Effect of Nitrogen Doping on the Migration of the Carbon Adatom and

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Effect of Nitrogen Doping on the Migration of Carbon Adatom and Monovacancy in Graphene Zhufeng Hou, and Kiyoyuki Terakura J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp512886t • Publication Date (Web): 10 Feb 2015 Downloaded from http://pubs.acs.org on February 16, 2015

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The Journal of Physical Chemistry

Effect of Nitrogen Doping on the Migration of Carbon Adatom and Monovacancy in Graphene Zhufeng Hou∗,† and Kiyoyuki Terakura‡,† Department of Organic and Polymeric Materials, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 I6-31, Ookayama,Tokyo 152-8552, Japan, and Research Center for Simulation Science, Japan Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan E-mail: [email protected]

Abstract Nitrogen-doped graphene (N-graphene) has important implications in graphenebased devices and catalysts. Nitrogen incorporation into graphene via post-synthetic treatment is likely to produce non-negligible amount of defects and bond disorders and the resulting nitrogen content is usually dominated by graphitic N and pyridinic N. To understand the kinetic stability of doped N and the effect of doped N on the self-healing of monovacancy in graphene, we have performed density functional theory calculations to study the adsorption and migration of an adsorbed C atom on undoped and N-doped graphene with and without a monovacancy (MV). The effects of N doping and hydrogenation on the migration of a MV in graphene are also studied. Our results suggest that the graphitic N doped in the vicinity of MV is kinetically unstable and it could be transformed into a pyridinic N due to the migration of MV when N-graphene ∗

To whom correspondence should be addressed Tokyo Institute of Technology ‡ Japan Advanced Institute of Science and Technology (JAIST) †

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is through high-temperature annealing. The presence of a C adatom would easily repair the vacancy of defective graphene with MV and either restore perfect graphene or form a Stone-Wales defect. Similar repairing processes were also found in the case of a C adatom near MV with a pyridinic N.

Keywords Defect Migration, Vacancies, Nitrogen-Doped Graphene, Density Functional Theory

1

INTRODUCTION

Graphene, a carbon allotrope with a two dimensional (2D) honeycomb lattice, has attracted immense attention because of its 2D crystal lattice with atomic thickness and unique electronic structures. 1,2 It has opened up exciting opportunities for developing nanoelectronic devices. 3 In low dimensional systems, the chemical and physical properties of materials can be heavily affected by the lattice imperfection due to the structural defects. 4 Different types of structural defects in graphene have been observed in experiment by using transmission electron microscope (TEM) 5–7 and scanning tunneling microscope (STM). 8–11 Vacancies are one of the simplest intrinsic defects in graphene and they may be formed during the growth process or can be inevitably generated under irradiation conditions. 12 It was found that vacancy can alter the electronic, magnetic, and chemical properties of graphene sheet. 13–16 However, the properties modified by structural defects are sometimes harmful to the application of graphene in hyperfine nanoelectronic devices and thus the synthesis of high-quality graphene is desired, because graphene’s mobility is affected by various types of scatterers, that is, charge impurities and crystalline defects. 17,18 Recent experiments showed that graphene is able to restore and heal its vacancy defects because of the presence of hydrocarbon contamination or mobile carbon adatoms (which may be accompanied by the irradiationinduced vacancies), or even by the use of methane precursor. 10,12,17,19–22 To understand the 2 ACS Paragon Plus Environment

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self-healing of vacancies in graphene, it is important to study the adsorption and migration of carbon adatom on graphene as well as the migration of vacancy. 19,23–25 The incorporation of nitrogen into graphene is a simple approach to tailor the electronic properties of graphene. Nitrogen-doped graphene (N-graphene) has been demonstrated to have highly promising applications in the energy conversion/storage and in the nanoelectronic device. 26–29 N-graphene can be synthesized by using a bottom-up method from the N-containing precursors or through a post-treatment of graphene and graphite oxide (GO). 30,31 The experimental characterization of N-graphene by x-ray absorption (XAS), emission (XES), photoelectron (XPS) spectroscopies 32–37 as well as nuclear magnetic resonance (NMR) spectroscopy 38 indicated that the doped N atoms usually substitute for C atoms in graphene and take the forms of pyridinic, pyrrolic, and graphitic N bonding configurations. The pyridinic and pyrrolic N may lie at the edge or defect (for example, vacancies) sites, while the graphitic N is coordinated with three carbon atoms in the graphene plane.

Particularly during the synthesis process of N-graphene via the post-treatment

method, nitrogen doping is likely to induce non-negligible amount of defects and bond disorders. 34–37,39,40 The resulting nitrogen content is usually dominated by the graphitic N and the pyridinic N. Recent experiments showed that nitrogen ion bombardment of graphite or electron beam irradiation of N-graphene (and N-doped carbon nanotubes) can create a pyridinic N at monovacancy (MV). 22,41 By performing density functional theory (DFT) calculations we have extensively and systematically studied the energetic stability of doped N in graphene to understand the thermodynamical factors of N doping. 42–45 We found that the doped N and the native point defects interact attractively and display a cooperative effect and that the attractive interaction is strongest for MV among several structural defects such as MV, divacancy, Stone-Wales (SW) defect, grain boundary, and edges. 44,45 Because N-graphene is usually treated by hightemperature annealing during the synthesis, the actual nitrogen population distribution in N-graphene would be affected by the kinetic factor besides the thermodynamical one. How-



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ever the kinetic stability of doped N in graphene has not been studied so far. The self-healing of pyridinic N doped MV, which results in the formation of graphitic N, was observed in experiment by TEM. 22 It indicates that the atom migration could lead to the transformation among different N bonding configurations. Thus the atom migration affects the composition of nitrogen-containing moieties in N-graphene and alters the physical and chemical properties of N-graphene. In this work, we extend our previous DFT calculations to the study of the adsorption and migration of a C atom on N-graphene with and without a MV as well as the migration of a MV, which would enable us to understand the self-healing of vacancies in N-graphene and the kinetic stability of doped N. The remainder of this paper is organized as follows. In Sect. 2, we introduce computational methods. The results for the adsorption and migration of a C adatom on graphene as well as the migration of a MV in graphene are presented in Sect. 3. The conclusions are given in Sect. 4.

