure), the changes of bond lengths in electron hopping process are opposite with that in hole hopping process. The values of bond changes are, however, nearly the same. For C S bonds (1 and 2 as shown in the figure), however, they exhibit obvious differences. Bond 1 is greatly compressed during the hole transfer process, and it contributes to the most of the relaxation energies during hole transfer process. For the C O bonds (3 and 7 as shown in the figure), they are stretched during electron transfer process; they are, however, compressed during hole transfer process. Also, it can be seen that the changes of bonds 3 and 7 contribute more relaxation energies for electron transfer process than that for hole transfer process. This is shown that the introduction of atom S would increase reorganization energy during hole transfer process, or, the atom S would be good for improving the charge transfer mobility of n-type semiconductors. On the other hand, atom O would be good for p-type semiconductors. Atom N makes no obvious differences for either n- or p-type semiconductors. 5. Conclusion The charge transfer mobility of C8-NDTI is investigated in this work. The charge transfer mobilities during electron and hole transfer process are 0.127 cm2 V−1 s−1 and 0.407 cm2 V−1 s−1 , respectively. As for reorganization energy, different atom exhibits different manners during the hole and electron transfer process: atom O can reduce the reorganization energy during hole transfer process; atom S can reduce the reorganization energy during electron transfer process; and atom N makes no obvious differences for both hole and electron transfer process. Furthermore, atom O affects the electronic coupling significantly during electron process for its strong electric negativity attracting more LUMO orbits. The atom O causes that the charge transfer mobility in the hole transfer process is bigger than that in the electron transfer process.
Acknowledgments We thank Dr. T. Wu for helpful discussions. This work was supported by the National Natural Science Foundation (No. 11374191) and the National Basic Research Program of China (No. 2015CB921004).
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
[22] [23] [24]
S.R. Forrest, Nature 428 (2004) 911. K. Takimiya, S. Shinamura, I. Osaka, E. Miyazaki, J. Adv. Mater. 23 (2011) 4347. S. Chai, S. Wen, K. Han, Org. Electron. 12 (2011) 1806. J. Gao, R. Li, L. Li, Q. Meng, H. Jiang, H. Li, W. Hu, J. Adv. Mater. 19 (2007) 3008. J. Huang, S. Wen, K. Han, Chem. Asian J. 7 (2012) 1032. H. Geng, Q. Peng, L. Wang, H. Li, Y. Liao, Z. Ma, Z. Shuai, J. Adv. Mater. 24 (2012) 3568. S.H. Wen, W.Q. Deng, K.L. Han, Phys. Chem. Chem. Phys. 12 (2010) 9267. M. Zhang, G. Zhao, J. Phys. Chem. C 116 (2012) 19197. Y. Zhao, W. Liang, Chem. Soc. Rev. 41 (2012) 1075. S.H. Wen, W.Q. Deng, K.L. Han, Chem. Commun. 46 (2010) 5133. J.D. Huang, S.H. Wen, W.Q. Deng, K.L. Han, J. Phys. Chem. B 115 (2011) 2140. S.H. Wen, A. Li, J.L. Song, W.Q. Deng, K.L. Han, W.A. Goddard III, J. Phys. Chem. B 113 (2009) 8813. Y. Fukutomi, M. Nakano, J.Y. Hu, I. Osaka, K. Takimiya, J. Am. Chem. Soc. 135 (2013) 11445. R.A. Marcus, J. Chem. Phys. 24 (1956) 966. N.S. Hush, J. Chem. Phys. 28 (1958) 962. W.Q. Deng, L. Sun, J.D. Huang, S. Chai, S.H. Wen, K.L. Han, Nat. Protoc. 10 (2015) 632. R.A. Marcus, Annu. Rev. Phys. Chem. 15 (1964) 155. J.C. Sancho-Garcìa, Theor. Chem. Acc. 127 (2010) 605. E.F. Valeev, V. Coropceanu, D.A. da Silva Filho, S. Salman, J.-L. Brèdas, J. Am. Chem. Soc. 128 (2006) 9882. J.R. Reimers, J. Chem. Phys. 115 (2001) 9103. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, et al., Gaussian 03, Revision c.02, Gaussian, Inc., Wallingford, CT, 2004. C. Fonseca Guerra, J.G. Snijders, G. te Velde, E.J. Baerends, Theor. Chem. Acc. 99 (1998) 391. ADF2013.01, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands. Available from: http://www.scm.com. F. Hirshfeld, Theor. Chem. Acc. 44 (1977) 129.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Charge transfer mobility of naphthodithiophenediimide derivative: Normal-mode and bond length relaxation analysis Xiaoyan Liu, Yujuan Liu, Yujun Zheng ∗ School of Physics, Shandong University, Jinan 250100, China
