CARBON 94 (2015) 174–180

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CARBON

journal homepage: www.elsevier .com/locate /carbon

Electronic transport properties of selected carbon p-bowls with differentsize, curvature and solid state packing

http://dx.doi.org/10.1016/j.carbon.2015.06.0410008-6223/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: rmargine@binghamton.edu (E.R. Margine).

Bao-Tian Wang a, Marina A. Petrukhina b, Elena R. Margine a,⇑a Department of Physics, Applied Physics and Astronomy, Binghamton University-SUNY, Binghamton, NY 13902, USAb Department of Chemistry, University at Albany, State University of New York, 1400 Washington Avenue, Albany, NY 12222, USA

a r t i c l e i n f o

Article history:Received 15 April 2015Received in revised form 18 June 2015Accepted 21 June 2015Available online 22 June 2015

a b s t r a c t

First-principles calculations combined with the Boltzmann transport theory are used to investigate theelectronic transport properties of four members of the extended family of indenocorannulene molecularcrystals. The results for the electrical conductivity suggest that all indenocorannulene derivatives shouldexhibit transport characteristics significantly improved compared to the parent corannulene. In particu-lar, the transport properties of 1,2,4-triindenocorannulene crystal are found to be comparable for electrondoping and likely surpass for hole doping the values achievable in sumanene, assuming the same carrierlifetimes. The findings point to a large sensitivity of the charge-carrier conductivity to the size as well asstacking direction of the carbon-rich p-bowls and indicate that this class of corannulene derivatives canprovide new structural motifs that can be further tuned to achieve high-performance materials fororganic electronic devices.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Bowl-shaped polyaromatic hydrocarbons (PAHs) have emergedin recent years as promising new materials for important techno-logical applications: batteries, optoelectronic devices, photoactiveswitches and chemical sensors. These curved polyarenes (oftencalled p-bowls) are excellent electron acceptors, comparable toplanar PAHs [1,2] and fullerenes [3,4], and could serve as key anodecomponents in rechargeable Li-ion batteries. Corannulene, thesmallest non-planar fragment of C60 fullerene [5,6], was shownto exhibit high degree of lithium intercalation upon step-wisereduction [7–10] and corannulene-based anode materials havedemonstrated a high reversible lithium capacity, almost twice ashigh as that of fully lithiated graphite [11,12]. The family ofp-bowls also provides a natural platform for designing new organicmaterials with applications in light emitting-diodes [13–16],field-effect transistors [17–19], or photovoltaic cells [20]. Whileorganic semiconductors may still not compete with their inorganiccounterparts in terms of charge-carrier mobility or power effi-ciency performance, they do have the advantage of beinglow-cost, flexible, easily processable in solution, and compatiblewith many substrates [21,22].

First-principles calculations could provide unique designinsights upon which a wide array of materials properties could

be improved beyond the current state-of-the-art. Due to the com-plexity and size of organic molecular crystals, most theoreticalstudies up to date have only addressed the energetics of the inter-action between isolated molecular bowls with various metalcations [23–28] or the energetics of small assemblies such ascorannulene dimers [29–32] or p-bowl-fullerene binary systems[33–35]. Only recently, several studies have explored the opticaland vibrational properties of corannulene-based crystals[14,16,36,37]. To the best of our knowledge, no theoretical insightsinto the electronic transport properties of crystalline bowl-shapedpolyarenes have yet been provided.

In the recent years, the family of p-bowls has greatly expanded[38] and besides the smallest members, corannulene (C20H10) andsumanene (C21H12) [39,40], it now includes bowls as large as pen-taindenocorannulene (C50H20) [41] and a short capped carbon nan-otube (C50H10) [42]. The in-depth structural analysis of p-bowls byFilatov et al. [43] has revealed that variation in the curvature and sizeof the molecular building blocks leads to very different crystal pack-ing. In particular, p–p bowl interactions between molecules of theindenocorannulene family with strong dipole moments promote aone-dimensional (1D) columnar stacking which, in turn, shouldfavor an efficient channel for charge transport. Experimental studieson sumanene [44] and corannulene derivatives [17–20,45] haveindeed found strong anisotropy in the electronic transport proper-ties with high charge-carrier mobilities along the p-bowl stackingdirection. Given the lack of studies on the transport properties oflarge indenocorannulene bowls in the crystalline state, it is

Fig. 1. Molecular building block of the crystal structures. (A color version of thisfigure can be viewed online.)

