Theoretical Studies on the Structures and Opto-Electronic Properties of Fluorene-Based Strained Semiconductors

LIU Yu-Yu LI Jie-Wei BO Yi-Fan YANG Lei ZHANG Xiao-FeiXIE Ling-Hai,* YI Ming-Dong HUANG Wei,,*



Theoretical Studies on the Structures and Opto-Electronic Properties of Fluorene-Based Strained Semiconductors

LIU Yu-Yu1LI Jie-Wei2BO Yi-Fan1YANG Lei1ZHANG Xiao-Fei3XIE Ling-Hai1,*YI Ming-Dong1HUANG Wei1,2,*

(1;2;College of Mathematics and Information Science, Guangxi University, Nanning 530004, P. R. China)

[4]Cyclo-9,9-dimethyl-2,7-fluorenylene ([4]CF) was used as a model compound to explore the steric strain effect on the structures and photoelectrical properties of materials. A series of strained cyclic polyfluorene materials, []CFs (= 3−8), was designed. It was found that the strain energy decreased and the energy gap increased as the number ofand ring diameter increased. The ionization potential and electronic affinity tended to increase and decrease as the strain energy decreased at the same number of []CFs, respectively. With a balance between hole and electron reorganization energies in the system, these compounds demonstrated great potential as ambipolar materials. It was also found that []CFs showed an obvious blue shift in their emission spectra wavelengths (em2) as the strain energy decreased. Steric strain provides a powerful tool for the design of multifunctional semiconductors in organic optoelectronics.

Fluorene material; Organic semiconductor; Strained macrocycle; Opto-electronic property; Density functional theory calculation

1 Introduction

When atoms are too close to each other in molecule, strain energy can arise from the electron-electron repulsion of these atoms. Recently, high strain materials, fully conjugated cyclic oligomers, have attracted not only synthetic but also theoretical chemists for many reasons1−7. At first, these macrocyclic oligomers have played important role in supramolecular chemistry and nanotechnology. With shape-persistent, non-collapsible, they may self-assemble into high degree of order supramolecular structures by−stacking and concave-convex interactions, such as host-guest complexes8−10, metal-coordinated framework11, 1D nanotubes12, 2D porous surface networks13and 3D inclusion complexes14. Secondly, these fully conjugated cyclic molecules represent defect-free, infinite-conjugated systems and high strain energy which can exhibit special electrical and optical properties comparing with linear compounds. The unique properties of these molecules can develop potential applications to organic optoelectronic materials15−17.

Polyfluorenes have attracted much attention in the past decade as semiconductor materials in thin film devices due to wide-band gaps, high thermal stability, high photoluminescence (PL) quantum yields, good charge transport properties and easy processing, such as organic light-emitting diodes (OLEDs), organic photovoltaics (OPVs), organic field effect transistors (OFETs) and polymer memories18. However, most structures of polyfluorenes are linear structures, only a few reports on the cyclic compounds based on fluorene units19−22. In this regard, novel and alternative topological fluorene-contained-systems, such as fully fluorene-based strained macrocycles, are highly desirable to further explore new properties and opportunities of fluorene-based semiconductors in organic electronics. Recently, our group have synthesized a fluorene-based strained macrocycle, [4]cyclo-9,9-dipropyl-2,7-fluorenylene ([4]CF)21. Dramatically different from corresponding linear quaterfluorene, [4]CF showed a green emission at 512 nm with high efficiency. To the best of our knowledge, until now, systematic theoretical study in strained cyclic polyfluorenes have seldom been reported22. Therefore, a theoretical guide for such compounds is important and necessary to find new semiconductor materials in electronic devices. Herein, we used [4]CF(a−d) as modeling compound and designed a series of strained fluorene-based cyclic materials []CFs (= 3−8) to explore the steric strain effect onopto-electronic properties of compounds. The stain energy of employed molecules were estimated. An integrated approach has been employed to evaluate the relevant parameters for optical and electronic property, such as electrostatic potential (ESP), reorganization energies (), ionization potential (IP), electronic affinity (EA) and frontier molecular orbitals. The absorption and fluorescence spectra of these materials were also predicted and discussed

