Functionalizing Single- and Multi-layer Graphene with Br and Br2

J. Phys. Chem. C 2010, 114, 14939–14945

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Functionalizing Single- and Multi-layer Graphene with Br and Br2 Xiaofeng Fan,*,† Lei Liu,*,† Jer-Lai Kuo,†,‡ and Zexiang Shen† DiVision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological UniVersity, Singapore, 637371, Singapore, and Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, 10617, Taiwan ReceiVed: May 7, 2010; ReVised Manuscript ReceiVed: July 21, 2010

The structural and electronic properties of Br2/Br adsorption and intercalation of single-layer graphene (SLG) and multi-layer graphene (MLG) are studied by density-functional theory. As a result of charge transfer, the Br atom is found to be stable as adsorbed on the vertex or near bridge sites of graphene whereas the Br2 molecule will be more stable when adsorbed perpendicularly on graphene. Because of the interactions between Br2 molecules, the stable configurations of Br2 on graphene or intercalated in MLG are parallel to graphene. With the analysis of charge difference, the experimental observation that the lowest stage of Br2 intercalated graphite is the stage 2 compound is ascribed to the effect of localized dipoles on graphene induced by Br2. Although only slightly disturbing the orbitals of graphene atoms, the existence of Br2 molecules or Br atoms will still affect the electronic structures of both materials. As adsorbed on the single surface of graphene, Br2 will open its bandgap at the K (K′) point. While present on both surfaces, Br2 molecules will induce a much larger bandgap of graphene with the Fermi level shifted down into the valence bands. If Br atoms are absorbed on graphene, the significant amount of charge will transfer from graphene to Br atoms because of the strong electronegativity of Br. More importantly, the electronic properties of SLG/MLG with the absorbed Br2 molecules can be controlled by the ultraviolet light that decomposes the Br2 on SLG/MLG. Introduction Graphene, a monolayer of carbon atoms with honeycomb lattice, has attracted enormous attention because of its extremely high mobility of carriers and other fascinating physical properties,1-6 such as abnormal quantum Hall effects7,8 and massless Dirac fermions.9 In particular, the high mobility of electrical carriers in graphene may lead to the next generation of carbon-based nanoelectronics.1,10-16 Some prototype graphenebased devices have been fabricated successfully.17-22 However, for the wider electronic-device applications, such as as fieldeffect transistors, the control of type and concentration of carriers in graphene with an opened bandgap will be critical.23 The modulation of band structure has spurred an intense scientific interest, and many methods have been tested to control the electronic behaviors of graphene, including electrostatic gating,24,25 bilayer graphene,11,12,15,26 graphene-substrate interaction,27-29 contact with metals,30 hydrogenation,31 and intercalation/interaction with chemical molecules.17,18,32-35 Furthermore, the nearly transparent optical properties of this semimetal membrane make it a good candidate material for the optoelectronic devices, for example, as a solar cell.19 As a 2D membrane, the whole surface of graphene can be used to interact with metal atoms or chemical molecules, and this may functionalize graphene further with the desirable electronic properties.36,37 Through chemical absorption, the Fermi level of graphene can be shifted because of the chargetransfer process, and the transport of its charge carriers can be controlled accordingly.18 Without introducing substitutional impurities to disrupt the conjugated network, the adsorptioninduced chemical doping would be an ideal way to scissor the * Corresponding authors. E-mail: [email protected], [email protected]. † Nanyang Technological University. ‡ Academia Sinica.

band structure and control the π-electron conduction of graphene.33 It has been known that intercalating alkaline metals into MLG can take up the Fermi level and result in electron doping.17 On the other hand, with the intercalation/absorption of halogen molecules in MLG or on SLG, hole doping with opened gap is expected to be obtained.33 The construction of intercalation compounds usually needs a host material with highly anisotropic layered structures.38 In the early study of intercalation compounds, graphite, with weak interplanar interactions, has been considered as a ideal host for the insertion of atomic or molecular layers.38 Actually, the notion of doping MLG or SLG with chemical absorption is the extension of the concept of intercalated graphite compounds. Halogen molecules, such as Cl2, Br2, and I2, are considered to be more electronegative than sp2-hybridized carbon, and they will induce a positive doping by charge transfer. For example, I2 can be absorbed on fullerenes39 and carbon nanotubes.40,41 Charge transfer between Br2 and double-walled carbon nanotube has been confirmed.42-44 I3- anions can be obtained by induced iodide anions on the carbon substrate. However, Br2 is the only diatomic homopolar halogen molecule that intercalates readily into MLG/graphite.38 Therefore, the clear understanding of the structural and electronic properties of SLG/MLG intercalated or absorbed with Br atoms or Br2 molecules would be helpful to explore a new way to chemically functionalize graphene layers. In this work, we report our systematic first-principles investigations on the absorption/insertion effect of SLG/MLG with Br atoms or Br2 molecules. With the analysis of electronic structure, charge transfer, and redistribution of charges of graphene, we suggest that, with the activation of ultraviolet light, the conversion between Br atoms and Br2 molecules adsorbed on graphene will result in the effective change of electronic properties of graphene.

