CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201301050

Functional Corannulene: Diverse Structures, Enhanced Charge Transport, and Tunable Optoelectronic Properties Somananda Sanyal,[a] Arun K. Manna,[a] and Swapan K. Pati*[a, b] Chemical functionalization of various hydrocarbons, such as coronene, corannulene, and so forth, shows good promise in electronics applications because of their tunable optoelectronic properties. By using quantum chemical calculations, we have investigated the changes in the corannulene buckybowl structure, which greatly affect its electronic and optical properties when functionalized with different electron-withdrawing imide groups. We find that the chemical nature and position of functional groups strongly regulate the stacking geometry, p-stacking interactions, and electronic structure. Herein, a range of optoelectronic properties and structure–property relationships

of various imide-functionalized corannulenes are explored and rationalized in detail. In terms of carrier mobility, we find that the functionalization strongly affects the reorganization energy of corannulene, while the enhanced stacking improves hopping integrals, favoring the carrier mobility of crystals of pentafluorophenylcorannulene-5-monoimide. The study shows a host of emerging optoelectronic properties and enhancements in the charge-transport characteristics of functionalized corannulene, which may find possible semiconductor and electronics applications.

1. Introduction Organic materials have shown remarkable technological importance in recent times. Displays for smartphones, colourful light sources, portable solar cells, and curved television screens are just a few examples of the increasing presence of organic electronics in our day-to-day lives. Though organic semiconducting molecules and polymers still cannot compete well with their inorganic counterparts in terms of charge-transport characteristics and industrial development, they hold key unparalleled advantages, such as reduced production costs, versatility of synthetic procedures, and compatibility with many substrates. The self-assembly formation of p-stacked organic molecules and their functionalized derivatives, such as benzene, naphthalene,[1] perylene,[2] and coronene,[3] have been shown to form 1D columnar aggregates that exhibit good charge-carrier mobility and optical properties with applications in the field of organic electronics.[4] Corannulene (C20H10),[5] or dibenzo[ghi,mno]fluoranthene,[6] a fragment of buckminsterfullerene,[7] has attracted the attention of chemists for quite some time now, along with the smallest hexagonal graphene quantum dot, coronene.[8] Its electronic properties and various functionalized derivatives and their optoelectronic applications are in[a] S. Sanyal, Dr. A. K. Manna, Prof. S. K. Pati Theoretical Sciences Unit Jawaharlal Nehru Centre for Advanced Scientific Research Jakkur P.O., Bangalore-560064 (India) [b] Prof. S. K. Pati New Chemistry Unit Jawaharlal Nehru Centre for Advanced Scientific Research Jakkur P.O., Bangalore-560064 (India) Fax: (+ 91) 80-22082766/2767 E-mail: [email protected] Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201301050.

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teresting studies.[9] The curvature in the molecule gives rise to two distinct surfaces (convex and concave), and this result in variations in the ionization potential and metal-binding nature of this molecule compared with its planar prototype, the coronene system. In our earlier study, we showed how functionalization of imide groups in coronene to form different numbers of imide rings changes the optoelectronic nature of the system and the charge-carrier properties.[10] These buckybowl molecules provide accessibility on both concave and convex faces, in contrast to fullerene for which only the convex face is accessible. Even corannulene-derived ferrocene donor–acceptor systems are reportedly synthesized to show H···p interactions and slipped p-stacking interactions.[11] The X-ray structure of corannulene shows no longrange stacking order and is extensively dominated by CH···p interactions that give rise to packing without any columnar order,[5] but functionalization in many cases, for example, tetrabromocorannulene, di-, tetra- and penta-substituted arylalkynyl corannulenes, cyclopalladation or imide functionalization gives proper columnar p-stacking.[12] The corannulene fragment has also been used for the synthesis of novel blue emitters, namely 1,2-bis(corannulenylethynyl)benzene and 1,4-bis(corannulenylethynyl)benzene[13] and as a buckycatcher by acting as molecular clips and tweezers for guest fullerene cages.[14] Corannulene can be charged with one or two electrons to affect its geometry[15] and its deca-heterosubstituted counterpart (general structure 1,3,5,7,9-penta-X,2,4,6,8,10-penta-Y-corannulene; X = alkoxy, aryl, aryloxy, etc. Y = Cl, Br, etc.)[16] can be used in fascinating synthetic applications. In addition to the interest of synthetic chemists in this corannulene molecule, various theoretical studies have also been of significance. Density functional theory (DFT) studies have ChemPhysChem 2014, 15, 885 – 893

