Theoretical Investigations into the Electron and Ambipolar Transport

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Theoretical Investigations into the Electron and Ambipolar Transport Properties of Anthracene-Based Derivatives Gui-Ya Qin, Li Fei Ji, Jian-Xun Fan, Ning-Xi Zhang, PanPan Lin, Shou-Feng Zhang, Lu-Yi Zou, and Ai-Min Ren J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00846 • Publication Date (Web): 22 Mar 2019 Downloaded from http://pubs.acs.org on March 23, 2019

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The Journal of Physical Chemistry

Theoretical Investigations into the Electron and Ambipolar Transport Properties of Anthracene-Based Derivatives Gui-Ya Qin,† Li-Fei Ji,† Jian-Xun Fan,†,‡ Ning-Xi Zhang,† Pan-Pan Lin,† Shou-Feng Zhang,† Lu-Yi Zou,† Ai-Min Ren* † †Laboratory

of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University,

Changchun 130023, China. E-mail: [email protected] ‡College of Chemistry and material, Weinan Normal University, Weinan, 714000, China.

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Abstract: To obtain anthracene-based derivatives with electron transport behavior, two series of anthracenebased derivatives modified by trifluoromethyl groups (-CF3) and cyano groups (-CN) at the 9,10positions of anthracene core were studied. Their electronic structures and crystal packings were also analyzed and compared. The charge carrier mobilities were evaluated by quantum nuclear tunneling theory based on the incoherent charge-hopping model. Our results suggest that, introducing -CN groups at 9,10-positions of anthracene core is more favorable than that of -CF3 in keeping great planar rigidity of anthracene skeleton, decreasing more LUMO energy levels (0.45~0.55 eV), reducing reorganization energies and especially forming a tight packing motif. Eventually, the excellent electron transport materials could be obtained. The molecule 1-B in Series 1 containing -CF3 groups is an ambipolar organic semiconductor (OSC) material with 2D transport network, and its value of μh-max/μemax

is 1.75/0.47 cm2 V-1 s-1 along different directions; 2-A and 2-C in Series 2 with -CN groups are

excellent n-type OSC candidates with the maximum intrinsic mobilities of 3.74 and 2.69 cm2 v-1 s-1 along π-π stacking direction, respectively. Besides, the Hirshfeld surface and QTAIM analyses were applied to reveal the relationship between noncovalent interactions and crystal stacking.

1. Introduction -2ACS Paragon Plus Environment

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Organic semiconductor (OSC) materials display quite a few desirable properties, for instance, low cost, ease of processing and synthesis, good flexibility and so on.1-4 Hence, it is no surprise that, as active layer material, they have been rapidly and widely utilized in smart electronic devices like organic light-emitting diodes (OLEDs),5-6 organic filed effect transistors (OFETs),7-8 organic semiconductor sensors (OSCSs) and organic photovoltaic cells (OPVCs).9 The performances of these electronic devices are mainly dominated by the charge transport property of active OSC materials. Therefore, the OSC materials with large carrier mobility have been the goal that researchers are pursuing. Compared with the polymers, small molecular semiconductors own the advantages of easy modification and processing, high purity and ordered packing, which are key factors for high quality OSCs. In recent years, derivatives based on acenes (thienoacenes), naphthalene diimide (NDI) or perylene diimide (PDI) have been extensively investigated to serve as p-type (hole) and n-type (electron) charge transport materials, respectively.10-16 Among various small molecules, acenes, such as naphthalene,17 anthracene,18 tetracene,17 and pentacene,17, 19-20 with highly planar π-conjugated skeleton have received the most attention from both academic and industrial communities. The linearly extended π-conjugated skeleton of a higher acene can enhance the intermolecular π-orbital overlaps in the solid state and lead to efficient charge carrier transport and high mobility. However, π-conjugated size of naphthalene is too small to offer sufficient intermolecular π-π overlap. Although tetracene and pentacene can make up for this defect, their low solubility in organic solvents, poor air stability and synthesis technology prevent these higher acenes from applying in electronic devices. Anthracene (Ant), consisting of three rigid fused benzene rings, possesses the best solubility and stablity among the acenes.21 It can be easily modified with phenyl, naphthyl, and thienyl groups at its active end- and peri-positions through common organic synthesis reaction, such as Heck coupling, Stille coupling or Suzuki coupling reaction and so on.21-23 These chemical modifications of Ant would extend the π-conjugated backbone, tune the molecular packing and thus change transport properties. As a result, the Ant has been given great consideration for electronic devices. Up to now, Ant’s hole mobility in single crystal field-effect transistors (SC-FETs) has reached about 3 cm2 V−1 s−1.18, 24 Many excellent p-type Ant-based derivatives have also been reported. For example, Meng group reported the p-type Ant-based derivatives, 2,6-bis(4-hexylthienyl)anthracene, which showed high hole mobility of 0.48 cm2 V-1 s-1;25-26 A series of triisopropylsilylethynylanthracene -3ACS Paragon Plus Environment