2 Computational section

The fluorene can be considered as dibenzocyclopentadiene, in which two benzene rings are embedded, similar to cycloparaphenylenes (CPPs). So the ground state molecules in our system were optimized by density functional theory (DFT) calculation at the B3LYP/6-31G() level23-24. And this method was widely used in the quantum chemical studies of fully conjugated cyclic oligomers systems25. We also calculated the structure of [4]CF (d) on the B3LYP/6-311++G(,). Compared with two molecular structures on different levels, the largest difference between the bond lengths of the two levels is less than 0.0002 nm. It indicates that the 6-31G() basis set used in this work is accurate enough. For the sake of reasonable computational cost, molecular structural calculations on other compounds were all performed at the B3LYP/6-31G() level. The ionization potential (IP), electronic affinity (EA) and reorganization energies () were calculated by the unrestricted formalism (UB3LYP)/6-31G() according to literature publications26. All the optimized conformations are not exhibited imaginary frequencies and all transition state structures are shown one imaginary frequency (Table S1, in Supporting Information) in harmonic vibrational frequency analysis. The electronic absorption and emission spectra were simulated by Gaussian functions with a half-width of 1900 cm−1based on the 25 lowest singlet energies from TDDFT/B3LYP/6-31G() calculations. All the quantum chemistry calculations are carried out using the Gaussian 09 program suite27.The charge density difference (CDD) maps implemented in Multiwfn 3.3 were employed to investigate electronic transition28,29.

3 Results and discussion

3.1 Optimized ground-state geometries and strain energies

First of all, for the sake of reasonable computational cost, the optimized conformational structures of [4]CF with methyl group as alkyl groups at the 9 site of fluorene segments were investigated by DFT calculation at the B3LYP/6-31G() level. Four stable conformers of [4]CF were found and shown in Fig.122. Due to steric effect, the structures with fluorene moieties no-alternating (a)and part-alternating (b, c) had reasonable stability comparable to all-alternating (d) (Δ= 18.8−30.6 kJ·mol−1, Δ= 18.4−31.0 kJ·mol−1). And the all-alternating structure (d) turned out to be the most stable geometry of [4]CF. The average fluorenyl-fluorenyl dihedral angle of d was around 38.9°, larger than that of difluorene (33.6°) calculated at the B3LYP/6-31G() level. Due to the way of rotation of a fluorene moiety, the two racemization pathways of isomers of [4]CF using B3LYP/6-31G() had been investigated. As shown in Fig.2, three transition states were identified and located along the isomerization pathway of each set. Four conformers could be transformed with each other by the rotation of fluorene moieties. In the first isomerization pathway with lower activation energy for racemization, the transition state for the isomerization of [4]CF between the conformer a and its isomer c (TSac, green) was observed, in which two dihedral angles of fluorene moieties (green and blue) was ca 67°. The rotation barrier of TSacwas calculated to be 92.1 kJ·mol−1. Besides, the rotation of fluorene (blue and pink) by about 180° led to the conformational structures of b and d, and the rotation barriers of TSbcand TScdwere lower than TSac, about 86.7 and 77.0 kJ·mol−1, respectively. In the second isomerization pathway, the rotation barrier of TS'acin which two dihedral angles were ca 59.4°, was calculated to be 242.4 kJ·mol−1higher than that of TSac. These values implied that the increased steric strain of fluorene moiety could increase the ring strain. Other transition states (TS'bcand TS'cd) were calculated to be 239.5 and 232.8 kJ·mol−1, respectively. These results indicated that fluorene moiety in [4]CF could rotate rather freely through first way at room temperature. This was consistent with the experiment observation of three and six signals at the aromatic region in1H and13C NMR spectra for [4]cyclo-9,9-dipropyl-2,7-fluorenylene ([4]CF (f) at room temperature on the NMR time, respectively21. The strain energy of [4]CF were estimated about 322.0, 313.6, 309.8 and 291.4 kJ·mol−1for the conformers a−d using homodesmotic reactions (Scheme S1, Table S2)24. The isomer d has lower strain energy than [8]CPP (302.3 kJ·mol−1)24.

