Effect of dihydropyrazine on structures and charge transport properties of N-heteropentacenes matters: A theoretical investigation

Organic Electronics 13 (2012) 2832–2842

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Effect of dihydropyrazine on structures and charge transport properties of N-heteropentacenes matters: A theoretical investigation Xian-Kai Chen, Lu-Yi Zou, Jian-Xun Fan, Shou-Feng Zhang, Ai-Min Ren ⇑ State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China

a r t i c l e

i n f o

Article history: Received 12 July 2012 Received in revised form 15 August 2012 Accepted 18 August 2012 Available online 18 September 2012 Keywords: N-heteropentacenes Charge transport Organic field-effect transistors Kinetic Monte-Carlo simulation Carrier mobility

a b s t r a c t A family of N-heteropentacenes acted as promising candidates for organic semiconductor materials is of immense interest. It should be attributed to the following reasons that (1) the positions, numbers and valence-states of N atom in N-heteropentacenes can effectively tune their electronic structure, stability, solubility, and molecular stacking; (2) diverse intermolecular interaction and p-stacking motifs appear in their crystals. The effect of the position and number of the 6-p-pyrazine on their structures and charge-transport properties has been systematically investigated in our previous work (J. Phys. Chem. C 115 (2011) 21416). Therefore, in this work, the study on the role of 8-p-dihydropyrazine with another valence-state N atoms is our focus. Density functional theory, Marcus electron transfer theory and Brownian diffusion assumption coupled with kinetic Monte-Carlo simulation are applied into this investigation. Our theoretical results indicate that in contrast with pyrazine, dihydropyrazine introduced is more helpful for promoting p-type organic semiconductor materials. For molecule 4, hole mobility of its single crystal theoretically reach 0.71 cm2 V1 s1, and coupled with its fine hole-injection ability, it should be a promising candidate for p-type organic semiconductor materials. Although the lowest triplet-state energies of the molecules studied are very small, introduction of dihydropyrazine is very helpful for increasing the energies. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Organic p-conjugated materials are of immense interest. They have been extensively investigated for optoelectronic and microelectronic applications, such as organic light-emitting diodes (OLEDs) [1,2], organic field-effect transistors (OFETs) [3–5], and organic photovoltaic devices (OPVs) [6,7], which are often called organic semiconductors. Although traditionally, the room-temperature carrier mobilities (106–104 cm2 V1 s1) for organic semiconductors are much lower than that (102–103 cm2 V1 s1) for inorganic semiconductor Si single crystals, the advantages of organic semiconductors are low-cost, light-weight, and good capability of thin-film, large-area, flexible device fabrication [8]. Moreover, recent progresses have also ⇑ Corresponding author. E-mail address: [email protected] (A.-M. Ren). 1566-1199/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.orgel.2012.08.035

shown that some typical organic semiconductors have achieved mobility beyond 10 cm2 V1 s1 (such as pentacene and rubrene) [9,10]. The great interest in pentacene, a leading organic semiconductor material, has recently extended to a family of N-heteropentacenes [11–13]. To develop novel high-performance organic semiconductors, introducing N atoms into the backbone of pentacene is a very promising approach which can effectively tune its electronic structure, stability, solubility, and molecular stacking. The presence of N atoms makes various intermolecular interaction appear in these psystems, which suggests the possibility of promoting high carrier mobilities. Moreover, the change of the number, position and valence-state of N atom can, in principle, bring a large number of structurally related p-backbones, which makes us considerable freely design organic semiconductors based on N-heteropentacenes and provides good opportunities for studying structure–property relationships.