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derivatives with the hole mobility up to 4.1cm2 V-1 s-1 have been synthesized by Chung;27-28 and 2-(4hexylphenylvinyl)anthracene and 2,6-distyrylanthracene have been researched by Perepichka, which showed high hole mobility, the former is 2.6 cm2 V-1 s-1 in single crystals transistors; the latter is 0.75 cm2 V-1 s-1 in OLETs.29-30 Remarkably, Hu group reported an outstanding charge transport material 2,6-diphenylanthracene (2,6-DPA) in recent years. The SC-FET devises based on 2,6-DPA exhibit excellent hole transport behavior with mobility even as high as 34 cm2 V-1 s-1.31-32 Many other Ant derivatives with p-type transport properties have also been investigated, such as 2,6-diphenyl-9,10bisphenylethynylanthracene,32

2,6-bis(dibenzo[b,d]furan-3-yl)anthracene,33

2,6-bis(4-

methoxyphenyl)anthracene34 and so on.35-36 However, only a few Ant derivatives performed n-type or ambipolar behavior, and their mobilities are very low. For instance, the first Ant-based n-type semiconductors of, 2,6-bis(4-trifluoromethylphenyl)anthracene (1-B’, the molecule structure is shown in Figure S1) was reported by Ando et al. Its electron mobility in thin film is only 3.4 × 10-3 cm2 V-1 s-1 at 20 ℃ in OTFT with Au electrode.21 In recent years, Glowatzki synthesized 2,6-bis((E)-4(trifluoromethyl)-styryl)anthracene, which showed an electron mobility of 1.8 × 10−2 cm2 V-1 s-1 with Au electrode.37 Until recently, an ambipolar behavior was found from 2,6-di(2-naphthyl)anthracene, with the hole/electron mobilities of 1.10/0.87 cm2 V-1 s-1.38 It is well known that n-type and ambipolar OSCs play crucial roles in ambipolar transistors and complementary inverter circuits. Hence it is necessary to research n-type and ambipolar charge transport materials based on Ant core to provide new opportunities for both scientific studies and technological applications.39 Numerous experimental and theoretical studies showed that electron transport semiconductors can be obtained by introducing electron-withdrawing groups, such as cyano groups (-CN), trifluoromethyl groups (-CF3), into the π-conjugated backbone. This approach can decrease the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy levels, and enhance the environmental stability of radical anions. However, it is not clear how these substituents affect electronic structure and charge transfer behavior and which substituents are more advantageous for Ant. Recently, S. Yamada et.al and F. Glöcklhofer et.al synthesized a series of 9,10bis(trifluoroalkyl)anthracene derivatives

40

and 9,10-dicyanoanthracene (DCA) derivatives,41-42

respectively. These compounds provide favorable crystal structures to illustrate this issue. Among these derivatives, some representative molecules caught our attention (the molecules in Figure 1 -4ACS Paragon Plus Environment

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except 1-A and 2-A). On one hand, compounds 1-B/C/D and 2-B extend the π-conjugated backbone via substituents at 2,6-positions. On the other hand, 2-C in Series 2，which introduces –NO2 groups at 2,7-positions of Ant core for improving the solubility by decreasing symmetry, possess a potential n-type charge transport property with low LUMO level. In this paper, we designed 1-A and 2-A molecule for comparison and to understand the effect of the substituents of -CF3 and -CN on carrier transport properties. The geometrical structures ， electronic structures, charge injection, stability, molecular stacking motifs and charge carrier mobilities of these compounds in Figure 1 are explored by using Density Functional Theory (DFT) to obtain the excellent n-type or ambipolar materials based on Ant. In order to deeply understand the influence of noncovalent interactions on packing behavior, the intermolecular interactions are analyzed. We expect that this work can provide useful guidelines for devising novel Ant-based semiconductors with both high charge transport properties and environmental stability.

