Effect of Imide Functionalization on the Electronic, Optical, and Charge

Article pubs.acs.org/JPCC

Effect of Imide Functionalization on the Electronic, Optical, and Charge Transport Properties of Coronene: A Theoretical Study Somananda Sanyal,† Arun K. Manna,† and Swapan K. Pati*,†,‡ †

Theoretical Sciences Unit and ‡New Chemistry Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, 560064, India ABSTRACT: We investigate the energetics, electronic structure, optical properties, and charge transfer characteristics of coronene and its imidefunctionalized derivatives using quantum chemical calculations. We analyze the formation feasibility of pristine coronene and its different imide monomers, namely, coronene-5-diimide, coronene-6-diimide, and coronenetetraimide, from a common parental compound, coronene octacarboxylic acid, and find that the most favorable derivative is the pure coronene. Our results also show that coronene-6-diimide is preferred over other possible imide compounds, which is well in accordance with the relative experimental abundance of coronene-6-diimide. The absorption characteristics obtained for both the monomer and dimer of coronene imides show bathochromic shifts for the low-energy peak positions in comparison to the pristine coronene because of the presence of the electron withdrawing imide groups, and the trend in transition energy follows the order of the electronic gap. Interestingly, we find a larger extent of red shift for the absorption maxima of the synthetically more feasible coronene-6-diimide among others. Moreover, our analysis also shows that the extent of red shift strongly depends on the position and orientations of the imide groups, and the low-energy peaks solely correspond to the π−π* electronic transitions. Furthermore, we also calculate the charge (electron and hole) transfer integrals for the plausible stable dimers, and find that effective hole transfer integrals are significantly larger than the electron transfer integral except for the coronene-tetraimide, for which the electron transfer integral is found to be greater than the hole transfer integral. The calculated carrier mobilities for the coronene crystal show that the hole mobility is significantly larger, almost 15 times, than the electron mobility. Our study provides a detailed understanding of the tunable optical and charge transfer properties for imide-functionalized coronene derivatives, and suggests their potential use in optoelectronic and field effect transistor devices. materials.20 Oligoacenes21 forming molecular clusters of πconjugated network are finding increasing prominence in organic semiconductor industries. Moreover, functionalized organic compounds, such as various imides of oligoacenes anthracene, perylene, coronene,22 alternating thiophene based copolymers, polytriphenylamines,23 and dinaphthothienothiophenes,24,25 are of profound interest for the present-day fabrication of OFETs and organic thin film transistors (OTFTs) for better performance.26,27 Experimentally, various diimide derivatives have been synthesized and are being proposed for use in designing organic optoelectronics. Recently, perylene diimide (PDI) has been shown as a crystalline acceptor in association with electron donating hexa-peri-hexabenzocoronene (HBC) to build photovoltaic devices with remarkably high quantum efficiencies.28 Moreover, it was demonstrated that PDI can induce long-distance electronic couplings as well as assist in DNA base-pair melting.29 The two-dimensional covalent organic framework (COF), specifically COF-366 and COF-66

1. INTRODUCTION Possible applications of organic crystals and many discotic liquid crystalline materials in organic molecular electronic devices, such as in organic and polymer light emitting diodes (OLEDs and PLEDs),1−4 laser dyes,5,6 organic solar cells,7−9 and organic field effect transistors (OFETs),10−13 are of remarkable current research interest from both scientific and technological aspects. Hence, these carbon-based molecules are of increasing interest for designing optoelectronic devices, because they promise bulk manufacturing of flexible, large-area devices at low cost.14−16 Similar to crystalline organic compounds, the discotic materials17 also provide order and extensive π-conjugations promising high intrachain charge carrier mobility values. The low cost and flexibility of these organic semiconducting materials in device integration show their potential over relatively high-cost and less flexible inorganic semiconductors. Among many other organic semiconductors, organic pentacene,18 a linearly fused five benzene rings, shows remarkable charge carrier mobility, and has been shown to find field effect transistor applications14 and the same is true for single crystal tetracene.19 In 1998, a group at the Philips Research Laboratories in Eindhoven successfully produced an integrated circuit consisting purely of organic © 2012 American Chemical Society

Received: October 19, 2012 Revised: December 12, 2012 Published: December 19, 2012 825

dx.doi.org/10.1021/jp310362c | J. Phys. Chem. C 2013, 117, 825−836

The Journal of Physical Chemistry C

Article

π−π interactions along the stacking directions.59 Experimentally, high charge carrier mobility values have been found for the various functionalized coronenes, such as coronene monoimides, coronene diimides, and perylene diimides.60 In fact, it would be helpful to understand the microscopic pictures for large carrier mobilities and other photophysical properties of these functionalized organic compounds. In this work, we have studied the energetics and photophysical properties of coronene and its various imide derivatives using DFT methods. We have considered four representative systems, including both monomer and dimer of pure coronene and its three imide derivatives, namely, coronene-5-diimide, coronene-6-diimide, and coronene-tetraimide. The calculated absorption properties show bathochromic shifts for the lowenergy absorption peaks, for the imide-functionalized coronenes, in comparison to the pristine coronene which strongly depend on the imide group topology (i.e., position and orientations). Furthermore, we also consider calculating the extent of charge transfer integrals and reorganization energy, which determine the extent of carrier mobility values, for the various plausible stable dimeric forms, and have also examined how these quantities are susceptible to different imide group positions and orientations. Our results show that the introduction of imide functional group, an electron acceptor, strongly modulates the charge transfer behaviors of coronene. Additionally, we have also calculated the charge carrier (electron and hole) mobilities for the pure coronene crystal, considering molecular packing as found in the crystal structure. We find that the hole mobility is significantly larger than the electron mobility, which agrees well with recent experimental findings.

