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Solid State Sciences 28 (2014) 41e46

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Solid State Sciences

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Structures and electronic states of fluorinated graphene

Hiroto Tachikawa*, Tetsuji IyamaDivision of Materials Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan

a r t i c l e i n f o

Article history:Received 10 June 2013Received in revised form15 November 2013Accepted 16 December 2013Available online 24 December 2013

Keywords:Carbon nano-materialDensity functional theoryFluorinated grapheneFunctionalized graphene

* Corresponding author. Fax: þ81 11 706 7897.E-mail address: hiroto@eng.hokudai.ac.jp (H. Tach

1293-2558/$ e see front matter � 2013 Elsevier Mashttp://dx.doi.org/10.1016/j.solidstatesciences.2013.12.0

a b s t r a c t

Functionalized graphenes have been utilized as electronic devices and energy materials. In the presentpaper, the effects of fluorine-termination of graphene edge on the structures and electronic statesof graphene have been investigated by means of density functional theory (DFT) method. It wasfound that the ionization potential (Ip) and electron affinity of graphene (EA) are blue-shifted by the F-substitution. On the other hand, the excitation energy was red-shifted. The drastic change showsa possibility as electronic devices such as field-effect transistors. The drastic change of electronicstates caused by the F-substitution of graphene edge was discussed on the basis of the theoreticalresults.

� 2013 Elsevier Masson SAS. All rights reserved.

1. Introduction

Graphene has a possibility to interact with several species on thesurface and in the edge regions. Surface-modified graphene isknown as functionalized graphenes, and the electronic states ofgraphene are variously changed by the functional group added tothe surface [1e3]. Especially, the graphene has a high carriermobility [4]. Hence, these characters have been applied to theelectronic devices such as field-effect transistors. The edge-modified graphene is one of the functionalized graphenes. How-ever, the effect of edge-modification on the electronic states ofgraphene is scarcely known.

In the present paper, the effects of fluorine-termination of gra-phene edge (F-substitution) on the structures and electronic statesof graphene are investigated by means of density functional theory(DFT) method. We focus our attention mainly on the effects to theionization potential (Ip), electron affinity of graphene (EA), andexcitation energies of graphene.

Fluorine-modifies graphenes have received much attentionbecause the electronic structure is drastically changed by thefluorination. Fluorination of graphene [5e18] proceeds easily by achemical reaction and a mechanistic treatment. Robinson et al. [10]reported that a reaction of graphene with XeF2 leads to partial orfull fluorination of graphene and showed that the properties ofgraphene, such as the band gap, can vary considerably as a function

ikawa).

son SAS. All rights reserved.14

of the degree of fluorination. The reaction of graphene surface withF was found to significantly depend on reaction conditions; only25% coverage was observed when a single graphene surface isexposed to XeF2, but full (100%) coverage emerged when bothsurfaces were allowed to react with XeF2.

Delabarre et al. used fluorinated graphite as the cathode inprimary lithium batteries [19]. The higher capacity values wereachieved for low temperature fluorinated graphite. Halogenation ofcarbon materials is possible to open a new materials chemistry.However, the effects of halogen substitution of edge region ofgraphene on the electronic structure of the graphene are not clearlyunderstood.

In previous papers [20,21], we investigated diffusion dynamicsof lithium ion on the carbon materials such as the fluorinatedgraphene surface by means of direct ab-initio molecular dynamics(AIMD) method. We showed that the diffusion behavior of lithiumion on the F-graphene is significantly different from that on anormal graphene. In this work, the DFT method was applied to theF-graphene system to elucidate the effects of F-substitution on thegraphene.

2. Method of calculation

The sizes of fluorinated graphene used in the present studywerechosen as n ¼ 7, 14, 19, 29 and 37, where n means number ofbenzene ring in each graphene. The geometry of the fluorinatedgraphene was fully optimized at the B3LYP/6-31G(d) level. Thestructures of F-graphene including one lithium ion are illustrated in

Table 1Optimized geometrical parameters of F-GR’s calculated at the B3LYP/6-31G(d) level.Average CeF and CeC distances (in �A) are given.

n <r(CeC)> <r(CeF)>

7 1.429 1.33814 1.422 1.33819 1.421 1.33929 1.423 1.33837 1.425 1.339

H. Tachikawa, T. Iyama / Solid State Sciences 28 (2014) 41e4642

Fig. 1. The carbon atoms in the edge region are terminated byfluorine atoms in the F-graphene.