a r t i c l e
i n f o
Article history: Received 24 September 2015 In final form 17 December 2015 Available online 24 December 2015
a b s t r a c t In this letter, the charge transfer mobility of naphthalenediimide (NDTI) derivative is investigated. By employing the normal-mode analysis and bond length relaxation analysis, the influences of chemical elements on reorganization energies and intermolecular electronic couplings are investigated in NDTI derivative. The results show that the introduction of atom O would decrease reorganization energy in hole-hopping process and increase electronic coupling. This analysis encourages the molecular and material design in organic semiconductors. © 2015 Elsevier B.V. All rights reserved.
1. Introduction In recent years there is a resurgence of interest in organic materials since the organic materials have many advantages, such as, low costs, ease of processing, flexibility, and easy chemical modifications [1,2]. However, the low charge transfer mobility is the main limiting factor for the applications of organic semiconductors. Many investigations have taken to improve its charge transfer mobility [3–9]. The drift mechanism of charge transfer mobility for organic materials is quite different from that for inorganic materials. It is known that the charge transfer mobility in inorganic materials is the charge drift from one atom to another atom. For organic materials, however, the charges drift from one molecule to another molecule, or from one part to another part of the same organic molecule. Han et al. investigated the quantitative structure–activity relationship of charge mobilities in -stacked systems, such as acene, acene derivatives and rubrene by firstprinciples simulation based on Marcus–Hush theory [7,10–12]. As we all know that the molecular potential energy and molecular packing modes have a great influences on the charge transfer mobility. And, the molecular structures affect not only the molecular potential energy, but also the molecular packing modes. 1,4,5,8-Naphthalenediimide (NDI) is one of the widely used organic semiconductors. N,N -dioctyl-Naphthodithiophenediimide (C8-NDTI) (its structure is schematically shown in Figure 1), one of NDI derivatives with two fused thiophenes, is attracted much attention since it has interesting optical and
∗ Corresponding author. E-mail address: [email protected] (Y. Zheng). http://dx.doi.org/10.1016/j.cplett.2015.12.038 0009-2614/© 2015 Elsevier B.V. All rights reserved.
electrical properties, and possesses a rather small HUMO–LUMO energy gap (∼ 2.1 eV) [13]. In this latter, the charge transfer mobility of C8-NDTI during both electron and hole transfer process is investigated. C8-NDTI possesses many special elements, such as, O, S and N, the influences of molecular elements on reorganization energies and intermolecular electronic couplings are discussed using the normal-mode analysis and bond length relaxation analysis. The analysis of the influences of molecular elements on the charge transfer mobility provides some new sights in the design of high charge transfer mobility. 2. Theoretical and computational method Our simulation model is based on first-principle quantum mechanics calculations combined with Marcus theory, using the hopping mechanism to describe the charge mobilities [14–16]. The charge hopping between neighboring molecules is supposed as the normal diffusion. Based on the Einstein relation, the mobility can be expressed as follows: =
e D, kB T
(1)
where e is the charge of electron, D is diffusion coefficient. The diffusion coefficient D can be written as follows: D=
1 2 d Wp, 2n
(2)
where n is the dimension of electronic diffusion, d is the molecular central distance. And, W is the hopping rate, p is the hopping probability, we let p = 1 in this letter.