B.-T. Wang et al. / CARBON 94 (2015) 174–180 175

important and timely to carry out a careful theoretical investigationin order to understand their potential as active materials in organicelectronic devices.

In this work, we report the first systematic theoretical investi-gation of the electronic transport properties of a series of X-raycrystallographically characterized bowl-shaped PAH crystals fromthe indenocorannulene family [43] vs. those of the parent corannu-lene which lacks columnar p-stacking in the solid state [46,47] andsumanene which exhibits an efficient p-stacking in the crystallinestate [48]. Specifically, first-principles band structure calculationscoupled with the Boltzmann transport formalism are used to char-acterize the electronic transport properties of sumanene (C21H12),corannulene (C20H10), and four indenocorannulene crystals,namely monoindenocorannulene (mono-IC, C26H12), diindenoco-rannulene (ortho-di-IC and para-di-IC, C32H14), and triindenoco-rannulene (1,2,4-tri-IC, C38H16). The molecular building blocksare shown in Fig. 1. Comparison of the transport coefficients ofthe four indenocorannulene crystals with those of the parentcorannulene and well-known sumanene allows us to identify themost promising candidates for experimental conductivity studies.

2. Computational method

The calculations are performed within the local density approxi-mation (LDA) [49] to density functional theory and norm-conservingpseudopotentials [50] using the QUANTUM-ESPRESSO package [51].The valence electronic wave functions are expanded in a plane-wavebasis set with a kinetic energy cutoff of 60 Ry. We use at least2000/(number of atoms in unit cell) k-points distributed on aMonkhorst–Pack mesh [52] for ionic relaxations and a much densermesh of at least 35,000/(number of atoms in unit cell) for transportproperties calculations. We employ the experimental lattice param-eters for all crystal structures [43,46,48] and relax the atomic posi-tions until the force on each atom is smaller than 0.01 eV/Å. Wechecked and found that for the 1,2,4-tri-IC system the effect of fullstructural relaxation on the electronic band structure is negligible.

The conventional unit cells of three-dimensional (3D) crystalstructures of sumanene, corannulene, mono-IC, ortho-di-IC,para-di-IC, and 1,2,4-tri-IC are shown in Figs. 2 and 3 and the

experimental X-ray crystallographic parameters are listed inTable 1. Sumanene crystallizes in the trigonal R3c space group withN = 6 molecules in the unit cell stacked along the c-axis[Figs. 2(a) and 3(a)]. Corannulene crystallizes in the monoclinicP21/c space group with N = 8 molecules in the unit cell[Figs. 2(b) and 3(b)] without any preferential stacking orientationof the C20H10 bowls. Mono-IC crystallizes in the monoclinic spacegroup P21/n [Figs. 2(c) and 3(c)]. There are N = 4 tortoise-shapedinequivalent molecules in the unit cell and they are stacked alongthe a-axis. Ortho-di-IC crystallizes in the orthorhombic spacegroup Pnma and there are N = 4 inequivalent molecules in the unitcell. The molecular bowls are stacked along the c-axis[Figs. 2(d) and 3(d)]. Para-di-IC crystallizes in the polar orthorhom-bic space group Cmc21. There are N = 4 molecules in the unit cellwith a preferential stacking orientation along the c-axis[Figs. 2(e) and 3(e)]. [We note that the primitive unit cell ofpara-di-IC has only N = 2 inequivalent molecules and all electronicand transport properties in this work are calculated for the primi-tive unit cell.] 1,2,4-tri-IC crystallizes in the polar orthorhombicspace group Pmn21 with N = 2 non-planar herringbone inequiva-lent molecules in the unit cell [Figs. 2(f) and 3(f)]. The moleculesare stacked along the c-axis. More details about the crystal struc-tures will be given in the next section in connection with the trans-port properties.