10.1021/jp1041537  2010 American Chemical Society Published on Web 08/18/2010

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Figure 1. Schematic representation of six high-symmetry adsorption sites for Br2 molecules on a fragment of graphene. vertex site (A), center site (B), and bridge site (C) for the models with molecular axes perpendicular to the graphene plane. Center to center (D), vertex to vertex (E), and bridge to bridge (F) for the models with molecular axes parallel to the graphene plane.

Structures and Method 1. Model Structures. To simulate the coupling between Br atom/molecule and graphene, the supercell approach is used to build the model structures. Three supercells containing 8, 16, and 32 carbon atoms per single Br2/Br are considered to test the effects of the interaction between Br2 molecules absorbed on graphene. In order to avoid the spurious vertical coupling between graphene layers, the vacuum separation in the model structures is set to more than 10 Å. For the supercells with 8 and 32 carbon atoms, the graphene layers are constructed from hexagonal 2 × 2 and 4 × 4 unit cells, respectively. The supercell of 16 atoms is constructed by a rectangular cell with the lattice parameters 2a and 2
3a, where the lattice constant, a, is that of the primitive cell for graphene. Br2 molecules are considered either perpendicular or parallel to the graphene plane. For both perpendicular-to-graphene and parallel-to-graphene models, six possible configurations with high-symmetry adsorption sites are simulated as shown in Figure 1. 2. Calculation Details. In the present work, the interaction between Br2/Br and the graphene layers is simulated with the plane-wave package of VASP.45 The total energy and the electronic density of the systems are calculated on the basis of the density-functional theory (DFT) within the local-density approximation (LDA) for exchange and correlation.46 Ultrasoft pseudopotentials and the plane-wave basis with a kinetic energy cutoff of 550 eV are employed, and all the model structures are fully relaxed. The proper k-point mesh under tetrahedron scheme for Brillouin-zone integration is tested to ensure that the total energy converged to 1 meV/atom. In the calculation of the hexagonal 4 × 4 unit cells, a 4 × 4 × 1 Monkhorst-Pack k-point mesh is used for the structural relaxation, and a 6 × 6 × 1 mesh is used for the calculation of electronic structure. After relaxation, a lattice constant for graphene of a ) 2.44 Å is obtained, which is near the experimental value (2.46 Å) at low temperature. For the distance between two graphene planes, the obtained parameter c ) 6.73 Å is also very close to the experimental value of 6.71 Å. The accuracy of the calculated lattice parameter c of graphite suggests that LDA may handle the weak interaction between graphene layers as an accidental case. This could be attributed to the counteraction between the long-range exchange-correlation effect and the van der Waals interactions which are largely neglected under LDA. It is expected that the interaction between Br2 molecules and graphene planes can be simulated appropriately with LDA, because the scale of such an interaction is between the chemical bonding and the van der Waals force due to the charge transfer and redistribution processes (see the next subsection for details).

Fan et al.

Figure 2. Potential-energy curves for Br2 molecule as a function of the distance between Br atoms (shown by black squares in panel A). Adsorption energies of Br atoms on graphene as a function of the separation between graphene and Br at different sites, including center, bridge, and vertex sites (A). Potential-energy curves of Br atom adsorbed on graphene (B), following two paths (from center to vertex site shown by red circles and from center to bridge site shown by black squares), with the center site defined as the zero position.