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CHEMPHYSCHEM ARTICLES been performed alongside X-ray structural characterization on 1,3,5,7,9-penta-tert-butylcorannulene, which has shown how addition of bulky groups helps to flatten the curved molecule and affects the crystal packing.[17] In another study, Dobrowolski et al. studied the aromatic stabilization of coronene and corannulene and reported their data based on 20 diverse homodesmotic reactions; they found that the mean aromatic stabilization energy is 44.5 and 58.4 kcal mol1 for coronene and corannulene, respectively.[18] Among the variety of studies done on this particular interesting molecule is another study to analyze whether it is a good diene or a dienophile.[19] Three possible isomers of [R-C20H10] + (R = H, CH3, CH2Cl, CHCl2, and CCl3,) as hub-, rim-, and spoke-functionalized corannulene derivatives[20] and the importance of p–p stacking of corannulene dimers in the supramolecular chemistry of curved conjugated complexes[21] are also widely studied by using DFT methods. Recently, Schmidt et al.[22] reported the synthesis and electronic properties of N-substituted imide-fused corannulene and predicted that the imide-fused molecules are promising ntype semiconductors due to the presence of noncovalent interactions in these species. These materials find applications in the fabrication of optoelectronic devices. Even the large p–p overlap for these complexes is similar to that of the much studied n-type perylene diimides and important for synthesis of air-stable electron transporters because the architecture excludes the presence of oxygen and moisture. Herein, by using density functional theoretical calculations, we provide a detailed theoretical study of the effect of functionalization of pristine corannulene with electron-withdrawing imide functional groups to form either a six- or a five-membered imide group and then subsequent substitution of the N atom of the imide with a pentafluorophenyl group, which has been experimentally synthesized as well. For further substitution effect studies, we substituted the H on the N atom of the 5-imide moiety with methyl, phenyl, and pentachlorophenyl groups. Diimide functionalization of the corannulene rim has been taken into account. Herein, we have also explored the changes in the optical properties of pristine corannulene with functionalization and also how the charge-transfer characteristics change when

www.chemphyschem.org the CH···p-stacked corannulene crystal becomes an ordered columnar stack with imide functionalization.

2. Results and Discussion 2.1. Structural and Energetic Stability We first present a discussion on the structural aspects of all monomers considered herein. The monomer of corannulene was modeled from its three-dimensional crystal configuration and the imide-functionalized corannulene systems were constructed from the pristine one. The initial structure of pentafluorophenyl-corannulene-5-imide was modeled from the available experimental X-ray crystal data for the N-substituted imide-fused corannulene reported by Schmidt et al.[22] It is found that they form a neat p-stacked structure that exhibits a convex–concave columnar arrangement, whereas the pristine corannulene crystal shows a disordered close-packed arrangement of monomer molecules stabilized mainly through CH···p interactions.[5, 23] All the model structures were fully optimized by using the dispersion-corrected density functional wB97XD with 6-31 + g(d,p) basis sets without imposing any constraint. It has been reported previously that corannulene tends to form a regular columnar stack when functionalized at the rim positions.[24] Therefore, to compare how imide functionalization changes the columnar packing of corannulene and its effects on optoelectronic properties, we have considered a few representative systems herein. These include corannulene-5-monoimide, corannulene-6-monoimide, corannulene-5-diimide, corannulene-6-diimide, corannulene-bisimide (with both 5-monoimide and 6-monoimide), phenylcorannulene-5-monoimide (without F substitution), methylcorannulene-5-monoimide, and pentachlorophenylcorannulen-5-monoimide (F atoms are replaced by Cl atoms in the phenyl ring; see Figures 1 and S1 in the Supporting Information). We analyze all these systems and compare and contrast with the results obtained for pristine corannulene. To quantify the structural changes introduced by different functionalization, we calculated the bowl depth, which is de-

Figure 1. Top view of optimized monomer (upper panel) and dimer (lower panel) structures of i) pristine corannulene; ii) corannulene-5-monoimide; iii) corannulene-6-monoimide; iv) corannulene-bisimide; v) corannulene-5-diimide; and vi) corannulene-6-diimide. The white, gray, blue, and red spheres represent hydrogen, carbon, nitrogen, and oxygen atoms, respectively. Note: The stick structure in the lower panel represents the second/lower fragment of the dimeric structure.