2

METHOD AND COMPUTATIONAL DETAILS

In the present work, the DFT calculations have been performed with the PWSCF code of the Quantum ESPRESSO suite. 46 We have employed ultrasoft pseudopotentials generated with the Rappe-Rabe-Kaxiras-Joannopoulos recipe 47 and the Perdew-Burke-Ernzerhof 48 approximation to the exchange correlation functional. The spin-polarization is taken into account if it exists. The electronic wave functions are expanded in plane waves with an energy cutoff of 35 Ry while for the charge density the energy cutoff is taken to 350 Ry. A 9 × 9 supercell of graphene hexagonal lattice with a 3 × 3 k -point grid is used for the calculations. A 12.0 ˚ A of vacuum in the normal direction of graphene sheet is included to decouple periodic images. The dipole correction energy of a single C (and N) adatom on the graphene surface is found to be in the order of 1 meV and thus it is neglected. The more details of the computational setup and the associated convergence tests were given in our previous paper, 44,45


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which showed that the above setup is sufficient to ensure the accuracy in the present study. To study the effect of doped N on the migration of an adsorbed C atom and a MV, we have calculated the energy barrier for their migration via ab initio techniques. The climbing image nudged elastic band (CI-NEB) method 49,50 is used to seek the saddle points and minimum energy path. Three or more images are employed between two end points. Each image is relaxed until the forces on atom are less than 0.02 eV/˚ A. To assess the stability of a point defect (and or an impurity) in graphene, we calculate its formation energy by using the following definition:

∆Ef (D) = Et (D) − nC Et (G) −

nN Et (N2 ), 2

(1)

where Et (D) is the total energy of a graphene supercell with a defect (and/or an impurity), Et (G) the total energy per atom of perfect graphene, Et (N2 ) the total energy of an isolated N2 molecule, and nC and nN the numbers of C and N atoms in the graphene supercell, respectively. As supplementary information, the adsorption energy ∆Ead for a single X (X = C or N) adatom on graphene is calculated with respect to the total energy Eatom (X) of an isolated X atom as below:

∆Ead (X) = Et (X + substrate) − Et (substrate) − Eatom (X),

(2)

where Et (X + substrate) and Et (substrate) are the total energies of a substrate (undoped or N-doped graphene) after and before adsorbing an X atom, respectively. To quantitatively describe the interaction and aggregation of two individual point defects (D1 and D2) in graphene, we estimate their interaction energy as

Eint (D1, D2) = ∆Ef (D1D2) − ∆Ef (D1) − ∆Ef (D2),

(3)

where ∆Ef (D1), ∆Ef (D2), and ∆Ef (D1D2) are the formation energies of the individual



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point defects D1 and D2, and the complex defect D1D2, respectively. A negative (positive) value of Eint indicates that two individual point defects D1 and D2 are energetically favorable (unfavorable) to aggregate.

3

RESULTS AND DISCUSSION

3.1

Effect of Nitrogen Doping on the Adsorption and Migration of a Carbon Adatom on Perfect Graphene

We first examine the energetic stability of a single C atom adsorbed on perfect graphene. Three possible adsorption positions (the bridge, on-top, and hollow sites as shown in Figure 1a) are considered for the adsorption of a C atom. The calculation results for a C atom adsorbed on perfect graphene are summarized in Table 1. It is found that the adsorbed C atom (Cad ) energetically prefers the bridge site rather than the on-top and hollow sites. 51 Our results are in good agreement with the previous ones by others. 52–56 Hereafter we mainly discuss the bridge site for the adsorption of a C atom on graphene. Figure 2 shows the formation energy of a complex defect of a single C adatom (Cad ) and a single graphitic N in graphene for the C adatom at different bridge sites. Based on our calculations, it is found that in N-doped graphene a C adatom prefers a bridge site between the first and second nearest neighboring C atoms (C1 and C2) of the doped N. This could be understood from the charge compensation between the graphitic N dopant (electron donor type) and the adsorbed C atom (electron acceptor type), as explained below. It is known that a single graphitic N in graphene acts as an electron dopant. The doped electron is mainly localized on the C atoms in a sublattice site different from that for the doped N, 57 that is, on C1, C3, C4, and C7, as shown in the simulated scanning tunneling microscope (STM) image under a bias voltage of Vb = −0.2 V (see the upper inset of Figure 2) for a single N substitution in graphene. This simulated STM image can provide the spatial distribution of local density of states (LDOS) in a certain energy range from the Fermi level (EF ) to −0.2 6 ACS Paragon Plus Environment

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eV below EF . It is noted that the state localized on C1 is polarized more toward C2 rather than toward the doped N. This is because the pz orbital of an N atom is more localized and has a deeper energy level than that of a C atom. As discussed below, a single C adatom at a bridge site on perfect graphene acts as a hole dopant and forms an sp2 hybridization with the bonded two substrate atoms. Therefore, the adsorbed C atom is energetically favorable to sit at the bridge site of the C1−C2 bond and efficiently compensates the doped electrons by the graphitic N as expected from the spatial distribution of LDOS in the STM image of Figure 2. In addition, the bond lengths between Cad and the bonded substrate atoms in the case of Cad at the bridge site of C1−C2 bond are about 0.02 and 0.04 ˚ A shorter than those in the case of Cad at the bridge site of C1−N bond. The most stable configuration of a complex defect with a C adatom and a graphitic N is denoted as Cad, NG and shown in the lower inset of Figure 2. The formation energy of Cad, NG is about 6.39 eV, which is less than the sum of the formation energies of a single N substitution in and a single C adatom on perfect graphene by −0.79 eV. The interaction between these two individual impurities is attractive, indicating that the adsorption of a C atom on graphene can enhance the N doping and vice versa. Figure 1g shows the energy evolution for the migration of a C adatom from a bridge site to a nearest neighboring one on perfect graphene and for the case of an N adatom. The energy barrier for the migration of a C adatom on perfect graphene is about 0.55 eV and it is smaller than that of an N adatom by 0.31 eV, indicating that a C adatom is easier than an N adatom to diffuse on the graphene surface. Figure 3 shows the energy evolution for the conversion from an N adatom to a complex defect of a substitutional N and a C adatom and for the migration of a C adatom on N-doped graphene along different reaction paths. The N adatom could push down one of the underlying C atoms to form a substitutional N accompanied by a C adatom on the opposite side of graphene. 58 In this reaction path the energy barrier is about 3.55 eV. It is noted that the backward energy barrier is about 0.83 eV, which is larger than that (0.43 eV) for the migration of a C adatom from the bridge