X. Liu et al. / Chemical Physics Letters 645 (2016) 92–96
93
In this letter, dushin program [20] is employed to take the normal-mode analysis. In dushin, the vibrational modes are included in , and =
1
2
k Q2 ,
(8)
where k is the force constant, Q is the displacement between the neutral and charged molecules for normal mode (NM) . The geometry optimizations of C8-NDTI are carried out by Gaussian package with b3lyp/6-311g(d,p) basis [21] in this letter. The intermolecular electronic couplings are calculated employing the Amsterdam density functional (ADF) program in PW91/TZP basis [22,23]. 3. Results and discussion
Figure 1. The structure of N,N -dioctyl-NDTI.
3.1. Reorganization energy
The hopping rate can be evaluated using Marcus–Hush theory [17]: V2 W=
− e 4kB T , kB T
(3)
where V is the electronic coupling, corresponding to the frontier orbits (HOMO or LUMO) interaction, is the total reorganization energy which is the total of relaxation energies, T is temperature (we set T = 300 K here) and kB is Boltzmann constant. The reorganization energy is the total geometry relaxation energies when a charge is added and removed in a molecule [18]. It can be obtained by four-point method ∗ = 1 + 2 = (E0∗ − E0 ) + (E± − E± ),
(4)
where E0 and E± represent the energies of the neutral, cationic and anionic species in their lowest-energy geometries, respectively. E0∗ ∗ denote the energies of the neutral and charged species in and E± the geometries of the charged and neutral species, respectively. The charge transfer mobility, after considering Eqs. (1)–(3), can be written as follows: =
e 2
2
− (dV ) √ e 4kB T . (kB T )
3
(5)
From Eq. (5), it can be seen that the charge transfer mobility is concerned with three factors: the reorganization energy , the electronic coupling V and the intermolecular distance d. This represents that small reorganization energy, big electronic coupling and long intermolecular distances are good for getting high charge transfer mobility. However, long intermolecular distance d is not favor for big intermolecular electronic coupling. The intermolecular electronic coupling V is given by [19]:
J − 1 (e + e )S ˛ˇ 2 ˛ ˇ ˛ˇ V = , 2 1 − S˛ˇ
(6)
where S˛ˇ is the spatial overlap, J˛ˇ is charge transfer integral, e˛ and eˇ are energies at site ˛ and ˇ, respectively. They are defined as follows: S˛ˇ = ϕ˛ |ϕˇ , J˛ˇ = ϕ˛ |H|ϕˇ ,
(7)
e˛ = ϕ˛ |H|ϕ˛ , where H is the Kohn–Sham Hamiltonian, and ϕ˛(ˇ) is the monomer HOMOs (for hole transport) or LUMOs (for electron transport) with Lowdin’s symmetric transformation, which can be used as the orthogonal basis set for calculation [19].
The reorganization energy is usually composed of two parts: the inner reorganization energy and the outer reorganization energy. The outer reorganization energy is the influence of charge transfer on the molecular solids, which can be neglected for organic crystals. The inner reorganization energy is the molecular geometry relaxation during charge hopping process. In this letter, the inner reorganization energies are simulated by four-point potential method (Eq. (4)). Also, to take the normal-mode and bond length relaxation analysis, the reorganization energies are investigated via normal-mode analysis method. The geometry of C8-NDTI is optimized using b3lyp/6-311g(d,p) by Gaussian. The results of reorganization energies are listed in Table 1. From the table, it can be seen that the results from the two methods are nearly identical. The reorganization energy during hole-hopping process is significantly smaller than that of electron-hopping process. This means that C8-NDTI could be a good p-type semiconductor rather than n-type semiconductor in the view of values. 3.2. Electronic couplings Besides reorganization energy, the electronic coupling is another main factor determining charge hopping rate, which is connected with the molecular orbitals of the conjugated molecules. And the site energies (e˛ and eˇ ), spatial overlap (S˛ˇ ) and charge transfer integrals (J˛ˇ ) for one dimer are computed by employing the Amsterdam density (ADF) program with the PW91 exchangecorrelation functional and the TZP basis [22,23]. Based on Eq. (6), the electronic couplings of LUMO and HOMO are listed in Table 2. The electronic couplings of LUMO (for electron transport) (70.86 meV) Table 1 Reorganization energies and relaxation energies 1 and 2 of C8-NDTI.a Reorganization energies
Four-point method Normal-mode method a
Electron hopping
Hole hopping
1
2
1
2
0.141 0.140
0.141 0.142
0.282 0.282
0.075 0.077
0.072 0.070
0.147 0.147
The energies are in unit of eV.
