Design of novel tetra-hetero[8]circulenes: a theoretical study of electronic structure and charge transport characteristics

In the present work, a series of new tetra-hetero[8]circulenes were theoretically designed in which heteroatoms include O, S, Se and N. Their electronic structure and characteristics of charge transport were investigated using DFT based computational methods. Except for the compounds containing Seatoms (3a and 3b), all remaining compounds exhibit planar and highly symmetrical structures featuring novel aromatic features: the inner eight-membered ring is anti-aromatic and the outer fused rings are aromatic. The predicted UV spectrum and reduction potential of 1a agree well with available experimental values. Following replacement of H-atoms by F-atoms, the energy levels of the frontier orbitals of 1b–4b are consistently decreased as compared to those of 1a–4a. Based on the calculated properties of electrochemistry and charge transport, the molecules 1a–4a and 4b are suggested to be good candidates for p-type semiconductors. More importantly, the molecules 1b–3b are revealed to be potential ambipolar organic semiconductors.


Introduction
[n]Circulenes, which consist of compounds having two concentric annulene rings, have attracted much attention as an intriguing family of aromatic polycyclic hydrocarbons. Three members of this family, including [5]circulene (corannulene), 1 [6]circulene (coronene) 2 and [7]circulene 3 (pleiadannulene), have experimentally been prepared for a long time and the characteristics of their electronic structure, chemical bonding and adsorption spectra were well determined. Although earlier theoretical studies suggested that [8]circulene is unstable, 4 this molecule was recently successfully synthesized by Wu and coworkers. 5 Their shapes interestingly change from a bowled shape for [5]circulene to a planar structure for [6]circulene and saddled shapes for [7] and [8]circulenes.
Recently, the family of hetero [8]circulenes appears to be even more intriguing. Replacing the outside benzene fused-rings by heterocyclic rings such as furan, thiophene. results in planar heteropolycyclic compounds with highly p-conjugated electronic structures which can eventually be used in many important applications. Octathio [8]circulene, named as sunower, (C 16 S 8 ) in which all outside fused benzene rings are replaced by eight fused thiophene rings, was for the rst time synthesized in 2006, 6 and found as a good p-type organic semiconductor by both experiment and theory. 7,8 Subsequently, the electronic structure and charge transport properties of its analogues molecules such as C 16 S 4 Se 4 and C 16 X 8 with X ¼ O, Se, NH, CH 2 , PH and PF were also extensively studied. [9][10][11][12] They were suggested as either p-type or n-type organic semiconducting materials with high rate of charge hopping. More recently, Datta and his co-workers 13 designed similar molecules, named as Siand Ge-sulower, in which C-atoms of C 16 S 8 were replaced by either Si-atoms or Ge-atoms. These molecules were found to be bowled structures and exhibit a large number of metallic-like states with weak optical absorption. In a recent study, we theoretically designed a series of new hetero [8]circulenes containing borole units. 14 These heteropolycyclics feature some intriguing aromatic characteristics at both inner and outer rings. Such interesting results stimulated us to further design of new p-conjugated materials based on the [8]circulene framework.
Tetra-hetero [8]circulenes in which only four fused benzene rings are replaced by four fused hetero-rings, have recently emerged as promising p-conjugated materials for organic electronic devices. In fact, tetraoxo [8]circulene was already found by experiment since 1960s, 15 but its applicable properties were not properly explored. Recently, Minaev and his coworkers performed a series of theoretical and experimental studies on electronic structure, spectroscopic properties, aromaticity and bonding characteristics of tetraoxa [8] circulenes and its derivatives. 16,17 Pittelkow et al. 18 reported the preparation of a series of p-extended tetraoxa[8[circulenes and their optical and electrochemical properties. These compounds showed high thermodynamic stability and can be used as promising materials for the development of blue organic lightemitting diodes (OLEDs). More recently, some planar cyclooctatetraenes such as azatrioxa [8]circulenes and diazadioxa [8]circulenes in which one and two O-atoms were replaced by N-atoms were successfully synthesized. Their characteristics of single-crystal X-ray structure, aromaticity, and spectroscopy were investigated in both experiment and theory. 19 In other way, Minaev et al. 20,21 reported theoretical results on the one-and two-dimensional nano-materials containing tetraoxa [8]circulene monomers. The authors found that these materials can be used as ambipolar organic semiconductors with high mobility for both hole and electron charge carriers.
In order to further explore this intriguing class of heteropolycyclic compounds, we herein performed theoretical studies of structural characteristics, electronic and charge transport properties of tetraoxo [8]circulene 1a and its derivatives in two different series 2a-4a and 1b-4b using DFT-based computational methods. The derivatives are designed by simply replacing oxygen atoms of 1a with sulfur (2a), selenium (3a) and NH-groups (4a). Additionally, replacement of H-atoms of compounds 1a-4a by uorine results in peruoronated compounds 1b-4b that are expected to have reduced LUMO energy levels and can thus be used as effective n-type organic semiconductors. Our results show that most of designed molecules exhibit the planar structures with high degree of p-conjugation and high rate of charge hopping.