Electronic transport coefficients are computed with theBoltzTraP code [53] that solves the semi-classical Boltzmann trans-port equations (BTEs) in the constant relaxation-time and rigidband approximations [54]. The known difficulties of describingthe finite lifetime of charge carriers due to various scatteringmechanisms, have led to adopting the constant relaxation-timeapproximation in many theoretical studies [54–57]. This approxi-mation is based on the assumption that the relaxation-time doesnot vary significantly in energy over the Brillouin zone, i.e. si,k = s.Moreover, within this approach, the Seebeck coefficient S, is inde-pendent of s and can be calculated on an absolute scale. Despite itssimplicity, the method has been shown to work rather well evenfor systems with substantially anisotropic conduction [58] and itis also the scheme adopted in this work.

3. Results and discussions

Fig. 4 shows the calculated electronic band structure and the den-sity of states (DOSs) for the six p-bowl systems. The calculated bandgaps are 2.80 eV for sumanene, 2.68 eV for corannulene, 1.97 eV formono-IC, 1.87 eV for ortho-di-IC, 1.73 eV for para-di-IC, and 1.50 eVfor 1,2,4-tri-IC. It can be noticed that in going from corannulene to1,2,4-tri-IC crystals, the energy band gap decreases monotonicallywith the increase in the number of indeno-group substituents andthe size of the bowl. As expected for traditional DFT, the calculatedenergy band gaps are underestimated by approximately 2 eV withrespect to experimental values, but in good agreement with othertheoretical studies at the same level of theory [16]. However, weshould note that the exact magnitude of the band gap is not a criticalparameter in this work and the transport coefficients are notaffected as long as the size of the band gap is large enough comparedto the temperatures considered. At room temperature, mostly carri-ers in a small energy window (approximately 0.1 eV) below thevalence band maximum (VBM) and above the conduction band min-imum (CBM) contribute to the charge-transport properties. In allcases, except corannulene, a large dispersion is observed at VBMand CBM along the crystallographic direction corresponding to thepreferential p-stacking of the bowl-shaped molecules. Negligibleband dispersions are found along the directions perpendicular tostacking, reflecting the molecular nature of the solid. From Fig. 4,we extract the bandwidth of the highest valance band (lowest

Fig. 2. Top view of three-dimensional conventional unit cell crystal structures for (a) sumanene, (b) corannulene, (c) mono-IC, (d) ortho-di-IC, (e) para-di-IC, and (f) 1,2,4-tri-IC. (A color version of this figure can be viewed online.)

Fig. 3. Side view of three-dimensional conventional unit cell crystal structures for (a) sumanene, (b) corannulene, (c) mono-IC, (d) ortho-di-IC, (e) para-di-IC, and (f) 1,2,4-tri-IC. Note that for visualization purposes the unit cells were doubled along the stacking direction in (c), (d), and (f). (A color version of this figure can be viewed online.)

176 B.-T. Wang et al. / CARBON 94 (2015) 174–180

conduction band) along the high-symmetry direction correspondingto the p-stacking of molecules. The bandwidth values are: 0.19(0.16) eV along the C� A direction for sumanene, 0.25 (0.30) eValong the Y � H direction and 0.28 (0.29) eV along the C� X direc-tion for mono-IC, 0.28 (0.07) eV along the C� Z direction forortho-di-IC, 0.15 (0.08) eV along the C� Z direction for para-di-IC,and 0.47 (0.34) eV along the C� Z direction for 1,2,4-tri-IC.Therefore, the band structure calculations suggest that all corannu-lene derivatives will exhibit anisotropic charge-transport propertiessimilarly to what was found experimentally in the case of sumanene.

The calculated electrical conductivity r at 300 K for the set ofsystems under consideration is shown in Figs. 5 and 6. Since thereare no available experimental data on the transport properties ofindenocorannulene derivatives, we computed the electrical con-ductivity for a range of charge carrier concentrations. To simulateelectron and hole doping, the position of the chemical potentialis shifted up and down relative to the bottom of the conductionband and the top of the valence band, respectively. For sumanene,the electrical conductivity is found to be highly anisotropic with adominant contribution along the z-axis which coincides with the

Table 1Experimental unit cell parameters (a, b, c, a, b, c) along with space groups and number of molecules in the conventional unit cell (N).