2. Theoretical Methods 2.1 Transport mechanisms and computational methods Generally, the charge carrier transport in organic semiconductors mainly takes place via an incoherent hopping regime between neighboring molecules at room temperature (300 K), causing by the small electronic couplings and large electron–phonon couplings.43-44 Every hopping event is deemed as a self-exchange electron-transfer reaction: M + M+/- = M+/-+ M, where M is the molecule undergoing the charge transfer. The corresponding transfer rate can be deduced by the Fermi Golden Rule (FGR),45 when the nuclear tunneling eﬀect is considered from the quantum nature of vibrations between localized molecular states, the rate formula of full quantum charge transfer (CT) can be expressed as: 𝑘𝐶𝑇 =

|𝑉|2 ∞ ∫ d𝑡 ℏ2 ―∞

here, 𝑛𝑗 = 1/(𝑒

ℏ𝜔𝑗 𝑘𝐵𝑇

exp{ ― ∑𝑗𝑆𝑗[(2𝑛𝑗 + 1) ― 𝑛𝑗𝑒 ―𝑖𝜔𝑗𝑡 ― (𝑛𝑗 + 1)𝑒𝑖𝜔𝑗𝑡]}

(1)

―1) is the occupation number for the jth vibrational mode with frequency  j , and

S j represents the Huang–Rhys factor, which evaluate local charge–phonon coupling strength for the

jth mode, and V is the electronic coupling. The reorganization energy (λ) is one important parameter for charge transfer, which consists of -5ACS Paragon Plus Environment


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two parts: one is the internal reorganization energy ( int ) and the other is external reorganization energy ( ext ), and total reorganization energy is the sum of them:   int  ext . Generally, the intermolecular reorganization energy is much smaller than the intramolecular reorganization energy in pure organic condensed phases. Hence, the external part is neglected in this study and only the inner ones are considered.46 Two methods can be used to calculate the intramolecular reorganization energy: one is from the adiabatic potential surfaces (AP) of neutral/charged species, which is shown as:

h / e = int1 + int 2 = (E* /   E+/  )+(E*  E)

(2)

here, the int1 ( int 2 ) respect to the geometry relaxation energy of one cation/anion (neutral) molecule from the most stable geometry of the neutral(cation/anion) state to the lowest energy geometry of the ionic(neutral) state; E and E+(E-) stand for the energies of the neutral and cation(anion) molecules in their lowest geometries, respectively, E* is neutral state species with the geometries of the cation and anion. 𝐸 ∗+ and 𝐸 ∗― are the energies of the cation and anion monomers with the geometries of neutral species, respectively. At the same time, the adiabatic ionization potential (AIP), adiabatic electron affinity (AEA), the vertical ionization potential (VIP), and vertical electronic affinity(VEA) can be obtained by the following equations:

AIP  E  E

(3)

VIP  E+*  E

(4)

AEA  E  E

(5)

VEA = E*  E

(6)

The other method is the normal mode analysis (NM),47-50 where contributions of every vibrational mode to  can be obtained: 𝑘𝑖

𝜆h/e = ∑𝜆𝑖 = ∑ℏ𝜔𝑖𝑆𝑖 = ∑ 2 Δ𝑄2𝑖

(7)

here, ki and ωi are the corresponding force constants and vibrational frequencies, severally. Qi is the displacement along normal mode i between the equilibrium stable geometries of the neutral and ionic molecules, and Si represents the Huang–Rhys factor which could evaluate local electron– phonon coupling strength for the ith mode. -6ACS Paragon Plus Environment

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The transfer integrals43 V for the nearest-neighboring dimers along the transfer pathways in the crystals can be calculated directly by site-energy overlap correction method:

V=

H ij



1 Sij  H ii  H jj  2 1  Si2j

(8)

H is the Kohn-Sham Hamiltonian of the dimer system which consists of two monomers and  i / j represents the monomer HOMOs (for hole transport) or LUMOs (for electron transport). Hii and Hjj are the site energies, defined as H ii =  i | H | i , H jj =  j | H | j , Sij and Hij are the spatial overlap and charge-transfer integral, defined as Sij   i |  j , H ij   i |H | j , respectively. The charge transfer process is usually regarded as a random diffusion process of Brownian particle’s, the carrier mobility can be denoted by the Einstein equation:51



e D k BT

(9)

here, D is the charge diffusion coefficient and defined as the specific value between the mean-square displacement x  t 

2

and the diffusion time t, which can be obtained by kinetic Monte Carlo

simulations:52-53

1 x t  D  lim 2n t t 

2

(10)

where n is the spatial dimensionality, t is the total simulation time. The anisotropic charge carrier mobilities54-55 are computed by the formula as below: x  t  cos 2 cos 2 i    e  lim  2k BT t  t 2

anisotropic

(11)

where  is the relevant angle between layers of the organic crystal molecular packing to the reference charge transport direction, and for 2D organic plane,    , i is the ith angle in one layer corresponding to the conducting channel relative to the same reference axis. Generally, the angle  is chosen from the reference axis to the horizontal position.

2.2 The analysis methods for noncovalent interactions Understanding the nature of noncovalent interactions between a self-defined center molecule and -7ACS Paragon Plus Environment


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its neighboring molecules is not only theoretical interesting but also important for practical purposes, such as crystal structure prediction and designing more potential organic semiconductor materials. Hence, in order to deeply understand the synergy between different types of noncovalent interactions responsible for the crystal packing, the weak interactions between nearest the compounds in the crystal structures were characterized by Hirshfeld surface analysis;56 and the adjacent molecular pairs picked out from crystal structures were analyzed by Bader’s quantum theory of atoms in molecules (QTAIM)57 at the theoretical level of B3LYP/6-31+G(d, p) using the Multiwfn 3.4 program.58 The bond critical points (BCPs) of intermolecular contacts or valence bonds are characterized by electron density and its Laplacian (∇2ρ(r)) and the total electron energy density (H). Meanwhile, to measure the strength of the interaction quantitatively, the interaction energies of the main neighboring dimers were calculated by using a super molecular approach: ΔE = Edimer-2Emonomer. But the standard density functionals are not enough to capture the long-range dispersion effect from the attractive van der Waals interactions in large π-conjugated systems, the D3(BJ) (D3 with Becke–Johnson damping) dispersion correction and the method of B3LYP/6-31G(d, p) were combined to calculate the interaction energies of the nearest-neighboring dimers. Meanwhile the basis-set super position error (BSSE) was taken into account by using counterpoise (CP) correction method due to basis set inconsistency in such calculations.59

Figure 1. Molecular structures of Series 1 and 2.

3. Results and Discussion 3.1 Molecular structures, frontier molecular orbitals and carrier injection The gas-phase optimized molecular geometries for the ground state of all studied compounds are depicted in Figure 2. For Series 1, due to the steric hindrance and intramolecular F···H interaction (as -8ACS Paragon Plus Environment