(p-type), has been found to possess the highest hole mobility among the organic crystalline polymers known to date, with the only exception found for perylene and its derivatives, which show large electron mobility.30−32 Interestingly, the charge carrier mobility in single crystal rubrene was measured to be 20 cm2/(V s), and the value is predicted to be highest among all others.33 On the other hand, theoretically, many π-conjugated systems are being studied for exploring their optoelectronic, photophysical, and charge transfer characteristics using many sophisticated levels of theories. A previous theoretical study on octathio[8]circulene (sulflower) showed high carrier (both electron and hole) mobilities (μhole = 3.5 cm2/(V s) and μelectron = 2.6 cm2/(V s)), suggesting its ambipolar nature.34 Moreover, studies on diacene-fused thienothiophenes showed large charge carrier mobilities of about 100 cm2/(V s).35 Circumacenes and oligorylenes converge, at infinite one-dimensional limits, to zigzag and armchair graphene nanoribbons, respectively, and hold good promise in molecular and organic electronics applications.36 Additionally, density functional theory (DFT) and time-dependent density functional theory (TDDFT) have been employed for exploring the ground states and electronic excited states, respectively, of many interesting organic compounds, such as perylenes, coronenes, tripheylene derivatives, phenacenes, circumacenes, and oligorylenes. These studies enabled the comparison of photoabsorption in the visible part of the spectrum, mostly used in photovoltaic applications.37,38 Importantly, a single crystal of coronene, synthesized experimentally,39,40 was studied theoretically exploring its electronic and charge carrier properties.41 Firstprinciples calculations on the electronic properties of solid coronene are also reported recently, which has demonstrated superconductivity with potassium doping.42−44 Beyond organic materials, many studies have also been devoted to analyzing the charge transfer properties in biological systems, particularly DNA with both natural and modified nucleobases.45−49 End functionalization of these π-conjugated organic molecules with suitable functional groups can result in exotic electronic and charge transfer properties, which may differ from those of their parent compounds, and consequently, have potential applications in OFETs.50 Zhao et al. reproduced the electronic excitation energies of PDI crystals using timedependent Hartree−Fock (TD-HF) theory on dimeric structures, which provides good evidence in support of the fact that the electronic excited states do not have significant charge transfer character.51 Similarly, anthracene diimides possessing six-membered imide rings have also been found to exhibit better electron-accepting properties.52 It was also shown that the functionalization and substitution of the bay region helps in modifying the optical and electronic properties of the various organic molecules, such as those observed for perylene diimide.53−55 However, still they show substantial electron mobility.56 Bredás et al. have also analyzed how the variations in the solid state packing and nature of the substituents affect the molecular energy levels and reorganization energy (λ), influencing the charge transport properties of a few organic molecules.57,58 Introduction of imide functional groups and expanding the core along the short axis of PDI result in “coronene diimides”, which have drawn remarkable attention because of their increased solubilities and lower isotropization temperatures for better processing of the liquid crystalline phase. A high charge carrier mobility is also expected due to the enhanced

2. COMPUTATIONAL DETAILS In this work, all the quantum chemical calculations are performed using density functional theory (DFT) as implemented in the Gaussian 0961 software package. We use the Becke, three-parameter, Lee−Yang−Parr (B3LYP)62,63 hybrid exchange and correlation functional for all the calculations involving the monomers, and the dispersion corrected energy functional, ωB97XD, is utilized for the geometry optimization of the dimers to account for the dispersion interactions, which have a significant role in determining the stacked geometry. However, for the computations of the reorganization energy, we have used a sufficiently larger basis set with more diffuse functions, i.e., 6311++g(d,p), to properly take into account the polarization effects important for the charged species. All the optimized geometries are confirmed to be in local minimum energy structures by analyzing the vibrational frequencies. To understand the aromatic nature, we calculate nucleus independent chemical shifts (NICS) to assess the magnetically defined aromatic character of coronene and its imide derivatives by the gauge-invariant atomic orbital (GIAO) method at the B3LYP/6-31+g(d,p) level of theory.64−66 B3LYP is chosen as the preferred functional as it has been found to be most apt for the prediction of electronic structures of polycyclic aromatic hydrocarbons.67 Further, to examine the effects of imide functionalization on the absorption properties of the conjugated coronene monomers and their π-stacked dimers, time-dependent density functional theory (TDDFT) calculations are carried out using B3LYP/6-31+g(d,p). Frequencydependent polarizability (α) values are also computed with the laser frequency of 0.043 au at the same level of theory. 826



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In addition, we have estimated the charge (hole and electron) transfer integrals for a deeper understanding of their use in device applications. In general, for organic semiconductors, the hopping process is modeled through a nonadiabatic electron transfer process within the semiclassical Marcus−Hush formalism.68−70 At a given temperature, the rate of charge transfer between neighboring molecules (W) depends on the reorganization energy (λ) as well as the electronic coupling matrix elements between two pairs of molecules (Jij), where i and j are two adjacent molecular indices present in a crystal. The reorganization energy for electron and hole injection is calculated using the following formulas:

Jeff = Jij −

⎛1⎞ ⎜ ⎟S (ε + ε ) j ⎝ 2 ⎠ ij i

where Jij and Sij denote the transfer integral and spatial overlap matrix element between the ith and jth molecular fragment orbitals (highest occupied molecular orbital (HOMO) for hole transfer and lowest unoccupied molecular orbital (LUMO) for electron transfer), while εi and εj represent the site energies of the two molecular orbitals where charges are localized. With this approach, the dimer molecular levels are represented as the linear combination of individual monomer molecular orbitals and the charge transfer integral is obtained as the off-diagonal elements of the Kohn−Sham Hamiltonian, HKS = SCEC−1. In addition, the rate of charge transfer is expressed mathematically as

* − E) λelectron = (E−* − E−) + (Eanion

* − E) λhole = (E+* − E+) + (Ecation

where E represents the ground state energy of the optimized geometry of the neutral molecule, E− (E+) is the energy of the optimized anionic (cationic) species, E−* (E+*) is the energy of the anionic (cationic) molecule in neutral geometry, and E*anion (E*cation) is the energy of the neutral molecule in anionic (cationic) geometry. Closed-shell calculations for singlets and open-shell calculations for doublets (cationic and anionic geometries) have been carried out for reorganization energy (λ) calculations at the B3LYP/6-311++g(d,p) level of theory for individual molecules. Optimized geometries of the neutral molecules at the same level of theory are shown in Figure 1.

