1 Introduction

Lithium–air batteries have attracted considerable recent attention as a highly promising energy storage system that could replace Li-ion batteries owing to their markedly superior theoretical energy density and low cost [1, 2]. However, the development of lithium–air batteries is still at its initial stage, and there are many technical challenges limiting their practical uses, such as low round-trip efficiency, poor rate capability and low cycle life [1, 2]. These problems mainly result from the sluggish kinetics of the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) at the cathode.

In an effort to enhance the kinetics at the lithium–air cathode and hence improve the overall performance of the battery, much intensive research has been devoted to the development of high-performance cathode materials [3]. Among the many potential cathode materials, graphene has been considered as one of the most interesting materials because of its unique properties such as large surface area, high electrical conductivity, and good chemical and thermal stability [4]. In addition, graphene can be easily tailored by diverse modification methods. Hence, further developments involving modifying the surface of graphene have been made in order to promote the electro-catalytic activity of the graphene electrode during the ORR and thus improve the specific capacity and cycling performance of the battery [5–25].

Among the various potential surface modifications, doping heteroatoms into graphene has attracted substantial interest due to its effectiveness at tailoring the electronic and chemical properties and enhancing catalytic activity [11, 12]. The N atom in particular is one of the most promising candidates for doping because its atomic size is closest to that of the C atom, and hence can be relatively easily made to substitute for a C atom in the lattice of hexagonal rings of graphene. Therefore, N-doped graphene has been more easily synthesized than have other types of doped graphene, and its synthesis has recently been actively carried out using several different methods, such as chemical vapor deposition (CVD) [26], thermal treatment [27, 28] and plasma treatment [29]. Furthermore, N-doped graphene has been found to be an even more excellent catalyst for the ORR than have noble metal (Pt, Au) and transition metal oxides (MnO2, Fe2O3, Co3O4) due to its availability and comparatively low price and hence suitability for large-scale production and commercialization [13–22]. However, the catalytic activity of N-doped graphene is still a subject of debate, and the molecular-scale mechanism by which LixO2 lithium oxides adsorb on N-doped graphene during the ORR has not yet been fully clarified.

Herein, we used density functional theory (DFT) calculations to gain an understanding of the mechanism of the adsorption of LixO2 lithium oxides on N-doped graphene. This mechanism was investigated by calculating the adsorption energies of ORR reactants O2 and Li and of ORR products LiO2 and Li2O2 on N-doped graphene and analyzing the accompanying electronic structures and properties, such as the band structure, density of states (DOS), derived electrostatic and chemical (DDEC) charge distribution, and electronic charge density distribution.

2 Computational methods

All calculations were performed within the DFT framework as implemented in the Vienna ab initio simulation package (VASP) [30, 31] to solve the Kohn–Sham equations with a plane-wave basis set, with a kinetic energy cutoff of 500 eV. The projector augmented wave (PAW) potential [32] was applied to describe core electrons. The spin-polarized generalized gradient (GGA) approximation with the Perdew–Burke–Ernzerhof (PBE) functional [33, 34] was employed to treat the exchange–correlation energy of interacting electrons. The GGA–PBE functional has been widely used to investigate carbon-based materials [35–42]. The 4 × 4 supercell model of graphene, which was set to 9.84 Å × 9.84 Å × 15 Å, was used. We selected the N-substituted graphene due to the lowest formation energy compared with other N-doped defect graphene including pyridinic or pyrrolic configuration [43]. The calculations were performed within the periodic boundary conditions, with 15 Å of vacuum space included, large enough to avoid direct interactions between the original structure and its periodically repeated image along the c-axis. The Brillouin zone was sampled with 5 × 5 × 1 k-point meshes centered at the gamma point using the Monkhorst–Pack scheme. Atomic positions were fully relaxed until the forces on each atom were smaller than 0.01 eV/Å and the total energies were converged within 10−6 eV. For all geometrical optimizations, a dipole correction was applied to compensate for the dipole interactions along the c-axis direction. The DFT-D3 correction of the Grimme scheme was incorporated with the PBE functional to account for the van der Waals interactions [44]. The adsorption energy of each system (∆E adsorption) was calculated by using the definition.

$$\Delta E_{\text{adsorption}} = E_{\text{total}} - (E_{{n - {\text{graphene}}}} + E_{\text{adsorbate}} )$$
(1)

where E total is the total energy of the system, E n-graphene is the energy of the N-doped graphene and E adsorbate is the energy of the adsorbate species in a vacuum, respectively. Please note that, according to this definition, a negative value of the adsorption energy indicates that adsorption is favorable, whereas a positive value indicates that it is unfavorable. To evaluate the quantitative charge distributions between the adsorbate species and graphene surface, the density-derived electrostatic and chemical (DDEC) method [45] was performed. To study the diffusion of Li atom on N-doped graphene, we used the climbing image nudge elastic band (CI-NEB) method.

