Charge Transfer Properties of Organic Semiconductor Molecules of Perylene Derivatives①

TAN Ying-Xiong LIU Jian-Bo LI Quan ZHAO Ke-Qing

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Charge Transfer Properties of Organic Semiconductor Molecules of Perylene Derivatives①

TAN Ying-Xiong LIU Jian-Bo LI Quan②ZHAO Ke-Qing

(610066)

The charge transfer rates of perylene and its four derivatives were studied at the level of B3LYP/6-31G** by density functional theory. The results showed that the perylene and its four derivatives belonged to the semiconductor molecules, which released energy when electron was injected. Therefore, they were suitable to be used as the electron injection material. The introduction of OH group can improve the electron transfer rate significantly. The formations of intramolecular hydrogen bonds were unfavorable to the hole transfer, but conducive to the electron transfer. The perylene derivatives, 2,5-3,4,5-(trifluorophenyl)ethynyl-8,11-3,4,5-trihydroxyphenyl ethynyl, designed in this article had the hole transfer rate of 1.57 cm2/V·s-1. Therefore, this kind of material will be potential hole transfer material with high transfer efficiency.

perylene derivatives, density functional theory, hole transfer,electron transfer, organic semiconductors;

1 INTRODUCTION

The organic-conjugated materials have been widely used in the field of optoelectronics and microelectronics, such as organic light-emitting dio- des (OLEDs), organic field-effect transistors (OFETs) and organic photovoltaic devices (OPVs)[1-3]. The organic semiconductor materials can be divided into organic crystal, conjugated polymer material and liquid crystal semiconductor. The liquid crystal semiconductor has the characteri- stics such as high degree of ordering, molecular self-assembly and self-repair, and can be made by solution processing. Compared with the crystal material, it has the advantages of high charge transfer rate and low cost of device processing. The organic semiconductor materials can be designed and synthesized by molecules. The performance can be further enhanced. The organic compounds con- taining conjugated-electrons are typical semicon- ductor materials, which have received extensive attention. Polyacene and polythiophene are polyme- rized organic semiconductors. The triphenylene, truxene and perylene derivatives are the discoid organic semiconductor materials with bright pro- spect[4-6]. Perylene derivatives are a group of organic compounds with larger-electron structure. They have been proved to have excellent photoelectric properties recently. For these properties, they have found wide applications in the fields of charge transfer, organic light emitting and solar cells, and there are extensive studies in synthesis, characteri- zation and computational of perylene derivatives[7-9].

Charge transfer is an important factor influencing the behavior of organic semiconductor materials, and charge carrier mobility is at the center of organic electronic devices[10-12]. According to the energy band theory, the movement of charge carrier, known as the charge transfer or charge migration, is an important factor for the characterization of semi- conductor materials. The holes, electron injections and transfer properties of four perylene derivatives were discussed through theoretical calculations in this article. The four perylene derivatives were perylene, 3,9-difluorine perylene, 3,9-dihydroxy perylene, 3,9-dihydroxy-4 and 10-difluorine per- ylene. The relationship between charge transfer properties and the structures of four perylene derivatives is studied, which contributes to the design and synthesis of perylene derivatives with high performance.

2 THEORETICAL METHODS

2. 1 Charge injection

The process of electron injection is described with the following formula[13].

The electron affinity of semiconductor molecule is expressed as, where(M-) and(M) denote the energy associated with negative ion and molecular geometry, respectively.represents that a molecule gains the energy released by an electron. The smaller the(the more negative), the easier the electron injection will be. This kind of material is suitable as the candidate material for the electron transfer layer.

The process of hole injection is generally repre- sented by electron stripping.

The performance of hole injection is generally described with the ionization energy

where(M+) and(M) denote the energy asso- ciated with cation and molecular geometry, respect- tively. The ionization energyrepresents the energy required by a molecule to ionize one electron. The magnitude of ionization energy has a negative correlation with hole injection properties. The smaller the ionization energy is, the easier the ionization will be, and more suitable to be used as the material for the hole transfer layer.

2. 2 Charge transfer

The mobility of charge carrier can be obtained by the Einstein equation:

The mobility of charge carrier is expressed as

＝e/(kB) (1)

where e is the electron charge, kBis the Boltzmann constant,is the absolute temperature, andis the average diffusion coefficient of the charge starting from a molecule and towards all directions in three-dimensional space, as given by Formula (2):

The diffusion coefficient is expressed as

＝(2)

The small-molecule discotic liquid crystal material, as a kind of organic semiconductor ma- terial, has the properties of one-dimensional charge carrier migration. The average diffusion coefficient can be simplified as=2, whereis the disk spacing between adjacent discotic molecules, andis the constant of charge transfer rate between adjacent molecules. The carrier mobility is obtained by substituting into formula (1).