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Recently, many experimental and theoretical groups are dedicated to investigate the structures and charge-transport properties of N-heteropentacenes. Bunz et al. demonstrated that the oligoacenes with aromatic 6-p-pyrazine should be promising candidates for excellent n-type OFET materials because of their large electron affinities and various intermolecular interaction [11,14]. Miao’s group also systemically investigated the effect of the number and position of pyrazine in the silylethynylated N-heteropentacenes on their electronic energy levels, molecular stacking and charge-transport properties [15–18]. Their results indicated that these molecular materials exhibited electron mobility up to 3.3 cm2 V1 s1 [17]. They considered that high electron mobility should be attributed to their low LUMO levels and dense molecular p-stacking in a 2-D brickwork arrangement. In the theoretical investigations, Houk et al. detailedly investigated their structures, electron affinities, excitation, ionization, and reorganization energies for the oligoacenes with pyrazine by theoretical calculation. Their results showed that the above some molecules possessed large electron affinities (up to 3 eV) and small electron reorganization energies (<0.20 eV), which makes them become promising candidates for n-type semiconducting materials [19]. Meantime, our group also showed that the pyrazine in the silylethynylated N-heteropentacenes played a very important role in keeping the molecular planarity, enhancing the stability of organic radical anions and decreasing the electron injection barriers [20]. More importantly, it is very helpful for prompting the molecular p-stacking, and hence gives rise to large intermolecular electronic coupling and electron mobility. Unfortunately, only few investigations focus on the influence of dihydropyrazine on the structures and charge-transport properties of the silylethynylated N-heteropentacenes. Very recently, Miao’s group indicated that the introduction of dihydropyrazine can form the classical H-bonds (N  NAH) in some crystals of N-heteropentacenes which are in principle more powerful in directing the molecular packing [21]. However, it is not clear how its introduction influences the electronic structures and charge-transport properties of N-heteropentacenes. So the problem is our investigation focus in this work. On the basis of these previous investigations, we systematically investigate the effects of dihydropyrazine on their geometrical and electronic structures, molecular stacking motifs, carrier injection and transport properties for the silylethynylated N-heteropentacenes presented in Fig. 1 by theoretical methods here. Through our theoretical study, different roles played by dihydropyrazine and pyrazine in their charge-transport properties are revealed, which can provide a fertile theoretical ground with the rational molecular design and synthesis of the desired organic semiconductor materials.

2. Theoretical and computational methodology There are mainly two types of carrier-transport mechanisms in organic electronic materials: (1) the coherent band mechanism and (2) the incoherent hopping mechanism [8,22–26]. In low temperature, the band mechanism dominates for highly-ordered organic crystals. The carrier moves

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as a highly delocalized plane wave in an energy band [8]. The interaction between the nearest-neighbor molecules is larger compared with dynamic structural disorder, for instance, reorganization energy resulting from charge transfer process from one molecule to another [25,26]. At high temperature (probably at room temperature) or in polycrystalline (or less-ordered) systems where intermolecular interaction is mainly from weak van der Waals force, charge carriers are expected to be localized on a single molecule and thus the band mechanism may be invalid [8]. The transport mechanism can be described here in terms of sequential jumps of the relaxed charges between adjacent molecules, that is, the mechanism can be referred to as hopping mechanism. Extensive experimental evidences, particularly the observed thermal signatures and optical spectra, are consistent with this assumption [27–29]. Here, each hopping event is viewed as a non-adiabatic charge transfer reaction, i.e. charge transfer process between two adjacent molecules follows the reaction M + M+/ = M+/ + M (see Fig. 2a). Charge transfer rate between neighboring molecules can be expressed by standard Marcus theory by the following equation [30]:

k¼

  4p2 V2 k pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp  4kB T h 4pkkB T

ð1Þ

where k is reorganization energy, and V is transfer integral between the two species M and M+/, T is the temperature and kB is the Boltzmann constant. 2.1. Reorganization energy From Eq. (1), charge transfer rate is mainly determined by two important parameters: reorganization energy (k) and transfer integral (V). Here, reorganization energy (k) is evaluated directly from the adiabatic potential-energy surfaces of neutral/cation or neutral/anion species in Fig. 2b (depicted in the Supporting information). k contains the internal and external contributions. The internal k reflects the geometric relaxation associated with going from the neutral to the ionized state, and vice versa. The external k describes the relaxation of the surrounding medium. The external k for organic crystals is commonly neglected because this value is small relative to the internal reorganization energy [8,31]. In the following sections, reorganization energy merely refers to the internal contribution. It is well-known that B3LYP functional is widely applied into the calculations of the geometrical optimization, ionization potentials, electron affinities and reorganization energies [25,26,32–35]. The geometries of the neutral and ionized states of all the studied molecules were optimized by B3LYP functional and its unrestricted formalism (UB3LYP) coupled with 6-31G(d, p) basis set, respectively [20,34–36]. Following each optimization, the vibrational frequencies were calculated and the results showed all the optimized structures were stable. To characterize the energies of these studied species more accurately, a single-point calculation on every specie was carried out at the B3LYP/6-31++G(d, p) level. On the basis of the above calculations, the corresponding ionization potentials (IPs), electron affinities (EAs) as well as reorganization energies

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Fig. 1. Chemical structures of the molecules investigated in this study.