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fined as the shortest distance between the centroid of the five interior carbon rings from the mean plane comprised of ten rim carbon atoms. The bowl depth for 5-monoimide-functionalized corannulene (0.87 ) is almost same as the value found for pristine corannulene (0.88 ).[5] For 5-diimide and pentafluorophenylcorannulene-5monoimide systems, we find large decrease in bowl depth (0.84 ) due to the presence of two bulky groups on opposite sides that tend to flatten the Figure 2. Top views and side views of optimized geometries of monomers and dimers of corannulene, corannulene-5-monoimide, and pentafluorophenylcorannulene-5-monoimide as obtained by using wB97XD/6-31 + G(d,p). curvature. This indicates that there can be a decrease in the bowl inversion barrier for the systems under study, as was also and diimides are modeled from optimized pristine corannulene reported in an earlier study.[9c] However, the bowl depth inboth for the monomers and stacked dimers. All the monomer creases for all other systems studied, with the 6-monoimideand stacked-dimer geometries are fully relaxed by using the and 6-diimide-functionalized derivatives showing large values dispersion-corrected density functional wB97XD with 6-31 + of 0.95 and 1.00 , respectively (see data in Table 1). Overall, g(d,p) basis sets. Note that the fully optimized geometries obthe calculations suggest that various imide functionalizations tained by using DFT are at 0 K temperatures, whereas the crysimpose different structural distortions as quantified by bowl tal structures were reported at finite temperatures. Thus, we depth. considered optimizing the dimer configuration initially modNext, we look at the structure and energetic stability of eled from the respective crystal geometries. All stable geomethese p-conjugated systems that form stacked dimers. We contries are shown in Figures 1 and 2. sidered the AB stacking configuration for the pristine corannuFrom the dimer-optimized geometries, we find that the lene modeled from X-ray crystal data reported by Petrukhina stacking distance (shortest distance between the two bottomand co-workers and published in 2005.[25] This is a monoclinic most points) decreases with imide functionalization and is less crystal with P21/c space group and the monomer has C5v pointfor 5-monoimide (3.62 ) than for 6-monoimide (3.65 ). The group symmetry. The corannulene crystal has two independent effect is much for the pentaflurophenylcorannulene-5-monomonomer molecules with a close-packed configuration stabiimide (3.58 ). The decrease in stacking distance is consistent lized mainly by CH···p-type interactions. However, the full gewith the flattening of the bowl shape (i.e. decreased bowl ometry optimizations of a corannulene crystal dimer result a pdepth) with functionalization. It is important to understand the stacked configuration in a convex–concave fashion (see energetic stability of these p-stacked dimer configurations, and Figure 2). For corannulene-pentafluorophenyl-5-monoimide, it is expected that these systems are stabilized mainly by longwe considered the dimer configuration from the reported crysrange electrostatic and short-range van der Waals and dipole– tal structure.[22] The initial geometries of all other monoimides dipole interactions. The binding energy (Eb) of the dimeric

Table 1. Equilibrium stacking distance (Req), BSSE-corrected binding energy (Eb), dispersion (D) and dipole–dipole (Edip–dip) contributions to the Eb value and bowl depth for corannulene and its imide-functionalized derivatives, as calculated by using wB97XD/6-31 + G(d,p). The monomer dipole moment (m) is also indicated. System

Req []

Eb [kcal mol1]

D [kcal mol1]

Edip–dip [kcal mol1]

Bowl depth[a] []

Bowl depth[b] []

m[b] [Debye]

pristine 5-monoimide 6-monomide bisimide 5-diimide 6-diimide pentafluorophenyl-5-monoimide pentachlorophenyl-5-monoimide methyl-5-monoimide phenyl-5-monoimide

3.63 3.62 3.65 3.69 3.59 3.76 3.58 3.63 3.62 3.62

16.39 24.35 24.55 30.31 30.01 26.14 22.72 22.32 25.76 27.64

10.98 14.20 14.53 17.05 16.85 14.70 12.58 14.29 15.11 16.27

0.0039 0.0065 0.0098 0.0004 0.0063 0.1300 0.5715 1.5722 0.0009 0.0247

0.86 0.83 0.92 0.93 0.81 0.95 0.87 0.87 0.82 0.84

0.88 0.87 0.95 0.93 0.84 1.00 0.84 0.85 0.89 0.86

2.2 3.9 5.9 2.1 2.3 3.4 5.8 5.1 3.4 3.5

[a] For the dimer. [b] For the monomer.

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complex reflects their energetic stability and is quantified as [Eq. (1)]: E b ¼ E dimer 2  E monomer

ð1Þ

in which Edimer and Emonomer are the optimized total energies of dimer and monomer at the wB97XD/6-31 + G(d,p) calculation level. Also, we have corrected the Eb value for the basis set superposition error (BSSE) as formulated by the Boys and Bernardi counterpoise correction (CP)[26] procedure. We note that the BSSE corrections are found to be small for the systems studied. We find that the binding stability (i.e. negative binding energy) for the functionalized corannulene system is larger than for pristine corannulene (see data in Table 1). The diimides show greater binding strength compared with the monoimide analogues. Maximum stability is found for corannulene bisimide (Eb = 30.31 kcal mol1). The enhanced binding stability is mainly associated with changes in electronic polarization, which strongly modulates the electrostatic interactions. In addition to electrostatic stabilization, the formation of these pstacked structures is largely governed by the dispersion and dipole–dipole interactions within the reduced length scale (i.e. small inter-planar separation). Thus, to quantify the extent of dispersion interactions (D) acting on each stacked dimer, we calculate D by using the BSSE-corrected binding energy differences obtained with (wB97XD) and without (wB97X) dispersion-corrected density functional (see Table 1). Further, we find that dipole moment (m) of corannulene is 2.2 Debye and the dipole moment increases with different imide functionalizations (see m values in Table 1), with a resultant dipole direction perpendicular to the bowl-depth direction. Thus, the direction of the molecular dipole is no longer along the bowl-depth direction, as was the case for pure corannulene. The intrinsic dipole moment of corannulene combined with the effect from imide functionalization adds to the van der Waals dispersion interactions for enhanced p–p-stacking interactions and thus helps to form highly ordered columnar crystal packing. In addition to the dispersion interactions, we also calculated the dipole–dipole interaction energy (Edip–dip) by using a point-dipole approximation defined as [Eq. (2)]: Edipdip ¼

