Theoretical Investigations on Charge-Transfer Properties of Novel

Article pubs.acs.org/JPCC

Theoretical Investigations on Charge-Transfer Properties of Novel High Mobility n‑Channel Organic Semiconductors − Diazapentacene Derivatives Xin Wang College of Chemistry, Sichuan University, Chengdu 610064, China

Kai-Chung Lau* Department of Biology and Chemistry, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong S Supporting Information *

ABSTRACT: The charge-transfer properties of three diazapentacene derivatives, including 5,7,12,14-tetrachloro-6,13diazapentacene (TCDAP), 5,7,12,14-tetrachloro-6,13-diaza-6,13-dihydropentacene (TCDAHP), and 5,7,12,14-tetrafluoro-6,13diazapentacene (TFDAP), have been studied using density functional theory. The performance of five pure GGA and seven hybrid GGA functionals and G3MP2B3 method on the reorganization energy (λ) and mobility (μ) predictions of TCDAP has been examined. Both the B3LYP functional and the G3MP2B3 method give reliable predictions for the λ value. Using the reorganization energy at the G3MP2B3 level together with the transfer integral by BHandH, BHandHLYP, and M06-2X functionals yields electron mobilities of 3.44, 3.32, and 3.29 cm2 V−1 S−1 for TCDAP, respectively, which come fortuitously close to the experimental value of 3.39 cm2 V−1 S−1. Other density functionals also give mobility predictions in agreement with the experimental value to a factor of ∼2. The TCDAHP, a −NH derivative of TCDAP, is predicted to have a large hole and electron mobility of 2.30 and 3.89 cm2 V−1 S−1, respectively. Our results suggest that TCDAP is an n-channel material, while TCDAHP is an ambipolar organic semiconductor with simultaneous hole and electron transport properties. By the substitution of chlorine with fluorine in TCDAP, we find that TFDAP is very similar to TCDAP in terms of the molecular and crystal structure and HOMO/LUMO property. TFDAP is an n-type semiconductor but with a larger electron mobility of 3.51 cm2 V−1 S−1. All theoretical predictions are based on the crystal structures obtained with PBC model and B97D functional. The transfer integral calculations along the four dominant hopping pathways reveal that the hole and electron transport processes occur via the parallel routes between two neighboring molecules with π-stacking interactions. On the basis of the angular resolution anisotropic mobility analyses, TCDAP, TCDAHP, and TFDAP show remarkably different anisotropic behaviors in comparison with the 6,13-dihydro-6,13-diazapentacene (DHDAP). conductors.11,12 Because of the great importance of n-type materials in plastic electronic devices such as OFETs,11 highperformance n-channel materials are in huge demand, and the understanding of the charge transport mechanism in these nchannel organic semiconductors is of fundamental interest.

1. INTRODUCTION Organic field-effect transistors (OFETs), field effect transistors using an organic semiconductor in transport channels, have gained tremendous interest due to their potential applications in low-cost, large-area, and tunable electronic properties.1−3 There has been important progress in the development and rational design of OFETs in the past decades.4−10 Most attention has been paid to p-type (hole-transporting) materials, whereas less studies are found on n-type (electron-transporting) semi© 2012 American Chemical Society

Received: July 20, 2012 Revised: October 8, 2012 Published: October 9, 2012 22749

dx.doi.org/10.1021/jp309226z | J. Phys. Chem. C 2012, 116, 22749−22758

The Journal of Physical Chemistry C

Article

Figure 1. Molecular structures of diazapentacene and its derivatives.

structural predictions of nucleic acid base dimers with strong π−π stacking interactions.46 Such π−π interactions should play an important role in molecular and crystal structures of TCDAP, TCDAHP, and TFDAP. In addition to this, four pure GGA and five hybrid GGA functionals are selected for the performance assessments of transfer integrals predictions. We compare the μ− and μ+ predictions with available experimental data20,21 and assess the performance of different functionals in charge transport property and mobility predictions for TCDAP, TCDAHP, and TFDAP. We aim at understanding the interplaying role of various factors affecting the charge transport property and hope to give insight for potential n-type semiconductors with high mobility.