W=

2Jij 2 h

⎛ −λ ⎞ π3 exp⎜ ⎟ λkBT ⎝ 4kBT ⎠

where kB is the Boltzmann constant and T is the temperature of the crystal (for our case, taken as 300 K). The diffusion coefficient (D) which is related to the hopping rate is given by 2 2 1 ∑i ri Wi D= 2d ∑i Wi

Here d is the dimensionality of the crystal (d = 3 in our case), and r is the stacking distance between the adjacent molecules. D is normalized over the total probability of charge transfer. Then, the final drift mobility (μ) is calculated using the Einstein relation, as follows: e μ= D kBT For all the calculations performed using ADF, we have used the generalized gradient approximation (GGA) within Perdew−Burke−Erznerhof (PBE) as the exchange and correlation functional, and a large triple ζ with double polarization (TZ2P) basis set for all the atoms. Moreover, we explicitly take into account the dispersion interactions for calculating the charge transfer integrals since they have a significant role in π-stacked dimers.

3. RESULTS AND DISCUSSION 3.1. Structure, Stability, and Electronic Properties. Before we discuss the detailed electronic structures and optical properties of coronene and its imide derivatives, we focus on comparing the extent of formation feasibility for all the monomers from a common parental compound, namely, coronene octacarboxylic acid. For this, we calculate the enthalpy change in forming different compounds from coronene octacarboxylic acid, and term it the formation energy (Ef). The results are presented in Table 1. Also, a schematic indicating the formation of different compounds is shown in Figure 1. As can be seen from Table 1, the relative energy cost for the formation of pristine coronene is less than that for the other derivatives. We also find that coronene-6-diimide is preferred to form among the others. The formation energies for all four compounds were found to be −82.41, −52.24, −67.82, and −27.72 kcal mol−1, for coronene, coronene-5-diimide, coronene-6-diimide, and coronene tetraimide, respectively. The larger formation extent for the 6-diimide over 5-diimide can be accounted for by the least energy changes in introducing

Figure 1. Schematic for the formation of (a) coronene, (b) coronene5-diimide, (c) coronene-6-diimide, and (d) coronene-tetraimide from coronene octacarboxylic acid.

The charge transfer integrals or hopping matrix elements, site energies, and spatial orbital overlap have also been calculated employing the Amsterdam Density Functional (ADF) program71 and the effective charge transfer integral (Jeff) is calculated using the formula 827



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Table 1. Formation Energy (Ef), HOMO−LUMO Gap (ΔEH−L), Polarizability (α), Quadrupole Moment (Q), and Adiabatic Electron Affinity (EA) Values for Coronene and Its Imide Derivativesa system

Ef (kcal mol−1)

ΔEH−L (eV)

α1avg (×10−3) (au)

α2avg (×10−3) (au)

Q (D Å)

EA (eV)

coronene coronene-5-diimide coronene-6-diimide coronene-tetraimide

−82.41 −52.24 −67.82 −27.72

4.02 3.17 3.14 3.27

0.30 0.40 0.40 0.49

0.31 0.41 0.42 0.51

128.32 197.02 206.71 269.72

0.54 2.28 2.48 3.01

a 1 αavg

and α2avg correspond to polarizability at frequencies (ω) 0.00 and 0.043 au, respectively.

Figure 2. Optimized monomeric structures of (a) coronene, (b) coronene-5-diimide, (c) coronene-6-diimide, and (d) coronene-tetraimide.

a six-membered ring rather than a five-membered ring for the imide functionalization. Moreover, the energy cost for the tetraimide formation is higher (−27.72 kcal mol−1) because of the introduction of four imide groups simultaneously. However, coronene-6-diimide is found to be the most synthetically feasible among other imide derivatives, which also conforms to the various synthetic procedures adopted in synthesizing the 6diimide derivative and also with varying alkyl groups attached to the core of coronene-6-diimide.60,72 Next, we present the structural details and electronic properties of all the monomers studied. We present the optimized structures in Figure 2, indicating all the important bond length values. As can be seen from Figure 2, the imide functionalization does not significantly change the C−C bond lengths, highlighting their similar structural stabilities, such as pure coronene possesses. A very small change (∼0.01 Å) is only found for the peripheral C−C bonds. To compare and contrast the local aromatic nature of these compounds, the concept of nucleus-independent chemical shift (NICS), introduced by Schleyer et al.,64 is adopted in the present study. Note that a higher negative NICS value indicates larger aromatic character for a given ring of interest. Moreover, it is practical to analyze NICS(1) and its only z-component NICS(1)zz calculated at 1 Å above or below the ring for examining the ring aromaticity rather than NICS(0), which is calculated at the basal plane of the ring. This is because, for NICS(0), there is a significant contribution from the σ-bonding framework, whereas for NICS(1) the sole contribution comes from the π-bonding network. The latter one is more relevant and important for judging the local ring aromaticity. The values of NICS(1) and NICS(1)zz calculated at the central benzene ring (R1), which are lower than the values calculated at the peripheral ring (R2) of coronene, indicate the lesser aromatic character of the central ring in comparison to the peripheral ring. As given in Table 2, the NICS(1) values for R1 and R2 are found to be −4.42 and −11.99, respectively. As

Table 2. Calculated NICS Values of Coronene and Its Imide Derivatives at Different Ring Centers, Calculated at Distances of 0 and 1 Å from the Molecular Plane system coronene coronene-5-diimide

coronene-6-diimide

coronene-tetraimide

ring no.