Table 2 The calculated electronic coupling Ve and Vh for transfer (in meV), the intermolecular ˚ the transport mobility e and h (in cm2 V−1 s−1 ) of center-of-mass distance d (in A), C8-NDTI. (The corresponding experimental result from Ref. [13] is in parentheses.) Parameters
C8-NDTI
Electronic couplings
Distance
Transfer mobility
Vh
Ve
d
h
e
56.13
70.86
3.56
0.407
0.127 (0.055)
94
X. Liu et al. / Chemical Physics Letters 645 (2016) 92–96
Figure 2. (a) Highest occupied molecular orbitals and (b) lowest unoccupied molecular orbitals of optimized C8-NDTI dimer.
Figure 4. Side view of C8-NDTI structure for clarity, octyl groups are omitted (a); the intermolecular center-of-mass distance for P pathway of the C8-NDTI (b).
bigger electronic negativity of atom O. That is, the electronic coupling during electron transfer process is much bigger than that during hole transfer process. Atoms N and S have little influence on the intermolecular van der Waals interactions. 3.3. Charge transfer mobility
Figure 3. Optimized structure of a dimer for C8-NDTI.
is larger than that of HOMO (for hole transport) (56.13 meV), which means C8-NDTI is more suitable to be used as n-type organic semiconductor in the view of HOMO/LUMO values. The HOMO and LUMO orbital distributions of C8-NDTI are shown in Figure 2, where we can see strong overlaps of -conjugating in HOMOs and LUMOs. Figure 3 shows the optimized structure of a dimer for C8-NDTI by employing the Materials Studio. We can note that there are 1.5 ring displacements along long molecular axis and a small displacements along short molecular axis. This kind of position is good for the overlap of LUMOs, which indicates the electronic coupling during electron hopping process is very strong. This kind of position is, however, not good for overlap of HOMOs. Therefore, the electronic coupling in the hole hopping process is much smaller than that of the electron hopping process. The contributions of the each element to the intermolecular interactions can also be analyzed by employing Crystal Explorer [24]. The relative contributions of H-all, C-all, O-all, S-all and Nall contacts to the Hirshfeld surface are listed in Table 3. From the Hirshfeld surface analysis, it is shown that atom O is very important in the intermolecular contacts, except for C and H atoms. And, there are more distributions of LUMO orbits on atom O for the Table 3 van der Waals interactions of C8-NDTI.a Contacts
H-all
C-all
O-all
S-all
N-all
%
74.7
14.2
7.7
2.5
0.9
a The values represent the contacts between the element and adjacent molecules account for the percentage of van der Waals interactions of the whole molecule.
A obvious characteristic in the molecular structure of C8-NDTI is the high planarity of the NDTI core (see Figure 4). From Eq. (5), we can see that the charge transfer mobility is partly dependent on the distance (d) between two molecular centroids in one dimer by using the Materials Studio. Our numerical simulation ˚ it is indicated in shows that the distance of the C8-NDTI is 3.56A, Figure 4. The charge transfer mobility can be obtained by using Eq. (5). The results of the hole and electron transport mobility of C8NDTI are listed in Table 2. For comparison, the experimental result of electron mobility by Fukutomi et al. [13] is also listed in the table, it is 0.055 cm2 V−1 s−1 . As noted in Ref. [13], the experimental results are depending on the substrate surface treatment and the substrate temperature during film deposition, the electron mobility extracted from the saturation regime was somewhat varied [13]. Our theoretical results in this letter are taken under the ideal conditions at room temperature. Our theoretical results provide the reliable results and assist to better understand the intramolecular and intermolecular charge transport behaviors. As shown in Table 2, the charge transfer mobility for hole transfer process is quite bigger than that of electron transfer process. As noted by Marcus–Hush theory, the small reorganization energies and high electronic couplings are good for getting high charge transfer mobility. For C8-NDTI, the electronic coupling is much strong during electron transfer process, and the reorganization energy is also bigger, the charge transfer mobility of electron transfer is much smaller than that during hole transfer process. This depends on the molecular compositions and bond natures. The concrete analysis is shown in the following section. 4. Normal-mode and bond length relaxation analysis To further understand the difference of the reorganization energies between hole/electron hopping process, we first
X. Liu et al. / Chemical Physics Letters 645 (2016) 92–96
95
Figure 5. The relaxation energies () spectra of C8-NDTI for hole and electron transfer process. Panels (a) and (b) are the relaxation energies for neutral and charged states during electron transfer process; panels (c) and (d) are the relaxation energies for neutral and charged state during hole transfer process.