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site of C−N bond (see Figure 3c) to a nearest neighboring bridge site of a C−C bond (see Figure 3e). For the conversion from an N adatom to a substitutional N accompanied by a C adatom on the same side of graphene, it needs to overcome an energy barrier of 4.31 eV (see Figure S1 in the Supporting Information). The energy barriers in both cases of the conversion from an N adatom to a substitutional N are much larger than that (0.86 eV) for the migration of an N adatom on graphene surface. Therefore, the formation of a graphitic N from an N adatom on defect-free graphene is very unlikely even under the high temperature annealing. On the other hand, a complex defect of a graphitic N and a C adatom would be kinetically stable once it is formed. For a C adatom in the most stable configuration of Cad, NG (see Figure 3e), the energy barriers for its migration to the bridge sites of a nearby C−N bond (see Figure 3c) or a nearby C−C bond (see Figures 3g and 3i) are 1.02 eV, 1.23 eV, and 1.05 eV, respectively. The migration of a C adatom by passing through the top site of a substitutional N (see Figures S1c, S1d and S1e in the Supporting Information) is also studied and the associated energy barrier is high up to 1.13 eV. All of them are larger than the energy barrier for the migration of a C adatom on undoped graphene. Therefore, N doping suppresses the migration of a C adatom on defect-free graphene.

3.2

Electronic Structure of Graphene with a C Adatom in the Absence and Presence of a Graphitic N

Now we discuss the influence of N doping on the electronic structure and magnetic property of a C adatom on graphene because it has interesting characteristics. The adsorption of a single C atom at the bridge site on perfect graphene (denoted as Cad, 0 ) induces magnetization, which is also found in the case of Cad, NG . The induced magnetic moments and the spin polarization energies of both cases are given in Table 1. In the cases of Cad, 0 and Cad, NG , the induced magnetic moments are about 0.44 µB per cell and 1.0 µB per cell, respectively, and the corresponding spin polarization energies are about −0.08 eV and −0.32 eV for the 9×9 supercell, indicating that the induced magnetization by a C adatom is enhanced after N 8 ACS Paragon Plus Environment

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doping. As pointed out by Lehtinen et al., 52 the spin polarization has no significant effect on the migration of the adsorbed C and N atoms on perfect graphene, which has been also found in our calculations. The distributions of spin density for Cad, 0 and Cad, NG are presented in Figures 4a-c and they clearly indicate that the induced magnetic moments mainly come from the spin polarization of the pπ orbitals of the adsorbed C atom in both cases, where this pπ orbital is perpendicular to the plane crossing the C adatom and the bonded two substrate atoms. As pointed out by Lehtinen et al., 52 the two substrate C atoms attached to the C adatom protrude out of the graphene substrate and have a mixture of sp 2 and sp 3 hybridization, while the C adatom is sp 2 hybridized. Among the three sp 2 orbitals of the C adatom, two of them contribute to the covalent bonds with the two substrate C atoms accommodating two electrons of the C adatom and the remaining one is a dangling bond pointing perpendicular to the substrate. The state associated with this dangling bond should be deep in the σ band range of graphene and accommodates two electrons of the C adatom. Note, however, that due to the double occupancy of the dangling bond, the Coulomb repulsion brings this state at about 1.5 eV below the Fermi level (see Figure S2 in the Supporting Information). Therefore, four electrons of the C adatom have been already accommodated and if the pπ orbital is located above the Fermi level, no carrier doping and no spin polarization will be observed. We confirmed that this is realized in the spin unpolarized state. However, in the lowest energy state, the Fermi level is located in the valence band (Figure 4e) and the spin polarization is observed. An important point in this regard is that as the pπ orbital is orthogonal to the graphene π orbitals at the nearest substrate C atoms, it has only very weak hybridization with the substrate π bands and has almost flat bands. 52 Because of this flat band nature of the pπ state, the spin polarization is self-consistently stabilized by the level lowering of the majority spin state due to the exchange splitting. Therefore, the partial occupation of the pπ state leads to the hole doping. We make here a brief comment on the reason why the spin polarization of a very flat band of the pπ orbital is not integer but fractional. First we note that the pπ band is



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not perfectly flat because the pπ orbital has some small hybridization with the substrate π states. From Figure 4e and Figure S2 in the Supporting Information, we see that the Fermi level is pinned at the majority spin pπ level. In this case, the total number of holes per supercell is equal to the number of electrons in the majority spin pπ level, i.e., the spin polarization and additionally the actual level position of the pπ orbital is adjusted according to its occupation. Therefore, the Fermi level and the pπ level coincide self-consistently. For example, consider the use of a larger supercell. If the spin polarization is fixed, the number of holes per substrate C atom becomes smaller and the Fermi level will shift up. This will lead to an increase in the electron population in the pπ state and then the pπ level will shift up to suppress the increase in the electron population due to the electron-electron repulsion. This trend is clearly seen in Figure 5a where the k -point sampling dependence of the spin polarization is shown for some different supercell sizes. We see that the spin polarization is always around 0.45 to 0.50 µB . However, it is still difficult to predict the large supercell limit of the spin polarization. This is because the hybridization between the adatom pπ orbital and the substrate state becomes smaller, making the pπ band dispersion-less as the supercell becomes larger. In the limit of the flat band, fractional occupancy is unlikely. Moreover, the supercell size dependence as shown in Figure S3a in the Supporting Information suggests that the majority spin pπ level will be located below the Dirac point whereas the Fermi level must coincides with the Dirac point in the limit of large unit cell size. If this is the case, the spin polarization of a C adatom will become 1.0 µB . In the case of Cad,NG , the additional electron of the graphitic N completely fills the majority state of the pπ orbital, leading to the magnetic moment of 1.0 µB and no carrier doping. Finally, we briefly discuss the electronic structure of an N adatom on perfect graphene (denoted as Nad, 0 ) to make a comparison with Cad, 0 . In both cases, the adsorbed N and C atoms have the same bonding picture. Because an N adatom has one more electron and a deeper potential than that of a C adatom, the flat band of the pπ orbital of an N adatom shifts to a lower energy (see Figure 4g) and is more than half occupied. The minority spin