~ r Þð~ rÞ ð~ m~ m1~ m2 m~ 3 1 1 5 2 2 r r3

ð2Þ

in which ~ m1 and ~ m2 are the two dipole moment vectors (for two monomer units) and r is the distance between molecular

centers 1 and 2. r1 and r2 are vector quantities defined as the molecular axis for each of the monomers. For dipolar molecules, the strongly allowed transition is to the lowest exciton state, for which the coupling interactions are approximated at large distances by a point-dipole model. To compute the Edip–dip value, we used a converged SCF charge density separately computed for each monomer unit present within a stacked dimer configuration. The dipole–dipole interactions for individual systems are also listed in Table 1. The results show that the binding stability is largely governed by the van der Waals dispersions and small effects arise from dipole–dipole interactions for the imide-functionalized derivatives. A relatively large Edip–dip contribution to the binding stability is predicted for the pentafluoro(chloro)-5-monoimide dimer. This is because of the large monomer dipoles created by the presence of strong electron-withdrawing groups.

2.2. Ground-State Electronic Properties To delve deep into understanding the electronic properties of a fragment of buckminsterfullerene, that is, corannulene and its imide-functionalized derivatives in various positions, we analyzed a few low-energy frontier molecular orbitals (FMOs); the HOMO (highest occupied molecular orbital), HOMO1, LUMO (lowest unoccupied molecular orbital), and LUMO + 1 for individual systems. For completeness, we also present and compare the results found for a planar coronene analogue. Perdew and Levy[27] and Casida[28] had verified Koopman’s Theorem[29] that is, the HOMO energy is equal to the negative of the ionization potential (IP), and the LUMO energy corresponds to electron affinity (EA), when the discontinuity in exchange correlation potential, Dxc = 0, and by using long-range corrected functionals, DFT satisfies Koopman’s Theorem.[30] Our results also show that the long-range corrected version of the hybrid functional B3LYP, namely CAM-B3LYP, and the dispersion-corrected functional wB97XD gives a result that is very close to Koopman’s theorem compared with the B3LYP functional, with CAM-B3LYP giving better results (see data in Table 2). The condition was shown to be satisfied by the long-range corrected density functional in DFT.[30] Thus we adopt the CAM-B3LYP functional for examining ground- and excited-state electronic properties of the molecules investigated here. We first compared the low-lying FMOs calculated for the curved corannulene and its planar analogue coronene. As shown in Figure S2, both pristine corannulene and coronene possess a twofold doubly degenerate HOMO and LUMO due

Table 2. IP and EA values for corannulene and pentafluorophenyl-5-imide-corannulene calculated by using B3LYP, wB97XD, and CAM-B3LYP functionals. All values are in eV. System IP