Compound Space group Unit cell parameters

a (Å) b (Å) c (Å) a b c N

Sumanene [48] R3c 16.642 16.642 7.724 90 120 90 6Corannulene [46] P21/c 13.156 11.671 16.293 90 102.17 90 8Mono-IC [41] P21/n 3.871 31.278 12.244 90 93.42 90 4Ortho-di-IC [41] Pnma 22.801 19.793 3.907 90 90 90 4Para-di-IC [41] Cmc21 26.018 9.256 7.691 90 90 90 41,2,4-tri-IC [41] Pmn21 17.238 14.184 4.197 90 90 90 2

Fig. 4. Electronic band structure and density of states for (a) sumanene, (b) corannulene, (c) mono-IC, (d) ortho-di-IC, (e) para-di-IC, and (f) 1,2,4-tri-IC. The zero of the energyin the figures is chosen as the middle of the calculated band gap that separates the bonding valence bands from the antibonding conduction bands. The density of states is inunits of states/(eV atom). The labels and coordinates of the high-symmetry k-path points in the Brillouin zone were obtained from Ref. [59].

B.-T. Wang et al. / CARBON 94 (2015) 174–180 177

molecules stacking direction (Fig. 3a). The estimated anisotropicratio varies from 10 to 15 for the electron-doped system for carrierconcentrations in the 1018 to 1021 cm�3 range. These values are invery good agreement with the experimental finding of a 9.2 aniso-tropic ratio for the electron mobility reported by Amaya et al. [44].In comparison, for corannulene, the electrical conductivity isalmost isotropic and an order of magnitude lower than that ofsumanene. This behavior is consistent with the lack of anybowl-to-bowl stacking arrangement in the crystal structure ofcorannulene (Fig. 3b).

The situation changes considerably in the case of indenocoran-nulene derivatives. The attachment of one or more indeno-groupsto the corannulene core leads to the formation of one-dimensionalcolumnar p-stacking of the bowls in a concave-to-convex fashionin their solid state structures (Fig. 3c–f). As a result, for mono-IC,para-di-IC, and 1,2,4-tri-IC crystals, the largest contribution tor/s is found along the stacking direction and only negligible contri-butions along the other two directions. Despite these similarities,however, there are noticeable differences in the magnitude of theelectrical conductivity due to the unique packing features that eachindividual crystal structure shows with respect to the orientationof the indeno-groups and the directions of the convex bowlsurfaces.

1,2,4-tri-IC, having three indeno-groups, has the largest surfacearea and the most effective packing with all bowls oriented in thesame direction in all stacks as shown in Fig. 3f. As one wouldexpect, 1,2,4-tri-IC indeed exhibits the best performance among

the corannulene derivatives investigated here and its electricalconductivity reaches 1.4 � 104 (X m fs)�1 and 1.1 � 104

(X m fs)�1 for hole and electron doping, respectively, at a carrierconcentration of 1021 cm�3. The larger conductivity valuesobtained under hole doping are consistent with both a largerDOS and a more disperse band at the top of the highest valenceband compared to the bottom of the lowest conduction band.These results suggest that 1,2,4-tri-IC crystals are expected to showa high anisotropic mobility comparable to (or even exceeding) thatof sumanene.

Para-di-IC has the most loosely packed crystal structure of thefour indenocorannulene family members and the p-bowls in thecolumns are significantly shifted with respect to one another.However, when viewed down the crystallographic c-axis, all bowlspoint in the same direction similarly to 1,2,4-tri-IC and a substan-tial overlap can still take place between the carbon p-surfaces ofthe molecules in the 1D stack (Fig. 3e). This latter aspect has animportant impact on the electrical conductivity which turns outto be about one-half and one-third of that of 1,2,4-tri-IC for thehole- and electron-doped systems, respectively. The difference inconductivity between hole and electron doping can be traced backto the almost twice larger bandwidth along the p-stacking direc-tion of the bowls at the top of the valence band compared to thebottom of the conduction band.