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state of the pπ band is partially filled with creating holes in the substrate. Figure 5b shows the k -point sampling dependence of the spin polarization for some different supercell sizes. In this case, the spin polarization may converge to 1.0 µB in the large supercell limit, meaning that the minority spin pπ band may become empty. This is supported by Figure S3b which shows the supercell size dependence of the majority spin pπ level. According to this figure, the pπ level will be located above the Dirac point and will be empty in the limit of large supercell size. Nevertheless, the physical reason of this supercell size dependence is not obvious. One possibility is that the inter-pπ orbital interaction between supercells is reduced as the supercell becomes larger. This may lead to the stronger localized nature of the pπ orbital and enhances the Coulomb repulsion in the orbital to shift up the minority spin level.

3.3

Effect of Nitrogen Doping on the Adsorption and Migration of a Carbon Adatom on Defective Graphene with a Monovacancy

For a MV in undoped graphene, as three electrons are accommodated to three dangling σ orbitals, the three carbon atoms next to a vacancy site would undergo a Jahn-Teller (JT) distortion, that is to say, two of them (labeled C5 and C50 in the inset of Figure 6a) would form a new bond and thus the D3h symmetry of vacancy site changes into Cs symmetry. This is, in fact, what the DFT calculations 13–15,59,60 have predicted and the experiment 10 has corroborated. The remaining one carbon atom (labeled C1 in the inset of Figure 6a) has a dangling σ state. The reconstructed MV consists of an enneagon and a pentagon. Figure 6 shows the formation energies of a single C atom adsorbed on different bridge sites around MV after relaxation, in which the geometry optimization starts from the initial atomic structures of the C adatom sitting at the bridge sites of different symmetry-inequivalent C-C bonds around MV and all atoms are allowed to relax. The structures for the C adatom occupying the bridge sites of C−C bonds associated with C2 atom (a nearest neighbor of



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C1 atom, see the inset of Figure 6a) converge after relaxation to the same stable structure (denoted as Cad, MV ) as shown in Figure 6b, in which the adsorbed C atom is bonded with C1 atom to form a C−C dimer protruding out of the graphene substrate. The Cad −C1 bond length is about 1.32 ˚ A, which is much smaller than the distance (1.98 ˚ A) between Cad and C2 atoms. The adsorption of the C adatom at the bridge site of the C5-C6 bond (see Figure 6e) leads to a symmetry-equivalent structure of Figure 6b. The adsorbed C atom at the bridge sites of C5−C50 and C6−C7 bonds spontaneously moves toward the vacancy site to heal the vacancy, thus repairing graphene. The adsorption of a C atom at the bridge site of C4−C5 bond results in the formation of a SW defect as shown in Figure 6d. Indeed, SW defects were observed in the high-resolution TEM image of graphene under electron irradiation. 19 The relaxed structure of Cad, MV shown in Figure 6b is less stable than SW defect, but more stable than the relaxed structures of a C atom adsorbed at the bridge sites of remaining C−C bonds considered here. Recent experiment showed that nitrogen ion bombardment of graphite (or graphene) or electron beam irradiation of N-graphene can create a pyridinic N at MV. 22,41 If the ejected C atom falls on N-graphene sample and not far away from the vacancy site, it may form an adatom around N-doped MV. Figure 7 shows the formation energies for the relaxed structures of a single C atom adsorbed on different bridge sites of C−C bonds (and N−C bond) around a pyridinic N doped MV. We find that the adsorbed C atom at the bridge sites of the C−C bonds of the pentagon [(5, 50 ), (5, 6), and (6, 7) in Figure 7a] moves spontaneously on plane and toward the vacancy site to heal the vacancy, resulting in the formation of a graphitic N from the doped pyridinic N. The adsorption of a C atom at the bridge site of C4−C5 bond leads to the formation of an N-doped SW defect as shown in Figure 7d, where the doped N is located in a pentagon ring and shared by the neighboring heptagon and hexagon rings. This structure of N-doped SW defect is metastable and its formation energy is about 0.42 eV less than that of the most stable one, in which the doped N is located in a pentagon ring and shared by two neighboring hexagon rings. 44 Single N dopant in a pentagon ring of the SW