Electronic structure calculations
Optimizations of the relevant geometries and calculations of their harmonic vibrational frequencies are fully performed using DFT. The hybrid functional B3LYP [22][23][24] are used in conjunction with the 6-31G(d,p) basis sets. 25,26 For open-shell systems such as cations and anions, the unrestricted formalism (UB3LYP) is used. This popular functional was proved to be reliable in predicting geometrical parameters and charge transport properties of many p-conjugated systems. For each species considered, the neutral, anionic and cationic states are characterized. All electronic structure calculations are carried out using the Gaussian 09 (ref. 27) suite of programs.

Charge transport properties
In order to probe the charge transport properties, the hopping model is used. [28][29][30][31][32][33] Accordingly, the hole and electron carriers can be jumped between the adjacent molecules of the organic crystals. The rate of charge hopping (K) is estimated by using the Marcus-Hush eqn (1): 34 where t is the transfer integral between two adjacent molecules, l the reorganization energy, k B Boltzmann constant and T the temperature (298 K in our calculations). Accordingly, a high rate of charge hopping K is obtained when the transfer integral (t) between two molecules is high, and the monomers have low reorganization energy (l).
The transfer integral is dened by the following expression (2): [35][36][37] where f 0,site1 i and f 0,site2 j present the HOMO (or LUMO) of isolated molecules 1 and 2, respectively. F is the Fock operator (F ¼ SC3C À1 ) of the dimer with a density matrix from non-interacting dimer, where S is the intermolecular overlap matrix, C and 3 are the molecular orbital coefficients and energies, respectively, from one-step diagonalization without iteration.
The transfer integral for hole (t h ) is calculated as half of the energy difference between the HOMO and HOMO À 1 of the dimer, while the transfer integral for electron (t e ) is half of the energy difference between the LUMO and LUMO + 1 of the dimer. These orbital energy levels are obtained using density functional theory (DFT) with the PW91PW91 functional 38,39 in conjunction with the 6-31G(d,p) basis set. This approach has been shown to be suitable and effective in calculations of the transfer integrals of many organic compounds. [40][41][42][43][44][45][46][47][48] We should note that the transfer integral is functional dependent property and their values systemically depend on the fraction of nonlocal HF exchange incorporated in a functional. Sutton et al. 48b showed that the amount of HF exchange substantially affects the transfer integral in a linear fashion with respect to the fraction of nonlocal HF exchange incorporated in a standard hybrid functional.

Reduction and oxidization potentials in solution
The reduction and oxidization potentials of compounds in solution are calculated by using a protocol recently developed by Davis and Fry. 49 Firstly, optimizations of geometries and calculations of vibrational frequencies of each compound in the neutral, anionic and cationic charge states are performed at the B3LYP/6-31+G(d) level. Their single point electronic energies are obtained using a larger basis set, B3LYP/6-311++G(2df,2p). Addition of a set of diffuse functions in the basis set is necessary to describe the structures of the ions involved in the evaluation. The SMD/IEF-PCM solvation model 50 in acetonitrile solvent is used to probe the solvent effects. These methods were proven to be effective to obtain the reduction and oxidation potentials of PHA compounds in solution. 49,51 Davis and Fry 49 showed that using eqn (4) and (5) results in a mean absolute deviation (MAD) for the polycyclic aromatic hydrocarbons (PAHs) of 0.023 and 0.032 mV, respectively.
The absolute potentials at 298 K are obtained using the following eqn (3): where E calc 298 is calculated from the difference in free energy (G) at 298 K between the couples neutral/cation and anion/neutral. The value of 0.03766 accounts to small thermal correction for a free electron at 298 K. 52 The reduction potential is predicted in MeCN solution for the ferrocene-ferrocenium (Fc/Fc + ) pair, and the standard redox couple are calculated by using the expressions (4) and (5): Oxidation:

Electronic structure and aromaticity of compounds
Geometric optimizations and calculations of harmonic vibrational frequencies of all compounds are performed using the hybrid functional B3LYP in conjugation with the polarized 6-31G(d,p) basic set. This method was demonstrated to provide reliable geometries and charge transport properties of the organic semiconductors in many previous studies. [53][54][55][56][57][58] The chemical structures of all compounds are shown in Fig. 1, whereas their shapes are given in the ESI le. † Among the eight compounds considered, 1a is the only one which has been well described by both experiment and theory. The computed C-O bond length of 1a of 1.385Å agrees well with the experimental value of 1.392-1.402Å. 13 The distances between C and hetero atoms of ve-membered rings change somewhat, and in the ordering of C-O $ C-N < C-S < C-Se. Consequently, our calculations show that the compounds containing furan (1a and 1b), thiophene (2a and 2b) and pyrrole (4a and 4b) exhibit planar structures whereas the compound containing selenophene (3a and 3b) is slightly distorted out of the structural plane due to the large C-Se distances. Following attachment of one excess electron into the molecules to form anionic species (or detaching one electron from the molecules to form cationic species), the geometries of the charged species only change somewhat, except for the case of 3a whose cationic state shows a large distorted shape. Consequently, we can expect that these compounds will have low reorganization energies that can dominate the rate of charge hopping.
Aromaticity is used to describe electron delocalization in compounds. Aromatic compounds usually exhibit high stability, planar and symmetrical structure and good electron delocalization. These are key properties for high charge mobility of p-conjugated organic molecules. Thus, evaluation of aromaticity of a compound gives us more insight into its electronic properties. Aromatic character is evaluated here using the nuclear independent chemical shi (NICS) index. 59,60 The NICS(0) values are calculated on ghost atoms located at center of rings 1, 2 and 3 as shown in Fig. 1. It is also known that the NICS(0) values can be affected by distribution of s-electrons of compounds. 54 Thus, the NICS(1) values that are calculated on ghost atoms located at 1Å distance out of the structural plane can give us more reliable indications.
Computed results in Table 1 showed that the inside eightmembered rings of compounds are anti-aromatic with positive NICS values, whereas all outside rings exhibit aromaticity with negative NICS values. There is negligible difference in aromatic character of molecules with different hetero atoms. In addition, replacing H-atoms of 1a-4a by F-atoms of 1b-4a only change somewhat the aromatic feature of compounds. These aromatic features are similar to those of the sulower C 18 S 8 and its derivatives. 45 Thus it is expected that these compounds are characterized by high p-conjugation, and thereby good ability of intramolecular charge transport.

Absorption UV spectra of compounds
The absorption UV spectra of all compounds are predicted using the time-dependent (TD-DFT) method with the B3LYP functional in conjunction with the 6-31+G(d,p) basis set. This method was evaluated to give reliable predictions for optical spectra of organic compounds. 61,62 The plots of absorption UV spectra of all compounds are displayed in Fig. 2.
There is a good agreement between our theoretical predictions and the available experimental and theoretical results. Accordingly, the UV spectrum of 1a shows two local peaks with high intensity centered at 255 and 261 nm which agree well to the experimental value of 260 nm. 18 Another local peak is   18 Our calculations also reveal a local peak at 416 nm which agrees well with the experimental value of 415 nm. This peak actually corresponds to a p-p* transition from HOMO to LUMO. However, this absorption has low intensity in both experimental and theoretical spectra. The low absorption intensity corresponds to a small transition moment between the ground and excited states. The transition moment is derived mainly from the integrals of the dipole moment acting on both states. In this case, it is characterized by the small overlap between the transition orbitals HOMO and LUMO. Similar observations were also found for the UV spectra of remaining compounds.
More interestingly, Fig. 2 shows that the UV spectra of compounds considered tend to be red-shied when O-atoms of 1a and 1b are replaced by S-and Se-atoms. Two high intensity peaks at 267 and 383 nm were found in the UV spectrum of 2a, whereas the 3a is characterized by two local peaks at 285 and 415 nm. Following peruorination of compounds 1a-3a, the rst local peaks in UV spectra of 1b-3b is red-shied, while their second local peaks are blue-shied as compared to those of 1a-3a, respectively. The UV spectra of 4a and 4b are similar to those of 2a and 2b, respectively.

