First-principles calculation of the electronic properties of graphene clusters doped with nitrogen and boron: Analysis of catalytic activity for the oxygen reduction reaction

Recent studies suggest that the carbon-alloy catalyst with doped nitrogen may be a powerful candidate for cathode catalyst of fuel cell. In this paper, we aim to clarify the microscopic mechanisms of the enhancement in the catalyst activity caused by nitrogen doping using a simple graphene cluster model. Our analysis is based on the density-functional electronic-structure calculations. We analyze modifications in the electronic structures and the energetical stability for some different configurations of N doping. We extend the analysis to the case of codoping of nitrogen and boron and propose two possible scenarios explaining the further enhancement of catalytic activity by N and B codoping.

Figure 1

Spin-density distribution of a pure graphene cluster. The contour for a given spin density of $0.003{\mu }_B/{\text{Bohr}}^3$ is plotted. Magnetic moments are large along the zigzag edge and decay fast into the interior of the cluster. Magnetic moments on opposite edges are antiparallel. For example, light (dark) shadow denotes up- (down-) spin magnetic moments. The horizontal and vertical dot-dashed lines denote the presence of mirror planes.

Figure 2

(Color online) The circles in the right panel are the magnetic moment of atoms at the edge of pure graphene cluster. The crosses are the total energy of N-doped graphene cluster for different site of doped N. The case with doped N located nearly at the center of the graphene cluster (labeled as “C”) is taken as the reference of the total energy.

Figure 3

(Color) The middle panel shows the TDOS of a pure graphene cluster which is shown as the right middle panel. The upper black (lower red) lines denote the up- (down-) spin states. Some orbitals near the Fermi level are shown. Red (blue) means positive (negative) parts.

Figure 4

(Color online) TDOS and LDOS of pure graphene cluster. Upper peaks and lower ones show the DOS of spin-up and spin-down component, respectively. There are edge states near the Fermi level on the atoms along the zigzag edge, which show opposite spin polarization along the opposite edge. The number shown for each spin state of each atom in the DOS panel denotes number of electrons in the particular spin state and the number in the parentheses denotes the total number of electrons for each atom. Cc is the carbon atom nearly at the center of the cluster and $\text{C}{3}^{\prime }$ is a counter site of C3 along the opposite zigzag edge.

Figure 5

(Color online) Position dependence of stability of doped N. The total energy for an N atom sitting nearly at the center of the cluster is taken as the reference. The relative total energy in eV for different site of doped N is listed. The results show that the doped N favors the zigzag edge sites.

Figure 6

(Color online) TDOS and LDOS of N-doped graphene cluster. N dopant denoted as N1 is located along the zigzag edge. $\text{C}{3}^{\prime }$ is along the other zigzag edge. The edge states near the Fermi level on the neighboring atoms along the zigzag edge are largely suppressed.

Figure 7

(Color) The middle panel shows TDOS of an N-doped graphene with N located at the zigzag edge as shown in the right middle part. The upper black (lower red) lines denote the up- (down-) spin states. Some orbitals near the Fermi level are shown. Blue (red) means positive (negative) parts.

Figure 8

(Color online) TDOS and LDOS of N-doped graphene cluster. N dopant denoted as N2 is located at a site next to the zigzag edge. $\text{C}{3}^{\prime }$ is along the other zigzag edge. The zigzag edge states near the Fermi level on the neighboring atoms along the zigzag edge are largely enhanced.

Figure 9

(Color online) A screening mechanism for N2 in Fig. 8. (a) The original LDOS and the carbon potential in pure graphene cluster are schematically shown. “edge C” denotes a carbon atom along a zigzag edge, for example, C1 and C3, and “edge-1 C” denotes a carbon atom located at a site next to a zigzag edge, for example, C2 in Fig. 4. (b) “edge-1 N” denotes N2. A deeper potential of N than C cannot pull down the unoccupied edge state but increases the amplitude of wave functions of occupied states at N2 so that the charge neutrality is satisfied at N2. This causes the deficiency in the electron number at the neighboring carbons C1 and C3. The situation is illustrated in the right bottom panel. (c) The electron deficiency at C1 and C3 produces attractive potential which pulls down the unoccupied edge states to be filled. The charge neutrality at every site is thus approximately achieved.

Figure 10

(Color) The middle panel shows TDOS of an N-doped graphene with N located at a site next to the zigzag edge as shown in the right middle part. The upper black (lower red) lines denote the up- (down-) spin states. Some orbitals near the Fermi level are shown. Red (blue) means positive (negative) parts.

Figure 11

(Color online) Graphene cluster with two N dopants. One of the two N dopants is always located at the site numbered “0” along the zigzag edge. The total energy of the system with two N dopants is measured with reference to the case where the second N dopant is located at the center of the cluster. The number shown at each site denotes the relative total energy (in eV) of the system where the second N dopant is located at the site. The inset plot denotes the interaction energy (in eV) between two N dopants, the first one being at the site labeled as 0 and the second one at another site.

Figure 12

(Color online) Position dependence of stability of doped B. The total energy for a B atom sitting nearly at the center of the cluster is taken as the reference. The relative total energy in eV for different site of doped B is listed. The results show that the doped B also favors the zigzag edge sites.

Figure 13

(Color online) TDOS and LDOS of B-doped graphene cluster. B dopant denoted as B1 is located along the zigzag edge. $\text{C}{3}^{\prime }$ is along the other zigzag edge. The zigzag edge states near the Fermi level on the neighboring atoms along the zigzag edge are largely suppressed.

Figure 14

(Color online) TDOS and LDOS of B-doped graphene cluster. B dopant denoted as B2 is located at a site next to the zigzag edge. $\text{C}{3}^{\prime }$ is along the other zigzag edge. The zigzag edge states just above the Fermi level on the neighboring atoms along the zigzag edge are largely enhanced.

Figure 15

Energetic stability of configurations of B and N codoping. For (a) to (d), the B dopant (open circle) is first located along the zigzag edge and the N dopant (filled circle) is put at some different sites. In the configuration (e), N is located along a zigzag edge site. The number outside parenthesis is the relative total energy of each configuration with the configuration (a) taken as the reference. The interaction energy between two dopants is estimated by an equation similar to Eq. (1) and is listed in the parenthesis.

Figure 16

(Color online) TDOS and LDOS for a B-N complex in a graphene cluster. $\text{C}{3}^{\prime }$ is along the other zigzag edge. At the edge carbon C3 next to N, the weight of zigzag edge states just below the Fermi level is enhanced compared with that for pure graphene. Some weight of edge states can also be observed at B1.

Figure 17

(Color online) TDOS and LDOS for a N-B complex in a graphene cluster. $\text{C}{3}^{\prime }$ is along the other zigzag edge. At the edge carbon C3 next to B, the weight of zigzag edge states just below the Fermi level is nearly the same as that for pure graphene.

Figure 18

Relative energetic stability of (N-B, N) complexes. Open circle denotes B and filled one N. The configuration (a) is taken as a reference.

Figure 19

(Color online) TDOS and LDOS for a (N-B, N) complex in a graphene cluster. The B dopant is located along the zigzag edge, and two N dopants are next to it. $\text{C}{3}^{\prime }$ is along the other zigzag edge. At the edge carbons C3 and C5 next to N, the weight of zigzag edge states near the Fermi level is enhanced compared with that of pure graphene cluster. Some weight of zigzag edge states can also be observed at B1.