Results and Discussions 1. Adsorption of Br/Br2 on Graphene. The bond length of an isolated Br2 molecule is calculated to be 2.27 Å, which agrees with the experimental value of 2.283 Å within a 2% error.47 The potential-energy curve of Br2 molecules is plotted in Figure 2A, which indicates that its binding energy is about 3 eV. The interaction between Br atoms can be neglected because their interdistances are more than 5.5 Å. A supercell of one Br atom or Br2 molecule per 32 carbon atoms is constructed, where the distances between the adjacent Br atoms or Br2 molecules are about 9.8 Å and 7.7 Å, respectively. Such separations are large enough to eliminate the interaction between Br atoms or Br2 molecules. Three possible configurations, shown in the inset of Figure 2A, are selected for simulating the interaction of Br on graphene at high-symmetry positions, where the Br atom is adsorbed on the hexagonal center, the midpoint of a carboncarbon bond (bridge site), or a carbon atom (vertex site). The energy curves of the interaction between a Br atom and the graphene along the z direction for the three cases are plotted in Figure 2A. It is found that the binding energies of the three absorbed sites are almost the same, about 400 meV. The curves achieve a minimum at about 2.9 Å. For separations larger than this value, the energy rises and reaches its asymptotic value at 6.5 Å. Therefore, the interaction between Br atom and graphene is strong and has exceeded the limit of the van der Waals force between graphene layers. To study the absorption of Br on a graphene plane, we simulate the potential-energy curves along two paths: one is from the center site to the vertex site, and the other is from the center site to the bridge site. In order to obtain the binding energy of each site in the path, the Br atoms are free to move along the z direction only in the optimization process. As shown in Figure 2B, the energy maximum and minimum are located at the hexagonal center and the vertex, respectively, with an energy difference of about 35 meV. When following the path from center site to bridge site, the energy minimum is near the bridge site. Hence, at room temperature, the Br atoms can move easily along the edge of the hexagonal benzene on graphene. This can be understood by the facts that the pz π orbitals of graphene distribute mainly along the localized benzene circle, and the charge is transferred from graphene into the emptied pz orbital of Br atom after absorption. Because the binding energy of Br2 molecules are rather high, the interaction between Br atoms and graphene will not

Functionalizing Single- and Multi-layer Graphene with Br and Br2

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TABLE 1: Binding Energy (∆E), Bond Length (BL) of Br2 Molecule, and Distance (∆H) between Br2 and Graphene Plane Given for the Six Configurationsa perpendicular-to-graphene ∆E (meV) BL (Å) ∆H (Å)

parallel-to-graphene

A

B

C

D

E

F

460 2.309 2.80

210 2.281 3.011

311 2.305 2.809

213 2.268 3.325

183 2.270 3.416

177 2.270 3.416

a For the molecular axis perpendicular to the graphene plane, the three sites considered are vertex site (A), center site (B), and bridge site (C). For the molecular axis parallel to the graphene plane, the three sites considered are center to center (D), vertex to vertex (E), and bridge to bridge (F).

decompose the Br2 molecules, and Br2 will be the stable state as absorbed on graphene. In order to study the stability of Br2 molecules absorbed on graphene, six possible configurations are analyzed by considering that the bond length of the Br2 molecule is close to the interdistance of the hexagonal centers in graphene. As shown in Figure 1, configurations A, B, and C belong to the perpendicular-to-graphene models, and configurations D, E, and F belong to the parallel-to-graphene models. After all atomic positions in the supercells are fully relaxed, the stable structure of each configuration can be obtained, and the structural properties of the six configurations are tabulated in Table 1. It is found that the distances from the Br2 molecule to the graphene plane in configurations of A, B, and C are smaller than those in configurations D, E, and F. In the three parallel-to-graphene models, the bond lengths of Br2 molecules are found to be almost identical to that of an isolated Br2 molecule, and those of three perpendicular-to-graphene configurations are found to be larger than that of an isolated Br2. The binding energies of Br2 molecules to graphene in configurations A and C are larger than those in configurations B, D, E, and F. This can be understood by considering the larger amount of charge transferred between Br2 and graphene in configurations A and C. The surplus charge from graphene will occupy the empty bromine antibonding state of ppσ*. As a result, the bromine bond strength will be weakened, and the bond length will be elongated. This agrees with the observation by Jhi et al. that the extra electrons transferred from carbon can result in the redshift of the Br2 stretching vibration frequency.44 In fact, from the change of bond length, we can deduce that the amount of charge from carbon to bromine decreases quickly as their interdistance increases. Moreover, the fact that the binding energy of configuration D is larger than that of configurations E and F may indicate that bromine atoms of configuration D are located at the energy canyon connecting two hexagonal centers of graphene. In order to study the interaction between Br2 and graphene, the interaction energy curves of four configurations are analyzed as plotted in Figure 3A. In these calculations, the bond length of the Br2 is fixed at 2.27 Å, that is, the bond length of the free molecule. The calculations show that, for all the four proposed models, the energy curves have reached their asymptotic values at a distance of 6.5 Å. The curves of the perpendicular-tographene configurations of A, B, and C merge rapidly with each other and become indistinguishable for a Br2-graphene separation of about 4.5 Å, whereas the curve of configuration D has a relatively slow asymptotic behavior. The different asymptotic behaviors of the perpendicular-to-graphene and parallel-tographene models illuminate that the center-to-center model of D is the most stable configuration as the distance between Br2 and graphene plane exceeds 3.3 Å. Furthermore, because the