According to the semi-classical model of Marcus charge transfer, the constant of charge transfer rate between adjacent molecules is expressed as the following formula[14, 15]:

＝(42h)2(4πkB)-0.5exp[-/(4kB)](4)

whereis the charge transfer matrix element,is the absolute temperature,is the charge reor- ganization energy, h is the Planck constant and kBis the Boltzmann constant.

The reorganization energy is calculated by the adiabatic potential energy surface. That is, the reorganization energy of hole transfer+and reorganization energy of electron transfer-are calculated as follows[10-12, 16]:

+＝(PE+/PE) –(PE+/PE+) ＋

(PE/PE+) –(PE/PE) (5)

-＝(PE￣/PE) –(PE￣/PE￣) ＋

(PE/PE￣) –(PE/PE) (6)

where(PE+/PE) represents the total energy of PE+ions in PE configuration optimization.(PE+/PE+) represents the total energy of PE+ion configuration optimization. The denotations of other symbols are similar.

The charge transfer matrix element characterizes the coupling strength of electron-electron interaction, and several methods have been proposed to evaluate the transfer integral within a molecular dimer. The simplest way is the frontier orbit energy level splitting method[10-12,16]. That is, the closed shell system was formed by adding one electron to the molecular/molecular cation system. The energy level splitting of HOMO and HOMO-1 at the transition state was calculated. One half is the hole transfer matrix element t+. The closed shell system is formed by reducing one electron from the molecular/molecular anion system. The energy level splitting of LUMO and LUMO＋1 at the transition state is calculated. One half is the negative charge transfer matrix element t-.

3 RESULTS AND DISCUSSION

3. 1 Molecular structure and charge injection

The geometrical structure optimization and energy calculation for the five molecules and molecular ions of perylene derivatives as shown in Fig. 1 were performed by the B3LYP/6-31G** the- oretical level in the Gaussian 09[17]. The results are shown in Table 1. D molecule was the perylene molecule not substituted; e molecule was 3,9- difluorine perylene; f molecule was 3,9-dihydroxy perylene; and g1 and g2 molecules (g2 contains F···H–O intramolecular hydrogen bond) are the derivatives, in which the Nos. 3 and 9 positions are substituted by F, and Nos. 4 and 10 positions by hydroxyl group. The binding energy of hydrogen bond was calculated as 19.69 kJ/mol. The bond lengths of O–H in the g1 and g2 molecules and their vibration frequencies are shown in Table 2.

Table 1. Energy Gap Eg of Perylene Derivatives Molecules. Ionization Energy E(IP), Electron Affinity E(EA) and Recombination Energy (kJ/mol)

TH, F-TH and OH-TH are triphenylene, fluorine-substituted triphenylene, and hydroxyl-substituted triphenylene respectively, as shown in literature [16].

Table 2. Hydroxyl Bond Length R (O-H) (nm) in the g1 and g2 Molecules and Stretching Vibrational Frequency V (O-H) (cm-1)

d：R1＝R2＝H；e：R1＝H，R2＝F；f：R1＝H，R2＝OH

g1：R1＝F，R2＝OH； g2：R1＝F，R2＝OH

Fig. 1 . Molecular structures of perylene derivatives

As seen from the data in Table 1, the energy gap of five perylene derivatives molecules is about 285 kJ/mol (2.95 eV). The derivative molecules be- longed to the organic semiconductor molecules. A hole injection for the molecules will absorb higher energy (600 kJ/mol). Therefore, the molecules of derivatives were not suitable to be used as the hole injection materials. The electron affinities were ne- gative, which indicated that the energy release was required for electron injection. The amount of released energy was related to the types of sub- stituent. The substitution of e molecules of perylene derivatives by the electron-withdrawing fluorine atoms released the most energies, while the sub- stitution of f molecules by electron-donating hydroxyl group released the least energies. It is easier to achieve the electron injection of g2 molecule than that of g1 molecule, due to the formation of intramolecular hydrogen bonds. Therefore, the perylene derivatives were suitable to be used as electron injection materials. In terms of recombination energy, the introductions of elec- tron-withdrawing F or electron-donating OH were not conducive to electronic transfer or hole transfer, which was also the case for triphenylene derivatives. For either the hole transfer or electron transfer, the recombination energies of perylene and its deriva- tive molecules were smaller than those of tripheny- lene and its derivatives. It was thus indicated that perylene and its derivatives were more suitable to be used as charge transfer material than tripheny- lene and its derivatives.

