Theoretical Study on the Electronic Structures and Charge Transport

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C: Energy Conversion and Storage; Energy and Charge Transport

A Theoretical Study on the Electronic Structures and Charge Transport Properties of a Series of Rubrene Derivatives Li Fei Ji, Jian-Xun Fan, Gui-Ya Qin, Ning-Xi Zhang, Pan-Pan Lin, and Ai-Min Ren J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07018 • Publication Date (Web): 28 Aug 2018 Downloaded from http://pubs.acs.org on August 28, 2018

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The Journal of Physical Chemistry

A Theoretical Study on the Electronic Structures and Charge Transport Properties of a Series of Rubrene Derivatives Li-Fei Ji,† Jian-Xun Fan,†,‡1 Gui-Ya Qin,† Ning-Xi Zhang,† Pan-Pan Lin,† Ai-Min Ren*† Correspondence to: Ai-Min Ren (E-mail: [email protected]) Authors’ affiliation: †: Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, P. R. China

1

College of Chemistry and Material, Weinan Normal University, Weinan 714000, P. R. China 1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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ABSTRACT: The charge transport properties of a series of rubrene derivatives were systematically investigated by density functional theory (DFT) and molecular dynamics (MD) simulations. It was found that functionalizing electron-withdrawing groups (-CN, -CF3, or fluorination) on the peripheral phenyls not only enhance the chemical stability of materials but also favor electron injection by lowering the energy levels of frontier molecular orbitals and increasing the electron affinities. Derivatives 2-5 and 9, exhibiting similar packing motifs to rubrene but closer -stacking distances, possess large hole and electron transfer integrals, significant bandwidths and small effective masses, suggesting excellent ambipolar semiconductor behavior. The maximum hole(electron) mobilities in the Marcus hopping mechanism based on kinetic Monte Carlo simulation can reach 14.0~16.5(1.6~3.5) cm2 V-1 s-1. Interestingly, the antiparallel 2-D brick stacking and twisted backbones of fluorinated derivatives 11 and 12 result in nearly 1-D percolation network but balanced hole and electron transport property. In contrast, the parallel 2-D brick stacking of 14 leads to 2-D percolation network. Their maximum hole and electron mobilities fall in the range of 0.5~3.6 and 2.0~4.8 cm2 V-1 s-1. Furthermore, MD simulations show that dynamic disorder is strongly detrimental to the hole transfer but has a little influence on the electrons transfer for 1-5. And severely twist of backbones of 9 leads to almost one order of magnitude lowered mobility. In addition, the influences of different substituents on the molecular structure, packing motif and intermolecular reorganization energy are discussed.

2


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1. INTRODUCTION Organic semiconductor (OSC) materials, especially the π-conjugated molecules, have gained great interest in the past years for their implementation in electronic and optoelectronic devices ranging from field-effect transistors to light-emitting diodes, and solar cells.1-3 Compared with inorganic semiconductors, OSCs have enormous advantages in cost and processability. 4, 5 In practical applications, the efficiency of the organic active layer is dependent on the charge carrier mobility of organic material. As one of the most promising OSCs, rubrene’s hole mobility in single crystal field-effect transistors (SC-FETs) has been reached 18 cm2 V−1 s−1. 6 This large mobility has led to extensive rubrene-focused studies in an effort to better understand the nature of charge transport. 7-13 Theoretical and experimental studies have shown that the outstanding transport property of rubrene was mainly attributed to its packing motif (orthorhombic crystal) 14, which presents substantive spatial overlap between the π-conjugated tetracene backbones leading to strong intermolecular electronic coupling (~100 meV evaluated by density functional theory methods) 11. However, poor stablility (easy photo-oxidizes)15 and modest solubility of rubrene hinder its application into real electronic devices. These limits prompted researchers to design and synthesis rubrene analogues and derivatives owning good oxidation resistance, enhanced stability and efficient charge transport property.16-26 In most cases, small changes in molecular structure can induce a large impact on crystalline structure and electrical performance. Recently, Douglas and his coworkers synthesized and crystallized a series of rubrene derivatives by modifying peripheral phenyl rings with alkyl or fluorinated groups.16-18 As we know, due to the strong electronegativity of fluorine, fluorination is a popular strategy to reduce the sensitivity to oxidation, even converts the p-type 3