discuss the influences of elements on reorganization energies in this section. The reorganization energy spectra are taken using DUSHIN [20], it is shown in Figure 5. For anionic state, the contributions of normal modes to reorganization energy are mainly coming from high frequency modes of 1500–1800 cm−1 . These modes correspond to the bond length stretching vibrations. For cationic state, however, the contributions of normal modes to reorganization energy are rather small for high frequency modes. For electron hopping process, the reorganization energy 1 and 2 are nearly identical. The main contributions of normal modes for 1 are 1593 cm−1 , 1759 cm−1 , 1435 cm−1 and 287 cm−1 , they correspond to C C stretching vibrations in molecular backbone, C O stretching vibrations, the stretching vibrations of hydrogen bond O H and the bending vibrations of molecular backbone, respectively. For 2 , the modes 1708 cm−1 , 1596 cm−1 , 613 cm−1 and 281 cm−1 contribute the most of the relaxation energies. Among these modes, 1708 cm−1 , which corresponds to the stretching vibrations of C O bond, makes the biggest contributions. The other three normal modes are the stretching vibrations of C C in molecular backbone, the stretching vibrations of hydrogen bond O H and the bending vibrations of molecular backbone, respectively. For hole hopping process, however, the main contributions of normal modes to 1 are 1560 cm−1 , 706 cm−1 , 1387 cm−1 and 1759 cm−1 . The four normal modes are composed of the stretching vibrations of C C in molecular backbone, S C stretching vibrations, the stretching vibrations of hydrogen bond O H and the stretching vibrations of C O bond, respectively. The stretching vibrations of C C bond at 1560 cm−1 contributes to the most of reorganization energies. As for 2 during hole hopping process, the main contributions of normal modes are 1441 cm−1 , 1477 cm−1 , 1374 cm−1 and 393 cm−1 . The normal modes of 1441 cm−1 , 1477 cm−1 and 1374 cm−1 are the vibrations of hydrogen bond O H.
Figure 6. The bond numbers in C8-NDTI for C O, C S and C N.
By the above analysis of reorganization energies, it can be seen that the bond length stretching vibrations contribute to the most of the reorganization energies. As shown in Figure 6, the bonds of C X (X stands for atoms of O, S and N) are numbered. The changes of C X bond lengths in anionic and cationic state are displayed in Figure 7. The changes of their lengths are calculated via subtracting the bond length of the neutral state from the bond length of charged states.
Figure 7. The bond lengths of C O, C S and C N in C8-NDTI.