Atomic charges of carbon and fluorine atoms of F-GR werecalculated by means of natural population analysis (NPA). Thestructures and electronic states of graphenes were calculated bymeans of DFT method at the B3LYP/6-31G(d) level using Gaussian09 program package [22]. The excitation energy and band gapwere calculated by means of time dependent (TD) DFT method.The electronic states of all molecules were obtained by naturalpopulation analysis (NPA) and natural bond orbital (NBO)methods at the B3LYP/6-31G(d) level. These levels give a reason-able electronic state of the graphene as shown in previous cal-culations [23e26].

Fig. 1. Structures of fluorinated graphenes (F-GR) with n ¼ 7, 14, 19, 29, and 37.

Fig. 2. Ionization potentials (Ip in eV) and electron affinities (EA in eV) of F-GR plottedas a function of n.

Fig. 4. Excitation energies of F-GR and H-GR plotted as a function of size of graphene(n). The values were calculated by TDDFT (B3LYP/6-31G(d)) method.

H. Tachikawa, T. Iyama / Solid State Sciences 28 (2014) 41e46 43

3. Results

3.1. Structures of F-graphene

The optimization structures of F-GR’s for n ¼ 7, 14, 19, 29 and 37were illustrated in Fig. 1. Hereafter, the fluorinated and normal

Fig. 3. NPA atomic charges of carbon and fluorine atoms of F-GR (n ¼ 37). The valuesare plotted as a function of center-of-mass distance of atom (Rcm). The atomic chargesare calculated by natural population analysis (NPA) at the B3LYP/6-31G(d) level. Lowerpanel shows an illustration of carbon and fluorine atoms of F-GR, and definition of Rcm.

hydrogen terminated graphenes are expressed as F-GR and H-GR,respectively. The average CeF and CeC distances in each graphenesize are given in Table 1. The average CeC distance was calculatedonly for the central region of F-GR. All the F-GR’s shows a pureplanar structure. The average CeF distances are 1.338�A (n ¼ 7) and1.339 �A (n ¼ 37), indicating that the CeF bond length is indepen-dent on the graphene size (n). The average CeC distances are1.338 �A (n ¼ 7) and 1.339�A (n ¼ 37). The CeC distances are almostconstant in all GR’s.

3.2. Ionization potential (Ip) and electron affinity (EA)

The vertical ionization potential (Ip) and electron affinity (EA) ofF-GR are plotted in Fig. 2 as a function of n. Ip and EA are defined asfollows;

Ip ¼ E�F� GRþ

�� EðF� GRÞ

Fig. 5. Orbital energies of F-GR and H-GR. DE mean HOMOeLUMO gaps.

Fig. 6. Spatial distribution of frontier orbitals of F-GR and H-GR.

H. Tachikawa, T. Iyama / Solid State Sciences 28 (2014) 41e4644

Table 2Excitation energies (Eex in eV) and configuration state functions (CSFs) of F-GRcalculated at the TD-DFT(B3LYP)/6-31G(d) level.

State CSF and CI vector Eex/eV

1B2u þ0.512f(HOMO � 1 / LUMO) �0.512f(HOMO / LUMO þ 1) 2.111B1u þ0.494f(HOMO / LUMO) þ0.494f(HOMO � 1 / LUMO þ 1) 2.261B2u þ0.512f(HOMO / LUMO þ 1) þ0.512f(HOMO � 1 / LUMO) 2.741B2u þ0.425f(HOMO � 1 / LUMO þ 1) �0.425f(HOMO / LUMO) 2.74

Fig. 7. Model of change of electronic states of graphene by F-substitution.

H. Tachikawa, T. Iyama / Solid State Sciences 28 (2014) 41e46 45

and

EA ¼ E�F� GR�

�� EðF� GRÞ;

where, E(F-GR) means total energy of F-GR at the stable point. E(F-GRþ) and E(F-GR�) are the energies at the vertical ionization andelectron capture points from F-GR.

Ip’s of F-GR decrease gradually as size of F-GR is increased:Ip(n¼ 7) ¼ 7.74 eV and Ip (n¼ 37)¼ 6.32 eV. On the other hand, EAincreases with increasing n: EA(n ¼ 7) ¼ 1.16 eV andEA(n¼ 37)¼ 2.54 eV. For comparison, Ip and EA of H-GR are plottedin Fig. 2 as dashed lines. Both Ip and EA are blue-shifted by the F-substitution of graphene. The energy shifts of Ip and EA caused bythe F-substitution are þ0.89 eV and þ0.97 � (þ1.13) eV,respectively.

3.3. Electronic states of the F-GR

The NPA atomic charges of F-GR with n ¼ 37 are given in Fig. 3.The NPA charges are plotted as a function of Rcm, where Rcm isdefined by a distance of each atom from the center-of-mass of F-GR.The atoms on the surface can be classified to four groups: carbonatoms in bulk region (bulk carbon), in the inner edge region (baycarbon), in the outer edge region (CeF carbon), and the fluorineatom in edge region (F atom).