EA

corannulene

7.63

0.63

pentafluorophenyl-5imide-corannulene

8.06

2.20

B3LYP HOMO

wB97XD HOMO

LUMO

IP

EA

6.28

1.88

7.85

0.45

6.80

3.25

8.26

2.08

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CAM-B3LYP HOMO

LUMO

IP

EA

8.20

0.21

7.83

0.50

7.63

0.80

8.69

1.59

8.25

2.15

8.14

2.18

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to the high molecular symmeTable 3. Transition wavelength, oscillator strength, and significant molecular orbital contributions (Ci) for UV/ tries, fully consistent with the Vis spectroscopy of the monomers [yMO = SCiAOs] calculated by using CAM-B3LYP/6-31 + G(d,p).[a] previous studies.[31] The doubly System Transition Oscillator HOMO!LUMO DEH–L degenerate HOMO and LUMO of wavelength [nm] strength (contribution) [eV] both the molecules are fully decoronene 269.57 1.05 H!L + 1 (0.38) 6.16 localized over the whole system. H1!L (0.38) In our system, both HOMO and corannulene 252.59 0.45 H3!L + 1 (0.46) 6.83 LUMO are degenerate because H2!L (0.46) the corannulene molecule has 5-monoimide 267.06 0.48 H3!L + 1 (0.53) 6.04 6-monomide 312.82 0.14 H3!L (0.63) 6.22 high symmetry for the five- and bisimide 329.24 0.19 H2!L (0.60) 5.90 six-membered rings that are in5-diimide 277.27 0.56 H2!L + 1 (0.57) 5.89 terconnected, thereby breaking 6-diimide 272.58 0.59 H3!L + 1 (0.47) 6.06 the alternating structure (the sopentafluorophenyl-5-monoimide 324.37 0.10 H2!L (0.49) 5.96 pentachlorophenyl-5-monoimide 323.20 0.10 H2!L (0.48) 5.99 called “bipartite” structure). This methyl-5-monoimide 267.61 0.54 H2!L + 1 (0.52) 6.07 is clear from the FMOs diagram phenyl-5-monoimide 269.13 0.70 H2!L + 1 (0.44) 6.02 provided in Figure S2. The [a] H and L indicate highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively. HOMO and LUMO consist of p (bonding) and p* (anti-bonding) molecular orbitals comprised of mainly C pz orbitals. The calculated HOMO–LUMO electronic different positions of corannulene (see Figure 3). As expected, the negative electron cloud is found to be spread towards the gap (DEH–L) for corannulene and coronene is 6.83 and 6.16 eV, functional group, whereas the electronic charge density is horespectively. The relatively large electronic gap found for cormogeneously distributed over the whole corannulene moleannulene is because its curvature induces less p-electron decule. The presence of these functional groups strongly affects localization and thus it is expected to exhibit large photostabilthe intrinsic IP and EA of corannulene. The adiabatic ionization ity. Similar findings were reported in previous studies.[9e, 10, 31] potential (IP = EcationEneutral) of corannulene (7.83 eV)[32] is Now we discuss the effects of different imide functionalization on the FMOs nature and the electronic DEH–L gap. We find found to be less than the pentafluorophenyl imide derivative (8.25 eV) and the adiabatic electron affinity (EA = EanionEneutral) significant changes in low-lying FMOs with varying extents induced by the different functional groups. It is found that the of corannulene (0.5 eV) is much higher than for pentafluoroHOMO is mainly localized over the main carbon framework of phenyl 5-imide corannulene (2.15 eV). This suggests a greater corannulene, whereas the LUMO is spread over the imide funcelectron-accepting tendency for the functionalized derivative tional group (see Figure S5). Moreover, as expected, introducthan the pristine corannulene moiety. Note that the pristine tion of functional groups removes the HOMO and LUMO orbicorannulene can accommodate up to four electrons (to form tal degeneracy. The results show relatively small DEH–L values a tetraanion) and is aromatic.[33, 34] Thus our results suggest that for all functionalized corannulene systems studied compared the functionalized systems investigated herein may have high with the pristine analogue (see data in Table 3). This is attributpotential for the electron transport through the crystal. ed to the energetic stabilization of both HOMO and LUMO, Next we compare and contrast the local aromatic character with LUMO being more stabilized. The comparatively small of the different corannulene systems studied. We considered HOMO–LUMO gap and possibility of low-energy charge-transcalculating the NICS (nucleus-independent chemical shift),[35] as introduced by Schleyer et al. in 1966. Note that a more negafer types of excitations (HOMO!LUMO) suggest the low photostability of these functionalized molecules. Furthermore, the electronic charge density distribution would help us to qualitatively understand the electrostatic interactions between various molecules in a crystal environment. For this, we calculated the electrostatic potential (ESP) surfaces for individual molecules and compare them. The ESP surfaces computed for different systems display the shift in negatively charged p-electron cloud distribution due to the presence of Figure 3. Electrostatic potential surfaces for the studied monomer systems calculated by using wB97XD/6different functional groups at 31 + G(d,p).  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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CHEMPHYSCHEM ARTICLES tive NICS value indicates a greater presence of induced diatropic ring current and thus a greater extent of local aromatic nature. A positive NICS value reflects a paratropic ring current, which suggests local antiaromaticity. We choose calculation points that are 1.0  above the five- and six-membered ring centers for the corannulene exo-side.