The improvement in charge-transfer mobility is the prime goal of OFET material development. Several notable n-type semiconductors used in OFETs such as C60 and its derivatives,13,14 naphthalene diimide (NDI) derivatives,15 perylene diimide (PDI) dervativies,16 perfluoropentacene,17 fluorinated metal phthaloyanines,18 and oligothiophenes19 have been reported. Among them, only the derivatives of C60, NDI, and PDI13−16 were reported to have electron mobility (μ−) as high as 6 cm2 V−1 S−1, and many other n-channel semiconductors have relatively low mobilities.11,12,17−19 Quiet recently, Tao and co-workers have reported a novel n-channel heteroaromatic oligomer, 5,7,12,14-tetrachloro-6,13-diazapentacene (TCDAP, see Figure 1) with a μ− value of 3.39 cm2 V−1 S−1.20 The hole mobilities (μ+) of TCDAP and its −NH derivatives, 5,7,12,14-tetrachloro-6,13diaza-6,13-dihydropentacene (TCDAHP, see Figure 1), have also been reported. They found that TCDAHP has a significantly larger hole mobility than TCDAP.21 TCDAP and TCDAHP are the respective chlorinated derivatives of 6,13-diazapentacene (DAP) and 6,13-dihydro-6,13-diazapentacene (DHDAP) (see Figure 1). DAP is a poor p-type semiconductor,22 and DHDAP has a field-effect hole mobility of 0.45 cm2 V−1 S−1 on octadecyltrichlorosilane (OTS)-treated SiO2 substrate.23 These studies point out that halogen substitution on the diazapentacene could potentially form a class of n-type semiconductor with high mobility. It is known that the charge transport properties of semiconductors are affected by a number of factors such as molecular structure, mode of crystal packing, film morphology, and material stability, etc.1,7 As the crystal packing and molecular structures of TCDAP and TCDAHP are similar, we believe that TCDAHP may have a high electron mobility and behave as an n-type semiconductor. In light of this, we perform theoretical calculations to study the charge-transfer properties of TCDAP and TCDAHP. In addition, it has been demonstrated that fluorination is also a useful strategy to convert a p-type semiconductor to an n-type one because of the lowering of the LUMO energy in the molecule.24−26 Thus, we substitute the chlorine in TCDAP with fluorine and carry out similar prediction on 5,7,12,14-tetrafluoro-6,13-diazapentacene (TFDAP). The hole and electron mobilities of the TFDAP molecule have not been reported yet. By optimizing the crystal structures of TCDAP, TCDAHP, and TFDAP using periodic boundary condition (PBC) and density functional theory (DFT), we obtain reorganization energy (λ) at the G3MP2B327 level for the μ− and μ+ predictions using various functionals such as PW91,28 B3LYP,29 and M06-2X.30 Both the PW91 and the B3LYP functionals have been used extensively for mobility prediction in the community.31−45 The M06-2X method30 is a density functional developed for organic molecules, especially for

2. COMPUTATIONAL DETAILS The prediction of charge mobility of organic semiconductors is a grand challenge to theoretical and computational chemists. There has been great progress in the developments of theoretical models for quantitative prediction of charge mobility.47 There are mainly two types of charge transport mechanisms: incoherent hopping and coherent band mechanisms.7,48 At high temperature (probably at room temperature), when the charge-transfer integral (t) is smaller than the reorganization energy, the charge carriers likely localize on a single molecule at the weak-coupling limit, and thus the transport process can be described by the hopping model.47−49 Under this situation, the Marcus−Hush model50,51 can be applied for charge mobility predictions and has been proved to be successful on many organic semiconductors.31−45 However, electron and charge transport is known to be a bulk property. When the transfer integral is dominant over the reorganization energy, it is possible that the charge is delocalized over several molecules. In this regard, the charge-transfer properties should be more appropriately described by coherent band mechanism and Holstein−Peierls model.47 In the present molecules, the reorganization energies are found to be larger than the transfer integrals. For examples, the λ+ value of 195.7 meV is larger than the value of t+ = 28.1 meV along the P1 dominant hopping pathway of TCDAP at the M06-2X level. We believe that a localized description on the charge transport process by the Marcus−Hush model is adaquate for the mobility predictions of TCDAP, TCDAHP, and TFDAP. In hopping mechanism, the charge carriers are expected to localize and jump between neighboring molecules to migrate across the organic layer. The hole transfer and electron transfer are represented by the following reactions, respectively:

22750

M + M+ → M+ + M

(1)

M + M− → M− + M

(2)



Article

where the M, M+, and M− are the neutral molecule, cation, and anion, respectively. The μ of hopping at a temperature (T) can be evaluated from the Einstein−Smoluchowski relation: e μ= D kBT (3) where e is the electron charge, kB is the Boltzmann constant, and D, diffusion coefficient, is a sum of the individual diffusion coefficient along the ith hopping pathway: D=

1 2n

∑ ri2kiPi i

(4)

Here, n = 3 is the space dimensionality, i represents a specific hopping pathway, ri is the hopping distance, ki is the hopping rate of the charge carrier in the ith pathway, and Pi is the relative probability for charge carrier hopping to a particular ith neighbor. Recently, some studies52,53 have shown that eq 4 may give unreliable global mobility for the diffused charge transports in annelated β-trithiophenes-type organic semiconductor. However, given that qualitative mobility predictions have been obtained by eq 4 for various organic semiconductors such as pentacene,32−34 rubrene,34 anthracene,35 oligothiophenes,36 perylene,38 pyrazines,40 and α-oligofuran,41 eq 4 should be applicable to describe the charge transport processes in TCDAP, TCDAHP, and TFDAP in the first approximation. The rate of charge transfer between two adjacent molecules, ki, is expressed by Marcus theory50,51 as: ki =

⎛ −λ± ⎞ 4π 2 2 1 ti exp⎜ ⎟ h ⎝ 4k bT ⎠ 4πλ±k bT

Figure 2. P1, P2, T1, and T2 hopping pathways in TCDAP.

and TPSSh) are chosen to give complete performance evaluation of density functionals.