Fig. 2. (a) Schematic representation of a charge exchange reaction pathway for hole transfer through a transition state by weak (nonadiabatic) coupling. The solid curves are the adiabatic surfaces, while the dashed lines refer to diabatic surfaces. (b) Schematic description of internal reorganization energy for hole transfer. The reaction coordinate Q is an ensemble of geometric modifications of the dimer system.

(ks) were obtained. The calculations of the above quantities were performed using the GAUSSIAN09 program package [37]. 2.2. Transfer integral The transfer integrals (V) for the nearest-neighbor dimers along transfer pathways in their crystals were calculated by using a fragment orbital approach [38] in combination with a basis set orthogonalization procedure

[39]. Transfer integral can be calculated from the spatial overlap (SRP), charge transfer integral (HRP) and site energies (HRR, HPP). Transfer integral V is given as follows:

V¼

HRP  0:5SRP ðHRR þ HPP Þ 1  S2RP

ð2Þ

where HRP = hwR|H|wPi, HRR = hwR|H|wRi, HPP = hwP|H|wPi and SRP = hwR|wPi; H is the system Kohn–Sham Hamiltonian of the dimer system, and WR(P) means the monomer’s LUMO (for electron transport) with Löwdin’s symmetric

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transformation, which can be used as the orthogonal basis set for calculation [8]. All the calculations of transfer integrals were performed with PW91/TZ2P method [34–36,40], using the ADF (Amsterdam Density Functional) package [41]. The study of Huang et al. showed that PW91 functional gave the best description for the bandwidth of organic solid [40] and some groups et al. also obtained very good results using PW91/TZ2P method in the similar investigations [34,35]. 2.3. Carrier mobility Here, charge transport is modeled as a Brownian motion described by a particle diffusion process. The mobility can be obtained by the Einstein equation [42]:

l¼

e D kB T

ð3Þ

where l is the carrier mobility, D is the isotropic charge diffusion coefficient, and e is the electronic charge. Here, kinetic Monte-Carlo (KMC) simulation method of carrier mobility used by Shuai et al. is employed [42]. We take the experimental molecular crystal as a reference structure and an arbitrary molecule as the initial charge center. The charge is only allowed to hop between the nearest-neighP boring molecules with a probability is Pa = ka/ aka. The hopping time along this pathway is 1/ka, and the hopping distance is taken to be the intermolecular mass-center distance. At each step in the simulation, a random number r is generated, uniformly distributed between 0 and 1. If Pi1 Pi a¼1 pa < r < a¼1 pa (accumulated probability), then the charge is allowed to go along the ith pathway. Each simulation lasts 10 ls. We save the squared displacement every 100 ns, which is much larger than the time cost in the charge hopping between the neighbors. Then, the diffusion constant is obtained as D ¼ limhlðtÞ2 i=6t, where hl(t)2i is t!1 the mean squared displacement. 2000 trajectories were simulated to obtain a converged diffusion constant, namely, a linear relationship between the square of the diffusion distance and the diffusion time. 3. Results and discussions 3.1. Geometry and reorganization energy All the geometries of the neutral molecule optimized exhibit the planar and rigid skeletons. The reorganization energy is originated from the geometrical relaxation accompanying charge transfer from one molecule to another. Therefore, hole (electron) reorganization energies are closely related to the geometries of cation (anion) states. Table 1 lists reorganization energies (kh for hole and ke for electron) of the studied molecules. The reorganization energies are in proportion to the deformation of the geometries in charge transfer process. Through our calculation, bond length change (BLC) is dominant in the reorganization energies for these rigid and planar molecules, so it is mainly discussed here. The bond length change between the neutral and ionized geometries is presented in Fig. S1 (in supporting information). For these molecules (1–7), the main deformations of bond lengths both for cation