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defect was observed very recently by the atomic-resolution scanning TEM measurement of N-graphene even at elevated temperatures. 61 The adsorption of a C atom at the bridge site of N−C2 bond forms a stable structure (denoted as Cad, N-MV ) as shown in Figure 7b, which is less stable than a graphitic N in perfect graphene and the N-doped SW defect, but more stable than the relaxed structures of C adatom adsorbed at the bridge sites of the remaining C−C bonds considered here. Figure 8 shows the energy evolution for the migration of a C adatom around MV before and after N doping. Due to a small energy barrier (0.36 eV and 0.18 eV for undoped and N-doped MVs, respectively), the adsorbed C atom tends to migrate close to the C1 atom. The subsequent migration of the C adatom from the stable structure of Cad, MV could restore the perfect graphene and the corresponding energy barrier is about 0.45 eV. We can also see that the migration of the C adatom from the stable structure of Cad, N−MV could result in the formation of a graphitic N and the energy barrier is about 0.40 eV. Therefore, N doping slightly reduces the energy barrier for the self-healing of MV. As mentioned above, the geometry optimization for the adsorption of a C adatom at the bridge site of C4−C5 bond leads to the formation of a SW defect spontaneously and the adsorption of a C adatom at the bridge site of C4−C10 bond is more stable than at that of C3−C4 bond. To further examine the kinetic stability of a SW defect, we have studied the C atom migration associated with the structure of a C adatom adsorbed at the bridge site of C4−C10 bond. The results are shown Figure 9. The formation of a SW defect caused by the migration of the lattice C4 atom (denoted as an in-plane mechanism) has much lower energy barrier (0.19 eV) than that (1.22 eV) by the migration of the C adatom (denoted as an on-plane mechanism). The same trend is also found in the case of N-doped MV. Moreover, the energy barrier for the formation of a SW defect caused by the migration of the lattice C4 atom in the case of N-doped MV is slightly reduced to 0.14 eV. We also find that the energy barrier for the formation of a SW defect caused by the in-plane 90◦ direct rotation of a C−C bond next to a graphitic N is about 8.89 eV and the one for the backward process is about 4.58 eV (see



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Figure S4 in the Supporting Information). Therefore, the presence of a C adatom around N-doped MV can enhance the formation of N-doped SW defect and its kinetic stability.

3.4

Effect of Nitrogen Doping and Hydrogenation on the Migration of a Monovacancy in Graphene

The migration of a MV in graphene corresponds to the migration of the atoms next to the vacancy site. Now we discuss the effect of N doping and hydrogenation on the migration of atoms around MV. Figure 10 shows the energy evolution for the migration of C atoms (C1, C5, and C50 shown in Figure 10a) next to a vacancy site in the reconstructed MV. The reconstructed MV from one pattern of Figure 10a to an equivalent pattern (see Figure 10c) needs to overcome an energy barrier of 0.19 eV. Such a small energy barrier could lead to the reconstruction of MV being dynamical, namely, the swapping of the reconstructed bond between two of the three C atoms next to vacancy site. This has been proposed to explain the observation of symmetric MV in the STM image. 10,59 The migration of a MV in graphene was observed in the TEM images in experiment, where the MVs were created by sputtering graphene with the use of a high current density electron beam. 10 The migration of C1 atom toward the center of C5−C50 bond (Figure 10d), thus shifting the vacancy to an adjacent lattice position (Figure 10e), needs to overcome an energy barrier of about 0.99 eV, which is in agreement with the value reported by others. 59,62–64 For N substitution around a MV, our previous study 44 showed that the doped N energetically prefers to substitute for the C atom (i.e., C1) with a dangling σ state and to form a pyridinic type. For the MV doped with a pyridinic N, the energy evolution for migration of N and C atoms next to the vacancy site is presented in Figure 11g. We can see that the migration of the doped N toward the center of C5−C50 bond [from panel (c) to panel (a) in Figure 11] needs to overcome an energy barrier of about 3.47 eV, which is much larger than that of the corresponding C1 atom in the undoped MV. Our results also show that a pyrrolic 14 ACS Paragon Plus Environment

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N (see Figure 11b) at MV is unstable. Alternatively, compared with the doped N atom the C atoms next to the vacancy site migrate [from panel (c) to panel (e) in Figure 11] with a lower energy barrier (for example, 2.75 eV for C50 atom), which is, however, still larger than that of C atom in undoped MV. On the other hand, the corresponding backward energy barrier for C atom migration is 0.77 eV. Our results suggest that a pyridinic N next to MV can lift the energy barrier to suppress the migration of MV and that a graphitic N near MV more or less lowers the energy barrier to enhance the migration of MV. Even if a graphitic N is doped in the vicinity of MV, the C atoms next to vacancy site could migrate with a lower energy barrier, resulting in the formation of a pyridinic N from a graphitic N near a MV when the N-graphene is through high-temperature annealling. Therefore, besides the thermodynamical stability a pyridinic N at MV is also kinetically stable. So far we have discussed the stability of a graphitic N versus a pyridinic N at MV separately in the presence and absence of a C adatom. From Table 2, which summarizes the energy barriers for the atom-migration-induced conversions among different forms of N dopants in N-graphene, we can find that the conversion from a pyridinic N at MV to a graphitic N caused by the on-plane C adatom migration in the presence of a C adatom has a much lower energy barrier (0.40 eV) than the one caused by the in-plane C atom migration in the absence of a C adatom (2.75 eV). This suggests that the conversion from a pyridinic N to a graphitic N is more favorably caused by the C atom migration in the presence of a C adatom. The TEM measurement of N-graphene under electron beam irradiation showed that the electron beam damage is initiated by displacement of C atoms next to the N dopant, leading to a conversion of the graphitic N dopants into the pyridinic ones. 22 It was also found that the vacancy created during the imaging was refilled to restore the graphitic N because of the adatom migration. 22 A very recent experiment showed that the conversion of pyridinic N to graphitic N in N-graphene/Ni system with an intercalated layer of gold can be effectively promoted at an appropriate temperature (e.g., T ≈ 580◦ C used there). 65 This conversion was ascribed to the migration of the dissolved C atom in Ni substrate and the activation