96
X. Liu et al. / Chemical Physics Letters 645 (2016) 92–96
As shown in Figure 7, the changes of bond lengths in stretching vibrations of C X present big differences during electron and hole hopping process. For C N bonds (4, 5 and 6 as shown in the figure), the changes of bond lengths in electron hopping process are opposite with that in hole hopping process. The values of bond changes are, however, nearly the same. For C S bonds (1 and 2 as shown in the figure), however, they exhibit obvious differences. Bond 1 is greatly compressed during the hole transfer process, and it contributes to the most of the relaxation energies during hole transfer process. For the C O bonds (3 and 7 as shown in the figure), they are stretched during electron transfer process; they are, however, compressed during hole transfer process. Also, it can be seen that the changes of bonds 3 and 7 contribute more relaxation energies for electron transfer process than that for hole transfer process. This is shown that the introduction of atom S would increase reorganization energy during hole transfer process, or, the atom S would be good for improving the charge transfer mobility of n-type semiconductors. On the other hand, atom O would be good for p-type semiconductors. Atom N makes no obvious differences for either n- or p-type semiconductors. 5. Conclusion The charge transfer mobility of C8-NDTI is investigated in this work. The charge transfer mobilities during electron and hole transfer process are 0.127 cm2 V−1 s−1 and 0.407 cm2 V−1 s−1 , respectively. As for reorganization energy, different atom exhibits different manners during the hole and electron transfer process: atom O can reduce the reorganization energy during hole transfer process; atom S can reduce the reorganization energy during electron transfer process; and atom N makes no obvious differences for both hole and electron transfer process. Furthermore, atom O affects the electronic coupling significantly during electron process for its strong electric negativity attracting more LUMO orbits. The atom O causes that the charge transfer mobility in the hole transfer process is bigger than that in the electron transfer process.
Acknowledgments We thank Dr. T. Wu for helpful discussions. This work was supported by the National Natural Science Foundation (No. 11374191) and the National Basic Research Program of China (No. 2015CB921004).
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
[22] [23] [24]
S.R. Forrest, Nature 428 (2004) 911. K. Takimiya, S. Shinamura, I. Osaka, E. Miyazaki, J. Adv. Mater. 23 (2011) 4347. S. Chai, S. Wen, K. Han, Org. Electron. 12 (2011) 1806. J. Gao, R. Li, L. Li, Q. Meng, H. Jiang, H. Li, W. Hu, J. Adv. Mater. 19 (2007) 3008. J. Huang, S. Wen, K. Han, Chem. Asian J. 7 (2012) 1032. H. Geng, Q. Peng, L. Wang, H. Li, Y. Liao, Z. Ma, Z. Shuai, J. Adv. Mater. 24 (2012) 3568. S.H. Wen, W.Q. Deng, K.L. Han, Phys. Chem. Chem. Phys. 12 (2010) 9267. M. Zhang, G. Zhao, J. Phys. Chem. C 116 (2012) 19197. Y. Zhao, W. Liang, Chem. Soc. Rev. 41 (2012) 1075. S.H. Wen, W.Q. Deng, K.L. Han, Chem. Commun. 46 (2010) 5133. J.D. Huang, S.H. Wen, W.Q. Deng, K.L. Han, J. Phys. Chem. B 115 (2011) 2140. S.H. Wen, A. Li, J.L. Song, W.Q. Deng, K.L. Han, W.A. Goddard III, J. Phys. Chem. B 113 (2009) 8813. Y. Fukutomi, M. Nakano, J.Y. Hu, I. Osaka, K. Takimiya, J. Am. Chem. Soc. 135 (2013) 11445. R.A. Marcus, J. Chem. Phys. 24 (1956) 966. N.S. Hush, J. Chem. Phys. 28 (1958) 962. W.Q. Deng, L. Sun, J.D. Huang, S. Chai, S.H. Wen, K.L. Han, Nat. Protoc. 10 (2015) 632. R.A. Marcus, Annu. Rev. Phys. Chem. 15 (1964) 155. J.C. Sancho-Garcìa, Theor. Chem. Acc. 127 (2010) 605. E.F. Valeev, V. Coropceanu, D.A. da Silva Filho, S. Salman, J.-L. Brèdas, J. Am. Chem. Soc. 128 (2006) 9882. J.R. Reimers, J. Chem. Phys. 115 (2001) 9103. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, et al., Gaussian 03, Revision c.02, Gaussian, Inc., Wallingford, CT, 2004. C. Fonseca Guerra, J.G. Snijders, G. te Velde, E.J. Baerends, Theor. Chem. Acc. 99 (1998) 391. ADF2013.01, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands. Available from: http://www.scm.com. F. Hirshfeld, Theor. Chem. Acc. 44 (1977) 129.