3. RESULTS AND DISCUSSION Crystal and Molecular Structures of TCDAP, TCDAHP, and TFDAP. The TCDAP single crystal structure has a planar π system packing in a monoclinic lattice with a space group P21/ n.20 The TCDAHP has a similar crystal structure but slightly larger cell.21 Listed in Table 1, the optimized crystal cell parameters of TCDAP, a = 3.936 Å, b = 12.38 Å, c = 17.35 Å, and β = 95.2°, are in good agreement with the corresponding experiment data:20 a = 3.919 Å, b = 12.18 Å, c = 16.99 Å, and β = 94.8°. The computed cell parameters of TCDAHP also come very close to the experiment results.21 Encouraged by the good agreements in the predictions of TCDAP and TCDAHP crystal structures, we are confident that the crystal structure of TFDAP obtained at the same level of theory should be reliable. In fact, the optimized cell parameters (a = 3.906 Å, b = 12.24 Å, c = 17.23 Å, and β = 94.9°) of TFDAP are very similar to those of TCDAP and TCDAHP. The π−π distances (Figure S3 in the Supporting Information) between two neighboring molecules along P1 pathways in TCDAP (3.372 Å) and TCDAHP (3.473 Å) are very similar and become slightly shorter in TFDAP (3.367 Å). The molecular structures of TCDAP, TCDAHP, and TFDAP are also similar (see geometrical parameters in Figure S4 in the Supporting Information). These results suggest that substitution of chlorine by fluorine in TCDAP does not change the crystal and molecular structure of TFDAP significantly. As found in Figure 3, the HOMO/LUMO of TCDAP and TFDAP is similar to those of DAP and pentacene,21 but the HOMO and LUMO energy levels of TCDAP and TFDAP are significantly stabilized by the halogen substitutions. The lowering of HOMO and LUMO energy is an important indicator for TCDAP and TFDAP to be high-mobility material. A similar situation is found between DHDAP and TCDAHP: both HOMO/LUMO patterns of DHDAP and TCDAHP are similar, whereas the HOMO and LUMO energy levels of TCDAHP are stabilized by chlorine substitution. Reorganization Energy of TCDAP, TCDAHP, and TFDAP. According to eqs 3−5, the reorganization energy λ and transfer integral t are the two dominant quantities governing the mobility. To study the performance of different theoretical methods for the predictions of λ (and its effect on μ), we have performed λ predictions using the PW91, B3LYP, and M06-2X density functionals and at the G3MP2B3 level. The G3MP2B3 method is a simplified version of the composite Gaussian 3 (G3) methodology,65 which approximates the electronic energy at the QCISD(T) level. The G3MP2B3 has an accuracy of ∼1.25 kcal/

(5)

where ti denotes the transfer integral between neighboring molecules in each individual hopping pathway, and λ± is the reorganization energy for hole (λ+) and electron (λ−) transports as: λ+ = E0(Q +) − E0(Q 0) + E+(Q 0) − E+(Q +)

(6)

λ− = E0(Q −) − E0(Q 0) + E − (Q 0) − E−(Q −)

(7)

where E0(Q0), E+(Q+), and E−(Q−) are the respective energies of optimized neutral, cationic, and anionic structures. E0(Q+)/ E0(Q−) is the neutral energy of the optimized cationic/anionic structure of the molecule, and E+(Q0)/E−(Q0) is the cationic/ anionic energy of the optimized neutral structure. A highly accurate G3MP2B3 method27 is used to predict the reorganization energy with the Gaussian 09 program.54 The crystal structures are optimized with the PBC model at the B97D/6-31G(d) level. The transfer integrals, based on the unique fragment approach,55,56 at 300 K are computed with the Amsterdam Density Functional (ADF 2010) package.57 There are a total of 11 hopping pathways found in the crystal structures of TCDAP (see Figure S1 in the Supporting Information), TCDAHP, and TFDAP, and only four dominant hopping pathways (P1, P2, T1, and T2 in Figures 2 and S2) are considered in this work. In addition to the PW91,28 B3LYP,29 and M06-2X30 methods, we have included the following density functionals for the performance evaluation in transfer integral predictions: four pure GGA functionals, BP86,58 BLYP,29b,59 PBE,60 and TPSS,61 and five hybrid GGAs, BHandH, 62 BHandHLYP,62 PBE0,63 mPW1K,64 and TPSSH.61 Both the classical GGA functional (BP86) and some newly developed functionals (such as mPW1K 22751



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Table 1. P21/n Crystal Lattice Parameters Obtained with PBC Model and at the B97D/6-31G(d) Levela

a

compound

a (Å)

b (Å)

c (Å)

β (deg)

π−πb (Å)

π−πc (Å)

TCDAP TCDAHP TFDAP

3.936(3.919) 4.032(4.05) 3.906

12.38(12.18) 12.43(12.13) 12.24

17.35(16.99) 17.35(17.11) 17.23

95.2(94.83) 91.75(90.97) 94.94

3.396(3.37) 3.481(3.45) 3.367

2.786(2.778) 2.780(2.768) 2.757

The experimental values are given in parentheses. bπ−π distance is along the P1 pathway. cπ−π distance is along the P2 pathway.