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energy was associated with the penetration of C atom from substrate to graphene. 65 It should be pointed out that in the present study we consider the atom migration only in (and on) the monolayer graphene and do not take into account the substrate and temperature effects, which will be studied in our future work. Nevertheless, our results provide a hint that the presence (or use) of additional carbon source could be an effective way to increase the population of graphitic N in N-graphene during its high-temperature treatment. Our previous study 44 showed that monohydrogenation can reduce the formation energy of a MV by 1.95 eV. The monohydrogenated MV is denoted as H-MV and shown in Figure 12c, in which the C1 atom with a dangling σ state is terminated by one H atom to form a sp2 hybridized C−H bond and the C5 and C50 atoms next to the vacancy site still form a weak bond. Figure 12g presents the energy evolution for the migration of atoms next to the vacancy site in H-MV. We can see that the migration of H atom from the passivated C1 atom to the unpassivated C5 (or equivalent C50 ) atom needs to overcome an energy barrier of about 1.22 eV, which is larger than that (0.19 eV) of a transformation between two equivalent patterns of a bare reconstructed MV. This suggests that the hydrogenation of MV, which may be due to the existence of H contaminant, could prevent the swapping of the reconstructed bond around the vacancy site (i.e., the oscillation of the MV reconstruction). 10 If an H atom is adsorbed on a C atom away from the vacancy site (see Figure S5c in the Supporting Information), it would migrate to the C atom next to the vacancy site due to a small energy barrier of about 0.29 eV. On the other hand, the energy barrier of the migration of an H atom around H-MV is smaller than that of the migration of C atoms (for example, 3.43 eV for the migration of C50 atom and 2.33 eV for the simultaneous migration of C5 and H atoms) next to the vacancy site. Therefore, the H atom in H-MV is easier to migrate than the lattice C atom. It is also noted that the hydrogenation of MV raises the energy barrier for the migration of the vacancy site. Our results suggest that the hydrogenation can stabilize the reconstructed pattern of MV both thermodynamically and kinetically, making it observed more easily in experiments (e.g., the TEM measurement 10 ).


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The N substitution in an H-MV 44 or the monohydrogenation of a pyridinic N doped MV is energetically favorable to form a pyridinium-like N at MV (denoted as pNH-MV and shown in Figure S6a in the Supporting Information), which is aromatic and does not induce any carrier. 57 In view of the above findings that both the pyridinic N and the hydrogenation significantly raise the energy barrier of the C atom migration next to the vacancy site with respect to the one in the bare MV and that the H atom in H-MV is easier to migrate than the lattice C atom, only the migration of an H atom was examined in the case of pNH-MV to discuss the kinetic stability of a pyridinium-like N versus a pyridinic N at a MV. The energy evolution for the migration of an H atom in the case of pNH-MV is presented in Figure S6 in the Supporting Information. It is found that the migration of the H atom from the N dopant to the unpassivated C atom (C5 or C50 ) needs to overcome an energy barrier of 0.86 eV and the corresponding backward energy barrier is 0.52 eV. Therefore, once the pyridinium-like N is formed at a MV, it would be kinetically stable.

4

CONCLUSION

The adsorption, migration, and electronic structure of a C adatom on graphene with and without a monovacancy (MV) before and after N doping have been studied by performing DFT calculations. The migration of a MV in graphene before and after N doping (and hydrogenation) is also studied. Our results show that a C adatom on graphene energetically tends to be adsorbed at a bridge site of a C−C bond next to the doped N because of their attractive interaction. Doped N can suppress the migration of a C adatom on defect-free graphene. The C adatom adsorbed on defective graphene with a MV tends to migrate toward the vacancy site to repair it even after N doping. Depending on the site of the C adatom, the repaired system may be either defect free graphene or graphene with a SW defect. The conversion from a pyridinic N at MV to a graphitic N caused by the migration of C atom in the presence of a C adatom has an energy barrier lower than that caused by the



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in-plane migration of lattice C atoms in the absence of a C adatom. The use or existence of additional carbon source during the high-temperature annealing of N-graphene could repair the vacancy so as to increase the population of graphitic N. This is supported by the very recent experiment. 65 In contrast to the case of a graphitic N doped in the vicinity of a MV, a pyridinic N doped at a MV can suppress the migration of MV. Our results suggest that pyridinic N at MV is thermodynamically and kinetically very stable in the absence of either C adatom or H contaminant. Besides the energetically favorable aggregation of multiple pyridinic N atoms at vacancies, 44 this may be one of the reasons why the population of pyridinic N in N-graphene is so high as to be comparable with that of graphitic N. Without the use of additional carbon source, the high-temperature annealing of N-graphene could lead to an increase of pyridinic N but a decrease of graphitic N because of the migration of a MV near a graphitic N.

Supporting Information Available Additional results are presented: (1) energy evolution along the reaction path for the conversion of an N adatom to a substitutional N and a C adatom on the same side of graphene; (2) energy evolution along the reaction path for the migration of a C adatom by passing through the top site of a graphitic N in graphene; (3) partial density of states for a C adatom on perfect graphene; (4) supercell size dependence of the majority spin pπ level of a C adatom and of the minority spin pπ level of an N adatom with respect to the Dirac point; (5) energy evolution along the reaction path for the formation of a SW defect caused by the in-plane 90◦ direct rotation of a C−C bond next to a graphitic N; (6) energy evolution along the reaction path for the migration of an H atom toward the vacancy site in the undoped MV. (7) energy evolution along the reaction path for the migration of an H atom around an N-doped MV. This material is available free of charge via the Internet at http://pubs.acs.org/.


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Acknowledgement This work was performed under Project 08003441-0 at the New Energy and Industrial Technology Development Organization (NEDO). The computation was performed using the supercomputing facilities in the Center for Information Science in JAIST. Parts of the computations were done on TSUBAME Grid Cluster at the Global Scientific Information and Computing Center of the Tokyo Institute of Technology.

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Table 1: The formation energies ∆Ef (in eV) and adsorption energies ∆Ead (in eV) of a single C adatom on perfect graphene and N-doped graphene (Cad, NG ) as well as a single N adatom on perfect graphene (Nad, 0 ). da−s is the bond length (in ˚ A) between the adsorbed atom and its bonded substrate C atoms. Mt is the total magnetic moment (µB per cell) induced by the adsorption of a single C (or N) atom. ESP is the corresponding spin polarization energy (in eV) defined as the total energy difference between the spin-polarized state and the non-spin-polarized state. The interaction energy Eint (in eV) between a Cad, 0 and a single N substitution is calculated by Eq. 3. System Adsorption site Figure No. ∆Ef ∆Ead da−s

C adatom on perfect graphene Bridge On-top Hollow 1(b) 6.40 6.86 7.51 −1.23 −0.79 −0.15 1.51 1.58, 3.46 1.56a 2.24b 0.44 1.95 2.21 −0.08 −0.08 −1.18

Cad, NG Nad, 0 Bridge Bridge 2, inset 1(d) 6.39 4.26 −2.05 −0.67 1.47c 1.46 1.55d Mt 1.00 0.73 Esp −0.32 −0.16 Eint −0.79 a Bond length between Cad and a C atom next to the substrate C atom just below the top site. b Non-spin-polarized calculation result. c dCad −C1 , C1 and C2 are the first and second nearest neighboring C atoms of doped N. d dCad −C2 .