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shown in Figure S2 and Table S1),60 it is quite interesting to note that the Ant conjugated planes are bent, which are much different from the single molecular geometries in solid state. In contrast, the molecules in Series 2 keep the flat Ant structures, and the gas-phase optimized molecular geometries are largely the same as that in the crystal. Therefore, in order to simulate the solid surroundings effect for the bent structures, the ground state structures of all molecules were optimized again by the quantum mechanics and molecular mechanics (QM/MM) approach,32, 61-63 which can be realized in Gaussian 09 ONIOM module.64 In the QM/MM model, as shown in Figure 3, the central molecule is regarded as the high layer and it was calculated by the quantum mechanical method at the B3LYP/631G(d, p) level, while the surrounding molecules were served as the low layer calculated by molecular mechanics with the Universal Force Field (UFF). In addition, the “frozen optimization” was adopted in the optimization for getting access to the frequency, which signified that the optimization only happened to centered molecule was and the other surrounding molecules were frozen.61 The optimized molecular geometries for ground state of all compounds (except 1-A) by using QM/MM model are depicted in Figure S3. The angles between the plane of the benzene ring at both ends of the Ant core (the angle between α and α’, β and β’) are defined to depict the distortion degree of Ant core; and the dihedral angles between peripheral phenyls and Ant core (θ1 and θ2) are defined to describe the conjugation degree between Ant core and substituents (shown in Figure 4). The parameters are listed in Table 1. It was found that the structures calculated by QM/MM are closer to that in solid accumulations. Take the molecule 1-B for example, in solid stacking, the angles between plane α and α’, β and β’ are 14.1° and 12.9°, respectively; and the dihedral angles between peripheral phenyls and Ant core, θ1 and θ2, are 32.4° and 27.2°, respectively. Correspondingly, the four torsional angles obtained by QM/MM model are 12.3°, 10.6°, 32.2°, and 24.7°, respectively. But under the gas-phase optimization, as seen in Figure 2, the four parameters are larger than that in solid stacking, which means a more severe torsional deflection. When the peripheral phenyls are replaced by small-sized thienyl (1-C) and alkynyl (1-D) groups with smaller steric hindrance, the Ant core is almost planar in solid and the whole molecular conjugated plane is extended. In fact, a good rigid π-conjugated structure is one of main requirements for useful organic electronic materials. Hence when the H-atoms at 9,10positions of Ant are substituted by -CF3, the selection of other substituents at 2,6-positions is need to consider for reducing the undesired repulsive interaction with the hydrogen atoms at the peri-position of Ant core. In contrast, -CN substituted Ant has a perfect planar rigid structure, for 2-B with phenyls, -9ACS Paragon Plus Environment


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the dihedral angles between planes α and α’, β and β’ are zero, and the θ1 and θ2 obtained by QM/MM (29.7° and -29.7°) is closer to that in solid environment (30.1° and -30.1°) than that by gas-phase optimization(36.3° and -36.3°). The structures of 2-A and 2-C obtained by both gas-optimized and QM/MM model are same to that in the solid.

Figure 2. The optimized molecular structures for all compounds in gas phase at the B3LYP/6-31G(d, p) level.

Figure 3. The QM/MM model and the profile view structures of 1-B in gas phase optimization, QM/MM optimization as well as solid accumulation.

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Figure 4. The defined planes on Ant skeleton(plane α,α’,β, and β’) and the dihedral angles between peripheral substituent groups and Ant core (θ1 and θ2). Table 1. The dihedral angles between planes α and α’ (α-α’), β and β’ (β-β’) as well as θ1 and θ2 obtaining through gas optimization, QM/MM optimization and solid accumulation. Gas optimization

QM/MM optimization

Solid accumulation

α-α’

β-β’

θ1

θ2

α-α’

β-β’

θ1

θ2

α-α’

β-β’