Fig.1 (A) Four conformations of [4]CF (a−d) (ΔG in kJ·mol−1, based on d), (B) conformations of difluorene.

We next optimized all possible conformations of []CF (= 3−8). As the same of [4]CF, all-alternating structures were the most stable ones for even-number []CF (= 6 and 8) (Fig.S1). For odd-number []CF (= 3, 5, and 7), the conformation with more alternating fluorene moieties had lower energy value in each case due to steric effect. At the same time, the unsubstituted fluorene cyclic oligomer [4]CF (e) was also optimized to observe the substituent effect. The major axis and the minor axis of all employed molecules were evaluated (Table S2). For even-number []CF, the most stable structures have perfect symmetry. The strain energies of []CF were also estimated by hypothetical homodesmotic reactions and the result shown in Table S224. It was found that the strain energy decreased as the diameters and numbers of []CF increasing. When= 3, the strain energy was 418.7 kJ·mol−1. When= 5, the strain energy was 232.4 kJ·mol−1. The strain energy of [4]CF (e) was 285.5 kJ·mol−1, which was smaller than [4]CF (a−d). This could be explained by steric effect. The strain energy are inversely proportional to the number and diameter, which indicates the limit of strain energy for [∞]CF is about 0 kJ·mol−1.

3.2 Frontier molecular orbitals and electronic properties

The isosurfaces of wave functions of the frontier orbitals from HOMO − 2 to LUMO + 2 of [4]CF (a−d) at0were illustrated in Fig.3(A). The HOMO and LUMO were delocalized over the ring of [4]CF with2dsymmetry. It was found sixteen pairs of positive and negative wave functions laid vertically on the backbone in HOMO and twenty-four horizontal wave functions in LUMO. The rest of four orbitals were delocalized two opposite sides withCsymmetry. Other compounds were found to have similar trends (Fig.S3). At the same time, Energy levels of LUMO, LUMO + 1, LUMO + 2 and HOMO, HOMO − 1, HOMO − 2 orbitals of [4]CFs and [4]LF (d) were listed in Fig.3(B). For [4]CFs, the relevant pairs of frontier orbitals; HOMO − 1/HOMO − 2 and LUMO + 1/LUMO + 2 were found degeneracy in energy levels. When the 9-positions were unsubstituted, the calculated energy levels of HOMO and LUMO of [4]CF (e) were 0.01 eV lower and 0.03 eV higher than that of [4]CF(d) respectively. When the strain energy became smaller to 0 kJ·mol−1, the calculated energy levels of HOMO and LUMO of [4]LF (e) were 0.16 eV lower and 0.22 eV higher than that of [4]CF (e). The LUMO level increased and the HOMO level decreased as the strain energy of molecules increasing. This made the energy gap increase with the strain energy decreasing. In other words, the energy gap was increased as the size of ring increasing. It is distinct that the energy levels of HOMO and LUMO orbital as well as their energy gap could be remarkably tuned by the strain of the ring. Other cyclic compounds were confirmed this deduction (Fig.S4 and S5). This trend is analogous to []CPPs30. The reason of this phenomenon of the []CPPs has speculated with the very recent study by Itami.23. In this study, it was explained from three factors; length effect, bending effect, and torsion effect. The same as []CPPs, the HOMO of []CF is mainly localized within individual fluorene units and independent from the inter-ring angle, the LUMO localized on the C―C bonds connecting two fluorene units in our system, which strongly affected by the-orbital alignment between the two carbon atoms. It can be deduced that the bending effect are more influenced in HOMO energies, while the LUMO energies are more pronounced by the torsion angles of neighboring fluorene units.