[36] The choice was made to avoid the influences that may arise from the s electrons and other rings (large effects for endo-side).The NICS calculations were performed by using the B3LYP/6-31 + g(d,p) level of theory. For comparison, we also provide the NICS values calculated for planar coronene. All the NICS values with the respective molecular diagrams are shown in Figure S3 and a NICS scan plot up to 2  on either side (exo and endo) of the central five-membered ring of corannulene and functionalized corannulene is presented to understand the trend of NICS values (see Figure S4). The NICS values calculated at the five-member ring centers for all the corannulene systems show moderate positive values and thus they exhibit anti-aromatic character (see values in Figure S3). The negative values obtained for the peripheral sixmember rings indicate local aromatic nature (see Figure S3). Significantly small negative NICS values suggest less peripheral ring aromaticity for the curved corannulene than its planar coronene analogue. We note that a direct comparison between the curved corannulene and planar coronene is difficult. However, considering the local aromaticity of the peripheral sixmember ring p electrons, we believe that the comparison is reasonable because of negligible influences from s electrons and other rings. The curvature from the presence of the core five-member ring largely reduces the local aromatic nature for corannulene. In addition, we find that the presence of imide groups at different positions mostly reduces the negative NICS values for the peripheral six-member rings further and thus suggests reduced local aromatic character compared with pristine corannulene. However, the aromatic nature of the peripheral six-member ring directly attached to the five-member imide group increases due to the enhanced p delocalization. 2.3. Excited-State Properties We now look at the excited-state properties of these systems and analyze the effects of functionalization on the low-energy optical absorption of corannulene. As has already been mentioned, we have chosen the LRC CAM-B3LYP functional over B3LYP and wB97XD because it satisfies Koopmans’s theorem. This LRC functional has been proven to produce accurate energetics for charge-transfer excitations.[30, 37] Pristine corannulene shows optical absorption at a higher energy of l  253 nm and has two degenerate low-energy peaks. The electronic promotion associated with these excitations mainly occurs between occupied (HOMO3, HOMO2) to unoccupied (LUMO, LUMO + 1) molecular orbitals (see Table 3). Its planar analogue, coronene, exhibits redshifted degenerate optical absorption at l  269 nm (see data in Table 3). The corannulene curvature causes blueshifted absorption, fully consistent with its higher DEH–L gap value than coronene. Imide functionalization causes corannulene to absorb at low  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org energy (for corannulene-5-monoimide lmax = 267 nm and for corannulene-6-monoimide lmax = 313 nm). This is corroborated with the small HOMO–LUMO gap values of these functionalized systems (see Table 3). Furthermore, corannulene-bisimide absorbs at much lower energy (l  329 nm). However, corannulene-5-diimide and -6-diimide show absorption peaks at l  277 and 272 nm, respectively. To understand the nature of low-energy excitations, we analyze the FMOs as shown in Figure S5. As listed in Table 3, the prominent absorption peaks characterized by large oscillator strengths occur due to the electronic promotion between an occupied molecular orbital (OMO) to an unoccupied molecular orbital (UMO). Now, when a phenyl/methyl group is added to the N atom of 5-imide, the lmax is around 267–269 nm, but when a pentafluorophenyl/pentachlorophenyl ring is added to the N atom of 5-imide, UV/Vis absorption is hugely redshifted to higher wavelengths (lmax = 324.37 nm for pentafluorophenyl-5-imide corannulene and lmax = 323.20 nm after addition of pentachlorophenyl). We analyzed the FMOs to understand the nature of low-energy electronic excitations. A signature of charge-transfer transitions is clear from the low-lying FMOs (see Figure S5). In these systems, the HOMO is mainly concentrated on the corannulene curvature, whereas the LUMO is delocalized over the imide substitution as well, although the pentafluorophenyl ring is almost perpendicular to the corannulene-imide system and does not contribute to the LUMO. As expected for dimeric systems, increased p delocalization in the LUMO results in lower HOMO–LUMO gap values (see data in Table S1) and also the absorption spectra is slightly shifted to higher wavelengths in comparison with their monomer analogue. The FMO natures relevant to the low-energy transitions are displayed in Figure S6. The HOMO is less affected by p-stacking interactions from neighboring units and was found to be mainly localized over each monomer unit and the enhanced p-electron delocalization is reflected in the low-lying unoccupied molecular orbitals. This highly stabilizes the unoccupied FMOs, which is in agreement with the small electronic gaps and redshifted absorption peak positions. Overall, the results suggest that corannulene 6-monoimide, -bisimide and -pentafluorophenyl-5-imide are the best choices for optoelectronic applications. 2.4. Reorganization Energy, Charge-Transfer Integrals, and Charge-Carrier Mobility It is known that the crystal packing of corannulene has a disordered arrangement of monomers. Unlike other aromatic crystals, it does not show a columnar aggregate arrangement. The charge-transport property of any organic semiconductor is dependent upon the degree of ordering in the system, the density of defects, molecular packing, temperature, electric field, pressure, and so forth.[38] The hopping matrix element and reorganization energy are integral parameters in understanding the charge-transport nature of a sample, whether it is a hole or an electron transporter. On a simpler note, charge transport by a hopping mechanism is an incoherent method of transport and takes place through transfer of charge (electrons or holes) ChemPhysChem 2014, 15, 885 – 893