NICS(0)

NICS(1)

NICS(1)zz

R1 R2 R1 R2 R3 R4 R1 R2 R3 R4 R1 R2 R3 R4 R5

−0.46 −9.98 −1.54 −9.68 6.39 −9.22 0.23 −9.17 −8.60 5.70 −0.42 −8.88 −8.78 5.93 5.58

−4.42 −11.99 −5.27 −10.97 2.59 −11.49 −4.11 −11.13 −11.12 1.67 −4.47 −11.07 −10.49 1.84 1.91

−7.62 −31.11 −9.36 −27.81 14.18 −29.07 −7.89 −28.46 −28.02 11.07 −8.06 −27.06 −25.53 11.37 12.15

expected, NICS(1) and NICS(1)zz follow a similar trend. Also, it is to be noted that the calculated NICS(1) for benzene is −10.25 within the same level of theory, which is very close to the value reported in the literature.73 This illustrates that the peripheral benzene ring (R2) of coronene and its derivatives is highly aromatic compared with the central one (R1), and the aromatic nature is even stronger than benzene’s aromatic character. The greater extent of aromatic behavior is due to the larger electron delocalization over the peripheral benzene rings. However, the coronene central ring (R1) shows very much less aromatic character as also found in a previous study74 and was shown to be weakly paratropic, although it has a (4n + 2)membered ring.75,76 Further reports on ring current measurements on coronene, corannulene, etc. have been measured in a few more studies as well.77−82 828



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Figure 3. Side views (above) and top views (below) of the optimized structures’ lowest energy π-stack dimers of (a) coronene, (b) coronene-5diimide, (c) coronene-6-diimide, and (d) coronene-tetraimide.

We find that introduction of imide functional groups slightly changes the ring’s aromatic nature compared to that of pure coronene’s rings. For 5-diimide, 6-diimide, and tetraimide coronene, the aromaticity of the central benzene ring (R1) is almost unaltered, while there is a reduction in NICS(1) values, i.e., less aromatic nature found for the peripheral rings in comparison to the corresponding rings’ aromaticity of pristine coronene. This is because the introduction of electron withdrawing imide groups strongly affects the peripheral ring’s electron distribution through direct conjugation rather than the central ring. However, as given in Table 2, the NICS(1) values calculated at the center of the five- and/or six- membered rings are found to be positive, indicating non- or antiaromatic behaviors. Further, we analyze the electronic properties of coronene and its imide-functionalized derivatives. The calculated electronic gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is 4.02 eV.83 In fact, experimental studies on fluorescence emission spectra of coronene have also been reported, and an optical gap of about 2.8 eV was found from electron energy loss spectroscopy (EELS) measurements.43,84 Note that the experimental estimate of the optical gap was found for a molecular aggregate of solid coronene, whereas the DFT calculated electronic gap is obtained for the isolated coronene in the gas phase. Our results agree well with the earlier theoretical predictions35,85 and experimental findings.84 However, as given in Table 1, the HOMO−LUMO gap decreases on imide functionalization. The gap values for the 5-diimide, 6diimide, and tetraimide are found to be 3.17, 3.14, and 3.27 eV, respectively. The reduction in the electronic gap is due to the stabilization of both the HOMO and LUMO orbitals with the larger stabilization found for the LUMO. As shown in Figure 4, the HOMO of pure coronene and its imide compounds is mainly delocalized over the peripheral benzene rings of the coronene moiety, whereas the LUMO is distributed over all the rings including peripheral imide as well as central rings of coronene, which leads to the larger stabilization of the LUMO. It is known that the larger the electronic gap, the greater is the stability, which means that the reactivity is lower and the compound with the higher gap value would be more stable.

Consequently, the pristine coronene and its tetraimide derivative are comparatively more stable than the other two compounds studied. Moreover, we find that coronene-5diimide and coronene-6-diimide show relatively lower and identical electronic gaps, highlighting their similar photophysical stabilities. Additionally, we calculate the static and frequency dependent dynamic polarizability (α) for pristine coronene and its imide derivatives. Our results show that,with the introduction of electron withdrawing imide groups, the α increases, indicating their greater extent of electronic charge density polarization/deformation upon imide functionalization. In addition, as can be seen from Table 1, the enhancement of polarization is dependent on the number of functional groups irrespective of their position. This is indicative from the similar α values obtained for the 5- and 6-diimides, while α for the tetraimide shows a relatively larger value. Further, we also estimate the values of the quadrupole moment (Q) for all the compounds, which are presented in Table 1. It is clear from Table 1 that Q increases with the introduction of imide groups to the coronene ring. Now, we discuss the structural stabilities and electronic properties of possible π-stacked dimers of coronene and its different imide-functionalized compounds (Figure 3). For pure coronene, we consider AB stacked dimers as found from the crystal structure.39 Since the crystal structure data for the imide derivatives are not available due to their gel-like nature, we also consider slipped-parallel, full-stacked, and antiparallel conformers (parallel or antiparallel with respect to the arrangements of imide groups of two monomers) for coronene-5diimide, while for 6-diimide and tetraimide we have considered slipped-parallel and antiparallel conformers. For this we rotated one molecule with respect to another, to get the structures, and we have optimized such dimeric configurations of all the compounds using the long-range dispersion corrected hybrid exchange and correlation functional, ωB97XD, to account for the dispersion interactions usually present for these π-stacked structures. Note that the fully optimized geometries obtained using the dispersion corrected DFT are considered at 0 K, whereas the crystal structure of pure coronene was reported at finite temperature. Thus, to compare and contrast our findings for the DFT optimized geometry of coronene dimer with the results obtained for the crystal structure geometry, we have also 829



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Figure 4. Frontier molecular orbital (FMO) plots of monomeric (a) coronene, (a), coronene-5-diimide, (c) coronene-6-diimide, and (d) coronenetetraimide. “H” and “L” represent the HOMO and LUMO, respectively.

calculated various properties for the crystal structure geometry using the same level of calculations. The geometries of all the stable dimers are shown in Figure 3. To analyze the stabilities of these dimeric compounds, we calculate the binding energy (Eb) defined as follows:

Table 3. Binding Energy (Eb), Equilibrium Distance (Req), and HOMO−LUMO (ΔEH−L) Gap Values for the Coronene Dimer and Its Imide-Functionalized Structures system coronene (DFT geometry) coronene (crystal geometry) coronene-5-diimide antiparallel slipped parallel full stacked coronene-6-diimide antiparallel slipped parallel coronene-tetraimide antiparallel slipped parallel

E b = Edimer − 2Emonomer

Here, Edimer and Emonomer are the total optimized energies of dimer and monomer, respectively. Since we use localized Gaussian orbitals as the basis sets, it is important to consider the basis set superposition error (BSSE).86,87 We calculate the binding energies using the above equation with and without BSSE corrections and present them in Table 3. As expected, BSSE corrections are found to be small and always increase the binding energy. It is well-known that the higher the modulus of the binding energy value, the lower is the stability. The BSSE corrected binding energy calculated for the dispersion corrected DFT optimized structure (crystal structure) of AB stacked coronene dimer is found to be −24.08 kcal mol−1 (−20.55 kcal mol−1), with the interplanar separation of 3.45 Å (3.51 Å)88 and a HOMO− LUMO gap value of 3.77 eV (3.78 eV).89 Note that the extent of binding strength is larger for the DFT optimized geometry than that found for the crystal geometry, with a slightly small interplanar distance. The slightly larger distance of separation and smaller binding strength obtained for the crystal geometry is because the coronene dimer structure is found to be stable

Req (Å)

Eb (kcal mol−1)

Eb + BSSE (kcal mol−1)

ΔEH−L (eV)

3.45

−27.19

−24.08

3.77

3.51

−23.08

−20.55

3.78

3.43 3.41

−37.49 −37.88

−32.88 −32.71

2.93

3.38

−37.27

−32.41

3.43 3.50

−39.86 −40.14

−35.09 −35.16

3.41 3.57

−51.01 −45.91

−43.75 −38.53

3.14

3.02

within the crystal packing environment at finite temperature. On the other hand, the DFT optimized geometry is obtained at 0 K for the isolated coronene dimer. However, our results compare fairly well with the previously reported binding energy/interaction energy for the coronene dimer, using 830



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different DFT methods: 22.64 kcal mol−1 with DFT-D2,90 17.45 kcal mol−1 with SAPT-DFT,91 and 22.38 kcal mol−1 with DFT.92,93 Among the three conformers for coronene-5-diimide studied, we find that the antiparallel structure is the most stable with binding energy −32.88 kcal mol−1 and a corresponding interplanar separation of 3.43 Å. Note that the energy differences among all three conformers are very small, suggesting their almost equal existence probability. Moreover, as can be seen from Figure 3, the 5-diimide groups for the two monomers are oriented in a perfect right angle with respect to each other and the central benzene rings are stabilized in a staggered conformation. We find that the slipped conformer of coronene-6-diimide is slightly more stable compared to the anticonformer. The estimated binding energy is −35.16 kcal mol−1 for the stable slipped-parallel geometry with the corresponding interplanar distance of 3.50 Å. However, the negligible difference in binding energies between the slipped-parallel and antiparallel conformers suggests their equal occurrence probability in an experimental synthesis. For the tetraimide compound, we find that the anticonformer is exclusively preferred over the slipped-parallel conformer with a difference in binding energy of 5.22 kcal mol−1. Among all the possible conformers studied for coronene imide derivatives, the anticonformer for tetraimide is predicted to have the largest binding energy with the relatively shorter distance (3.41 Å) of interplanar separation. In order to understand the increasing binding energy for the functionalized dimers compared with that of the pristine coronene dimer, we calculate and analyze the polarizability (α), quadrupole moment (Q), and charge transfer between the two-stacked monomers, if there is any. As expected, we do not find any interfacial charge transfer. Therefore, it is clear that there are no charge transfer driven Coulombic interactions for the enhanced stability. As can be seen from Table 1, the α and Q values increase with the introduction of imide functional groups to the coronene ring. These two quantities are strongly related to dispersion interactions. A higher value of α indicates that it is more easy to deform the charge density distribution on a molecule, which in turn results in larger dispersion interactions. Almost similar values of α and Q calculated for the 5-diimide and 6-diimide compounds result in very close binding energies. Moreover, the larger α and Q values found for the coronenetetraimide cause greater binding stability of its antiparallel dimer. Thus, the stability of these dimer structures mainly depends on the dispersion interactions, which is also expected for these stacked geometries. Additionally, we also calculate the electronic HOMO− LUMO gap using the B3LYP/6-31+g(d,p) level of theory to understand the effect of π-stacking interactions on the electronic properties. The HOMO−LUMO gap (ΔEH−L), for all the dimers considered here, is found to be less than the corresponding value obtained for the monomers, which agrees well with the concept that, in general, an aggregated system shows a lower HOMO−LUMO gap due to increased π−π interactions and extended π-electron delocalization over the two monomers present in a dimeric complex. Consequently, we find lower ΔEH−L with increased π-conjugation for the complexes studied. 3.2. Optical Absorption of Monomers and Dimers. To understand the optical absorption properties, we calculate the absorption spectra employing the TDDFT method as implemented in the Gaussian 09 package, using the B3LYP/ 6-31+g(d,p) level of theory. We consider calculating the