Fig.2 Potential energy diagram along the isomerization reaction pathway (ΔG in kJ·mol−1, based on d), color online.

Fig.3 (A) HOMO and LUMO of [4]CF (d), (B) calculated energy gap of [4]CFs and [4]LF(d), (C) ESP of [4]CF (d).

It was known that cyclic arrays oforbitals in normally conjugatedsystems are oriented perpendicular to the molecular plane, but the molecules with belt-like and loop-like shape possessed an unusual arrangement oforbitals, which align parallel to the molecular plane with radial pattern14. It made the electrostatic potential more negative in the concave face than in the convex one. The same effect was encountered in our system, as represented in Fig.3(C). It can also be observed that the electrostatic potential was positive in the upper and lower parts, similar to the other strain macrocycles (Fig.S6)31.

3.3 Ionization potential, electron affinity, and reorganization energy

The most important properties of optoelectronic compounds are charge-injection and -transport ability and their balance. It was well known that ionization potentials (IPs), electronic affinities (EAs) and reorganization energies () were evaluated the energy barrier for injection and transport rates of charge carriers. The IPs and EAs include both vertical excitations (v, at the geometry of the neutral molecule) and adiabatic excitations (a, at the optimized structures of neutral or charged molecule). The reorganization energy is a key indicator the charge-transport ability (the lower thevalues, the bigger the charge-transport rate). From the Table 1, three main trends in the IPs and EAs of [4]CF (a−e) could be observed. The first trend was found that the IPs increased gradually as the strain energy decreased at the same number of []CF while the EAs decreased inversely. The strain energy of [4]CF (a−d) increased gradually as follows, a > b > c > d. The IP(a) of [4]CF (a−d) were 5.63, 5.65, 5.68 and 5.74 eV, while those for the EA (a) of [4]CF (a−d) were 0.91, 0.88, 0.85 and 0.77 eV. The second one was that when 9-position of [4]CF had not any alkyl substitution, the IPs increased and EAs decreased. This could explain from steric effect. The third one was that the IPs of [4]CFs were lower than [4]LFs, but the EAs of those were higher than that. The difference between the IPs of [4]CF (d) and [4]LF (d) is 0.15−0.16 eV. The ionization potentials, electron affinities and reorganization energies for other [n]CFs and []LFs were investigated and resulted were listed in Table S3. It was also found that the IPs tended to decrease and EAs increase as the diameter and number of []CF increased. The IP (a) and EA (a) of [4]CF (d) is 5.74 and 0.77 eV, those for [5]CF is 5.68 and 0.88 eV. This phenomenon could be explained by the better stabilization of the charge by the larger ring due to its increased delocalization. The IPs and EAs of linear oligomer had the same regulation. It was also found thatdecreased with the length of the conjugated cyclic oligomers and linear oligomers. Compared with the reorganization energy of []CF, the difference betweenholeandelectronwas very small with the balance value betweenholeandelectron.It indicated these cyclooligomers would be potential candidates of ambipolar materials.

Table 1 Ionization potential (IP), electronic affinity (EA), and reorganization energy (λ) of [4]CFs and [4]LFs (all unit in eV)

aHole extraction potential (HEP) is the energy difference from M+ (cationic) to M (neutral molecule) using the M+ geometric structure,bElectron extraction potential (EEP) is the energy difference from M− (anionic) to M using the M− geometric structure.