The charge of carbon atom in the bulk region is almost zero,which is close to that of H-GR. The fluorine atom has negativecharge (�0.32). The carbon atom binding to the F atom has largerpositive charges (þ0.38to þ0.48). These feature indicates that alarge dipole moment caused by C(dþ)eF(d�) is formed locally inthe edge of F-GR. The charge of carbon atom in the bay region is aslight negative (�0.16) because the bay carbon is located in two CeFcarbon atoms. Thus, the F-GR has a specific electronic state, inparticular, the edge region of F-GR.

3.4. Excitation energy of F-GR

To elucidate the effects of F-substitution on the excitation en-ergy of graphene, TDDFTcalculations were carried out for F-GR. Tenexcited states were solved. The results were plotted in Fig. 4 as afunction of n. The excitation energy decreases with increasing n.The first excitation energy of H-GR is plotted by a dashed line forcomparison. It was found that the first excitation energy is uni-formly red-shifted by the F-substitution of H-GR: the excitationenergies at n ¼ 37 were calculated to be 1.67 eV for H-GR and1.58 eV for F-GR. The energy shift was calculated to be �0.09 eV inn ¼ 37.

3.5. Origin of the shift of excitation energy

The orbital energies of F-GR and H-GR are given in Fig. 5. Theoccupied molecular orbital (HOMO) and lowest unoccupied mo-lecular orbital (LUMO) of H-GR lay at �4.93 and �2.11 eV, respec-tively. In case of F-GR, HOMO and LUMO are �5.80 and �3.14 eV,respectively. The energy levels of HOMO and LUMO were signifi-cantly decreased by the F-substitution. The lowering of energy levelof LUMO was larger than that of HOMO. The HOMOeLUMO gaps inH-GR and F-GR were calculated to be DE ¼ 2.82 and 2.66 eV,respectively.

To elucidate the electronic states of F-GR inmore details, the TD-DFT calculation was carried out at the B3LYP/6-31G(d) level. Thespatial distributions of molecular orbitals around HOMO are illus-trated in Fig. 6, and configuration state functions (CSFs) contrib-uting to the electronic transition are given in Table 2. The spatial

distributions of HOMO and LUMO of F-GR are largely different fromthose of H-GR. The orbital of F-GR is widely distributed over the Fatoms in the edge region. On the other hand, the orbital is onlydistributed on the carbon plane. This difference is an origin of thered-shift of F-GR. The lowest excitation is assigned to aHOMO � 1 / LUMO transition (1Ag / 1B2u) and the excitationenergy is 2.11 eV. The strong intensity band is aHOMO / LUMO þ 1 transition (1Ag / 1B2u) at Eex ¼ 2.74 eV.

4. Discussion

In the present study, the effects of F atom-termination of gra-phene edge on the electronic states of graphene have been inves-tigated by means of DFT method. The Ip and EA increased by the F-substitution. On the other hand, the excitation energy was red-shifted.

As a summary of the present study, a schematic illustration ofthe effect of F-substitution on the electronic states of graphene isgiven in Fig. 7. This is a simple squirewell potential model. S1 and S2mean square measures depend on the size of graphene. Bothheights of S1 and S2 show the energy levels of pi-electron in H-GRand F-GR, respectively. These levels are approximately close to theenergy level of HOMO.

After the F-substitution, the energy level of S1 is changed to thatof S2 because the F atom attracts electron density of graphenesurface. This decrease of energy causes the increase of ionizationpotential of graphene: Ip(F-GR) > Ip(H-GR). The decrease of theenergy level of S1 also causes the increase of EA because capacity ofelectron increases with decreasing the level. The capacity of elec-tron is proportional to volume V ¼ S1[(Ip(F-GR) � Ip(H-GR))]. Thus,the simple model can reasonably explain the results.

Fig. 8. Model of the ion confinement effect on fluorinated graphene.

H. Tachikawa, T. Iyama / Solid State Sciences 28 (2014) 41e4646

A schematic illustration of diffusion model of positive metal ionon the F-graphene is given in Fig. 8. As shown in Section 3.3, theedge region of F-graphene is polarized as CþeF� because of elec-tron transfer from carbon to fluorine atoms. The positive chargedmetal ion can move freely the bulk region of F-graphene. However,the movement of the ion will be strongly restricted in the edgeregion because the ion feels potential barrier generated by thepolarized CeF bond. From this ion confinement effect, the positivemetal ion is trapped in the bulk region of F-graphene.