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and anion geometries appear in the CASi bonds, the central benzenes and heterocycles. The relations between BLC values and reorganization energies are shown in Fig. 3. Firstly, it can be found that the relative orders of BLC’s magnitude are almost agreement with those of reorganization energies both for hole and electron. Secondly, all BLC values for electron are larger than the corresponding values for hole, which directly results in larger ke values within the range 0.19–0.37 eV. Finally, for hole, the introduction of heterocycles into TIPS-PEN brings larger BLC values and hence larger kh values, however, they are so small within the range 0.15–0.22 eV that these molecules should be suitable for the application in hole transport materials in terms of Eq. (1). Only introducing pyrazines into TIPSPEN does not almost result in the change of ke values for molecules 1, 5 and 7. In addition, from Table 1 and Fig. 3, through comparing k values of some molecules pairs (molecules 4(6) and 5(7)), it is noted that dihydropyrazine introduced possesses the ability of increasing k values both for electron and hole. It should be a main reason that in comparison with pyrazine, dihydropyrazine brings more p-electron with rigid p-conjugated skeletons, which can result in larger geometrical deformation accompanying charge transfer. These facts suggest that the valence-states of N atom can largely affect their structures and chargetransport properties. To further understand it, the contribution of every atom to the corresponding highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for all the molecules studied is presented in Fig. S2. Larger contribution of atom to HOMO and LUMO should lead to larger deformation on those structures adjacent to it in charge transfer process [43]. As stated in the above section, CASi bonds, central benzene and heterocycles, accompanying large geometrical relaxation in charge transfer process, indeed possess large contributions to HOMOs and LUMOs for the molecules studied, especially dihydropyrazine. 3.2. Frontier molecular orbital, ionization potential, electron affinity It will be useful to examine the HOMO and LUMO levels of the studied molecules. The reorganization energy (the description of local electron-vibration coupling in charge transfer process) is closely related to molecular HOMO and LUMO [8]. The relative orderings of HOMOs and LUMOs energies provide a reasonable qualitative indication of the ability of hole and electron injection, respectively. The energies of HOMOs and LUMOs of all the studied molecules and their corresponding electronic density contours are shown in Fig. 4. From Fig. 4, the electronic density of all the studied molecules mainly distributes in their whole p-conjugated skeletons. It can be found that the introduction of heterocycles stabilizes their HOMO levels which are within the range 5.35 to 4.91 eV. More is the number of heterocycles, more stable is their HOMOs. Molecule 2 is an exception. It should arise from the terminal effect of dihydropyrazine which results in the localization of electronic density of its HOMO at the certain extent (see Fig. 4), and hence enhances the energy level. Through the comparison (mole-

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Table 1 Ionization potentials (IPs), electronic affinities (EAs), extraction potentials and reorganization energies (ks) of the studied molecules obtained in B3LYP/631++G(d, p) theory level (in eV). Species

IPv

IPa

HEP

EAv

EAa

EEP

khole

kelec

TIPS-PEN 1 2 3 4 5 6 7

5.97a 6.21 6.12 6.53 6.12 6.31 6.37 6.65

5.90a 6.12 6.00 6.42 6.02 6.22 6.27 6.54

5.84a 6.05 5.90 6.31 5.92 6.14 6.18 6.44

1.94a 2.20 1.54 1.20 0.93 2.33 1.35 2.66

2.03a 2.29 1.71 1.35 1.11 2.42 1.49 2.76

2.13a 2.39 1.90 1.52 1.30 2.53 1.65 2.87

0.13a 0.15 0.22 0.22 0.19 0.17 0.19 0.21

0.19a 0.19 0.37 0.32 0.37 0.20 0.30 0.20

The suffixes (v) and (a) respectively indicate vertical and adiabatic values. a Data form the Ref. [20].

Fig. 3. Illumination of the relation between their reorganization energies and geometrical deformation in charge transfer processes for the molecules studied.

Fig. 4. The energies of HOMOs and LUMOs of all the studied molecules obtained in B3LYP/6-31++G(d, p) theory level and their electronic density contours.