Reduction and oxidation potentials of compounds in the solution
The values of reduction and oxidation potentials, that are related to the energies of frontier molecular orbitals (FMO), play important role for applicability of organic semiconductors. The energy levels of HOMO (characteristic for p-type semiconductor) and LUMO (for n-type semiconductor) should be close to work functions (WF) in vacuum of electrodes in order to improve their charge transport ability. In experimental studies, some electrodes such as gold (Au) (WF $ 5.10 eV), calcium (WF $ 2.90 eV), and magnesium (WF $ 3.68 eV) are commonly used. 63 While the gold electrode is one of the best electrodes for organic electronic device, the calcium and magnesium electrodes are the preferred ones for n-type organic semiconductors due to the fact that this type of materials usually possesses a LUMO energy level of $3.0-4.0 eV. In this study, the reduction and oxidation potentials and energy levels of frontier orbitals of the molecules examined are calculated using the SMD/IEF-PCM solvation model 64 in acetonitrile solvent (see above). All computed values are given in the Table 2, while the shapes of frontier orbitals are displayed in Fig. 3.
The reduction potential of 1a is equal to À2.09 eV that is slightly higher than the highest experimental value of À2.39 eV of 1a. 18 It can be observed that the compounds containing group VIA elements 1a-3a and 1b-3b have comparable energy levels of frontier orbitals. The LUMO and HOMO of 4a and 4b containing pyrrole units are higher. Additionally, the HOMO energy levels of the 1a-4a vary in a range of (À5.27)-(À6.27) eV, and are in the sequence of 1a < 2a < 3a < 4a. A similar trend is found for the series 1b-4b. These values are close to the work function of 5.1 eV of gold electrode, and consequently they are expected to be good candidates for p-type semiconductors.
Replacement of H-atoms in 1a-4a by F-atoms consistently decreases the energy levels of both HOMO and LUMO of 1b-4b. More importantly, the LUMOs of 1b-3b have similar energy levels and are equal to $3.00 eV. These values are very close to that of 2.90 eV of the calcium electrode. The LUMO energy levels of 1a-3a are somewhat higher and close to 2.70 eV. Thus, the peruorinated compounds 1b-3b can act as ambipolar organic semiconductors. 1a-3a and compounds containing pyrrole 4a and 4b have high LUMOs, and accordingly they can only be suitable for p-type organic semiconducting materials.