The predictions by PW91 and M06-2X derive from the “estimated” λ+ value by −0.03 and +0.06 eV. Hole Mobility of Pentacene. Before the results are presented on the charge mobility of TCDAP, TCDHAP, and TFDAP, a performance assessment on the hole mobility of pentacene with different density functionals is done (see Table S1). The experimental hole mobility67,68 of pentacene has been reported to range from 3 to 7 and from 11.7 to 35 cm2 V−1 S−1 (depending on the homogeneity of current flow in the experiment sample),68 and pentacene has been used for performance assessment in numerous studies.32−34,69−72 The five pure GGA functionals (PW91, BP86, BLYP, PBE, and TPSS in category (3)) give μ+ values below 2 cm2 V−1 S−1, whereas the hybrid functional yields larger μ+, ranging from 1.81 to 3.27 cm2 V−1 S−1. Among these DFT methods, the μ+ values are increased to 3.31 (M06-2X), 3.56 (BHandH), and 3.34 (BHandLYP) cm2 V−1 S−1 by augmenting with diffuse functions. These three predictions are at the lower bound of the experimental values of 3−7 cm2 V−1 S−1. Electron and Hole Mobilities of TCDAP. The hole mobility predictions of TCDAP are grouped into four categories in accordance with the combinations of reorganization energy and transfer integral computed at various levels of theory and basis sets (see Table 3 and Table S2): (1) λ and t are obtained with the PW91, B3LYP, and M06-2X functionals; (2) λ and t are obtained with B3LYP and PW91 or M06-2X, respectively; (3) λ is obtained at the G3MP2B3 level and t is calculated with PW91, B3LYP, BHandH, BHandHLYP, and M06-2X functionals; and (4) λ is obtained at the G3MP2B3 level and t is calculated with B3LYP, BHandH, BHandHLYP, and M06-2X functionals but augmented with diffuse functions in the basis set. Under all four categories, the theory predicts that the μ+ ranges from 0.16 to 0.53 cm2 V−1 S−1. The hole mobilities of 0.01−0.13 cm2 V−1 S−1 along the rubbing direction and 0.07 cm2 V−1 S−1 in the direction perpendicular to the rubbing direction have been measured with a TCDAP thin film deposited on a rubbed monolayer of nnonyltrichlorosilane on the top of a SiO2/Si substrate by Tao and co-workers.21 A direct comparison between the experimental thin-film mobility and the theoretical mobility is not relevant because the packing structure in the thin film may not be completely transferable to the single-crystal structure. Nevertheless, both experimental and theoretical results clearly preclude TCDAP from being an efficient p-type semiconductor. In

Figure 3. HOMO, LUMO, and band gaps of pentacene, diazapentacene, and its derivatives at the B3LYP/6-31G(d) level.

mol,27 which is presumably superior to the DFT methods. Shown in Table 2 are the computed reorganization energies of hole (λ+) and electron (λ−) transports. Although the three functionals and the G3MP2B3 method give diversified results on reorganization energies, we find a few trends: (1) In general, the PW91 functional gives the smallest set of λ+/λ− values, while the λ+/λ− values by the M06-2X functional are the largest. (2) The B3LYP functional gives closer λ+/λ− predictions to the G3MP2B3 method. Numerous studies31−45 have reported that using reorganization energies at the B3LYP level gives prediction in quantitative agreement with experimental reorganization energies32 and thus the subsequent mobilities for a variety of semiconductors.37,38 (3) All methods predict that TCDAHP has the largest λ+ value (except M06-2X) and the smallest λ− value. The reorganization energy is a measure of geometrical distortion of the ionic forms from the neutral molecule. The neutral TCDAHP distorts (Figure S4) significantly in the pyrazine ring from the cationic form (leading to a larger λ+), whereas little geometry difference is found between the neutral and anionic forms of TCDAHP (resulting in a smaller λ+). Coropceanu et al.66 have reported the ultraviolent photoelectron spectra of pentacene and arrived at an “estimated” λ+ value of 0.0992 eV. This λ+ value, based on the vibrational contribution (0.0496 eV) of normal modes in the photoionization process and assuming that such vibrational contributions are identical for cationic and neutral pentacene, comes very close to the B3LYP and G3MP2B3 predictions of 0.0952 and 0.0892 eV, respectively.