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cules 4(6) and 5(7)), it can be found that the valence-states of N atom have little effect on HOMO levels. For LUMO levels, in comparison with TIPS-PEN, 8-p-dihydropyrazine possessing donating-electron ability largely enhances the LUMO energies of the corresponding molecules, up to 2.01 eV. It indicates that introducing dihydropyrazine should be adverse to electron injection because their high LUMO energies and hence small electron affinities in terms of Koopmans’ theorem. In contrast to the above molecules with dihydropyrazine, LUMO levels of molecules 1, 5 and 7 are very low within the range 3.15 to 3.49 eV. Through comparing molecule 1 with molecule 5, it is noted that the former with the terminal pyrazine possesses more stable HOMO and LUMO level, which suggests that the position of N atoms can possess large effect on electronic structures of these molecules. In the same time, the different valencestates of N atom also have large effect on the energy gaps (Eg) between the HOMO and LUMO levels of the molecules studied. From Fig. 4, we can find that the introduction of pyrazine can slightly reduce Eg values, while dihydropyrazine introduced largely increase the values, up to 3.07 eV. In our case that the interfacial vacuum energy shift is neglected, the energy barrier of electron (hole) injection from the electrode to the organic semiconductor is the energy difference between the electrode’s work function and LUMO (HOMO) of the organic material (the injection barrier UB = Um  |LUMO| (Um: the work function of the metal electrode) for electron injection; UB = |HOMO|  Um for hole injection) [44]. In the experiments, Au with a work function of about 5.1 eV in vacuum is widely applied to the electrodes of OFETs [44] and thus acted as the source and drain electrodes here. As expected by us, the electron injection barriers for the molecules studied are much larger than the corresponding hole ones. Our previous study had demonstrated that the introduction of pyrazine was helpful for improving the electron injection ability of these molecules [20]. Here, because the introduction of dihydropyrazine gives rise to very high LUMO levels of the corresponding molecules, it make them possess large barriers of electron injection, and the largest barrier reaches 3.09 eV for molecule 4. For hole injection, the introduction of N atoms enhances the energy barriers, and with the increase of their number, the barriers increase. Fortunately, hole-injection barriers of these molecules (1, 4 and 5) with single heterocycle are comparable with the values of excellent p-type organic semiconductor materials (such as oligoacenes). The ionization potentials (IPs) and electron affinities (EAs) of the molecules are the most important parameters that characterize their reduction and oxidation ability, respectively. Thus, IP and EA values are calculated and Table 1 also contains the ionization potentials (IPs), electron affinities (EAs), both vertical (v; at the geometry of the neutral molecule) and adiabatic (a; optimized structure for both the neutral and charged molecule), and extraction potentials (HEP and EEP for the hole and electron, respectively) that refer to the geometry of the ions. Because IPv (EAv) and IPa (EAa) values exhibit the same variational orders here, we only discuss the vertical values. From Table 1, compared with those values of TIPS-PEN, IPv values of molecules 1–7 are larger within the range

6.12–6.65 eV as the result of N atoms introduced. Meantime, it can be found that the effect of dihydropyrazine on the values is obviously weaker than that of pyrazine, and the value (6.12 eV) of molecule 4 is just 0.15 eV larger than that of TIPS-PEN. In contrary, the molecules with dihydropyrazine possess very small EAv values, which results in the instability of their radical anions in ambient atmosphere. It also suggests that introducing dihydropyrazine into TIPS-PEN is not a correct approach to obtain ntype OFET materials. Here, it is consistent with the result of our previous work that the introduction of pyrazine can efficiently promote the stability of radical anions for N-heteropentacenes [20]. 3.3. Molecular stacking character, transfer integral, and carrier mobility It is brought to light that charge-transport properties of organic crystals are highly sensitive to the relative orientations and crystal stacking characters of organic molecules involved [45–47]. Recently, the pentacene derivatives with the triisopropylsilyl substituents (such as TIPS-PEN or Nheteropentacenes) are of immense interest because they exhibit a fascinating molecular p-stacking motif in the crystal structures.[11,12,14–18,21]. The parameters of crystal structures for these molecules studied are listed in Table 2. Fig. 5 also shows their molecular stacking motifs in the crystals of the molecules studied except molecule 2. Through examining their crystal structures, it can be found the crystal structures of molecules 4(6) and 5(7) are very similar, which indicates that the valence-states of N atoms for these molecules should have small effect on their molecular stacking motifs. Meantime, compared with molecule 4(5), the crystal structure of molecule 6(7) shows some differences. It should be a main reason that the introduction of the second heterocycle into in another part of 4(5) gives rise to large change of charge in this area. In contrary, the crystal structures of molecules 1 and 3 have little difference. In addition, the terminal effect of pyrazine does not bring large change of their crystal structures for molecules 1 and 5. These facts also indicate that for these silylethynylated N-heteropentacenes, their molecular packing should be dominated by large triisopropylsilyl substituents. The minimal interplanar distances for 0 these molecular are within0 van der Waals radius (3–4 Å A) and are close to that (3.35 Å A) for graphite. It is powerful for yielding strong pAp interaction in their crystals, which is a crucial factor determining their charge-transport properties. Meantime, no intermolecular H-bonds are found in their crystal structures.