3.4 Optical property: absorption and emission spectra

In order to understand the optical properties of []CFs and []LFs, the absorption and fluorescence spectra in vacuum were performed by Gaussian functions from TDDFT calculations. The calculated absorption wavelengths, main transition configurations, and oscillator strengths for the most relevant excited states of [4]CFs and [4]LF were listed together in Table 2.Compared with the experimental absorption spectrum of [4]CF (f)21, all the absorption spectra exhibited absorption bands in the long-wavelength region around 450−499 nm (abs2) in addition to the intense absorption bands with the absorption maximum wavelengths of 347−363 nm (abs1). It was known that all of the electronic transitions of [4]CFs and [4]LF are of the→* type for the absorption spectra.Excited states 4 and 5 should correspond toabs1, and the other peak (abs2) should be identified with the excited state 1. For [4]LF, the1←0transitions are predominantly–* type involving delocalized HOMOs and LUMOs and had largest oscillator strength values. For [4]CFs, the lowest1←0transition involving HOMOs and LUMOs were forbidden due to the small oscillator strengths. They had the calculated maximum absorption from the initial state of HOMO, HOMO − 1 or HOMO − 2 to the final state of LUMO, LUMO + 1 or LUMO + 2. When the strain energy became smaller, theabs2showed an obvious blue-shift in the UV-Vis absorption spectra in [4]CF (a−e), while theabs1was constant around 350 nm. The absorption spectra of []CF (= 3,5) and []LF (= 3,5) were also calculated (Table S4). It was found the difference oscillator strengths between the cyclic and linear systems were significant. For []LFs, the oscillator strengths (excited state 1) increased sharply with the number of fluorene units. On the contrary, the oscillator strengths (excited state 1) for [4]CF (a) and [4]CF (d, e) were zero due to molecular symmetry. For an odd number of cyclic fluorenes ([3]CF and [5]CF) and [4]CF (b, c), the symmetry of optimized geometries reduced and the oscillator strengths were nonzero. As the number of fluorene units increasing, it was found that the strain energy became smaller and the absorption maximum wavelengths (abs1) of []CFs showed an obvious blue-shift duo to length effect. A little change in the absorption bands (abs2) of []CFs regardless of the ring size. This could be explained from the similar energy gap between HOMO and LUMO + 1 (2) or between HOMO − 1 (2) and LUMO. Compared with []LFs, []CFs showed an obvious blue-shift inthe absorption maximum wavelengths (~30 nm).

Table 2 Electronic transition data obtained by TDDFT methods (TD-B3LYP/6-31G(d)//B3LYP/6-31G(d)) for [4]CFs and [4]LFs.

Table 3 Electronic transition data obtained by TDDFT methods (TD-B3LYP/6-31G(d)//B3LYP/6-31G(d)) for the PL spectra of employed molecules.

The theoretical emission spectra of [4]CFs and [4]LFs were presented and the calculated emission wavelengths, main transition configurations, and oscillator strengths for the most relevant excited states of [4]CFs and [4]LFs were listed in Table 3.Compared to the experimental absorption spectrum of [4]CF (f)19, Excited states 4−5 should correspond toem1, and the other peak (em2) should be identified with the excited state 1. When the strain energy became smaller, theem2shown an obvious blue-shift in the emission spectra of [4]CF (a, b, d and e), while theem1was constant around 400 nm. The emission spectra of []CF (= 3 and 5) and []LF (= 3 , 5) were also calculated (Table S5). For []CFs, It was found that the oscillator strengths of0←1transitions were smaller than that of0←5transitions and0←4transitions and the Stoke shift of []CFs were decreased as theincreasing. Dynamic conformational change could deduce deformation symmetry to make the forbidden transition possible16,32, the peak ofabs2andem2could be observed in reality21. When= 4, the emission wavelength (em2) of [4]CF (f) is exhibited green photoluminescent in experiment. This phenomenon may be give new direction to explain the green band of polyfluorenes. Compared with []LFs, []CFs showed an obvious red-shift in the emission wavelengths of0←1.

To gain further insight into the charge transfer from the ground state to excited states, charge difference density (CDD) mapsofS←0for [4]CFs were calculated33. The result was shown in Fig.S7. The decrease in electron density was indicated in violet and the increase was in turquoise,respectively. From the analysis of all CDD maps, it was found that the hole and electron distributions covered the whole system and the excitation ofS←0for [4]CFs were identified as local excitation. The further theoretical investigation of optical properties for these strain semiconductors will be continued in our lab.