Table 2. Reorganization Energy (in eV) for Hole and Electron Transport of TCDAP, TCDAHP, and TFDAP Using Different DFT Functionals with the 6-311++G(d,p) Basis Set and the G3MP2B3 Method λ+

a

λ−

species

PW91

B3LYP

M06-2X

G3MP2B3

PW91

B3LYP

M06-2X

G3MP2B3

TCDAP TCDAHP TFDAP pentacenea

0.1052 0.1263 0.1199 0.0614

0.1303 0.1646 0.1602 0.0952

0.1957 0.2225 0.2353 0.1607

0.1175 0.1698 0.1460 0.0892

0.1283 0.1245 0.1431 0.0995

0.1739 0.1565 0.1880 0.1340

0.2407 0.1922 0.2541 0.1960

0.1591 0.1423 0.1681 0.1193

Reference 66. The λ+ of pentacene is estimated to be 0.0992 eV based on the ultraviolent photoelectron spectroscopic measurement. 22752



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formidable task. Under the approximations and limits47,49,69−72 of current theoretical models, it is unsurprising that the mobility predictions by density functional theory could differ from the experimental data by a factor of 2. The predictions by other pure and hybrid GGA functionals are given in Table S2 for a detailed comparison. In general, the pure GGAs predict a smaller value of mobility than the hybrid GGA functionals. Within the five pure GGAs, the hole and electron mobilities of TCDAP are consistent with the respective values around ∼0.23 and ∼1.50 cm2 V−1 S−1. Among the hybrid GGA functionals, the predicted μ+ falls into a narrow range from 0.3 to 0.6 cm2 V−1 S−1, while the μ− is in a larger range of 1.8−3.5 cm2 V−1 S−1. The new mPW1K functional does perform very well, as the μ− value of 3.00 cm2 V−1 S−1 still comes close to the experimental value of 3.39 cm2 V−1 S−1. On the basis of the performance assessments of various density functionals on the mobility predictions of TCDAP and pentacene, using reorganization energy at the G3MP2B3 level and transfer integral at the BHandH/ADZP or BHandHLYP/ ADZP or M06-2X/ADZP level should a give reliable and similar prediction of hole and electron mobilities. In the following, we will focus on the mobility results obtained from the G3MP2B3based λ’s and M06-2X/ADZP-based t’s for discussions. We should emphasize that using transfer integrals either at the BHandH/ADZP or at the BHandHLYP/ADZP level is not expected to give significantly different results that would alter the conclusions in this study. Electron and Hole Mobilities of TCDAHP and TFDAP. Four dominant hopping pathways are considered in the transfer integral predictions: P1 and P2 are the parallel hopping pathways between two neighboring molecules with π-stacking interactions, while T1 and T2 are the transverse hopping routes between two neighboring molecules in a perpendicular arrangement. In Table 4, it is found that the electron transfer integrals in the P1 route are larger than those in the T1 and T2 pathways for all three molecules. The relative probabilities for electron transfer along the transverse hopping pathways are minimal, and the transfers are dominant along the parallel pathways, with the relative probabilities [i.e., P1 in eq 4] being 99.6% (TCDAP), 95.1% (TCDAHP), and 99.8% (TFDAP) along the P1 pathway. The hole transfers are also dominant along the parallel pathways, and the relative probabilities are 56.9% (along P1 in TCDAP), 40.8% (along P2 in TCDAP), 99.8% (along P1 in TCDAHP), 18.6% (along P1 in TFDAP), and 80.9% (along P2 in TFDAP). The P2 route of TCDAP is a lot longer than the P1 pathway, but the hole transfer along the P2 make a comparable contribution (the hopping rate in P2 is very comparable with that in P1) to the hole mobility of TCDAP. If the contribution to the hole transfer processes along the P2 pathway is neglected, the hole mobility of TCDAP is reduced from 0.45 to 0.12 cm2 V−1 S−1, which is in agreement with the hole mobility prediction of 0.13 cm2 V−1 S−1 (this value is converted from a one-dimensional value in Table 2 of ref 21) by Tao and co-workers.21 The prediction by Tao and co-workers might have included the contribution along the P1 direction only. In the TCDAHP, the hole transfer coupling in the P2 route is almost negligible, and it occurs mainly in the P1 direction. Using the G3MP2B3-based λ+ and transfer integral at the M06-2X/ADZP level, the predicted hole and electron mobilities of TCDAHP are 2.30 and 3.89 cm2 V−1 S−1, respectively. The former value is larger than the experimental μ+ values of 1.4 (along rubbing direction) and 0.7 (in direction perpendicular to the rubbing direction) cm2 V−1 S−1 by Tao and co-workers.21

Table 3. Prediction of Electron and Hole Mobilities (in cm2 V−1 s−1) for TCDAP Using Various Combinations of Density Functionals (PW91, B3LYP, BHandH, BHandLYP, and M062X) and the G3MP2B3 Methoda functionals/method for

category (1)

(2) (3)

(4)

reorganization energy (λ)b

transfer integral (t)c

hole mobility (μ+)

electron mobility (μ−)

PW91 B3LYP M06-2X B3LYP B3LYP G3MP2B3 G3MP2B3 G3MP2B3 G3MP2B3 G3MP2B3 G3MP2B3 G3MP2B3 G3MP2B3 G3MP2B3 experiment

PW91 B3LYP M06-2X PW91 M06-2X PW91 B3LYP BHandH BHandHLYP M06-2X B3LYPd BHandHd BHandHLYPd M06-2Xd

0.27 0.26 0.16 0.19 0.36 0.23 0.31 0.53 0.50 0.43 0.34 0.57 0.57 0.45 0.01 − 0.13e 0.07f