The crystal structure of mono-IC also displays a preferentialstacking of the p-conjugated bowl cores along one crystallographicaxis (a-axis) as shown in Fig. 3c. However, unlike the solid state

Fig. 5. The electrical conductivity r=s along the stacking direction as function ofhole concentration for sumanene (solid, black), mono-IC (short dash, blue), ortho-di-IC (dash dot, olive), para-di-IC (dash dot dot, cyan), and 1,2,4-tri-IC (short dot,magenta). For corannulene (dash, red), the electrical conductivity is averaged overthe three crystallographic directions. The inset shows the electrical conductivity forortho-di-IC along the stacking direction (dash dot, olive) and perpendicular tostacking along the length of the molecules (short dash dot, olive). (A color version ofthis figure can be viewed online.)

Fig. 6. The electrical conductivity r=s along the stacking direction as function ofelectron concentration for sumanene (solid, black), mono-IC (short dash, blue),ortho-di-IC (dash dot, olive), para-di-IC (dash dot dot, cyan), and 1,2,4-tri-IC (shortdot, magenta). For corannulene (dash, red), the electrical conductivity is averagedover the three crystallographic directions. The inset shows the electrical conduc-tivity for ortho-di-IC along the stacking direction (dash dot, olive) and perpendic-ular to stacking along the length of the molecules (short dash dot, olive). (A colorversion of this figure can be viewed online.)

178 B.-T. Wang et al. / CARBON 94 (2015) 174–180

structures of 1,2,4-tri-IC and para-di-IC, the molecules are arrangedsuch that each column has one neighbor with the same and oneneighbor with the opposite direction of the bowls. In terms of chargetransport properties, the electrical conductivity of mono-IC is pre-dicted to be about one-quarter and three-quarters of that of1,2,4-tri-IC for the hole- and electron-doped systems, roughly theopposite to what is found for para-di-IC.

Finally, the picture considerably changes when ortho-di-IC crys-tals are considered. Addition of two indeno-groups in theortho-positions on the corannulene rim induces a clear alignmentof the bowls along the c-axis (Fig. 3d), similar to mono-IC and1,2,4-tri-IC. However, the solid-state packing of columns in thetwo directions perpendicular to stacking is completely unique tothis derivative. Viewed along the a-axis, the two indeno-groupspoint in the same direction (Fig. 2d), but the bowls alternate direc-tion in every other column (Fig. 3d). When viewed along the b-axis,on the other hand, the curved surfaces of all carbon bowls face inthe same direction (Fig. 3d), while the two indeno-groups alternatetheir orientation along this respective axis (Fig. 2d). Ortho-di-ICalso displays a distinctive behavior in terms of transport propertiesnot only when compared to the other three corannulene deriva-tives, but also under hole and electron doping. For thehole-doped system, the largest contribution to conductivity is

Fig. 7. The Seebeck coefficient as a function of hole concentration at 300 K forsumanene (solid, black), corannulene (dash, red), mono-IC (short dash, blue), ortho-di-IC (dash dot, olive), para-di-IC (dash dot dot, cyan), and 1,2,4-tri-IC (short dot,magenta). The calculated Seebeck coefficients are averaged over the three crystal-lographic directions. (A color version of this figure can be viewed online.)

detected along the stacking direction but there is also a noticeablecontribution along the a-axis coinciding with the direction alongthe length of the molecules (see inset Fig. 5). For theelectron-doped system, the direction of the largest conductivitycorresponds, in fact, with that of the a-axis, while the conductivityalong the stacking direction is almost a factor of three smaller (seeinset Fig. 6). The relatively flat bands along the stacking direction ofthe bowls at the bottom of the conduction band cause a very lowelectrical conductivity along the c-axis.