θ1

θ2

1-B

15.5

15.6

35.8

35.6

12.3

10.6

32.2

24.7

14.1

12.9

32.4

27.2

1-C

2.8

2.8

-26.0

26.0

4.8

4.8

-15.9

15.9

1.6

1.6

-13.5

13.5

1-D

15.7

15.7

-0.1

-1.4

3.6

3.6

3.1

-3.1

4.7

4.7

4.9

-4.9

The energy levels of frontier molecular orbitals (FMOs), including the HOMO and LUMO, are important parameters to evaluate the charge injection. For n-type OSCs, it is generally accepted that low LUMO levels facilitate electrons injection efficiently and guarantee the material’s stability in the environment as well. The ease of charge injection into OSC material depends on the matching degree between the energy of HOMO/LUMO of organic molecule and the work function (Φm) of the metal electrode. Small energy gap between HOMO and LUMO levels is required for the efficient hole and electron injection from the same metal electrode. For p- or n-type charge transport materials, it is fundamental to guarantee HOMO level above -5.0 eV, or LUMO level below -3.0 eV65-66 to match the commonly used Au electrode (Φm = -5.0 eV) in experiment. The energy levels of frontier molecular orbitals (HOMO/LUMO) calculated at the B3LYP/6-31G(d, p) level are shown in Table 2, and the results for QM/MM model are shown in Table S2. The orbital distributions of HOMOs and LUMOs are presented in Figure 5. For all compounds in Series 1, the LUMOs are mainly distributed on the Ant core, the orbital distributions of HOMO are delocalized over the whole π-conjugated skeletons. For 2-A in Series 2, both HOMO and LUMO are spread over the whole rigid π-conjugated skeletons (including Ant and -CN). The HOMO of 2-B is delocalized over the both phenyls and central rigid πconjugated skeleton, and the LUMO is only delocalized over the central rigid Ant core skeleton. For 2-C, the HOMO mainly delocalized over Ant core and -CN, but with little contribution on the -NO2, in contrast, the LUMO is delocalized partly on the -NO2 groups. The LUMOs/HOMOs of the compounds in Series 1 are in the range of -2.53~-2.64/-5.25~-5.88 eV. The isomer of 1-B, 2,6-bis(4trifluoromethylphenyl)anthracene (1-B’), is a typical n-type charge transport material.21 Its LUMO and - 11 ACS Paragon Plus Environment


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HOMO levels we calculated are -2.18 eV and -5.52 eV, respectively. The LUMO energy level of 1-B is 0.37 eV lower than that of 1-B’, suggesting that 1-B is more conducive to electron injection. It indicates that the compounds with similar LUMO levels in Series 1 have great possibility to inject electron. Meanwhile, for 1-B, 1-C and 1-D, the HOMO levels match well with Au electrode. Additionally, with the enhancement of planarity in Series 1, 1-C and 1-D have smaller energy gap than 1-B. Hence 1-C and 1-D might be the excellent ambipolar materials. For Series 2, due to the extended π-conjugated structure by the strong electron-withdrawing groups of -CN, the values of LUMO of all molecules are below -3.0 eV, which means facile electron injections from Au electrode， and the HOMO levels are below -5.91 eV, which means the materials are difficult to be oxidized, thus attaining better air stability. It is worth noting that the HOMO and LUMO values of 2-C reduce more drastically, because of the extra electron-withdrawing nitro- (-NO2) groups. There is no doubt that the LUMO of 2-C (-4.17 eV) is fairly suitable for efficiently injecting electrons into the semiconductor and ensuring the stability in air. In addition, through comparing 1-A with 2-A, and 1-B with 2-B, we found that -CN substitution at 9,10-positions could reduce the LUMO levels by about 0.45~0.55 eV compared with -CF3 substitution. In short, the two -CF3 groups at 9,10-positions of Ant contribute little to the HOMO and LUMO components in Series 1, only pull the HOMO and LUMO levels down; but the two -CN groups in Series 2 are fully involved in the conjugation of Ant rings in the HOMO and LUMO, not only lowering the HOMO and LUMO levels, but also modulating the polarized orientation of the electron cloud. Except for HOMO/LUMO, the charge injection also directly relies on the IP/EA, that depends on the nature of the semiconductor (p- or n-type semiconductor). IP and EA are the most important arguments to represent the reduction and oxidation ability, respectively. Large EAs indicate high air stability of anions against ambient oxidants (mainly O2 and H2O), which is a crucial requirement for n-type materials. By contrast, low IPs are desired for the p-type charge transport materials. As seen in Table 2, the EA of 1-A is too small (AEA/VEA:0.37/0.26 eV) to ensure stability of anion, and the HOMO level (-5.88 eV) is too low to match Au electrode for hole injection. Therefore 1-A is not qualified for charge transport material. For the other compounds in Series 1, the values of AEAs lie in the range of 1.40~1.53 eV which are larger than that of 1-B’ (1.09 eV), and the values of AIPs lie in the range of 6.17-6.80 eV. These data demonstrate the ambipolar characteristic of the compounds in Series 1 except for 1-A considering from the view of charge injection.59 For Series 2, the larger EAs - 12 ACS Paragon Plus Environment

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can be observed, especially, 2-C, it possess the largest AEA/VEA values (2.87/2.75 eV), which indicate an air-stable n-channel transport property in theoretical. Whereas the hole injection could be annihilated because of the high AIP/VIP (8.54 eV/8.61 eV). From the above analyses, it can be concluded that the reduction in HOMO/LUMO energy level by introducing -CF3 groups is modest, which is beneficial to regulate compounds to be ambipolar materials. Additionally, -CN groups have advantages over -CF3 groups in keeping good planar rigidity, decreasing LUMO level and improving air-stability. Through modifications of Ant core structures and functionalities, HOMO/LUMO energy levels can be finely tuned over 1.0 eV, allowing determination of the molecular orbital energetic windows governing carrier polarity and environmental stability.