2.22 1.65 1.06 1.23 2.37 1.48 1.99 3.13 2.96 2.86 2.17 3.44 3.32 3.29 3.39g

a

All calculations are based on the experimental crystal structure. bBasis set 6-311++G(d,p) is used; G3MP2B3 method uses predefined basis set and level of theory. cUnless specified, basis set DZP is used. dBasis set ADZP is used. Using PW91 with ADZP basis set encounters a numerical problem in the ADF program. eReference 21. This mobility was measured along the rubbing direction from a TCDAP thin film deposited on a rubbed monolayer of n-nonyltrichlorosilane on a SiO2/ Si substrate. fReference 21. This mobility was measured in the direction perpendicular to the rubbing direction from a TCDAP thin film deposited on a rubbed monolayer of n-nonyltrichlorosilane on a SiO2/Si substrate. gReference 20. This mobility was measured on the basis of the single-crystal form of TCDAP.

category (1), the predicted μ− value of TCDAP is around 1.06− 2.22 cm2 V−1 S−1, which is somewhat smaller than the experimental mobility of 3.39 cm2 V−1 S−1; the mobility was measured on the single-crystal form of TCDAP by Tao, Pola, and Islam.20 When the B3LYP-based reorganization energy is used for mobility prediction at the PW91 level [category (2)], the mobility (1.23 cm2 V−1 S−1) is still underestimated by 2.1 cm2 V−1 S−1. It is worthwhile to mention that a small change (about +46 meV) in λ− (from 0.1283 at PW91 to 0.1739 eV at B3LYP) decreases the μ− value of TCDAP by ∼1 cm2 V−1 S−1 (from 2.22 to 1.23). Given that most DFT methods have uncertainty from a few to a few tenths kcal mol−1, reliable prediction by DFT methods on hole and electron mobilities could be exceedingly difficult, and obtaining predictions in quantitative agreement with the experiments could be fortuitous. By using the G3MP2B3 reorganization energy in the category (3), the μ− value of TCDAP becomes 1.48 (PW91), 1.99 (B3LYP), 3.13 (BHandH), 2.96 (BHandHLYP), and 2.86 (M06−2X) cm2 V−1 S−1. The three values of ∼3 cm2 V−1 S−1, obtained with BHandH, BHandHLYP, and M06-2X transfer integrals, come very close to the experimental value (3.39 cm2 V−1 S−1). Upon including the diffuse functions in the transfer integral calculation [category (4)], the predicted electron mobilities of 3.44 (BHandH), 3.32 (BHandHLYP), and 3.29 (M06-2X) cm2 V−1 S−1 are in excellent agreement with experimental data. Given the good agreement obtained here, we are well aware that the quantitative description for charge transport processes in bulk organic materials is still a 22753



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Table 4. Summary of Hole and Electron Transfer Integrals (in meV) along the Hopping Pathways P1, P2, T1, and T2, and Hole and Electron Mobility (in cm2 V−1 s−1) Predictions at the M06-2X/ADZP Level with the Reorganization Energies Obtained via the G3MP2B3 Method distance (P1)d distance (P2) distance (T1) distance (T2) t+ (P1) t+ (P2) t+ (T1) t+ (T2) t− (P1) t− (P2) t− (T1) t− (T2) μ+

μ−

TCDAPa

TCDAPb

TCDAHPc

TCDAHPb

TFDAPb

3.919 12.799 10.765 10.501 28.1 −23.8 4.7 3.2 −192.5 −11.7 2.0 1.8 0.45 0.01−0.13e 0.07f 3.29 3.39g

3.936 12.988 10.693 10.980 28.4 23.0 −4.3 −1.0 185.0 10.8 2.0 1.7 0.43

4.050 12.788 10.708 10.653 −166.5 −9.9 0.6 0.1 −183.8 39.7 −0.2 13.4 2.30 0.7e 1.4f 3.89

4.032 13.068 10.812 10.908 −154.0 −6.0 −0.5 1.7 −174.7 27.5 11.5 −0.4 1.95

3.906 12.849 10.898 10.590 −11.7 −24.4 0.5 −1.9 −210.8 8.6 0.1 0.1 0.55

3.07

3.51

3.51

a

Based on the X-ray crystal structure in ref 20. bBased on the crystal structure obtained with the PBC method at the B97D/6-31G(d) level. Constructed using the cell parameters from the X-ray crystal structure in ref 21. dGiven as the center-of-mass distance, in Å, in the hopping pathways. eReference 21. This mobility was measured along the rubbing direction from a thin film deposited on a rubbed monolayer of nnonyltrichlorosilane on a SiO2/Si substrate. fReference 21. This mobility was measured in the direction perpendicular to the rubbing direction from a thin film deposited on a rubbed monolayer of n-nonyltrichlorosilane on a SiO2/Si substrate. gReference 20. This mobility was measured on the basis of the single-crystal form of TCDAP. c