Charge transport properties of compounds
3.4.1 Reorganization energy. In order to evaluate the charge transport characteristics for electron and hole of molecules, the reorganization electron energy is rst considered. A molecule exhibits a high rate of charge hopping when it has low reorganization energy. The reorganization energy is dened as the sum of geometrical relaxation energies when the species goes from the neutral state geometry to charged state geometry, and vice versa (eqn (6) and (7)): where l h and l e are reorganization energies for hole and electron, respectively; E(M + ) and E(M À ) the total energies of the cationic and anionic states with the optimized geometries of the neutral ground state, respectively; E(M) the total energy of the neutral state with the optimized geometries of the cationic species (for eqn (6)) and of the anionic species (for eqn (7)); E 0 (M), E 0 (M + ) and E 0 (M À ) the total energies of the neutral, cationic and anionic ground state species, respectively. In the present work, the reorganization energies for electron and hole of all compounds are calculated using the B3LYP/6-31G(d,p) method and the computed results are listed in Table 3. Except for the relatively large l h value of 3a (l h ¼ 0.35 eV, Table 3) which is due to a large distortion of its cationic state, the reorganization energies for hole and for electron of 1a-4a are quite low and vary in a range of 0.17-0.19 eV and 0.19-0.28 eV, respectively. As compared to the computed values of C 16 (PF) 8 (l h ¼ 0.30 eV and l e ¼ 0.22 eV) and peruoropentacene (PF-PEN) (l h ¼ 0.23 eV and l e ¼ 0.23 eV) which is a typical n-type organic semiconductor, the reorganization energy for hole (l h ) of 1a-4a are properly lower. Their l e values are close to those of PF-PEN and C 16 (PF) 8 . Although the peruorinated compounds 1b-4b showed the l h and l e values a bit higher than those of 1a-4a, they are also comparable to those of compounds previously reported.
3.4.2 Dimer interactions and rate of charge hopping (K). To further probe the behaviour of charge transport, we perform calculations of the dimer interactions of molecules considered. The geometries of dimers are constructed in a translational parallel motif (Fig. 4) and optimized by using the B3LYP-3D functional that contains dispersion energy (as denoted by-D) in conjugation with 6-31G(d,p) basis set.
The intermolecular interaction energy of dimers is dened by expression (8): where E monomer and E dimer are total energies of monomer and dimer, respectively. They are computed using the functionals B3LYP-3D and M06. These approaches were previously tested as effective for evaluating the dimer interactions. 12,45 To further consider the effect of basis sets used, we performed single point energy calculations on these optimized congurations by using functional M06 in conjuration with three different basis sets, including 6-31G(d,p), 6-311G(d,p) and 6-311+G(d,p). Our computed results pointed out that the intermolecular interaction energies of dimers tend to be increased as size of basis sets increased (Table S2, ESI †).
Adding polarized function only somewhat changes the interaction energies of dimers.
Our calculated results are given in Table 3 and compared with calculated properties of the previously reported C 16 S 8 . We should note that the molecular structures of the designed compounds 1a-4a and 1b-4b are in fact similar to that of sul-ower C 16 S 8 . Thus, a comparison between C 16 S 8 and the molecules designed in this work appears useful to understand their charge transport characteristics.
The strong interactions between monomers in dimers of all compounds were observed. The distances between monomers (D dimer ) vary in a small range of 3.62 O 3.95Å and are close to the value of 3.87Å of C 16 S 8 in the same interaction motif. The interaction energies between two monomers amount to 1.04-1.57 eV that is properly larger than the value of 0.98 eV of C 16 S 8 . Consequently, it can be seen that integral transfers for hole of compounds are comparable to that of C 16 S 8 , whereas their integral transfers of electron becomes much larger. Since the C 16 S 8 was reported as good p-type organic semiconductor, the compounds considered in this work are expected to be appropriate for both n-type and p-type semiconductors.

Conclusions
We theoretically designed a series of new tetra-hetero [8]circulenes based on an inner eight-membered ring. The electronic structure and characteristics of charge transport of all compounds were investigated using DFT based computational methods. Except for the compounds containing Se-atoms (3a and 3b), all remaining compounds exhibit planar and highly symmetrical structures with a novel aromatic feature: while the inner eight-membered ring is anti-aromatic, the outer fused rings are aromatic. The predicted UV spectrum and reduction potential of 1a agree well with available experimental values. Following replacement of H-atoms by F-atoms, the energy levels of frontier orbitals of 1b-4b are consistently decreased as compared to those of 1a-4a.
Based on the properties of electrochemistry and charge transport calculated, the molecules 1a-4a and 4b can be regarded as good candidates for p-type semiconductors. More importantly, the molecules 1b-3b are revealed to exhibit characteristics suitable for ambipolar organic semiconductors. Since the n-type and ambipolar organic semiconducting materials remain rare, we would hope that the present results will attract much attention from the experimental scientists.
At the time of nalizing this report, we interestingly found that tetrathio and tetraselono [8]circulenes were experimentally synthesized by Wong et al. 65 Table 3 Dimer distances (Å), interaction energies (eV), integral transfer (meV) and rate of charge hopping (s À1 ) of all compounds 1a-4a and 1b-4b Comp.
D dimer (Å) a These values obtained from ref. 10. Fig. 4 The translational parallel motif of dimers.