Figure 5. The diagrams of the frontier orbital energy levels for studied molecules.

Table 2.The calculated energies of HOMO and LUMO, Ionization Potential (IP), and Electron Affinity (EA) of Adiabatic/Vertical (A/V) at the B3LYP/6-31G(d, p). (unit: eV) Compd.

HOMO

LUMO

L-H

AIP

VIP

AEA

VEA

1-A 1-B 1-C 1-D 2-A 2-B 2-C

-5.88 -5.67 -5.55 -5.25 -6.17 -5.91 -7.15

-2.53 -2.55 -2.64 -2.57 -3.08 -3.02 -4.17

3.35 3.12 2.91 2.68 3.09 2.89 2.98

6.35 6.80 6.61 6.17 7.66 7.04 8.54

6.44 6.92 6.76 6.28 7.72 7.13 8.61

0.37 1.40 1.42 1.53 1.63 1.80 2.87

0.26 1.23 1.34 1.40 1.53 1.70 2.75

- 13 ACS Paragon Plus Environment


1-B’

-5.52

-2.18

3.34

6.75

Page 14 of 39

6.84

1.09

0.93

3.2 Reorganization energy The reorganization energy (λ) is an important parameter for electronic hopping rate. Small reorganization energy promises the ease of the charge carrier transport. In order to understand the effect of -CF3 and -CN on reorganization energy intuitively, the reorganization energies obtained by NM methods of three simple compounds, Ant, 1-A and 2-A were firstly studied under gas-phase optimization. The NM analyses were executed by Charge Transfer Modeling Package (CTMP) which is developed by our group.67-68 The contributions of each vibration mode to hole/electron reorganization energies (λh/λe) are shown in Table S3 and Figure S4. For Ant, the contributions for λh mainly derive from the high-frequency region of C–H bending vibration (1421 cm-1) and C=C stretching vibrations (1583 and 1683 cm-1). When substituted by -CF3 groups at 9,10-positions, the contributions of bending vibrational modes in low frequency region and the stretching vibrational motion of conjugated core along the molecular long axis (nearby 750 cm-1) increase. One remarkable increase of vibrational modes can be found in the range of less than 55 cm-1, which correspond to the rotation of -CF3, meanwhile the contributions of C–H bending vibration (scissoring) and C-C stretching vibrations (1236 and 1253 cm-1) also increase obviously. However, in the high-frequency region, remarkable reduction can be found especially for around 1580 cm-1. Whereas for 2-A, the main vibration modes that contribute to λh stem from C–H scissor bending vibration (1453 cm-1) and C=C stretching vibrations (1582 and 1668 cm-1), which is similar with Ant, and even smaller in each modes due to nonbonding character of -CN groups in FMOs.69-70 Hence, compared with Ant, the λh of 1-A is larger and that of 2-A is smaller. For λe of Ant, the contributions that differ significantly from λh appears at low frequency region (396 and 399 cm-1), which mainly derived from the conjugated core reverse stretching motion along the long-axis of molecule. For 1-A, except for the main increased contributions of rotation of -CF3 ( 1.25 Å and x ≈ 3.0–4.0 Å, y < 1.5 Å. Combined with the largest interaction energy range of the other two molecules, 1-B and 2-B, their regions are mainly distributed in function x/y >1.6 (x [0, 4], the unit is Å) and x < 4 Å, y 100 meV) are broader than 2-A and 2-B, they overlap the region with large intermolecular interaction energies by only a small amount. The overlapping regions are mainly located in x ≈ 3.0~4.0 Å and y

Theoretical Investigations into the Electron and Ambipolar Transport

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