Table 2 The crystal structural parameters for the molecules studied except molecule 2. Species

a/Å

b/Å

c/Å

a/°

b/°

c/°

Space group

1 3 4 5 6 7

7.6 7.5 7.7 7.7 8.1 8.1

7.9 7.9 7.7 7.7 10.5 10.5

16.9 16.9 16.9 17.0 12.8 12.8

78.2 78.2 78.0 78.2 99.8 99.8

89.3 89.1 88.8 88.8 100.8 100.8

79.5 79.7 81.7 81.8 101.5 101.5

P1 P-1 P1 P1 P1 P-1

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Fig. 5. Molecular stacking motifs and charge transfer pathways in single crystals of the molecules studied.

The p-stacking character probably gives rise to fine porbital overlap and hence large transfer integral value. All the identified hopping pathways for these molecules are also presented in Fig. 5 and the corresponding transfer integral values calculated by Eq. (2) are listed in Table 3. Indeed, the p-stacking of these molecules leads to large transfer integral values. Meantime, transfer integrals vary within very large range because the quantities are very sensitive to molecular stacking and closely dependent on the node of HOMOs or LUMOs of the molecules studied. The transfer integral is increased if both are bonding or anti-bonding interactions between the

p-atomic orbitals and decreased when there occurs a cancelation between bonding and anti-bonding overlaps [25]. Through examining their crystal structures, we find that dominant transfer pathways possessing large transfer integrals appear in a–b plane, and single crystals of molecules 1, 3, 4, and 5 exhibit obvious 2D transport properties, while those of molecules 6–7 possess 1D transport character. It is noted that crystal structures of molecules 4 and 5 are very similar, however, their charge transport properties are very different. For molecule 4, hole transfer integrals (Vh) are larger than the corresponding electron transfer integrals (Ve). Coupled with small kh value, single

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Table 3 0 Hole/electron transfer integrals (Vh/Ve in 104 eV) for molecules 1 and 3–7 along different hopping pathways calculated (P: the hopping pathway; d/Å A: the mass 2 1 1 center distance). lh/le (in cm V s ) is the average hole/electron mobility; the values in the brackets are the experimental results. P

1

3

4

5

6

7

Vh/Ve

d

Vh/Ve

d

Vh/Ve

d

Vh/Ve

d

Vh/Ve

d

Vh/Ve

d

1 2 3

78.1/971.4 170.9/771.5 3.2/0.5

7.9 9.9 16.9

79.1/313.5 90.1/375.7 2.4/0.9

7.9 9.9 16.9

688/180.6 437/333.1 0.4/0.9

7.7 10.1 16.9

40.8/1013.4 28/500 2.8/0.4

7.7 10.1 17

253.8/208.2 8.5/3.2 19.5/0.3

8.1 10.5 12.8

149.3/571.2 20.9/5.9 12.7/22.7

8.1 10.5 12.8

lh le

0.21 (0.3–1.2) [18] 5.01 (–) [18]

0.01 (0.3–0.7) [21] 0.07 (–) [21]

0.71 (0.02–0.07) [17] 0.03 (0.0003) [17]

crystal of molecule 4 exhibits fine hole transport property and its hole mobility theoretically reach 0.71 cm2 V1 s1. In contrary, electron mobility for single crystal of molecule 5 is as high as 1.24 cm2 V1 s1, which makes it become a promising candidate for n-type organic semiconductor material, as a result of very large Ve values and small ke value. The fact suggests that dihydropyrazine group should be more helpful for promoting p-type organic semiconductor materials, while the function of pyrazine ring is contrary. For molecules 6 and 7, the change trend of their mobilities is similar with that for molecules 4 and 5. It also demonstrates that dihydropyrazine and pyrazine play very different roles in charge transport properties of the silylethynylated N-heteropentacene materials again. Here, it should be mentioned that some groups have shown that the influence of defects on mobility is more pronounced in 1D conductors than in 2D or 3D ones [48]. So it is probably that single crystals of molecules 6 and 7 do not exhibit good charge-transport properties. Compared with molecule 5, the terminal effect of pyrazine makes single crystal of molecule 1 become excellent ambipolar transport materials—hole and electron mobilities are up to 0.21 and 5.01 cm2 V1 s1, respectively. For molecule 3, the introduction of dihydropyrazine largely reduces transfer integral values compared with molecule 1, and in combination with its large reorganization energies, its single crystal exhibits relative smaller carrier mobilities both for electron and hole. In addition, it must be mentioned that the above KMC simulation about carrier mobility actually gives the 3D averaged mobility although our calculations were based on the structure of single crystals. It is noted that organic crystals typically possess layered structures with weak couplings between layers [49], so their carrier mobilities show obvious anisotropic behavior. Meantime, many factors influence charge-transport properties of organic semiconductors, such as the presence and nature of defects or traps, the presence of interfaces, the applied external fields, and the temperature. Thus, the mobilities obtained by theoretical calculation possess some differences with experimental results from Table 3. However, there is currently a consensus that hopping theories employed describe in a qualitatively correct way how the electronic structure is related to the intrinsic mobility and they retain the ability to rationalize the differences between similar materials even when they are not the most suitable model [50]. Recently, Han et al. have used