excitation energy for both the monomers and dimers of coronene and its imide-functionalized compounds. Moreover, we look at the FMOs relevant for the low-energy-absorpton peaks in detail to unravel the microscopic origins of these peaks. Our results show that there are two degenerate low-energyabsorption peaks centered at ∼4.11 eV for the coronene moeity, which mainly result from the electronic transitions from HOMO (H) to LUMO + 1, and HOMO to LUMO (L), HOMO − 1 to LUMO + 1, respectively. With the introduction of the electron withdrawing imide groups, we see that the absorption peaks are bathochromically shifted to a lower energy region. For the 5-diimide monomer, the first transition occurs at ∼2.71 eV, a relatively lower energy transition compared to the coronene low-energy absorption (∼4.11 eV), and the origin of this peak is due to the electronic promotion from HOMO to LUMO. Additionally, we also find two other low-energy peaks in the absorption spectra, which are centered at 3.69 and 3.73 eV with the corresponding electronic excitations from HOMO and HOMO − 1 to LUMO + 2. However, as given in Table 4, the prominent absorption, indicative from the higher oscillator strength, occurs at 3.69 eV. For the coronene-6-diimide monomer, the calculated lowenergy-absorption peaks are found at ∼2.97 and 3.89 eV with the stronger electronic absorption for the former peak position. To find the origin for these absorptions, an analysis of the FMOs reveals that HOMO − 1 to LUMO and LUMO + 1 transitions are mainly responsible for these two low-energy excitations. Also, note that the prominent absorption peak obtained for the 6-diimide is at a lower energy (∼2.97 eV) than that found for the 5-diimide monomer (∼3.69 eV). This is fully consistent with the calculated electronic gap values for these two monomers: ∼3.17 and ∼3.14 eV HOMO−LUMO gaps are found for the 5-diimide and 6-diimide, respectively. This can also be rationalized to a greater extent of LUMO stabilization for the 6-diimide than for the 5-diimide coronene because of the presence of more preferred 6-member diimide groups.94 Interestingly, we find that the calculated gas phase absorption maxima (λmax = 416.82 nm) obtained for coronene-6-diimide corroborates well with the experimentally observed value of λmax = 421 nm, measured in toluene solvent,72 and this compound has been reported to show good absorption and emission behaviors with considerable absorption coefficients and fluorescence quantum yields. Note that coronene-5-diimide and 6-diimide contain two electron withdrawing groups. Inclusion of further imide groups may lead to much lower energy optically allowed transitions because of the presence of the large number of electronic pulling groups, which can stabilize the HOMO and LUMO much more than those found for 5- or 6-diimide analogues. To investigate this, we calculated the absorption properties of coronene-tetradiimide and the results are shown in Table 4. We find that this tetraimide derivative absorbs at a relatively higher energy in comparison to the absorption spectra calculated for the 5- and 6-diimide compounds. However, the low-energy-absorption peaks are still found to be at lower energy than that computed for the coronene monomer. The two low-energy peaks are found at ∼3.28 and 3.29 eV, with the major FMO contribution toward this electronic excitation originating from the HOMO − 1 to LUMO and LUMO + 1 transitions, respectively. These results are in accordance with the calculated trend in HOMO−LUMO electronic gaps. The energy associated with the low-energy 831



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dimer (λmax = 294.70 nm) is blue shifted compared to its monomeric counterpart (λmax = 301.67 nm) by ∼0.1 eV. Similarly, a considerable blue shift in the low-energy-absorption peaks is found for antiparallel coronene-5-diimide (λmax = 348.37 nm) compared to that for monomeric coronene-5diimide (λmax = 457.64 nm, shift ∼0.85 eV), for slipped-parallel coronene-6-diimide (λmax = 412.85 nm) compared to its monomeric form (λmax = 416.85 nm, shift ∼0.03 eV), and antiparallel coronene-tetraimide (λmax = 380.68 nm) in comparison to monomeric coronene-tetraimide (λmax = 378.53 nm). We find that the low-energy-absorption peaks for the imide-functionalized coronenes are red shifted when compared with those of the pure coronene dimer. This is due to the presence of electron withdrawing imide groups in these derivatives, which increases the π-electron delocalization on the LUMO, resulting in lower electronic gaps (see in Figure 5). However, this observed blue shift for dimer absorption rather than the monomer can be attributed to the presence of interstack interactions with varying strengths, which have a profound effect on the low-energy photophysics of stacked compounds. Thus, π−π interactions play a significant role in the changes in electronic structures of stacked systems and, thereby, modulation of absorption properties. 3.3. Charge Transfer Integrals, Reorganization Energy, and Mobility. The aromatic molecules present in a crystal or in discotic liquid crystalline materials form columnar aggregates through extended π-conjugation between the consecutive stacked layers, which indicates their propensity for exhibiting promising charge transport properties. Thus, these materials find large scale applications in organic electronics. The charge transport characteristics of organic molecules depend on the molecular packing, the degree of ordering in the structure as well as the density of defects, whether chemical or structural, temperature, and electric field, the presence of impurities, size/molecular weight, and pressure.27,95 Thus, over the past two decades, depending on the sample quality, the results for transport properties of organic crystals were varied. Microscopic understanding of charge transport leads to the importance of the hopping matrix elements and the reorganization energy. Hence, the charge transfer integral and reorganization energy calculations are of relevance for understanding their nature, either as a hole transporter or as an electron transporter. The reorganization energy is defined as the amount of energy required to distort the nuclear configuration of the reactants into the nuclear configuration of the products before any charge (electron or hole) is transferred, and has been understood within Marcus theory formalism.69 In general, the charge transport mechanism involves the transfer of electrons or holes from a charged species to an adjacent neutral moiety. The charge carrier mobilities depend mainly on two intrinsic quantities, namely, (1) reorganization energy (λ) and (2) effective charge transfer integrals (Jeff). Both λ and Jeff are calculated using the procedures described above. The reorganization energies for all the monomeric structures show that λhole < λelectron, indicating their potential for behaving as hole transporting materials. Note that the reorganization energy calculated is the internal reorganization energy considering only the isolated coronene and its imide derivatives and does not include any environmental effects (see below). For pure coronene, coronene-5-diimide, coronene-6diimide, and coronene-tetraimide, the reorganization energy is larger for electrons than for holes (λelectron > λhole), which means

Table 4. Transition Energy, Oscillator Strength, and Significant MO Contributions for Low-Energy Electronic Excitations system coronene

transition energy (eV) 4.11

oscillator strength Monomers 0.69 0.69

coronene-5diimide

coronene-6diimide

coronenetetraimide

coronene

coronene-5diimide

coronene-6diimide

coronenetetraimide

3.73

0.26

3.69

0.67

2.71 3.89

0.15 0.27

2.97

0.32

3.29

0.60

3.28

0.66

4.25

Dimers 0.16

4.23

0.50

4.21

0.68

3.56

0.21

3.56

0.21

3.79

0.13

3.75

0.14

3.00

0.33

3.44

0.32

3.43

0.45

3.35

0.13

3.26

0.13

MO contribution

ΔEH−L (eV)