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 2: The energy barrier ∆Eb (in eV) for a conversion between two of the different forms of N dopants in N-graphene. Nad (Cad ), gN, pN, pNH, and CH stand for an N (a C) adatom, a graphitic N, a pyridinic N, a pyridinium-like N, and a monohydrogenated C atom. Conversion Notation Host Nad gN + Cad defect-free Cad + pN gN MV, defect-free Cad + pN gN MV, SW defect pN gN MV pNH pN + CH MV a Nad and Cad are adsorbed on the

Figure No. ∆Eb Initial Final Forward Backward 3aa 3ea 3.55 1.42 8h 8j 0.40 9.61 9e 9h 0.14 5.25 11c 11f 2.75 1.17 S5a S5c 0.86 0.52 opposite sides of graphene sheet.


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/∗ ◦ (a)

(b)

E [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(c)

1.0 0.8 0.6 0.4 0.2 0.0

(g)

d b 0

(d)

(e)

e

f c

e N

ad

d b

C adatom 0.2

0.4

0.6

ato m

0.8

1

Reaction coordinate

(f )

Figure 1: (a) Top view of the adsorption positions (bridge, on-top, and hollow sites marked by the red star, blue triangle, and green circle, respectively) on perfect graphene. (b) and (c): local atomic structure configurations along the reaction path for the migration of a C adatom on perfect graphene from a bridge site to its nearest neighboring one. (d)−(f): local atomic structure configurations along the reaction path for the migration of an N adatom on perfect graphene from one bridge site to a nearest neighboring one. (g): energy evolution along the reaction paths. The atomic structures for points b0 , d0 , and e0 in panel (g) are equivalent to those in panels (b), (d), and (e), respectively. Grey and blue balls represent C and N atoms, respectively.



Ef [eV]

7.5

0 1 50

7.0

1E−4

N

2 4

3 6

7.5E−5

5

5.0E−5 2.5E−5

7

0.0

8

6.5

6.0 (6, 7)

(5 , 8)

(5, 7)

(4, 6)

(4, 5 )

(3, 5)

(2, 4)

(2, 3)

(1, 2)

(0, 1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Bridge site on the bond between atom i and atom j, (i, j) Figure 2: Formation energy ∆Ef of a complex defect of a single graphitic N and a C adatom for the C adatom at different bridge sites in N-doped graphene. The upper insets show the local atomic structure and simulated scanning tunneling microscope (STM) image (under a bias voltage of Vb = −0.2 V and with a sample-tip distance of d = 2 ˚ A) of N-doped graphene with a single graphitic N before adsorbing a C atom, where the non-zero integer number indicates the ith nearest neighbor of the graphitic N. The lower inset shows the local atomic structure for the most stable configuration of a C adatom on N-doped graphene.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


E [eV]

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(a)

(b)

(c)

(d)

(e)

(f )

(g)

(h)

(i)

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5a 0.0 0

b

(j)

0.2

0.4

c c

f

d

0.6

g i

e h

0.8

1

Reaction coordinate Figure 3: Local atomic structure configurations (a)−(i) and energy evolution (j) along the reaction paths for the conversion of an N adatom on perfect graphene to a substitutional N accompanied by a C adatom and for the migration of a C adatom on graphene with a graphitic N. The atomic structure for point c0 in panel (j) is equivalent to that in panel (c), where the C adatom on the opposite side of graphene.



(a)

(b)

N N

(c)

(d)

2.0 1.5 Energy [eV]

1.0

Minority spin Majority spin

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.5 0.0 -0.5 -1.0 -1.5 -2.0 K M

K M

K M

(e)

(f)

(g)

Figure 4: Isosurface (3 × 10−3 e/Bohr3 ) of spin density (yellow and cyan colors for majority and minority spins, respectively) of (a) top view and (b) side view for a single C adatom on perfect graphene, (c) a single C adatom on N-doped graphene (top view), and (d) a single N adatom on perfect graphene (top view). The band structures of graphene with (e) a single C adatom, (f) a single C adatom plus a single graphitic N, and (g) a single N adatom. Green circles indicate the fat bands derived from the 2pπ orbital (perpendicular to the plane crossing the adatom and the bonded two substrate atoms) of the adsorbed C or N atom. The zero of energy is set at the Fermi level.


0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40

(a)

1

2

0.90

9 × 9 supercell 12 × 12 supercell 15 × 15 supercell

3

4

5

6

7

8

Mt [µB/cell]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Mt [µB/cell]

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0.80 0.75 0.70

m × m k-mesh for a (3n × 3n) supercell containing a C adatom

9 × 9 supercell 12 × 12 supercell 15 × 15 supercell

0.65 0.60

9 10

(b)

0.85

1

2

3

4

5

6

7

8

9 10

m × m k-mesh for a (3n × 3n) supercell containing an N adatom

Figure 5: The k-point sampling dependence of the total magnetic moment Mt of a 3n × 3n (n = 3, 4, 5) supercell of graphene containing (a) a C adatom, (b) an N adatom. For each supercell size, the atomic structure is fixed at the one obtained by a geometry optimization with the smallest one of the tested k-point grids. Note that the changes in the total energies as a function of the tested k-point grids are less than 0.03 eV and 0.07 eV in the cases of a C adatom and an N adatom, respectively.