0.005 (0.02–0.05) [17] 1.24 (–) [17]

0.06 (–) [17] 0.02 (–) [17]

0.02 (1.0–3.3) [17] 0.25 (0.003) [17]

the following expression to calculate anisotropic carrier mobility [51]:

lU ¼

e X 2 r ka Pa cos2 ca cos2 ðha  UÞ 2kB T a a

ð4Þ

where ha and ca are the hopping angles along the specific transfer channel relative to the reference axis. From Table 3, due to small transfer integral values for the dimers along interlayer transfer pathways for molecules studied, only intra-layer (a–b plane) transfer pathways are considered, i.e. ca = 0°. Here, the reference axis is set as the crystallographic b axis, and the orientation angle along the specific conducting channel relative to the reference b axis is U. The illumination of the relative quantities and results for molecules 1, 3, 4 and 6 are presented in Fig. 6. Because their anisotropic carrier mobilities for single crystals of molecules 5 and 7 have been analyzed in our previous work in Ref. [20], they are not detailedly discussed here. It can be found that carrier mobilities for single crystals of the molecules studied show remarkable anisotropic behavior. Due to similar crystal structures and transfer pathways for molecules 1 and 3, their angle U dependences of mobilities show very similar trend, and their anisotropic le values are much larger than the corresponding lh values. For molecule 1, the highest le (lh) values are 5.85 (0.45) cm2 V1 s1 when U = 165°/345° (135°/315°), which makes it become a promising candidate for ambipolar organic semiconductor materials. In contrary, large difference between crystal structures of molecules 4 and 6 results in very diverse anisotropic behavior of their mobilities, and their anisotropic lh values are much larger the corresponding le values. Large anisotropic lh values (the largest value is 2.59 cm2 V1 s1 when U = 172.5°/ 352.5°) coupled with fine hole-injection ability make it meet the requirements of good p-type organic semiconductor materials. 3.4. Lowest triplet-state energy In electrophosphorescent OLEDs, the emissive layer (EML) is composed of a phosphorescent emitter dispersed within a host material in order to prevent concentration quenching of the phosphorescence. Thus, the development of host materials is as critical as that of emitters for the fabrication of efficient devices. An important criterion that the host needs to fulfill is that its triplet energy is larger than that of the phosphorescent guest, which facilitates an exothermic energy transfer from the host to the guest

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Fig. 6. Illustration of projecting different hopping pathways to a transistor channel in the a–b plane of 1, 3, 4 and 6 crystals, respectively. h1 and h2 are the angles of 1 and 2 dimers relative to the reference crystallographic axis b. U is the angle along a transistor channel relative to the reference crystallographic axis b; The anisotropy curves of the calculated mobilities.

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Fig. 7. The lowest triplet-state (T1) energies with and without zero point vibrational energy (ZPVE) corrections of the molecules studied, and their energy gaps (Eg) between HOMOs and LUMOs.

and prevents back energy transfer (that could lead to luminescence quenching). So far, most of the host materials are organic molecules with N atoms, therefore, the study on the lowest triplet-state (T1) energies of the silylethynylated N-heteropentacenes is very interesting here. The optimization of geometries in T1 states were performed at UB3LYP/ 6-31G(d, p) level using GUSSIAN09 package [52,53]. Vibrational frequency calculations were also carried out to confirm that all the optimized structures correspond to minima on the potential energy surfaces. The T1 energies were assessed on the basis of the optimized structures, and zero point vibrational energy (ZPVE) corrections were also considered. The results are presented in Fig. 7. The following several points can be found from Fig. 7: (i) T1 energies of the molecules studied are very small within the range 0.5–1.99 eV, which cannot meet the requirement of high T1 energies (–3 eV)[53] of the host materials. ZPVE corrections have little effect on all T1 energies in this work; (ii) the valence-states of N atom largely influence Eg values of the molecules studied in this work, and hence their T1 energies. From Fig. 7, it can be found that compared with pyrazine, the introduction of dihydropyrazine is more helpful for enhancing their T1 energies in this work, which should be attributed to large Eg values of the corresponding molecules [52]. The result also provides an efficient approach with the experiment scientists to obtain the host materials possessing high T1 energies. On the basis of the above result, the further design of the host materials with facile and balanced charge injection from the neighboring hole-transport layer and electron-transport layer is our investigation focus in the future. 4. Conclusions In summary, their geometrical and electronic structures, molecular stacking motifs, carrier injection and transport properties for the silylethynylated N-heteropentacenes were detailedly investigated by density functional theory coupled with Marcus electron transfer theory and Brownian diffusion assumption. The results indicate that