H → L+1 (0.39) H−1 → L+1 (0.39) H → L (0.39) H−1 → L+2 (0.66) H → L+2 (0.62) H → L (0.65) H−1 → L+1 (0.66) H−1 → L (0.66) H−1 → L+1 (0.54) H−1 → L (0.54)

4.02

H → L+1 (−0.11) H−3 → L+2 (0.35) H−3 → L+1 (0.33) H−1 → L+4 (0.40) H−1 → L+4 (0.40) H−1 → L+5 (0.29) H−7 → L+1 (0.17) H−2 → L+5 (0.52) H−3 → L+3 (0.37) H−1 → L+4 (0.46) H → L+4 (0.40) H → L+4 (0.43)

3.77

4.02

3.17 3.17 3.17 3.14 3.14 3.27 3.27

3.77 3.77 2.93 2.93 3.08 3.08 3.08 3.02 3.02 3.02 3.02

electronic excitation follows the order coronene > coronenetetraimide > coronene-6-diimide > coronene-5-diimide. In order to understand the effects of π−π stacking interactions on the absorption properties, we also consider calculating the absorption characteristics for the stable πstacked dimers of coronene and its imide compounds. Our results show that the low-energy electronic transition occurs at higher energy compared to the corresponding monomer’s transition. This is fully inconsistent with the calculated HOMO−LUMO gap values. To analyze the underlying reasons behind these findings, we find that, for all the π-stacked dimers, the low-energy absorption occurs because of the electronic excitations from occupied core molecular orbitals to relatively higher energy unoccupied molecular orbitals. The calculated first low-energy peak is found at ∼4.21, ∼3.56, ∼3.00, and ∼3.43 eV for all the stable dimers of coronene, coronene-5diimide, coronene-6-diimide, and coronene-tetraimide, respectively. The absorption maxima for the π-stacked coronene 832



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Figure 5. Top-view and side-view plots of FMOs of dimeric lowest binding energy structures of (a) coronene, (b) anti-coronene-5-diimide, (c)slipstacked-coronene-6-diimide, and (d) anti-coronene-tetraimide, using B3LYP/6-31+g(d,p).

Table 5. Effective Charge Transfer Integrals (Jeff) between the Two Monomers in a Dimer Structure and Reorganization Energy (λ) Calculated for Each Monomer J (eV) system coronene (DFT geometry) coronene (crystal geometry) coronene-5-diimide antiparallel slipped parallel full stacked coronene-6-diimide antiparallel slipped parallel coronene-tetraimide antiparallel slipped parallel

electron 0.0920 −0.05756

λ (eV)

Jeff (eV) hole 0.3284 0.22051

electron

hole

electron

hole

0.0653 −0.0409

0.1669 0.1103

0.1724 0.1724 0.2261

0.1294 0.1294 0.1946

0.2405

0.1802

0.2408

0.1829

0.0002 −0.0020 −0.1734

0.4031 −0.1917 −0.0706

0.0001 −0.0008 −0.0438

0.1968 −0.0087 −0.0438

−0.0007 −0.0953

−0.4108 −0.0269

−0.0004 −0.0565

−0.1946 −0.0129

0.1702 −0.1944

0.0890 −0.1280

0.0967 −0.1138

0.0429 −0.0644

electron withdrawing groups, such as imides, tend to tune the properties of p-type semiconductors to n-type, depending on the functional group position and concentrations. Note that, for pure coronene, the holes are the major charge carrier for the electronic transport. However, as given in Table 1, the adiabatic electron affinity (EA) of coronene increases monotonically with the introduction of electron withdrawing imide groups, suggesting their usage as n-type functional components in optoelectronic devices. Additionally, we also calculate the generalized charge (electron and hole) transfer integrals (Jeff) for the possible dimers considered, as has already been discussed. We find that Jeff calculated for holes is significantly larger than that calculated

that, for the structural rearrangement, the energy associated with putting an electron is greater than that for creating a hole, which in turn is supposed to enhance the hole mobility (μhole). As we introduce an electron withdrawing imide group, we notice that the λhole slightly increases, while λelectron increases significantly.96 Consequently, creation of holes and electrons on all these functionalized monomers will cost slightly higher energy compared to that on the pristine coronene moeity. However, the λhole is always lower than the λelectron for all the imide-functionalized coronenes. Conventionally, the smaller the λ value, the higher is the charge transfer rate. Thus, qualitatively, these materials may be said to be typically hole transporters. However, it is worth noting that the presence of 833



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Figure 6. (left) Unit cell of coronene crystal structure39 and (right) modeled molecular cluster containing five monomers taken from the crystal packing for calculating the charge transfer integrals.

Table 6. Charge Transfer Integrals for Five Fragments Cluster Considered from the Coronene Crystal Structure

a

R1ja

Jijelec (eV)

Jijhole (eV)

Jeffelec (eV)

Jeffhole (eV)

μhole (cm2 /(V s))

μelectron (cm2 /(V s))

4.70 8.40 10.01 11.14

0.0570 −0.0057 0.0161 −0.0054

−0.2217 −0.0006 0.0078 −0.0041

0.0399 −0.0004 0.0113 −0.0040

−0.1139 0.0016 0.0037 −0.0020

2.4589

0.1626

j = 2, 3, 4, 5.