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OSCs into n-type or ambipolar materials. Furthermore, fluorination can change the electronic and optical properties of a material and introduce several types of inter- or intra molecular interactions, such as C−H···F, C−F···F and C−F···π contacts, in the solid state packing. Based on a careful analysis on the intermolecular interaction in crystals, Douglas et al demonstrated that the symmetric intralayer and interlayer noncovalent interactions in the solid state are beneficial to stabilize and crystallize planar rubrene conformations, but imbalanced interactions cause a significant twisted tetracene backbone and large backbone-backbone distance, which drastically reduce the π-π overlap and thus destroy their charge transport capacity. 18,19 For example, functionalizing electron-donating methyl on the peripheral phenyls induces significant steric hindrance and electrostatic repulsion in rubrene derivatives 6 and 7 (see Figure 1), which leads to severely twisted tetracene backbone in solid state; whereas incorporating para-trifluoromethyl (para-CF3) on two peripheral aryl groups (at positions 5, 12 of tetracene core) obtained rubrene analogues 4 and 5 that packed similar to orthorhombic rubrene with a planar backbone. Subsequently, W. Xie investigated the ambipolar characteristic of 5 by employing carbon nanotube electrodes instead of Au electrodes.20 As a result, SC-FETs of 5 showed an intrinsic and balanced ambipolar behavior with mobilities up to 4.8 cm2 V-1 s-1 for holes and 4.2 cm2 V-1 s-1 for electrons. However, further increasing CF 3 substituents destroys the backbone planarity and packing arrangements, for instance 8. It is extremely interesting that when -5, -12 benzene rings displaced by perfluorophenyl groups, rubrene derivatives 11 and 12 display a 2-D brick motif with π-stack distances of 3.5~3.6 Å. However, as Anger and Zhang reported,21, 22 further fluorination or perfluorination can increase the stability of rubrene but lead to significant twisted backbone nearly with no overlap between tetracene cores. Uttiya introduced electron withdrawing substituents (–CN and –CF3) on the -5, -11 phenyls (2 and 3) or replacing 4


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phenyl rings with smaller thiophene rings (–Th) (9) to reduce the peripheral phenyl–phenyl steric repulsion.24 These compounds exhibit similar packing features to orthorhombic rubrene, and (except 9) display higher oxidation potentials and lower photo-oxidation reactivity than rubrene. What’s more, experimental measurement suggested that derivative 3 can display comparable charge conductivity with rubrene. 24 Combining perfluorination of phenyl rings with thiophene substituents in rubrene obtained a more stable compound 14 but with low mobility of 1.7310-4 cm2 V-1 s-1.25

5



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Figure 1. Chemical structures of the investigated rubrene derivatives.

However, to the best of our knowledge, no systematic investigations about these rubrene analogues or derivatives have been carried out. Theoretical characterization of a series of analogues is an appealing means to provide reliable insight into their intrinsic electronic structures and charge transport trend. Thus, in this work we studied the charge transport properties of a series of rubrene derivatives via quantum chemical calculations based on experimental X-ray crystals. In compounds 2, 6


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3 and 9, the 5-, 11- phenyls of rubrene are modified by cyano group, trifuoromethyl, or thiophene ring. In series of 4-6, the 5-, 12- phenyls are substituted with methyl or trifuoromethyl. In compounds 11-14, the phenyl rings of rubrene are fluorinated. In compounds 7, 8, 10, and 13, four phenyl rings are modified by same substituents. We firstly explored how the substituents influence the geometrical and electronic structures and redox properties of the isolated molecules. We then investigated the intramolecular and intermolecular parameters (reorganization energies and electronic couplings) that governing charge transport of rubrene derivatives and their electronic band structures. Finally, the mobilities were determined using kinetic Monte Carlo (KMC) simulations based on Marcus theory rates. Moreover, to evaluate the effect of thermal molecular motions (or dynamic disorder) on the charge transport properties, classical molecular dynamics (MD) simulations were performed.