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from a charged to a neutral species. Therein lies the importance of the internal reorganization energy parameter, in which a mobile charge on a molecular system distorts the nuclear geometry to generate a polaron and the effective charge-transfer integral. The reorganization energy (l) is calculated by using the formula mentioned in the Computational Details. As briefly mentioned in the Computational Details, the Marcus hopping mechanism adopted in our study for calcu- Figure 4. Monomer structure, crystal packing, and model cluster used for mobility calculations for corannulene[5] lating charge carriers rates is (upper panel) and pentafluoro-5-imide-corannulene[22] (lower panel). The white, gray, blue, red, and cyan spheres strictly valid at the so-called represent hydrogen, carbon, nitrogen, oxygen, and fluorine atoms, respectively. high-temperature limit, at which nuclear tunneling is expected to be negligible. The calculated small activation barriers (Ea Schmidt et al.,[22] these corannulene systems fused with an  0.07–0.12 eV), moderate reorganization energy (l  0.3– electron-withdrawing imide group show promising n-type 0.5 eV), and zero driving force (DE = 0.0 eV) are three key pasemiconductor properties. We speculate that these functionalrameters that govern the transfer process and suggest a nonized corannulene derivatives could find huge applications in inverted Marcus regime, in which the thermally activated prothe ever-growing field of organic field effect transistors and orcess is expected to be dominant. ganic electronics research due to their higher charge-carrier Herein, we have considered four corannulene monomer mobility. units modeled from the close-packed X-ray crystal structure, which is mainly stabilized through CH···p interactions, and the distances (r1j) from the central fragment are listed in Table 2. 3. Conclusion For pentafluorophenylcorannulene-5-imide, we considered a 1D chain that consists of five monomers along the stacking In summary, the low-energy optoelectronic and charge-transfer direction (see Figure 4). Because the charge-transfer integral characteristics of corannulene and its various imide-functionaldecreases to very low values beyond a distance of about 10 , ized derivatives have been studied by using density functional we have considered the fragments in both the systems within theory. The role of van der Waals and dipole–dipole interacthat range. For the pristine corannulene moiety, we find lhole tions in stabilizing the columnar p-stacked aggregates (molec(0.37 eV) > lelectron (0.32 eV), whereas the situation is reversed ular wires) that are suitable for enhanced charge-transport profor pentafluorophenyl-corannulene-5-monoimide (lhole cesses are analyzed in great detail. The study also explores the (0.41 eV) < lelectron (0.51 eV)). This suggests that corannulene diverse and tunable low-energy optical properties of corannuacts as an electron transporter, whereas pentafluorophenyl-corlene. We believe that the present study widens the applicaannulene-5-monoimide is expected to be a hole transporter. tions of these functional organic materials in optoelectronics However, the second factor, the charge-transfer integral values, and n-type semiconducting devices. dictates the overall transport nature. We find that Jelec,eff > Table 4. Reorganization energy (l), effective charge-transfer integrals (Jeff) and carrier mobility (m) for the coranJhole,eff changed to match symnulene 3D network and pentafluorophenylcorannulene-5-monoimide 1D chain. bols in Table 4, (see data in [a] [a] lelec r1j[a] Jhole,eff Jelec,eff melec mhole lhole Table 4) and the charge-carrier 1j 1j [eV] [eV] [] [eV] [eV] [cm2 Vs1] [cm2 Vs1] mobility for electrons is much corannulene higher than holes in both sys0.37 0.32 5.49 0.003 0.023 0.017 0.006 tems considered (melec = 0.017 7.62 0.006 0.001 2 1 and mhole = 0.006 cm Vs for 6.05 0.005 0.244 corannulene; melec = 0.1498 and pentafluorophenylcorannulene-5-monoimide 0.41 0.51 7.16 0.0032 0.0940 0.1498 0.003 mhole = 0.0031 cm2 Vs1 for penta7.35 0.0083 0.0004 fluorophenylcorannulene-5-mon7.15 0.0034 0.0937 oimide), thus making them 7.35 0.0083 0.0004 both n-type semiconductors. [a] j = 2, 3, 4 for corannulene and j = 2, 3, 4, 5 for pentafluoro-phenyl-corannulene-5-monoimide. Thus, as was predicted by  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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Computational Details Quantum chemical calculations have been performed by using density functional theory (DFT) as implemented in the Gaussian 09[39] software package. The long-range dispersion corrected energy functional, wB97XD, was used for the geometry optimization of the monomers and dimers to account for the dispersion interactions in the curved structures, which play a significant role in determining the stacked geometry. All geometry optimizations were carried out by using the basis set 6-31 + g(d,p) for all atoms. We confirmed the geometries to be in true local minima by analyzing the vibrational frequencies. Time-dependent density functional theory (TDDFT) calculations, as implemented in Gaussian 09,[39] have been performed by using a long-range corrected (LRC) version of B3LYP with the Coulomb-attenuating method [CAM-B3LYP][40] and 6-31 + g(d,p) basis set. The LRC density functional has been used to explore the possibility of any charge-transfer excitations within monomers and dimers of the systems studied. For the sake of completeness, we have also used hybrid B3LYP and compared the important findings. The reorganization energy (l) was calculated by using Equations (3) and (4):    *  E lelectron ¼ E*  E þ Eanion