These measurements were done on a TCDAHP thin film prepared on a rubbed monolayer of n-nonyltrichlorosilane on the top of a SiO2/Si substrate. Comparing the TCDAP with its −NH derivative, TCDAHP, the latter molecule has tremendously increased hole mobility (0.45 vs 2.30) and has a larger electron mobility (3.29 vs 3.89). Our prediction suggests that TCDAP should be an n-channel semiconductor, while TCDAHP, with its very large electron and hole mobilities, is potentially an ambipolar organic semiconductor.48 The hole mobility of TCDAHP has been reported previously,21 and its electron mobility (3.89 cm2 V−1 S−1) is reported for the first time. Examining the HOMO of TCDAP and TCDAHP (Figure 3) reveals that they are of different nature: the HOMO is localized in peripheral carbons of TCDAP (nodal planes are along the long molecular axes), whereas the HOMO is mainly in fused carbons of TCDAHP (nodal planes are perpendicular to the long molecular axes). As the HOMOs of TCDAP and TCDAHP resemble the respective LUMO and HOMO of pentacene, Tao and co-workers have compared the relative displacement of dimeric TCDAP and TCDAHP molecules along the longer molecular axes with that of pentacene and suggested that the very high hole mobility in TCDAHP is correlated with local maximal electronic coupling between the HOMO of TCDAHP dimer.70 The predicted μ+/μ− values of TCDAP/TCDAHP based on the optimized crystal structure are in qualitative agreement with the values based on the experimental crystal structure. This suggests that the optimized crystal structures obtained with PBC model at the B97D/6-31G(d) level should be reliable for the mobility calculations of the structurally similar TFDAP molecule. Both TCDAP and TFDAP have similar molecular and crystal structures and HOMO/LUMO properties; thus they should have near-identical hole and electron transfer properties. As compared to the TCDAP, the TFDAP has a slightly large hole mobility (0.55 vs 0.43) because of the predominant contribution

of the hole transfer along the P2 pathway over the P1 pathway. This enhanced contribution from P2 pathway or diminished contribution from P1 pathway is apparently due to the presence of fluorine atom in TFDAP. The predicted hole and electron mobilities of TFDAP are 0.55 and 3.51 cm2 V−1 S−1, respectively, suggesting that TFDAP should be a more efficient n-channel semiconductor than TCDAP. TCDAHP is the chloride-substituted derivative of DHDAP. Different charge transport properties between DHDAP and TCDAHP may be rationalized by the difference in crystal packing modes,23 HOMO/LUMO orbitals level, and overlaps. The experimental hole mobility23 of DHDAP is 0.45 cm2 V−1 S−1, and the respective predicted μ+ and μ− values are 0.41 and 1.11 cm2 V−1 S−1, using the transfer integral at the M06-2X/ ADZP level and G3MP2B3’s λ. The crystal packing of DHDAP (Figure S5) is similar to that of pentacene but very different from the TCDAHP. The μ− of TCDAHP (3.89 cm2 V−1 S−1) is found to be significantly larger than that of DHDAP (1.11 cm2 V−1 S−1). The increased electron mobility in TCDAHP is due to lowering of LUMO energy levels (Figure 3) and excellent π−π overlap of the LUMOs (Figure 4) in the TCDAHP dimer (as compared to

Figure 4. LUMOs of the P1 dimers in DHDAP, TCDAHP, TCDAP, and TFDAP at the B3LYP/6-31G(d) level. The isovalues for surfaces are set to MO = 0.015 and density = 0.0004. 22754



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Figure 5. (a) Illustration of projecting different hopping pathways onto a transistor channel in a−b plane of TCDAP crystals; θP1 and θP2 are the angles of P1 and P2 dimers relative to the reference crystallographic axis a; Φ is the angle along a transistor channel relative to the reference crystallographic axis a. (b) The predicted anisotropic hole (red curve) and electronic (blue curve) mobility on the a−b plane of TCDAP crystal.

Figure 6. Predicted anisotropic hole (red curve) and electronic (blue curve) mobility on the a−b plane of TCDAHP and TFDAP crystals.

the relatively poor π−π stacking in the DHDAP dimer). The high electron mobility in TCDAP and TFDAP is also contributed by the proper π−π overlap of their LUMOs in dimeric form. Anisotropic Mobility. At high temperature, the thermal molecular motions may lead to dynamic disorder−molecular disorientation in the crystal structures and positional fluctuation

over the time. This may cause fluctuations, attenuations, and even enhancements in the intermolecular transfer integrals.71,72 As a result, we have studied the anisotropic effect in TCDAP, TFDAP, and TCDAHP to understand how it affects mobility. The anisotropic effect in transport mobility was first observed in rubrene crystals by Sunder et al.73 Han et al. have developed a 22755