2. THEORETICAL METHODOLOGY The charge transport mechanism in solid state depends on the ratio of electronic coupling (V) to reorganization energy (λ). 27, 28 Generally, when V when V

 , the delocatized band transport dominates,

 , localized hopping model dominates. However, when V   , it is unclear whether

coherent band or incoherent hopping mechanism is dominant. In most OSC materials, the electron couplings between neighboring molecules are weak, plus the dynamic disorder resulting from thermal effects at higher temperatures, then the charge transport mainly occurs via hopping. Thus bulk charge transport was investigated according to the Marcus hopping theory29, which has been successfully applied to many systems of OSCs. 30 Marcus rate equation is as follows: 7



kCT

12   G   2  2Vij 2    ij     exp   h   k BT  4 k BT    

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(1)

where T is the temperature (set to 300 K in this work), kB is the Boltzmann constant, Vij is the electron coupling (or transfer integral) between adjacent molecules i and j , λ is the reorganization energy and Gij is the difference in free energies between the initial i and final states j . In the self-exchange reaction, the free energy difference G is often assumed to be zero. The charge transfer integral reflects the strength of the electronic interactions between neighboring molecules in crystal and thus is highly sensitive to the molecule packing motif. It can be evaluated by the site-energy overlap correction method 4:

V

J ij  0.5Sij  eii  e jj 

(2)

1  Sij 2



here, J ij is the transfer integral  i Hˆ  j overlap matrix element

   i

j

,

is the

ei  j  is the site energies



i

Hˆ  i

 , and

Sij is the

ohn–Sham Hamiltonians of a dimer and  i  j 

represents the LUMO (for electron transport) or HOMO (for hole transport) of the isolated molecule i(j). All these calculations of transfer integrals were performed in the ADF2016 package31 at PW91/DZP level.32 The reorganization energy includes intramolecular contribution in and intermolecular contribution out . The inner sphere part reflects the changes in molecular geometry during charge transport; and the latter is related to the electronic polarization of surrounding medium. For most organic crystals, however, out is small and usually neglected (i.e.,   in ).33,34 Thus, in this paper, only the intramolecular contributor has been considered. The reorganization energies were evaluated from the adiabatic potential-energy surfaces of isolated monomers (or four-points method)35 as the following equation: 8


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  E 0  G   E 0  G 0   E   G 0   E  G 

 

where, E 0 G 0

 

and E  G 

(3)

are the ground-state energies of molecule in its optimized neutral

 

and ionic state geometries, respectively, E  G 0 is the energy of the charged molecule at the

 

optimal geometry of neutral molecule, and E 0 G 

is the energy of the neutral molecule at the

optimal ionic geometry. All the neutral and charged molecular geometries were optimized by B3LYP functional 36 along with 6-31G(d,p)37 basis set in the Gaussian 09 software package. 38 The vibrational frequencies for the optimized geometries were calculated to ensure the minimum had been reached. In fact, the conformations of molecular neutral and charged states are also affected by the surrounding medium (or molecular packing), especially for the molecules with soft branch chains. The surrounding medium can restrict the freedom degree of molecule in some of extent, and then decreases the intramolecular reorganization energies.39, 40 As Douglas et al have demonstrated that whether the tetracene backbone of rubrene derivatives exhibit planar or twisted conformations is very sensitive to the molecular arrangement. Thus, the influence of the surrounding medium is also considered into in by using hybrid quantum mechanical/molecular mechanical (QM/MM) method. As shown in Figure 2, the center molecule labeled in red is set as the QM molecule, and its structures at different charged states are optimized by B3LYP/6-31G(d,p) method. The environment is treated as MM using the UFF force field41, and their coordinates are fixed during optimization. All the QM/MM calculations are implemented in Gaussian 09 ONIOM42, 43 module. The reorganization energy is also obtained by using four-points method.