ð3Þ

    * E lhole ¼ Eþ*  Eþ þ Ecation

ð4Þ

in which 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 *þ) is the energy of the anionic (cationic) molecule in neutral geometry, * ) is the energy of the neutral molecule in anion* (E cation and E anion ic (cationic) geometry. Note that we have ignored the external reorganization energy because we do not consider any environmental effects. In the arena of charge-induced deformation, mostly in case of organic semiconductor molecules, the hopping process is modeled through a nonadiabatic electrontransfer process and the hopping rate of a charge carrier can be defined by using Marcus theory formalism[7, 41] given as [Eq. (5)]:  2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi =h p=lkB T expðl4kB T Þ W ¼ 2Jeff

ð5Þ

in which kB is the Boltzmann constant and T is the absolute temperature of the crystal (T = 300 K herein). It is important to mention that the Marcus hopping mechanism adopted here is strictly valid at the high-temperature limit, at which the importance of tunneling effects are negligible. Furthermore, the driving energy for the transfer process is implicitly set to zero because of identical sets of monomer units present in the crystal studied here. The effective charge transfer integral (Jeff) was calculated by using Equation (6): Jeff ¼ Jij ð1=2ÞSij ðei þ ej Þ

 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

ð6Þ

in which Jij and Sij denote the transfer integral and spatial overlap matrix element between ith and jth molecular fragment orbitals (HOMO for hole transfer and LUMO for electron transfer); ei and ej represent the site energies of the two charge-localized molecular orbitals. In 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 = SCEC1. The diffusion coefficient (D), which is related to the hopping rate, is given by Equation (7)  D¼

1 2d

"X i

2 i

2 i

r W

, X

# Wi

ð7Þ

i

in which d is the dimensionality of the crystal (d = 1 for pentafluorophenyl-corannulene-5-monoimide-corannulene and 3 for corannulene) and r is the stacking distance between the adjacent molecules. D is normalized over the total probability of charge transfer. The final drift mobility (m) is calculated by using the Einstein relation, as follows [Eq. (8)]: m ¼ ðe=kB TÞD

ð8Þ

The charge-transfer integrals or hopping matrix elements, site energies, and spatial orbital overlap have been calculated by using the fragment orbital method in the Amsterdam Density Functional (ADF) program.[42] For all the calculations done by using ADF, we have used a generalized gradient approximation (GGA) within Perdew–Burke–Ernzerhof (PBE)[43] as an exchange and correlation functional, and a large triple zeta (&) with double-polarization (TZ2P) basis set for all atoms. Moreover, we have taken into account the dispersion interactions for calculating the charge-transfer integrals because it has a significant role in the p-stacked dimers.

Acknowledgements S.S. acknowledges JNCASR for financial assistance, A.K.M. acknowledges CSIR, Govt. of India, for a senior research fellowship and S.K.P. acknowledges DST, Govt. of India for research funding. Keywords: charge transfer · charge-carrier mobility · corannulenes · density functional calculations · optical properties · semiconductors [1] a) D. Polpanich, U. Asawapirom, R. Thiramanas, P. Piyakulawat, Mater. Chem. Phys. 2011, 129, 495 – 500; b) J. B. Bodapati, H. Icil, Photochem. Photobiol. Sci. 2011, 10, 1283 – 1293; c) R. Rybakiewicz, P. Gawrys, D. Tsikritzis, K. Emmanouil, S. Kennou, M. Zagorska, A. Pron, Electrochim. Acta 2013, 96, 13 – 17. [2] a) C. Li, H. Wonneberger, Adv. Mater. 2012, 24, 613 – 636; b) J. L. Segura, H. Herrera, P. Bauerle, J. Mater. Chem. 2012, 22, 8717 – 8733; c) F. G. Brunetti, R. Kumar, F. Wudl, J. Mater. Chem. 2010, 20, 2934 – 2948. [3] a) C. Kulkarni, R. Munirathinam, S. J. George, Chem. Eur. J. 2013, 19, 11270 – 11278; b) L. Hao, W. Jiang, Z. Wang, Tetrahedron 2012, 68, 9234 – 9239. [4] M. R. Wasielewski, Acc. Chem. Res. 2009, 42, 1910 – 1921. [5] J. C. Hanson, C. E. Nordman, Acta Crystallogr. Sect. B 1976, 32, 1147 – 1153.

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Received: November 12, 2013 Revised: December 20, 2013 Published online on March 3, 2014

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