As shown from Table 2, the formation of F···H-O hydrogen bond in the molecules leng- thened the O–H bond, and the stretching vibrational frequency decreases, which presented the typical characteristics of red-shifted hydrogen bonds.

3. 2 Charge transfer

When the molecules and ions with optimized structures overlapped, and the disk spacing was 0.45 nm, the molecules and ions were rotated by 0～180o, considering the symmetric structure of each molecule. The difference was 20o. The total energy E of molecular ion dimer and energy level splitting value were calculated in each rotation angle (ΔHOMO and ΔLUMO). Fig. 2 shows the relationship between the energy level splitting in charge transfer and rotation angle for each molecule.

Fig. 2 . Relationship between the energy level splitting value and rotation angle of perylene derivatives

The energy level splitting values (ΔHOMO or ΔLUMO) are determined by the couplings of molecules and ions (HOMO or LUMO). For ΔLUMO, when the molecules and anions were overlapped at certain angle and distance to form the transition state molecules, ΔLUMO was the dif- ference between LUMO＋1 and LUMO. If LUMO of molecules and ions had more overlapping in one-dimensional space, the molecular ion dimer formed had a lower LUMO. As a result, the accumulation of molecules and ions showed more prominent bonding characteristics. The ΔLUMO was also larger. Correspondingly, the charge transfer matrix element and the charge transfer rate increased. As shown in Fig. 2, the energy level splitting values of the hole or electron transfer presented regular changes with the rotation angle. The rotation angle was in the range of 0～180o. The images of energy level splitting values of charge transfer were symmetrical. When the disk spacing of molecules was fixed, the maximum values of energy level splitting of charge transfer for five molecules emerged within the range of rotation angle of 0o or 180o. The hole and electron transfer matrix elements were the maximum, given the maximum overlapped area of molecules and ions. When the rotation angle was in the range of 20～60o, the hole transfer matrix element was greater than that of the electron transfer. Within the range of 80～100o, the electron transfer matrix element was greater than that of the hole transfer. When the rotation angle was 0o, the hole transfer matrix element decreased successively from d, f, g2, e to the g1 molecules (the energy level splitting values are 0.147, 0.133, 0.111, 0.105 and 0.101 eV, respectively). It was indicated that the hole transfer matrix element for the perylene substituted by electron-donating group was greater than that of perylene substituted by electron-withdrawing groups. By comparison between g2 and g1, it was found that the hole transfer matrix element of g2 molecule was greater than that of g1 molecule, due to the better electronic delocalization of g2 mole- cule. There was a great difference with the previous research result of triphenylene. When the rotation angle was 0o, the electron transfer matrix element reduced successively from d, e, g2, f to the g1 mo- lecule (the energy level splitting values are 0.199, 0.188, 0.171, 0.132 and 0.114 eV, respectively). It was indicated that the introduction of electron- withdrawing group was more conducive to electron transfer than that of the electron-donating group. The formation of intramolecular hydrogen bonds was conducive to the electronic delocalization of rigid nucleus, which would increase the electron transfer matrix element.

According to the lowest energy principle, the overlapped disk spacing and rotation angle between molecules and molecular ions were selected. Then, the charge transfer matrix element and charge transfer rate were calculated. The calculation results are shown in Table 3.

Table 3. Relationship between Disk Spacing dis, the Lowest Energy of Charge Transfer (nm) and Rotation Angle θ (o). Relationship between the Charge Transfer Matrix Element T (kJ/mol) and Charge Transfer Rate (cm2/V·S-1)

For perylene molecule d, when the distance was 0.55 nm and the rotation angle was 100o, the molecule and molecular ions overlapped with the lowest energy. At this moment, the accumulation was in the optimal state. The electron transfer rate was 2.76 times greater than the hole transfer rate. Compared with the hole transfer rates of tripheny- lene and its derivatives[12], those of perylene and its hydroxyl or fluorine-substituted derivatives decrea- sed obviously. But the electron transfer rates were equivalent. The introduction of electron-withdraw- ing fluorine atoms or electron-donating hydroxyl group would result in the increase of hole transfer matrix element of perylene, thereby leading to the increase of hole transfer rate of perylene. The introduction of electron-donating OH increased the electron transfer matrix element significantly, which improved the electron transfer rate. Comparing g1 and g2 molecules, it was found that the formation of intramolecular hydrogen bonds was not conducive to the hole transfer. For the g2 molecule, the formation of intramolecular hydrogen bond was apparently conducive to the electron transfer.