9



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Figure 2. The center molecule displayed with ball and stick model (labeled in red) represents the region optimized by QM; and its nearest neighboring melecules displayed with wire model represent the region treated with MM.

Within the hopping mechanism, the average charge carrier mobility μ can be evaluated by the Einstein relation44 :   eD kB T , where e is the electronic charge and D is the diffusion coefficient. D is defined as the ratio between the mean squared displacement

x2

and diffusion time t , which

was computed by KMC simulations45: 2 1 x t  ,(n  1,2,3) D  lim t  2n t

(4)

The angular resolution anisotropic mobility in a two-dimensional (2-D) surface of single crystal was evaluated by following equation46:

x 2  t  cos2 i    e   lim  2k BT t t

(5)

here,  i (  ) are the angle of the transport channel i (the orientation angle of a specific transport direction) relative to the reference axis.

10


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To account for thermal disorder arising from low-frequency intermolecular vibrations (ω < 200 cm−1) in the crystal,4 MD simulations combined with QM evaluation of transfer integrals were carried out. All MD simulations were run on supercells of rubrene derivatives and performed in Material Studio package with the Discover module using the COMPASS force field.47 Additional details can be found in the Supporting Information. Band-structure

calculations

were

carried

out

with

Perdew–Burke–Ernzerhof

(PBE)

exchange-correlation functional 48 in VASP Package49,50 based on the experimental crystal structures. The kinetic energy cutoff on the wave function expansion was set to be 450 eV. The electron–ion interactions were described by using the projector augmented wave (PAW) potentials. 51 The Sperling’s centered difference method with dk = 0.01 Bohr-1 was used for effective mass calculations.52

1 1 2E  2 mij ki k j

(6)

In a broad band model, where the band width W is much larger than k BT (26 meV), the lowest limit of drift mobility can be evaluated by the equation53:

  20   300 T    m* m0  cm2 V-1s-1  1

(7)

here, m0 is the electron rest mass and T is the temperature in Kelvins. The m* is the effective mass for holes (mh *) at top of the valence band (VB) or for electronics (me *) at the bottom of the conduction band (CB). Ionization potentials (IPs) and electron affinities (EAs) are two key parameters that determine the efficiency of the charge injection from the electrodes and the reduced or oxidized ability of charged organic molecules.54 Large EA is beneficial for electron injection and stabilizing the organic radical anions. Low IPs facilitate hole injection, but too low values can produce unintentional doping. 11



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Thus, the adiabatic IPs and EAs for the isolated monomers were evaluated at the B3LYP/6-311+G(d,p)//B3LYP/6-31G(d,p) level with following equations:

IP  a   Eh G   E 0 G 0 

(8)

EA a   E 0  G 0   Ee G 

(9)

3. RESULTS AND DISCUSSION 3.1 Geometrical Structures and Intramolecular Reorganization Energies Firstly, we observe the influence of different substituents in the 5-, 6-, 11-, 12-position of rubrene on the backbone configuration and the relative position between substituents. The representative dihedral angles for the optimized rubrene molecules by QM and QM/MM methods are given in Table 1. The structures in experimental crystals are also listed in Table 1 for comparison. For the isolated molecules which are fully relaxed during optimization in gas phase, except molecules 1, 4, 5, and 13 with a planar backbone, most of the rubrene derivatives have a twisted tetracene backbone. The degree of twisting even reaches around 40. The strong repulsive interactions between substituents on the backbone lead to phenyl rings or thiophene rings slipping by each other to give a dihedral angle of 22~37°. We note that in molecules 25, and 9 which exhibit mild twisted or planar tetracene backbones, one of the phenyl rings in the same side is attached an electron-withdrawing group, the other one owns an electron-donating group or is replaced by thiophene ring. That seems to decrease the repulsive interactions between substituents to a certain extent. But, paradoxically, the molecules 1 and 13 with same substituents in the same side also have a planar backbone, and the molecules 11 and 12 attached two substituents with opposite electrical charge in the same side show a twisted backbone. 12


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Table 1. Dihedral angles for the backbone twist (: deg) and the out-of-plane substituents (: deg) of rubrene derivatives for the optimized molecules by QM and QM/MM methods and the molecules in crystals.

