1. Introduction

Organic semiconductors have received tremendous attention in recent years because of their potential application in organic light emitting diodes (OLED),organic solar cells and organic field-effect transistors (OFETs) ^{[1, 2, 3]}. Previous investigations demonstrate that designing molecules with donor-acceptor (D-A) moieties is a viable strategy to create organic semiconductors ^{[4, 5, 6]}. Zhang et al. report a new D-A-D molecule: BTBPD (Fig. 1) with bipyrrolylidene-2,2' (1H,1'H)-dione (BPD) as the electron-accepting core containing two benzo^[b]-thiophene moieties ^[7]. The OFET of BTBPD exhibits an outstanding hole mobility of up to 1.4 cm²V^-1s^-1.

Recently,a great deal of effort has been invested in the theoretical study on typical photoelectric material systems to understand the experimental phenomenon and design new photoelectric materials ^{[8, 9]}. In order to gain insight into the origin of the hole transfer property of BTBPD,its charge transport features were systematically investigated by the Marcus theory in this article.

2. Computational methods

The ground state and cationic state structures of BTBPD were fully optimized at density functional theory level with B3LYP functional and 6-31+g** basis set,which is recognized to successfully provide molecular geometries and accurately calculate the charge transport parameters for sulfur containing compounds ^{[10, 11]}. Harmonic vibrational frequencies were also calculated and confirmed that each optimized configuration was a minimum on the potential energy surface.

To describe the charge-transport properties of the compound, the Marcus electron transfer model was employed ^[12]. In this model,charge carrier diffuse by hopping from a charged molecule to an adjacent neutral one and each hopping step has been considered as a non-adiabatic electron-transfer reaction involving a self-exchange of charge between neighboring molecules. Thus the rate of charge transfer between neighboring molecules,kcan be expressed as:

Here,Vis the intermolecular transfer integral,λis the reorganization energy,h=h/2π,his the Planck constant.k_Bis the Boltzmann constant andTis the temperature. In this paper,the hole transfer integral of (V_h) is calculated with ADF software at the PW91/TZP level. The hole reorganization energy (λ_h) is evaluated from adiabatic potential-energy surfaces and given by,

E⁺(g⁰) and E⁰(g⁰) are the energy of the cationic and neutral states with the optimized geometry of the neutral molecule,respectively;E⁺(g⁺ ) and E⁰(g⁺) are the energy of the cationic and neutral states with the optimized cationic geometry,respectively.

Thus,the drift mobility of hopping,μ,can be evaluated from the Einstein relation:

Heren= 3 is the dimensionality,i is the all nearest adjacent molecules,d_i,k_i,P_i are the corresponding center-to-center hopping distance,hopping rate and the hopping probability due to the charge carrier to theith neighbor,respectively. Using Eqs. (1)-(5), the carrier mobility can be calculated.

3. Results and discussion 3.1. Geometric structure and molecular orbital

The schematic structure of BTBPD with the number of some key atom is shown in Fig. 1. The main geometrical parameters optimized at B3LYP level and the experimental results determined by the single-crystal X-ray diffraction are listed in Table 1.

The calculated structure shows that the BPD core adopts a transconfiguration at the C55C double bond and exhibits a nearly planar geometry. The thiophene rings form dihedral angles of 28.17° and 25.42° with BPD core and the benzo^[b]thiophene rings,respectively. The calculated bond distances are in good agreement with the experimental results determined by the single-crystal X-ray diffraction. Since the hole transport property is closely related to HOMO,we show the HOMO of BTBPD in Fig. 2. The results indicate that the HOMO with π-orbital features is mainly delocalized over the BPD core and two thiophene rings.