Figure 3. Potential-energy curves for Br2 approaching to the graphene layer in four different configurations (the axis of the molecule is perpendicular or parallel to the graphene plane) (A), and potentialenergy curves of the interaction between Br2 molecules in two different ways (B).

binding energy difference between configurations A and D is smaller than 87 meV, the perpendicular-to-graphene configuration will strongly compete with the parallel-to-graphene configuration, for those Br2 molecules adsorbed on graphene around room temperature. 2. Interaction between Br2 Molecules and Intercalation of Br2 in MLG/Graphite. It is well known that the two-zone vapor-transport method is usually used to intercalate Br2 into graphite.48 With the controlled growth temperature in the graphite side, liquid bromine is inserted into a temperaturecontrolled alcohol bath and then is transferred to the region of graphite for the intercalation. Thus, when the Br2 molecules are inserted into graphite, there is an interaction between Br2 molecules. This interaction will be important to understand how Br2 molecules are inserted into MLG/graphite. In Figure 3B, we depict two possible interactions between two Br2 molecules: (A) two molecules are parallel separated (parallel-direction model), and (B) the axes of two molecules is along the same line (axial-direction model). The calculated binding energies are almost identical for the two configurations. However, for the axial-direction model, the energy curve converges quickly to its asymptotic value at the interdistance of 4.3 Å. The energy curve of the parallel-direction model indicates that the parallel interaction between two Br2 molecules is relatively long-ranged. Under thermodynamic considerations, the Br2 molecules more easily form a layer structure with the molecule axes oriented along the layer plane. As we know, the low-pressure solid phase of bromine is an orthorhombic crystal of Br2 layers, and the in-plane Br2 molecules are arranged in zigzag in each layer. When considering the computational capacity, the interaction between Br2 molecules on graphene is analyzed by calculating the absorption of Br2 molecules in different-size supercell graphene with the same vacuum separation as that tabulated in Table 2. By comparing the binding energy of configurations A and D, we find that the parallel-to-graphene configuration will be the most possible way for the absorbed or intercalated Br2 molecules to stay on MLG/graphite, following the increase of Br2 concentration. For these parallel-to-graphene configurations, it is also found that the interaction between Br2 molecules will elongate the Br2 bond and shorten the distance between Br2 and graphene simultaneously. Thus, it is not difficult to understand that Br2 molecules are more easily inserted into the graphite/ MLG layers when they are parallel to graphene, when considering that the in-plane intermolecular interaction of Br2 on graphene is similar to the molecular interaction of solid bromine.

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TABLE 2: Binding Energy (∆E), Bond Length (BL) of Br2 Molecule, Distance (∆H) between Br2 and Graphene Plane, and Nearest Distance between Br2 Molecules (∆L) for Configuration A (conf. A) in the Perpendicular-to-Graphene Model and Configuration D (conf. D) in the Parallel-to-Graphene Model with Different Sizes of Supercells (8, 16, and 32 Carbon Atoms) in Order to Show the Effect of the Interaction between Br2 Molecules perpendicular-tographene conf. A