Based on the electrical conductivity results, it can be concludedthat all four indenocorannulene derivatives show significantlyimproved transport properties compared to the parent corannu-lene. In particular, the molecular building motif of 1,2,4-tri-IC exhi-bits the largest p-conjugated surface and enough spatial overlap toresult in a significant intermolecular coupling, and, thus, enhancedcharge-carrier transport, along the p-stacking direction. In addi-tion, 1,2,4-tri-IC could be considered a promising candidate fororganic electronic devices since its performance should be compa-rable for electron doping and likely surpass for hole doping that ofsumanene crystals, assuming the same carrier lifetimes and forcarrier concentrations in the limits of 1018–1021 cm�3.

We next evaluate the dependence of the Seebeck coefficient S asa function of the carrier concentration for hole and electron doping

Fig. 8. The Seebeck coefficient as a function of electron concentration at 300 K forsumanene (solid, black), corannulene (dash, red), mono-IC (short dash, blue), ortho-di-IC (dash dot, olive), para-di-IC (dash dot dot, cyan), and 1,2,4-tri-IC (short dot,magenta). The calculated Seebeck coefficients are averaged over the three crystal-lographic directions. (A color version of this figure can be viewed online.)

B.-T. Wang et al. / CARBON 94 (2015) 174–180 179

in all six systems at room temperature. Unlike the electrical con-ductivity which is strongly dependent on the transport direction,the Seebeck coefficient is almost isotropic. For hole doping, the cal-culated S decreases logarithmically with increasing carrier concen-tration as the position of the chemical potential moves down intothe valence band. From Fig. 7, we can see that the hole Seebeckcoefficient of corannulene is the largest in magnitude, while thatof para-di-IC is the smallest. This can be understood from the dif-ference in the density of states between the two structures sincethe system with the most rapidly changing DOS (sharper distribu-tion) is expected to have the largest Seebeck coefficient [60].Indeed, in comparison to para-di-IC, corannulene exhibits a muchsharper peak in the DOS near the top of the valence band. This isin accord with our earlier observation that in corannulene theenergy bands are almost flat over the entire Brillouin zone closelyresembling molecular-like states. The Seebeck coefficients for theother four systems fall in between those of corannulene andpara-di-IC and the curves lie almost on top of each other. Thisreflects the close similarity in their DOS dependence near theVBM. Overall, the estimated values for S are found to be in thesame range with measured hole Seebeck coefficients in planarhydrocarbons near room temperature, namely, thin films of pen-tacene and single crystals of rubrene [61].

The situation is almost identical for the electron doped systemsas shown in Fig. 8. The Seebeck coefficients follow a similar trendas for hole doping and the absolute value of S increases logarithmi-cally with decreasing carrier concentration. As before, there are nosignificant differences in S among the six systems and, overall, thevalues for S are only slightly smaller than those of the hole dopedcounterparts. The relatively large Seebeck coefficient and the pres-ence of both flat and dispersed bands around the Fermi level indi-cate that some of these organic semiconductors could potentiallyserve as active materials in thermoelectric devices.

4. Conclusions

In this work, we explore the relationship between the solid-statepacking and the charge-carrier transport properties in the extendedfamily of indenocorannulene molecular crystals. Usingfirst-principles calculations coupled with the Boltzmann transporttheory, we find that all four corannulene derivatives investigatedhere show significantly improved electrical conductivity comparedto the parent corannulene. In particular, 1,2,4-tri-IC is identified asa promising active material for organic electronic devices exhibitinga pronounced anisotropy in the electrical conductivity along thestacking direction of the p-bowls similar to the well-known suma-nene. The charge conductivity of 1,2,4-tri-IC is predicted to be com-parable for electron doping and likely surpass for hole doping thevalues achievable in sumanene, assuming the same carrier lifetimes.Further modification of the corannulene derivatives through incor-poration of functional groups as well as side chain engineering canlead to larger p–p overlap and extended p-network which shouldbe beneficial to the charge transport. Finally, the new class ofcarbon-rich bowl-shaped polyaromatic hydrocarbons should offerunique and yet unexplored opportunities in identifying organicsuperconductors with a high transition temperature since theirstructures constitute a direct link between zero-dimensionalfullerenes and two-dimensional planar hydrocarbons, and that canbring novel synergistic qualities.

Acknowledgment

This work was supported by SUNY RF (4E NoE).

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