Derivatives 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Isolated molecules

QM/MM

Crystals













0 7.8 7.8 0 0 42.1 42.5 41.3 8.5 42.7 38.0 37.8 0 40.8

29.9 32.5/22.6 32.8/23.0 29.4 22.7 37.2 37.4 37.1 21.9/32.5 37.0/36.8 32.6/32.5 33.0 24.6 33.2

0 0 0 0 0 0 28.3 27.8 25.4 0 28.7

24.8 26.1 27.4 22.2 26.2 22.9 32.2/29.3 22.7/18.2 18.3 30.0 26.7

0 0 0 0 0 41.2 42.8 18.6 0 28.8 30.8 28.9 0 42.0

25.0 26.6 26.3 21.5 23.0 41.5/32.3 35.0 13.6 22.0 31.0 17.2/17.1 16.9 27.0 24.7

When considering the impact of intermolecular interactions with surrounding molecules (or molecular packing) on the molecular configuration, the twisting degree of tetracene backbone tend to become smaller or even to be zero, such as 2, 3 and 9 molecules. Meanwhile, the distortion of side substituents diminishes by 5~10. These results illustrate that the molecular packing has a great influence on the molecular geometries just as demonstrated by W. A. Ogden et al 18; that is to say, the molecular packing has a great influence on the intramolecular reorganization energies during charge carrier occurs. Moreover, the geometries of rubrene derivatives obtained with QM/MM model are

13



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very similar to that in experimental crystals, indicating that our calculation method of B3LYP/6-31G(d,p) and QM/MM model are feasible and reliable. Table 2. Calculated intramolecular reorganization energies with isolated molecule model and QM/MM model for selected rubrene derivatives at the B3LYP/6-31G(d,p) level. isolated molecule

QM/MM

Derivatives λh (meV)

λe (meV)

λh (meV)

λe (meV)

1 2

152 142

208 289

129 125

173 174

3 4 5 9 10 11 12 13 14

154 166 258 207 275 194 187 272 272

257 266 344 201 179 218 272 231 202

141 138 143 130 178 153 154 140 185

192 185 189 175 181 192 207 199 192

We now turn to the intramolecular reorganization energy that is one of most important parameters for charge transport. Also it can provide important information about the geometry relaxations that occur during charge transport and offer an evaluation of electron-phonon coupling. The reorganization energies for hole ( h ) and electron ( e ) calculated by adiabatic potential surfaces method with isolated molecule model and QM/MM model are shown in Table 2. It can be seen from Table 2 that the molecular packing indeed has a great influence on the calculated intramolecular reorganization energies ( in ). The reorganization energies for the isolated molecules lie in the range of 142344 meV. When taking into account the molecular packing, the values of in reduce substantially. For example, for rubrene the h and e lower by 15% and 17%, respectively, and for molecule 5 both the h and e lower by 45%. From the Marcus transport rate equation, we 14