∆E (meV) BL (Å) ∆H (Å) ∆L (Å)

parallel-tographene conf. D

8

16

32

8

16

32

269 2.2925 2.863 4.88

303 2.300 2.84 4.88

460 2.309 2.80 9.792

667 2.446 3.293 2.446

246 2.2996 3.3065 3.9497

213 2.268 3.325 7.524

In earlier experimental studies about graphite-bromine compounds, it is suspected that it is possible to arrange orderly Br2 molecules between carbon layers and that the bromine layer could be commensurate with the graphite layer.49 However, because of the small energy difference between different configurations of the inserted Br2 molecules, the potential barriers for Br2 diffusion would be rather low. Actually, in a HOPG host material, the activation energy for the Br2 diffusion is just 5 kcal/mol.38 The low potential barrier will also result in the absence of bromine in the graphite/MLG, following the decrease of Br2 vapor pressure. Usually, about 30% of Br2 uptake at saturation remains in the resulting residue compound at ambient atmospheric pressure.48 Thus, only dilute Br2 molecules absorbed on graphene or inserted in MLG are located at the global energy-minimum state. This case is very interesting for the fabrication of graphene by exfoliating graphite with interaction of dilute bromine.50 The attractive force between graphite layers is rather strong; therefore, it is not easy to obtain graphene by exfoliating graphite, though such interaction is a weak van der Waals force. The inserted Br2 molecules will loosen the graphene layers and replace the layer interaction with the interaction between Br2 and graphene. Because two graphene layers are coupled by Br2 molecules, dilute Br2 molecules between them will weaken their interaction accordingly. Because the parallel-to-graphene configuration D is the most stable state, it is possible that the intercalation of Br2 molecule may change the AB stacking order in MLG or graphite. We consider two cases: one is Br2 molecules inserted into the bilayer graphene with AA stacking or AB stacking; another is Br2 molecules intercalated into AA-stacked or AB-stacked MLG. It is found that Br2 molecules will stay in MLG with a centervertex configuration as shown in Figure 4A and the AB stacking is held for the intercalation. Moreover, the bridge-bridge and vertex-vertex configurations (shown in Figure 4B,C) are found to be unstable and will be transformed to the center-vertex configuration. 3. Electronic Properties of Different Adsorption Sites. With sp2 hybridization, carbon atoms can form a stable 2D hexagonal sheet with strong σ bonds. The remnant pz orbitals

Figure 4. Top view of Br2-adosorbed AB stacked graphite/bilayer graphene with center-vertex configuration (A), bridge-bridge configuration (B), and vertex-vertex configuration (C).

Figure 5. Band structures of single-layer graphene (A), bilayer graphene (B), Br2-adosorded single-layer graphene (C), bilayer graphene with Br2 adosorption in the middle (D), single-layer graphene with Br2 adosored on both surfaces (E), and bilayer graphene with Br2 adosorption on both upper and lower surfaces.

between neighbor carbons connected with each other result in fantastic 2D electron states along the network of σ bonds. With the band theory, the coupling between the pz orbitals leads to π and π* orbitals, and the energy bands of π and π* orbitals cross at the K (K′) points of the Brillouin zone because of the equivalency of two carbon atoms in the unit cell. Moreover, because of the spin-orbit coupling effect and strong electronphonon coupling at the Dirac point, the bandgap of the prime graphene plane is opened weakly. However, a larger bandgap is desirable for the application of graphene in electronic devices. Typically, the effective method to open graphene’s bandgap in K (K′) points is to disturb its π electrons in some way. With the chemical absorption of small molecules on graphene, the gap is expected to open because of the localized redistributions of 2D electrons. Therefore, the absorption effect of the Br2/Br on the band structure of graphene deserves to be examined theoretically. With a 4 × 4 supercell of 32 carbon atoms, the band structure of graphene is folded in Brillouin zones as shown in Figure 5A. For graphene, the gap between the σ and σ* bands is rather large, and the π electrons dominate its low-energy (less than 5 eV) electronic behaviors. With Br2 adsorbed on graphene with

Functionalizing Single- and Multi-layer Graphene with Br and Br2

Figure 6. Band structures of Br2-inserted graphite with stage 2 (A), Br2-inserted graphite with stage 1 (B), Br-adsorbed graphene with center site (C), and Br-adsorbed graphene with vertex site (D).