14

(a)

6Ef [eV]

12 10

11

8 12 1

6

2

4 2

4 3 10 5 6 9 50 8 7

0 (7, 8)

(6, 9)

(5, 6)

(6, 7)

(5, 5v)

(4, 5)

(4, 10)

(3, 11)

(3, 4)

(2, 12)

(2, 3)

(1, 2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Bridge site on the Ci-Cj bond, (i, j)

(b)

(c)

(d)

(e)

Figure 6: (a) Formation energy ∆Ef for the relaxed structures of a single C adatom at different bridge sites around MV in graphene. The inset is the structure of MV before adsorbing a C adatom and the symmetry-inequivalent C atoms around a vacancy site are marked by integer numbers. The optimized local atomic structures for a single C adatom adsorbed at the bridge sites of (b) C1−C2 bond, (c) C4−C10 bond, (d) C4−C5 bond, and (e) C5−C6 bond. The atomic structures in panels (b) and (e) are equivalent. During the geometry optimization, the C adatom at the bridge sites of C2−C3 and C2−C12 bonds migrates to the bridge site of C1−C2 bond spontaneously.


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12

(a)

6Ef [eV]

10 11

8

2 12 3 4 10 1 5 6 9 50 8 7

6 4 2 0

(7, 8)

(6, 9)

(5, 6)

(6, 7)

(5, 5v)

(4, 5)

(4, 10)

(3, 11)

(3, 4)

(2, 12)

(2, 3)

(1, 2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Bridge site on the bond between atom i and atom j, (i, j)

(b)

(c)

(d)

Figure 7: (a) Formation energy ∆Ef of a single C adatom at different bridge sites around pyrindinic N doped MV in graphene. The inset is the structure of N-doped MV before adsorbing a C adatom and the symmetry-inequivalent N and C atoms around vacancy site are marked by integer numbers. The optimized local atomic structures for a single C adatom at the bridge sites of (b) N−C2 bond, (c) C4−C10 bond, and (d) C4−C5 bond. A single C adatom at any of (5, 50 ), (6, 7), and (5, 6) bridge sites will convert the pyridinic N to a graphitic N.



13

11 2

12 1

(a)

4

3

(b)

0

7

(c) 13 2

b

d

(k)

e 0

0.2

0.4

0.6

0.8

(j)

7

E [eV]

c

(i)

6

(h)

a

(e)

10

5 5

14 12 10 8 6 4 2 0 -2

4

3

0

(g)

(d)

11

12 1

(f )

10 6

5 5

E [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1

12 f 10 8 6 4 2 0 -2 0

Reaction coordinate

(l)

i

g h

j 0.2

0.4

0.6

0.8

1

Reaction coordinate

Figure 8: Local atomic structure configurations along the reaction paths for the migration of a C adatom near (a)−(e) undoped and (f)−(j) N-doped MVs. The energy evolution along the reaction paths for the migration of a C adatom near (k) undoped and (l) N-doped MVs.


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11 12 1

10

2 3 4 5 50

6

9 8

7

(a) 11 12 1

(c)

(d)

(f )

(g)

(h)

10

2 3 4 5 0 5

(b)

6

9 8

7

(e) 10 8a 6 4 2 0 0

(i)

b c

9

8

on-plane in-plane

E [eV]

E [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8 70

0.2

0.2

0.4

0.4

d

0.6

0.6

0.8

in-plane

e

4

7 6 5 40

2 0

1

f on-plane

(j)

6

0

Reaction coordinate

g h 0.2

0.2

0.4

0.4

0.6

0.6

0.8

1

Reaction coordinate

Figure 9: Local atomic structure configurations along the reaction paths for a C atom migration from the bridge site of C4−C10 bond around (a)−(d) undoped and (e)−(h) Ndoped MVs to Stone-Wales defects. The energy evolution along the reaction paths for a C atom migration from the bridge site of C4−C10 bond around (i) undoped and (j) Ndoped MVs to Stone-Wales defects. The arrow in panels (b), (c), (f), and (g) illustrates the migration direction of the C adatom (denoted as on-plane mechanism) and the substrate C4 atom (denoted as in-plane mechanism).



1.5

(a)

(b)

E [eV]

2 4 1 35 6 50 7

(c)

(f)

0.5

b

a 0

(d)

d

1.0

0.0

b

a

c 0.2

0.4

0.6

0.8

e 1

Reaction coordinate

(e)

Figure 10: Left panels (a)−(e): local atomic structure configurations along the reaction path for the migration of C1 atom (namely, a carbon vacancy migration) in an undoped MV. Right panel (f): energy evolution along the reaction path. The atomic structures for points a0 and b0 in panel (f) are equivalent to those in panels (a) and (b), respectively.

(a)

(b)

(g)

4

2 4 1 35 6 50 7

E [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 40

(c)

d

3 2 1 0

(e)

d e

f

c

a 0

(d)

b

0.2

0.4

0.6

0.8

1

Reaction coordinate

(f )

Figure 11: (a)−(c): Local atomic structure configurations along the reaction path for the migration of doped N atom (pyridine-like) at a MV. (c)−(f): Local atomic structure configurations along the reaction path for the migration of C atoms around N-doped MV. Right panel (g): energy evolution along the reaction path. The atomic structure for point d0 in panel (g) is equivalent to that in panel (d).


Page 39 of 40

2 4 3 1 5 6 50 7

(a)

(b)

Energy [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(c)

4 3a

(g)

b e

2

d

1 0

(d)

(e)

cv

c

0

0.2

0.4

0.6

f 0.8

1

Reaction coordinate

(f )

Figure 12: (a)−(f): Local atomic structure configurations along the reaction path for C and/or H atoms around a monohydrogenated MV. Right panel (g): energy evolution along the reaction path. The atomic structure for point c0 in panel (g) is equivalent to that in panel (c) and C5 atom is hydrogenated. Grey and cyan balls represent C and H atoms, respectively.



Graphical TOC Entry 2 Relative energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0

0.40

-2 -4

9.61

-6 -8 -10

Reaction coordinate


Page 40 of 40

Effect of Nitrogen Doping on the Migration of the Carbon Adatom and

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