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know that small decrease in  can lead to few-fold increase in the hopping rates. This means that when taking into account the molecular packing, the theoretically evaluated charge mobilities would be higher. Thus, in the later discussion we employed the values of reorganization energies calculated by QM/MM model. To explore how the molecular packing weakens the in , the torsion angles for tetracene backbone and side phenyl rings of rubre ne derivatives at neutral and charged states are checked, the results are listed in Table 3. The values for isolated molecules are given in Table S1 in the Supporting Information. It can be found from Table S1 that the isolated molecules undergo large conformational deformation from neutral to charged states. In contrast, in QM/MM model the conformations of molecules at neutral and charged states are very close, as shown in Table 3. In the presence of noncovalent forces from sounding medium, some of the molecule motions are restricted, which results lowered in . Additionally, we note that for the rubrene derivatives the reorganization energies for hole and electron are less than 200 meV, which is beneficial for charge transport. Only from the reorganization energy perspective, all the rubrene derivatives could exhibit well-balanced ambipolar transport property. This may be one reason for the material 5, which showed a balanced ambipolar behavior in SC-FETs20. Table 3. Dihedral angles for the backbone twist (: deg) and the out-of-plane substituents (: deg) at neutral and charged states for the center molecules of selected rubrene derivatives obtained by QM/MM methods. Derivatives

Neutral state

Cation state

Ion state













1

0

24.8

0

24.6

0

25.7

2

0

26.2

0

25.6

0

27.0

3

0

27.4

0

26.0

0

27.4

4

0

22.2

0

21.9

0

23.1

5

0

26.2

0

25.9

0

27.4

9

0

22.9

0

23.4

0

23.5

10

28.3

32.2/29.3

27.7

33.3/31.6

26.4

32.8/30.1

15



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11

27.8

22.7/18.2

29.0

23.9/19.0

27.3

24.1/19.1

12

25.4

18.3

26.1

18.7/16.5

24.9

19.3

13

0

30.0

0

29.9

0

30.3

14

28.7

26.7

29.8

27.6

26.2

27.5

We next evaluate how the internal reorganization energies change with different substituents on the external phenyl rings and different position of the substituted groups. It was found that the molecule 2 bearing two cyano (-CN) groups substituent exhibits nearly same  e/ h with the parent rubrene. However, other substituents on the phenyl rings induce increased reorganization energies. We find that compound 3 shows larger  than 4 by 3 meV for hole and 7 meV for electron. This suggests that trifuoromethyl attached on phenyl rings at 5-, 12-position of tetracene backbone is superior to that attached on the 5-, 11-positions phenyls. Compound 9 in which 5-, 11-positions phenyls are displaced by thiophene groups shows similar reorganization energies with parent rubrene. However, when all phenyl rings are displaced by thiophene rings the value of hole reorganization energy increases by 49 meV, obviously against hole transport. In addition, when the phenyls are fluorinated, compounds 11-14 achieved significantly increased reorganization energies especially for holes. The increase of λ values with fluorination, has been previously observed in other acenes such as tetracenes, pentacene,55 naphthalene diimide,56 or tri-isopropilsililpentacene derivatives 57. 3.2 Frontier Molecular Orbitals (FMOs), Ionization Potentials, and Electron Affinities Since the frontier molecular orbitals are closely related to the ability of charge injection, the energies of HOMO/LUMO for the isolated monomers of rubrene derivatives were calculated at the B3LYP/6-311+G(d,p)//B3LYP/6-31G(d,p) level. The results are listed in Table 4 and the available experimental values of FMOs are also listed in Table 4. The distribution diagram of frontier orbitals is shown in Figure S1 of Supporting Information. For all compounds, both HOMOs and LUMOs are 16


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mainly spread over the tetracene backbone, with little delocalization on side substituents. As expected, embellishing electron-withdrawing groups (-CN or -CF 3) on the peripheral phenyls can moderately lower the HOMO (LUMO) energies by 0.270.46 eV (0.250.46 eV) of rubrene, and introducing four para-CF3 or fluorinating the peripheral phenyls greatly reduce FMO energies by 0.51-1.16 eV. On the contrary, the electron-donating groups (-CH3) destabilize the HOMO and LUMO. In addition, introduction of thiophene groups also stabilizes the HOMO and LUMO by 0.10.28 eV with respect to rubrene. These suggest that compounds 6 and 7 are easier to oxidize than rubrene. Conversely, other derivatives should be slightly more difficult to oxidize but easier to reduce than 1. From Table 4, we note that for these derivatives the theoretical values of HOMO are in reasonable agreement with the experimental values. However, the evaluated LUMO energies are slightly higher than the experimental values and the energy gaps Eg are also increased. This may stems from the systematic error of computed method. So the HOMO−LUMO gaps of these derivatives should be smaller than our theoretical values (~2.5 eV). It can be found that the modification on the external phenyls of rubrene nearly does not change the energy gaps, except 10 with four thiophene groups on backbone which shows slight decrease. So it can be assumed that these rubrene derivatives possess similar HOMO−LUMO gaps with the parent molecule, rubrene (2.26 eV), or other analogues which have experimental values. This narrow energy gaps facilitate the injections of both the holes and electrons.