configuration D, the band structure around the Dirac point is disturbed, and a bandgap of about 120 meV is opened as shown in Figure 5C. The Fermi level is still in the bandgap with a slight shift of about 30 meV down to the valence bands due to the weak charge transfer. The localized impurity states near the Fermi level can be attributed to the ppσ* level mostly from Br2 molecule. For the Br2 molecules inserted into bilayer graphene, the center-vertex model with AB-stacking is considered. As shown in Figure 5D, the band structure is very different from the isolated bilayer graphene with AB-stacking as illustrated in Figure 5B. For the isolated bilayer graphene, the π electrons from both layers interact with each other, and this results in a split of π (and π*) bands which is similar to the energy band of graphite. After Br2 molecules are inserted, the upper graphene layer is taken up relatively, the graphene layers do not interact with each other directly because of the larger interlayer distance (about 6.7 Å), and the band structure shows a profile like that of the Br2-adosrped SLG. For Br2 intercalation of MLG, the stage 2 compound is considered to be the most stable stage. As shown in Figure 6A, the band structure of the stage 2 is simulated. We find that the energy bands near the Fermi level are very similar to those of graphite or bilayer graphene. This can be attributed to the fact that the interaction of graphene layers in the stage 2 modulate and split the π bands. The ppσ* states of the inserted Br2 molecules will induce an impurity band near the Fermi level. Therefore, the small charge transfer and the interaction between the impurity bands and the π bands near the Dirac point result in a small bandgap opening and down-shift of the Fermi level. For the Br2 intercalation of stage 1, it is found that its band structure is similar to Br2-inserted bilayer graphene, as shown in Figure 6B. Because of the interaction between Br2 molecules mediated by graphene layers, the two impurity bands are split, and this results in a larger down-shift of the Fermi level (about

J. Phys. Chem. C, Vol. 114, No. 35, 2010 14943 0.2 eV). In the recent experiments of Br2-intercalated fewerlayer graphene, charge transfer has been confirmed with the shift of graphene G peak which is sensitive to the shift of the Femi level.33 The relative large shift of the G mode in SLG is suspected to be due to the Br2 adsorption on both surfaces of graphene. Such a situation is simulated by considering that each surface of graphene adsorbs a Br2 molecule in a supercell with 32 carbon atoms. Comparing with the Br2 adsorption on one of graphene surfaces, a larger bandgap is opened, and a Fermilevel shift of about 0.2 eV is observed, as shown in Figure 5E. In Figure 5F, we also analyze the band structure of bilayer graphene with Br2 adsorbed on the upper and lower surfaces. Without the Br2 adsorption in the middle of two graphene planes, the band structure of π electrons should be similar to that of isolated bilayer graphene. However, it is interesting to note that the reduced π electrons on both graphene layers due to the charge transfer result in the reconstruction of energy bands near the Dirac point. Thus, two quasi-Dirac points are constructed with a Fermi level near the new Dirac points and the resulting hole doping. The change of the band structure of Br2-adsorbed graphene can be mostly attributed to the ppσ* states of Br2 molecules. Because the energy level of half-occupied pz orbitals of Br atom is lower than that of ppσ* states of Br2, it is possible to shift the Fermi level of graphene by the charge transfer between Br atom and graphene layer. Our calculations indicate that the binding energy of Br2 molecule is about 3 eV/molecule. The experimental value of the bond-dissociation energy is 1.99 eV/ atom. When considering that the adsorption energy of Br atom on graphene is about 0.8 eV, the Br2 molecule may decompose easily if activated by ultraviolet light. At the same time, two separated Br atoms can transfer and recombine easily among the different sits of the graphene carbon ring because of the small potential barrier.32 Thus, when controlled with ultraviolet light, the translation between Br2 and Br is easy to realize. Here, we also discuss the band structure of Br adsorbed on graphene. As plotted in Figure 6C, the band structure of two Br atoms located at the center positions of graphene, a 32-carbon-atoms model, shows a larger shift (∼0.6 eV) of the Fermi level. Because the Br atoms at the hexagonal center may diffuse to the low-energy vertex/bridge sites on graphene, the band structure for Br atom adsorbed on vertex is analyzed in Figure 6D. The Fermi-level shift is about 0.6 eV with a small bandgap (∼90 meV) opened. Two pz bands weakly interact with the π states of graphene and are split because of their coupling. In Figure 7A-D, the structures and projected charge densities of the Br2- and Br-adsorbed SLG are shown to illustrate the interaction between Br2/Br and the graphene layer. As shown in Figure 7C,D, the charge of graphene distributes mostly around the C-C bond. The charge of Br2 molecule is mainly around the Br atoms, and only a small part of it is located around the molecule axis, which means the Br-Br bond is weak. Thus, the two Br atoms are located at the center sites with lower energy in order to reduce the repulsive Coulomb interaction between charges. Therefore, it is possible that the absorption of Br2 molecules on SLG only results in a small amount of charge transfer between them, because most of the ppσ* states are near the Br atom. The transferred charges can be calculated by the charge difference formula:43,51