Acknowledgments

This work was partially supported by the Suhara memoriamfoundation. The author acknowledges partial support from a Grant-in-Aid for Scientific Research (C) from the Japan Society for thePromotion of Science (JSPS) (Grant Number 24550001). This workis partially supported by a Grant-in-Aid for Scientific Research onInnovation Areas “Evolution of Molecules in Space” (Grant Number2510800413).

References

[1] Y. Sun, S.-B. Yang, L.-P. Lv, I. Lieberwirth, L.-C. Zhang, C.-X. Ding, C.-H. Chen,J. Power Sources 241 (2013) 168.

[2] Y. Zhang, Y. Zhao, A. Konarov, D. Gosselink, H.G. Soboleski, P. Chen, J. PowerSources 241 (2013) 517.

[3] B. Kang, G. Ceder, Nature 458 (2009) 190.[4] Y.-M. Lin, C. Dimitrakopoulos, K.A. Jenkins, D.B. Farmer, H.-Y. Chiu, A. Grill,

Ph. Avouris, Science 327 (2010) 662.[5] S. Tang, S. Zhang, J. Phys. Chem. C 115 (2011) 16644.[6] H. Yang, M. Chen, H. Zhou, C. Qiu, L. Hu, F. Yu, W. Chu, S. Sun, L. Sun, J. Phys.

Chem. C 115 (2011) 16844.[7] S. Osuna, M. Torrent-Sucarrat, M. Solà, P. Geerlings, C.P. Ewels, G. Van Lier,

J. Phys. Chem. C 114 (2010) 3340.[8] D.W. Boukhvalov, Phys. E 43 (2010) 199.[9] S.-H. Cheng, K. Zou, F. Okino, H.R. Gutierrez, A. Gupta, N. Shen, P.C. Eklund,

J.O. Sofo, J. Zhu, Phys. Rev. B 81 (2010) 205435e205441.[10] J.T. Robinson, J.S. Burgess, C.E. Junkermeier, S.C. Badescu, T.L. Reinecke,

F.K. Perkins, M.K. Zalalutdniov, J.W. Baldwin, J.C. Culbertson, P.E. Sheehan,E.S. Snow, Nano Lett. 10 (2010) 3001.

[11] R. Stine, J.W. Ciszek, D.E. Barlow, W.-K. Lee, J.T. Robinson, P.E. Sheehan,Langmuir 28 (2012) 7957.

[12] O. Leenaerts, H. Peelaers, A.D. Hernandez-Nieves, B. Partoens, F.M. Peeters,Phys. Rev. B 82 (2010) 195436e195441.

[13] F. Withers, M. Dubois, A.K. Savchenko, Phys. Rev. B 82 (2010) 073403e073411.

[14] M. Klintenberg, S. Lebegue, M.I. Katsnelson, O. Eriksson, Phys. Rev. B 81 (2010)085433e085441.

[15] S.B. Bon, L. Valentini, R. Verdejo, J.L. Garcia Fierro, L. Peponi, M.A. Lopez-Manchado, J.M. Kenny, Plasma Chem. Mater. 21 (2009) 3433.

[16] S.-S. Lee, S.-W. Jang, K. Park, E.C. Jang, J.-Y. Kim, D. Neuhauser, S. Lee, J. Phys.Chem. C 117 (2013) 5407.

[17] A. Ueta, Y. Tanimura, O.V. Prezhdo, J. Phys. Chem. Lett. 3 (2012) 246.[18] C.-H. Hu, P. Zhang, H.-Y. Liu, S.-Q. Wu, Y. Yang, Z.-Z. Zhu, J. Phys. Chem. C 117

(2013) 3572.[19] C. Delabarre, M. Dubois, J. Giraudet, K. Guerin, A. Hamwi, Carbon 44 (2006)

2543.[20] H. Tachikawa, J. Phys. Chem. C 112 (2008) 10193.[21] H. Tachikawa, J. Phys. Chem. C 115 (2011) 20406.[22] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb,

J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson,H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino,G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda,J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven,J.A. Montgomery Jr., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers,K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari,A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam,M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts,R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski,R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador,J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz,J. Cioslowski, D.J. Fox, Gaussian 09, Revision A.1, Gaussian, Inc., WallingfordCT, 2009.

[23] H. Tachikawa, A. Shimizu, J. Phys. Chem. B 110 (2006) 20445.[24] H. Tachikawa, J. Phys. Chem. C 111 (2007) 13087.[25] H. Tachikawa, J. Phys. Chem. A 114 (2010) 4951.[26] H. Tachikawa, Phys. Chem. Chem. Phys. 13 (2011) 11206.