17



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Table 4. Calculated electronic structures for isolated monemers of rubrene derivatives at the level of B3LYP/6-311+G(d,p)//B3LYP/6-31G(d,p). (unit: eV) (a from ref. 26, b from ref. 24, c from ref. 20, d from ref. 25) Derivatives 1

HOMO -5.03

LUMO -2.47

Eg 2.56

HOMOexp a

LUMOexp b

-5.16 (-5.63 )

-2.90

a

Egexp

IP(a)

EA(a)

a

6.10

1.42

2.26

b

-

-

6.54

1.93

2

-5.49

-2.93

2.56

-5.76

3

-5.36

-2.79

2.57

-5.73b

-

-

6.42

1.79

4

-5.36

-2.79

2.57

-

-

-

6.42

1.79

5

-5.30

-2.72

2.58

-5.9c

-3.6c

2.3c

6.09

1.99

6

-4.91

-2.44

2.47

-

-

-

5.94

1.41

7

-4.85

-2.38

2.47

-

-

-

5.86

1.37

8

-5.63

-3.16

2.47

-

-

-

6.67

2.22

9

-5.15

-2.62

2.52

-5.19a (-5.68 b)

-2.98a

2.21a

6.20

1.57

a

a

6.13

1.71

a

10

-5.13

-2.75

2.38

-5.24

-3.08

2.16

11

-5.54

-3.07

2.47

-

-

-

6.60

2.04

12

-5.68

-3.24

2.44

-

-

-

6.73

2.26

13

-6.19

-3.60

2.59

-

-

-

7.09

2.55

14

-5.62

-3.20

2.42

-5.52d

-3.30d

2.22d

6.63

2.16

In experiments, gold (Au) electrodes are usually employed as the electrodes in amibipolar OFETs. But its low work function (-5.1 eV) does not seem to ensure efficient electron injection for majority of herein studied materials. This drawback can be overcome by employing electrodes with higher work function or surface modifiers to change the metal work function. For example, compound 5 showed ambipolar transport property with high hole mobility of 1.5 cm2 V-1 s -1 but low electron mobility of 0.28 cm2 V-1 s-1. When employing the single-walled carbon nanotube (CNT) either serving as a standalone electrode (-4.8 eV) or modifying the Au electrodes, the SC-FETs of 5 showed an intrinsic ambipolar electrical performance with mobilities up to 4.8 cm2 V-1 s-1 for holes and 4.2 cm2 V-1 s -1 for electrons.20 Hence, we infer that some of these derivatives with narrow Eg