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the valence-states of N atom can largely tune their structures and charge-transport properties. More is the number of heterocycles, more stable is their HOMOs. Owing to donating-electron ability of 8-p-dihydropyrazine, it largely enhances the LUMO energies of the corresponding molecules, which indicates that its introduction should be adverse to electron injection and stability of radical anions. Meantime, dihydropyrazine introduced possesses the ability of enhancing k values both for electron and hole. Fortunately, their kh values are very small within the range 0.15–0.22 eV. The fascinating molecular p-stacking in their crystals make some molecular crystals possess excellent charge-transport properties. In contrast with pyrazine, dihydropyrazine introduced is more helpful for promoting p-type organic semiconductor materials. Although their T1 energies are very small, introduction of dihydropyrazine is very helpful for enhancing their T1 energies. The theoretical investigation is a powerful tool providing a fertile theoretical ground with the rational molecular design and synthesis of the desired organic semiconductor materials. Acknowledgements This work was supported by the Natural Science Foundation of China (Nos. 20973078 and 21173099) and Fundamental Research Funds for the Central Universities, as well as Project No. 20121029 Supported by Graduate Innovation Fund of Jilin University. 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.orgel.2012.08.035. References [1] C.W. Tang, S.A. VanSlyke, Applied Physics Letters 51 (1987) 913. [2] P.K.H. Ho, J.S. Kim, J.H. Burroughes, H. Becker, S.F.Y. Li, T.M. Brown, F. Cacialli, R.H. Friend, Nature 404 (2000) 481. [3] H.E. Katz, Journal of Materials Chemistry 7 (1997) 369. [4] G. Horowitz, M.E. Hajlaoui, Advanced Materials 12 (2000) 1046. [5] C.R. Newman, C.D. Frisbie, D.A. da Silva Filho, J.-L. Brédas, P.C. Ewbank, K.R. Mann, Chemistry of Materials 16 (2004) 4436. [6] F. Padinger, R.S. Rittberger, N.S. Sariciftci, Advanced Functional Materials 13 (2003) 85. [7] C.J. Brabec, N.S. Sariciftci, J.C. Hummelen, Advanced Functional Materials 11 (2001) 15. [8] V. Coropceanu, J. Cornil, D.A. da Silva Filho, Y. Olivier, R. Silbey, J.-L. Bredas, Chemical Reviews 107 (2007) 926. [9] V.C. Sundar, J. Zaumseil, V. Podzorov, E. Menard, R.L. Willett, T. Someya, M.E. Gershenson, J.A. Rogers, Science 303 (2004) 1644. [10] M.E. Gershenson, V. Podzorov, A.F. Morpurgo, Reviews of Modern Physics 78 (2006) 973. [11] U.H.F. Bunz, Chemistry-A European Journal 15 (2009) 6780. [12] Q. Miao, Synlett (2012) 326. [13] Y.Y. Liu, C.L. Song, W.J. Zeng, K.G. Zhou, Z.F. Shi, C.B. Ma, F. Yang, H.L. Zhang, X. Gong, Journal of the American Chemical Society 132 (2010) 16349. [14] S. Miao, S.M. Brombosz, P.v.R. Schleyer, J.I. Wu, S. Barlow, S.R. Marder, K.I. Hardcastle, U.H.F. Bunz, Journal of the American Chemical Society 130 (2008) 7339. [15] Q. Tang, Z. Liang, J. Liu, J. Xu, Q. Miao, Chemical Communications 46 (2010) 2977. [16] Z. Liang, Q. Tang, J. Liu, J. Li, F. Yan, Q. Miao, Chemistry of Materials 22 (2010) 6438. [17] Z. Liang, Q. Tang, J. Xu, Q. Miao, Advanced Materials 23 (2011) 1535.

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