4 Conclusions

In this paper, DFT methods were adopted to investigate the structures and properties of the []CFs and []LFs. In this fully conjugated cyclic oligomers, For even-number []CFs (= 4, 6 and 8), all-alternating structures were the most stable one. For odd-number []CFs (= 3, 5, 7), the conformation with more fluorene moieties alternating gave lower energy value in every case. The structures could be transformed each other by rotation of fluorene moiety. The strain energy decreased and the energy gap increased as the number and diameters increasing. Due to the special geometry, the electrostatic potential was positive in the upper and lower parts, but somewhat negative at the convex face and considerably negative on the concave face. The IPs and EAs tended to increase and decrease as the strain energy of []CF decreased with the same. With the balance value betweenholeandelectronin system, this compound demonstrated great potential as ambipolar materials. From the absorption and fluorescence spectra, it was found that []CFs showed an obvious blue-shift in the emission spectra wavelengthsem2with the strain energy decreasing. And []CFs with special electrical properties might be found many applications in other optoelectronic devices such as OFETs and OPVs. Steric strain provides one powerful tool to design multifunctional semiconductors in organic optoelectronics. The theoretical and experimental investigation for these compounds will be continued in our group.

Supporting Information: available free of chargethe internet at http://www.whxb.pku.edu.cn.

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芴基张力半导体结构和光电性质的理论研究

刘玉玉1李杰伟2薄一凡1杨 磊1张效霏3解令海1,*仪明东1黄 维1,2,*

(1南京邮电大学信息材料与纳米技术研究院暨有机电子与信息显示国家重点实验室培育基地，先进生物与化学制造协同创新分中心，南京 210023；2南京工业大学先进材料研究院暨柔性电子重点实验室，先进生物与化学制造协同创新中心， 南京 211816；3广西大学数学与信息科学学院，南宁 530004)

通过对模型化合物环四-9,9-二甲基-2,7-芴及其系列的环芴衍生物[]CFs(= 3−8)的结构、张力能以及光电性质的研究来进一步探讨空间张力对材料光学及电学性质的影响。研究结果表明，随着化合物中芴基数量和直径的增加，张力能减小，能隙增大。具有相同芴基数目的环芴分子，随着分子中张力能减少，分子电离电势逐渐增加，而电子亲和能逐渐减小。通过对模型化合物的空穴和电子重整能研究发现，其数值很接近，说明该类材料是一类潜在的双极性传输材料。同时还发现[]CFs中，随着张力的减少，其第二发射峰的波长发生了蓝移。综上所述，空间张力为设计多功能有机半导体材料提供了有力工具。

芴类材料；有机半导体；张力大环；光电性质；密度泛函理论计算

O641；O649

10.3866/PKU.WHXB201705104

March 21, 2017;

May 3, 2017;

May 10, 2017.

XIE Ling-Hai, Email: iamlhxie@njupt.edu.cn. HUANG Wei, Email: iamwhuang@njupt.edu.cn.

The project was supported by the National Natural Science Foundation of China (U1301243, 2150314, 21602111), Doctoral Fund of Ministry of Education of China (20133223110007), Natural Science Foundation of Jiangsu Province of China (BM2012010, BK20150832), Program for Postgraduates Research Innovation in University of Jiangsu Province, China (CXZZ13_0470), Nanjing University of Post and Telecommunications, China (NY214176, NY215172, NY217082, 2016XSG03), Synergetic Innovation Center for Organic Electronics and Information Displays and Excellent Science and Technology Innovation Team of Jiangsu Higher Education Institutions, China (2013), the Priority Academic Program Development of Jiangsu Higher Education Institutions.

国家自然科学基金(U1301243, 2150314, 21602111), 教育部高等学校博士点专项科研基金项目(20133223110007), 江苏省自然科学基金(BM2012010, BK20150832), 江苏省高校研究生科研创新计划(CXZZ13_0470), 南京邮电大学(NY214176, NY215172, NY217082, 2016XSG03), 江苏省有机电子与信息显示协同创新中心, 江苏省高等学校优秀科技创新团队, 江苏省高校优势学科建设工程资助项目