3.2. Reorganization energy

In the cationic state,the molecular structure is almost coplanar. The thiophene rings form dihedral angles of 4.03°and 2.98° with BPD core and the benzo^[b]thiophene rings,respectively. Moreover,the structural distortions are mainly localized on the central BPD core,such as,the bond length of C₁-C₃and C₃-C₄changes by-0.039 Å and 0.046 Å ,respectively. The degree of bond length alteration (BLA) in the central BPD core, calculated as the difference between the average bond length of C₁-C₃,C₁-C₂ and the average bond length of C₁-C'₁,C₃-C₄, amounts to 0.077 Å in the ground state and 0.017 Å in cationic state. The smaller BLA in the cationic state indicates that the p-electron are delocalized and creates an enhanced quinoidal character to the conjugated backbone in the cationic state, which facilitates the hole transport. The adiabatic potentialenergy surfaces of neutral/cation species were adopted to evaluate the reorganization energy. The calculated hole reorganization energy based on the DFT/B3LYP method is 0.496 eV, which is much close to that of the typical hole transport material TPD (0.28 eV) ^[13]. The small hole energy reveals that the structural distortions induced by hole injection are negligible, which is in agreement with the discussions above about the geometrical structure. Since the hole injection ability of hole transport materials is known to heavily depend on the ionization potential (IP),the calculated adiabatic IP (5.68 eV) and vertical IP (5.96 eV) indicate that the hole injection would be facile.

3.3. Transfer integral

Fig. 3 illustrates four main hopping pathways obtained directly from the crystal structure of BTBPD. The hole transfer integrals of (V_h) calculated with ADF at the PW91/TZP level of theory are listed in Table 2. The results indicate that the magnitudes of hole transfer integrals are sensitive to the molecular stacking arrangements in crystal. TheV_hvalues in these pathways are large in the range of 10^-3eV to 10^-1eV. The statistical average value for V_h is 37.90 meV. In the parallel pathway 1 with theπ-πpacking orientation,theV_h(159.08 meV) is the largest,indicating that the

π-πpacking is favorable to the HOMO electronic coupling of neighbors and plays a major role in the hole mobility of the material. While for pathway 2 with the short S···S contact (3.522 Å ),the transfer integral is also large (12.43 meV). It is caused by the p-type interaction since the lone-pair electrons of the neighboring sulfur atoms arrange side by side,obviously contributing to the relatively large V_h values. Thus the S···S interaction is a supramolecular organization force that should drive the effective self-assembly and facilitate charge transfer.

In addition,basis set superposition error (BSSE) using a counterpoise correction scheme was taken into account to calculate the interaction energies for main pathways. The results show high intermolecular interaction energy with the values of 28.66 kcal/mol and 8.63 kcal/mol occur on pathways 1and 2, respectively,in which theV_hare big. This suggests that there is some correlation between the intermolecular interaction energy and the transfer integral.

3.4. Hole mobility

Combining the parameters mentioned above,we estimated the hole mobility by Marcus charge transfer model. The calculated hole mobility of BTBPD is large with a value of 0.29 cm²V^-1s^-1. ,which is ascribed to the smaller hole reorganization energy and large transfer integral. The calculated hole mobility is smaller than the experimental OFET result,which may be a result of the simplicity of the Marcus model. It is worth noting that this manuscript focuses on the structural and electronic properties in solid phase, and the accurate absolute hole mobility is not the aim of this work.So the Marcus theory could be still fully applicable,and the results presented in this work could shed light on materials design for organic semiconductors.

4. Conclusion

In summary,the structural,electronic and charge transport properties of BTBPD were systematically investigated by DFT calculations. The results show that the HOMO of BTBPD is mainly composed ofπ-orbital of the peripheral aromatic rings. The hole reorganization energy is small with a value of 0.496 eV. The hole transfer integrals of BTBPD are large,especially in the pathways 1 and 2 with π-π interaction and S···S interaction. Calculated hole drift mobility (0.29 cm²V^-1s^-1) suggests that BTBPD is a outstanding hole transport material and has potential applications in organic optoelectronic devices.

Acknowledgments

The authors acknowledge the financial support from the Ministry of Science and Technology of China (No. 09C26212203285) and the Project of Science and Technology of Jilin Province (No. 201115094).