3. 3 Design of a new type of perylene derivatives

According to the above research result, the h molecule of perylene derivative is shown in Fig. 3.

Fig. 3 . Structure of the h molecule

In h molecule, at Nos. 2 and 5 positions, the 3,4,5-(trifluorophenyl) ethynyl was introduced, and at Nos. 8 and 11 positions, the 3,4,5-trihydroxy- phenyl ethynyl was introduced. When the molecules and ions rotated by 180o, the large-interaction between the molecules and ions emerged due to the overlap of electron-deficient trifluorophenyl and electron-rich trihydroxyphenyl. Therefore, the elec- tron coupling increased.

The energy gap of h molecule was calculated on the basis of the optimized structures of molecules and molecular ions, which was 270.24 kJ/mol. The ionization energy and electron affinity were 590.64 and –151.39 kJ/mol, respectively. The recombina- tion energies of hole and electron transfer were 12.64 and 14.21 kJ/mol, respectively. It was indica- ted that the h molecule had semiconductor pro- perties. The performance of hole injection was poor, while the electron injection was accompanied by energy release. The recombination energies of hole and electron transfer were lower than those of d (perylene) molecule, which was beneficial to the charge transfer.

When the h molecules and molecular ions overlapped, and the disk spacing was set at 0.45 nm, the molecular ion dimer was rotated at a difference of 20o within the range of 0～180o. Then the energy and energy level splitting value at the transition state were calculated. The results are shown in Figs. 4 and 5, respectively.

As shown in Figs. 4 and 5, when the h molecule transferred the holes and electrons, the molecules and cations as well as the molecules and anions accumulated. The lowest energy value emerged at 40° and 140°. At this moment, the matrix element was the largest (energy level splitting value was also the largest), which was conducive to both the hole transfer and electron transfer. When the rotation angle of molecular ion dimer was set at 140°, and the distance between molecules and ions was changed to 0.34～0.45 nm, the energy of molecular ion system was calculated. The distance corresponding to the lowest energy was obtained. Moreover, the hole transfer and electron transfer matrix elements at this state were calculated, with the values being 5.78 and 3.81 kJ/mol, respectively. The hole transfer and electron transfer rates were 1.57 and 0.506 cm2/V·s-1, respectively. For either hole transfer or electron transfer, the transfer rate of h molecule was much greater than that of d, e, f and g molecules. Especially, the hole transfer properties were greatly improved. The reason was that the coupling degree of the electron-electron interaction was enhanced, while the recombination energy of transfer decreased, leading to the obvious increase of transfer matrix element. The hole transfer rate of h molecule was 3.1 times larger than the electron transfer rate. Thus, the h molecule can be used as the hole transfer material with high efficiency.

Fig. 4 . Relationship between energy and rotation angle of h molecules and molecular ion dimers

Fig. 5 . Relationship between energy level splitting value in charge transfer and rotation angle for the h molecule

4 CONCLUSION

The charge transfer rates of perylene and hy- droxyl and/or fluorine-substituted perylene deriva- tives were calculated theoretically. The following conclusions were derived:

(1) The molecules of perylene derivatives were organic semiconductor molecules and therefore unsuitable to be used as the hole injection material but suitable as the electron injection material. The substitution properties and the formations of intramolecular hydrogen bonds would all influence the electron injection ability.

(2) Compared with the hole transfer rates of triphenylene and its derivatives, those of perylene and its hydroxyl or fluorine-substituted derivatives were much lower. But the electron transfer rates were equivalent. The introductions of electron- withdrawing fluorine atoms or electron-donating hydroxyl groups could increase the hole transfer rate. The introduction of electron-donating OH would significantly improve the electron transfer rate. The formation of intramolecular hydrogen bonds was unfavorable to the hole transfer, but conducive to the electron transfer.

(3) The perylene derivative h molecules of 2,5-3,4,5-(trifluorophenyl)ethynyl-8,11-3,4,5- trihy- droxyphenyl ethynyl designed in this article had the hole transfer rate of 1.57 cm2/V·s-1, with the electron transfer rate to be 0.506 cm2/V·s-1.

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31 March 2014; accepted 5 January 2015

①Supported by the National Natural Science Foundation of China (No. 51273133), the Opening Project of National Key Laboratory of Theoretical Chemical Computation (No. K1202), and the Department of Education in Sichuan Province (No. 11ZB086)

. Li Quan, born in 1966, professor, Tel: 13808003581, E-mail: liquan6688@163.com

10.14102/j.cnki.0254-5861.2011-0312