responsible for hole and electron migration. In Figure 5, coronene-6-diimide and tetraimide, the LUMO exhibits more diffused electron distributions than the HOMO. The delocalized nature of the LUMO over the entire dimer facilitates enhanced electron transport for the two compounds. As expected, we also find the larger extent of electron transfer integrals for the stable dimers of these two compounds. The LUMO of the most energetically preferred 6-diimide dimer, as shown in Figure 5, shows the strong π−π overlaps, and this system along with its further alkyl-functionalized derivatives has reportedly been synthesized, showing comparatively higher electron mobility values.60 Further, the higher electron affinity and greater extent of interorbital overlaps, as indicated in the LUMO distribution, suggest that they can be good n-type semiconductors. This further strengthens the idea of realizing n-type semiconductor from a p-type one by the introduction of suitable electron withdrawing groups, such as imides, considered here. Although we gain a qualitative idea from the calculations of reorganization energy and charge transfer integrals in predicting charge transport properties, it is important to investigate the charge carrier’s mobility for these organic molecular crystals. The availability of crystal structure and the detailed structural orientations of all monomers present in the crystal of pure coronene help us to investigate its charge carrier mobility values. As discussed above, Jeffelec and Jeffhole are calculated to be 0.065 and 0.167 eV, respectively, for the stable dimeric arrangement. It is also important to consider the effect of the other monomers present in the crystal on Jeffelec and Jeffhole. For this, we have considered a molecular cluster consisting of five coronene monomers from the crystal structure, as shown in Figure 6. All the distances calculated from the central coronene and their corresponding Jeff values are given in Table 6. We have employed the hopping model for the calculations of charge carriers’ mobility as was also used in several other studies considering similar organic systems.31,34,38,97 Our results show that the hole carrier mobility is significantly larger, almost

for the electrons for coronene dimer structure, suggesting their potential for hole transport. This is true for both geometries of AB stacked coronene dimer considered, i.e., DFT optimized structure and crystal configuration. As has been discussed already, the crystal geometry was reported at finite experimental temperature, whereas the DFT optimized structure is at 0 K. Thus, it is important to compare the extent of charge transfer integrals for both of these structures. We present the results in Table 5. It is clear that the charge transfer integrals for both electron and hole are slightly larger for the fully relaxed DFT optimized coronene dimer geometry in comparison to the values calculated for the crystal configuration. This is expected because the slightly decreased interplanar distance induced greater π-stacking interactions for the DFT optimized dimer structure. For the antiparallel and slipped-parallel coronene-5diimide, we also find Jeffhole > Jeffelectron, a trend similar to that found for coronene, whereas an ambipolar nature is predicted for the full-stacked dimer. However, among all the dimers of coronene-5-diimide considered, the most stable antiparallel conformer exhibits the highest hole transfer integrals, highlighting its great promise as a hole transporting substance. The comparatively stable slip-stacked conformer for 6-diimide shows Jeffhole < Jeffelectron while it is reversed for the anticonformer. Note that the negligible difference in binding energies between these two conformers suggests their equal existing probability, and hence, together both conformers would contribute toward hole transport with the larger contribution arising from antiparallel structure. In contrast to these findings, for the tetraimide derivative, the order is found to be Jeffhole < Jeffelectron, for both conformations considered, and among the two dimers, Jeffelectron is estimated to be higher for the slippedparallel conformer because of the larger extent of LUMO delocalization. This is also consistent with the higher EA calculated for this tetraimide. In fact, the FMO characteristics are important for understanding the charge transfer rate and the majority carrier type in a given material. The extent of HOMO and LUMO wave function distribution is supposed to be 834



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Notes

15 times, than the electron mobility. However, as mentioned above, the charge transfer integrals for coronene crystal are calculated at the crystal structure geometry, which was reported experimentally at finite temperature. Note that we do not have specific crystal packing of all the imide-functionalized compounds. However, it is really important to compare the carrier mobilities of coronene and its 6-diimide derivative which is experimentally more feasible to form. Our results show that λhole for 6-diimide is higher compared to that for coronene. On the basis of the calculations performed on the dimers of these two compounds, it is found that the both the hole transfer integral and reorganization energy significantly increase upon imide functionalization to the coronene. However, these two intrinsic quantities compete with each other to give rise to the intrinsic carrier mobility. We conjecture that both the coronene and its 6-diimide would exhibit as hole transport materials in organic electronics.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.K.M. acknowledges CSIR, Government of India, for a senior research fellowship, and S.K.P. acknowledges DST, Government of India, and AOARD for research funding.

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4. CONCLUSIONS In summary, we have performed computational studies based on first-principles calculations on coronene and its imide derivatives, namely, coronene-5-diimide, coronene-6-diimide, and coronene-tetraimide. The formation feasibility of each molecule is examined by estimating the relative enthalpy cost for their formation from a common compound, coronene octacarboxylic acid. Our results show that coronene and coronene-6-diimide are most preferred to form among others, which corroborates well with the relative experimental abundance of coronene, coronene-6-diimide, and its further alkylated derivatives. We also focus on analyzing the effect of imide functionalization on electronic and optical absorption properties. The absorption characteristics obtained for both the monomeric and dimeric forms of coronene imides show bathochromic shifts of low-energy peaks in comparison to the pristine coronene due to the presence of the electron withdrawing imide groups, and the trend in transition energy follows the order of the electronic HOMO−LUMO gap. Interestingly, we find a larger extent of red shift for the synthetically more feasible coronene-6-diimide among the others. Moreover, our analysis also shows that the extent of red shift strongly depends on the position and orientations of the imide groups, and the low-energy peaks correspond to the π−π* electronic transitions from the highest occupied to lowest unoccupied frontier molecular orbitals. Furthermore, we also estimate the charge (electrons and holes) transfer integrals for the stable dimers, and we find that effective hole transfer integrals are significantly larger than the electron transfer integrals except for the coronene-tetraimide, for which the electron transfer integral is predicted to be greater than the hole transfer integrals. The charge carrier mobility calculated for the experimental crystal structure of coronene at room temperature shows that the hole mobility is significantly larger, almost 15 times, than the electron mobility. We believe that our study unravels the microscopic understandings for the tunable optical and charge transfer properties of functionalized coronene, and suggests a potential route in designing for optoelectronic and field effect transistor applications.

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