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functionals, this gives the most reliable predictions to the electron mobility of TCDAP. The respective electron mobilities, 3.29, 3.44, and 3.32 cm2 V−1 S−1, are in excellent and fortuitous agreement with the experimental value of 3.39 cm2 V−1 S−1. Other density functionals also consistently give predictions different from the experimental electron mobility of TCDAP by less than a factor of 2. As suggested in previous study and confirmed here, TCDAP is an n-channel but not a p-type semiconductor. The −NH derivative of TCDAP, TCDAHP, is found to have a large hole mobility of 2.30 cm2 V−1 S−1 and an even larger electron mobility of 3.89 cm2 V−1 S−1. The TCDAHP molecule should behave as an ambipolar organic semiconductor with simultaneous hole and electron transport properties. By the substitution of chlorine with fluorine in TCDAP, we find that the TFDAP is very similar to TCDAP in terms of the molecular and crystal structure and HOMO/LUMO property. Similarly, TFDAP is a n-type semiconductor but with a slightly larger electron mobility of 3.51 cm2 V−1 S−1; the prediction is based on the crystal structure obtained with PBC model and B97D functional. The transfer integral calculations among four dominant hopping pathways show that the hole and electron transport processes occur in parallel routes between two neighboring molecules with π-stacking interactions for all three molecules. On the basis of the angular resolution anisotropic mobilities analyses, TCDAP, TCDAHP, and TFDAP show similar anisotropic mobilities but remarkably different anisotropic behaviors in comparison with DHDAP.

model to compute the anisotropic mobility (μΦ) by projecting the hopping pathway onto the transistor channel relative to the reference axis of the molecular crystal.74 The angular resolution anisotropic mobility can be calculated by the following equation: μ=

e 2kBT

∑ Wri i2Pi cos2 γi cos2(θi − Φ) i

(8)

where γi is the angle of the ith hopping pathway relative to the transport plane of the crystal molecular stacking layer, and θi is the hopping angles along the ith conducting channel relative to the reference axis of crystal. As shown in Figure 5, the reference axis is set as the crystallographic a axis, and the orientation angle along the specific transistor channel relative to the reference a axis is Φ. Because of the smaller transfer integrals along the T1 and T2 transfer pathways in the TCDAP, we have only considered the P1 and P2 hopping channels in the mobility orientation function on the a−b plane, that is, the γi = 0°. Recently, Yin, Reimers, and co-workers have shown that eq 8 might give poor approximation to the magnitude and anisotropy of mobility for the crystalline and amorphous forms of mer-tris(8hydroxyquinolinato)aluminum(III).53 For organic semiconductors74 such as ruberene, pentacene, tetracene, 5,11-dichlorotetracene, hexathiapentacene, tetrathiofulvalene-7,8,8-tetracyanoquinodimethane,34 pyrazine, and bisindenoanthraziline derivatives,40,44 eq 8 was shown to give reasonable profiles for anisotropic mobilities. The angular plots of the anisotropic mobilities of DHDAP, TCDAP, TCDAHP, and TFDAP are shown in Figures S4, 5, and 6, respectively. We found that all four crystals exhibit remarkable angular dependence of mobilities and anisotropic behaviors. TCDAP, TFDAP, and TCDAHP have similar anisotropic electron mobilities on the a axis. At the Φ angle of 0° and 180°, maxima of electron mobility along the P1 hopping pathway are found, indicating that the electronic coupling of LUMOs is the strongest along the shortest center-of-mass distance between two monomers. In hole mobility, TCDAHP has the highest angular mobility at Φ = 0° and 180°, whereas the maxima of μ+ for TCDAP and TFDAP are at Φ = 110° and 290°. As compared to the TCDAHP, the DHDAP (with smaller hole and electron mobilities) shows different anisotropic behaviors. DHDAP has the largest hole and electron mobilities at Φ = 60°/240° and 10°/ 190°, respectively. The differences in angular anisotropic hole and electron mobility between TCDAHP and DHDAP can be explained by poor π−π stacking interaction in DHDAP dimer and the dominant hopping pathways in DHDAP being T1 (for hole transfer) and P (for electron transfer), rather than the P1 channels in TCDAHP.

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ASSOCIATED CONTENT

S Supporting Information *

Hopping pathways of TCDAP, TCDAHP, and TFCAP. The top and side views of the structures and HOMOs of P1 and P2 dimers. The predicted anisotropic mobility on the a−b plane of DHDAP crystal. The predictions of hole and electron mobility of pentacene and TCDAP using various density functionals. This material is available free of charge via the Internet at http://pubs. acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS X.W. is grateful for the support of the National Science Foundation of China under Grant No. 20503018 and the Open Project Program of State Key Laboratory of Physical Chemistry of Solid Surfaces (Xiamen University), China (201010). The work described in this Article was supported by a Strategic Research Grant from the City University of Hong Kong (Project No. 7002596).

4. CONCLUSIONS We have performed theoretical predictions to study the chargetransfer properties of novel diazapentacene derivatives, including TCDAP, TCDAHP, and TFDAP. The performance assessment among density functionals and G3MP2B3 method on the reorganization energy calculations points out that the reorganization energy of TCDAP predicted by B3LYP functional comes very close to the G3MP2B3 value. In fact, both theoretical methods give virtually no difference in reorganization energy when compared to the “experimental” estimation for pentacene. Five pure and seven GGA hybrid density functionals are selected for performance assessment of transfer integrals. When the reorganization energy at the G3MP2B3 level is coupled with the transfer integral with M06-2X, BHandH, and BHandLYP

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