∆CHA(r) ) CHABr2/Br-g(r) - CHAg(r) - CHABr2/Br(r) (1)

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Figure 7. Structures (A and B), distributions of charge density (arbitrary units) in the (010) plane (C and D), and charge-density difference (arbitrary units) in the (010) plane (E and F) of SLG with Br adsorbed on the center site and the Br2-adsorbed SLG with center-center configuration.

where CHABr2/Br-g(r), CHAg(r), and CHABr2/Br(r) are the realspace electronic charge distribution of the Br2/Br-adsorbed SLG, free SLG, and Br2/Br. In Figure 7E,F, we plot the chargedifference distributions in (010) plane of Br- and Br2-adsorbed SLG. A considerable charge redistribution for graphene layer near Br2/Br and a localized electronic dipole along the c axis are formed on the graphene layer because of the charge transfer and the localized weak static electric interaction between Br2/ Br and graphene. For Br atoms absorbed on graphene, the transferred charge is distributed at the outside of Br atom, and a relative large amount of charge is localized at the side of graphene because of the Coulomb interaction. For Br2-adsorbed SLG, the charge of Br2 is redistributed because of the interaction between the Br2 molecule and graphene, and the transferred charge cannot be observed clearly in Figure 7F. Furthermore, the fact that the electronic dipole is localized in graphene along the c axis can explain why the lowest stage of graphite obtained in experiments is not a stage-1 compound for Br2 intercalation.38 As illustrated in Figure 7F, the holes of graphene are localized at the side with Br2, and the electrons are localized at the other side. Thus, after the intercalation attains stage 2, the reversed electronic-dipole interaction of two graphene layers between two Br2 intercalation layers will block the intercalation of Br2 from forming the stage-1 compound. By integrating the charge difference of localized space around Br2/Br, a small amount of transferred charge can be found. Here, the charge difference is integrated in the region between 1.8 and 7 Å above the graphene plane. For the Br-adsorbed SLG with a cell of 32 carbon atoms, net charges of about 0.37 electrons per Br atom are transferred. For Br2-adsorbed SLG, the transferred net charge is only about 0.0045 electrons per Br2 molecule, which is similar to the condition of Br2-adsorbed carbon nanotube.44 The relatively large amount of charge transferred from graphene to the Br atom can be attributed to the fact that the energy level of half-empty pz orbitals is lower

than that of ppσ* states of Br2. As shown in Figure 5C, the small bandgap can be ascribed directly to the redistribution of charges near the Dirac point, and the weak shift of the Fermi level is consistent with the small amount of transferred charges between graphene and Br2. The redistributed charge of Br2 is still localized at the small region near the Br2 molecule and thus results in nondispersive levels around the Fermi energy in the band structure. At the same time, the larger shift (∼ 0.6 eV) of the Fermi level in Figure 6C is due to the relatively large amount of transferred charges. However, the bandgap is not opened effectively, though the charge of graphene is redistributed. This can be understood by the low energy level of half-empty pz state of Br atom. It is considered that this localized state is just coupled weakly to the bonding states of graphene with the same energy. Conclusion In summary, the effects of Br2/Br adsorption on graphene and Br2 intercalation of MLG/graphite have been studied by first-principles DFT calculations. It is found that Br atoms will be adsorbed at the vertex or near bridge sites of graphene with the stable low-energy states due to the charge transfer. For the same reason, Br2 on graphene adsorbed at the vertex or bridge sites with perpendicular-to-graphene configurations are more stable. It is found that Br2 adsorbed on SLG/MLG with a stable parallel-to-graphene configuration may be attributed to the interaction between Br2 molecules. This explains the experimental observation that Br2 molecules intercalated in graphite/MLG stay parallel to the graphene planes. With the analysis of charge distributions, the general phenomenon that the lowest stage of Br2 intercalation of graphite is a stage-2 compound can be ascribed to the local electronic dipole due to the interaction between Br2 and graphene. Our calculated results indicate that the Br2/Br adsorbed on graphene will not introduce basal-plane reactions to destroy the

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