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might be a potential ambipolar semiconductor, such as 24 which show similar electronic structures and molecular arrangement motifs to 5 (as described later in this work). The adiabatic ionization potentials IP(a) and adiabatic electron affinities EA(a) which characterize the redox ability of materials are also given in Table 4. As we know, large EA is beneficial for electron injection and ensure the environmental stability of materials, and low IP is helpful for hole injection. Without considering the polarizable environment and interface effect (or dipole interaction) between metal and organic semiconductor, the calculated IPs are always overestimated and EAs are underestimated with respect to the experimental ones. 58 Although the theoretical values can’t give exact information, but can provide a variation trend within a series of related derivatives. The IP(a) and EA(a) trends are in good agreement with the electronic structures. The IP(a)s and EA(a)s for these derivatives lie in the range of 5.86−7.09 eV and 1.37−2.55 eV, respectively. 6 and 7 show lower IP(a) and EA(a) than rubrene, which obviously impairs their air stability. On the contrary, other molecules show higher IP(a) and EA(a) than rubrene. Thus, fluorinating the peripheral phenyl rings, modifying para-trifluoromethyl or cyano group on phenyls, or replacing with smaller thiophene rings not only favor electron injection, but also help to enhance the chemical stability of materials. It is worth noting that derivative 5 shows a IP(a) similar to rubrene but a higher EA(a) than rubrene. That is why 5 can show ambipolar characteristic.

3.3 Crystal structures, Intermolecular Electronic Coupling and Electronic band structures The crystal parameters of rubrene derivatives obtained on experiment are tabulated in Table S2. Functionalizing rubrene with methyls or four trifuoromethyls and thiophenes leads to severely twisted backbones and destroys the preferred packing arrangements and efficient π-stacking between

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molecules. As shown in Figure S2, for 68 and 10 the distances between neighboring paralleled molecules even reach 10 Å, resulting in little overlap between tetracene cores. Besides, no overlaps between the peripheral phenyl rings and tetracene cores or the peripheral phenyl rings in two neighboring molecules are present. Obviously, these solid packing motifs are unsatisfactory. So the transport property in the four compounds was not discussed in here. The other derivatives’ crystal packing motifs are shown in Figure 3. As mentioned above, compounds 2-5 and 9 adopt a herringbone motif with predominant face-to-face stacking, similar to the orthorhombic rubrene57. But closer observation reveals that functionalizing the peripheral phenyls of rubrene with –CN and –CF 3 and –Th induces closer -stacking contacts compared to the parent molecule, rubrene (3.721 Å); the values of -stacking distances are 3.630 Å for 2, 3.529 Å for 3, 3.552 Å for 4, 3.508 Å for 5, 3.532 Å for 9, respectively. That’s because their introduction brings about stronger intermolecular interactions and hence reduces the separations, consequently will enhance the electronic coupling between adjacent molecules, as described below. It is interesting to note that the fluorinated rubrene derivatives 11, 12 and 14 display 2-D brick-like packing motifs, the most ideal stacking for high performance OSCs. Their π-stacking distances range from 3.5 to 3.9 Å. In addition, compound 13 exhibits a herringbone-like 1D π-stacking, but two distinct arrangements appear alternately, as shown in Figure 3, in column A the molecules exhibit a slipped face-to-face pattern with a small π-stacking distance of 3.632 Å, while in column B the molecules also exhibit a slipped face-to-face pattern but with a large π-stacking distance of 5.564 Å. This leads to two distinct transport channels A and B.

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Figure 3. The molecular packing motifs in the transport planes and the major hopping pathways in crystals of rubrene derivatives, and the face-to-face distances are labeled in black.

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Page 22 of 41

Based on the crystal structures, the major hopping pathways in crystals are defined in Figure 3, the corresponding electronic couplings between neighboring molecules were analyzed, and the calculated values for the disorder-free ideal crystals are given in Table 5. In case of 2-5 and 9, six nearest-neighboring molecules are found in the crystals. As expected, the largest transfer integrals for the -stacked dimers (pathways 1 and 2) of 2-5 and 9 are about 10-40 meV larger than that for rubrene (83.2 meV for hole and 40.4 meV for electron). The values for hole (electron) transfer integral along the cofacial -stacking direction are 100.5, 107.2, 111.1, 118.1 and 112.8 meV (48.0, 77.7, 60.8, 71.0, and 50.9 meV ) for 2, 3, 4, 5, and 9, respectively. In pathways 3-6, the adjacent molecules adopt an edge-to-face alignment, consequently the electronic couplings for these dimers are lower (

Theoretical Study on the Electronic Structures and Charge Transport

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