3 Results and discussion

3.1 Adsorption of O2 on N-doped graphene

In order to understand the adsorption mechanism of LixO2 lithium oxides, which are ORR products, we considered two possible pathways to produce these oxides: O2 → LiO2 → Li2O2 and Li → LiO2 → Li2O2. The former denotes an ORR pathway in which an O2 molecule initially adsorbs onto N-doped graphene and then Li atoms adsorb onto the N-doped graphene and adsorbed O2, whereas the latter indicates the initial anchoring of one Li atom on N-doped graphene that are then bound by an O2 molecule and a second Li atom. We aimed to predict which of the two pathways predominate by investigating the numerous possible adsorption structures.

First, we considered the various possible adsorption sites of the O2 molecule on N-doped graphene, as shown in Fig. 1. We considered the adsorption sites in which O2 spans a hexagonal ring that contains a doped N atom (configurations “O2_A” and “O2_B”) and in which O2 similarly spans an all-carbon hexagonal ring far from an N atom (configurations “O2_C” and “O2_D”). In configuration O2_A, the O2 molecule was initially made to form a bridge “over” the N-containing ring from the nitrogen atom to the opposing (para) carbon atom, whereas in configuration O2_B it was made to form a bridge between the midpoints of opposite C–C bonds. Similarly, O2 was started off bridging para-related carbons of the all-carbon ring in configuration O2_C and opposite C–C bonds of the all-carbon ring in configuration O2_D. The considered sites were: (1) site O2_1A, in which O2 lays across the midpoint of the C–C bond; (2) site O2_1B, in which O2 lays across two opposing carbon atoms; (3) site O2_1C, in which the O2 lays across two adjacent carbon atoms; and (4) site O2_1D, in which the O2 lays above the center of a hexagon ring. The adsorption energies, DDEC charge distributions, distance from the graphene to the center of mass of O2 and the bond length of O2 at various adsorption sites are given in Table 1.

Fig. 1
figure 1

Optimized structures of the various configurations of O2 adsorbed on N-doped graphene: a top and side views of O2_A, b top and side views of O2_B, c top and side views of O2_C, d top and side views of O2_D. The gray, red and blue colors denote carbon, oxygen and nitrogen, respectively

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Table 1 Adsorption energy, DDEC charge distribution, vertical distance from N-doped graphene to O2 and bond length of O2 for various adsorption configurations in the O2-adsorbed N-doped graphene
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The adsorption energies, charge distributions through DDEC charge analysis, vertical distance from the N-doped graphene to the center of mass of O2 and the bond length of O2 at the various adsorption configurations are given in Table 1. The adsorption energies for O2 adsorbed on the hexagonal ring containing an N atom in configurations O2_A and O2_B were calculated using DFT to be stronger than those for O2 adsorbed on the all-carbon ring in configurations O2_C and O2_D. The adsorption energies of the O2 molecule on N-doped graphene were in the range of −0.280 to −0.215 eV and hence stronger than the adsorption energies of −0.111 to −0.089 eV on pristine graphene in our previous study [46]. The distance between the O2 molecule and N-doped graphene (3.015 and 3.173 Å for the two configurations) was shorter than the distance between the O2 molecule and pristine graphene (3.204 and 3.284 Å). In addition, due to the higher electronegativity of O than C and N, substantial charge (−0.255 to −0.169e) was transferred from N-doped graphene to O2, compared with pristine graphene (−0.036e) [46]. Therefore, these results indicated that N doping enhanced the interaction between the O2 molecule and graphene, but O2 was still weakly physisorbed onto N-doped graphene.

3.2 Adsorption of Li on N-doped graphene

Next, we placed a Li atom on N-doped graphene in various possible adsorption configurations. As shown in Fig. 2, three high-symmetry adsorption sites were considered: (1) the site above the C atom nearest the N atom (configuration Li_A); (2) the site above the center of the hexagonal ring containing an N atom (configuration Li_B); and (3) the site above the center of the all-carbon ring farthest from the N atom (configuration Li_C). The adsorption energies of the Li atom onto N-doped graphene varied from −1.001 to −0.503 eV, as shown in Table 2. The site above the center of the all-carbon hexagonal ring farthest from the N atom (configuration Li_C) was the most favorable position for the adsorption of Li, with an adsorption energy of −1.001 eV and a distance of 1.683 Å, indicative of a strong Coulombic interaction. Note that increasing the distance between the adsorbed Li atom and the N atom resulted in stronger interactions between Li and graphene. However, in contrast to the adsorption energies of a Li atom (−1.079 to −0.768 eV) and the amount of transferred charge (−0.917 to −0.910 e) on pristine graphene [46], the adsorption energies and the amounts of transferred charge on N-doped graphene were decreased. These results may be explained by the Li atom having a tendency to readily lose an electron in order to attain a stable complete-shell electron configuration, whereas electron-rich N-doped graphene tends not to accept more electrons [47], resulting in the N atom on N-doped graphene and the Li atom repelling each other. However, the Li atom in our calculations still adsorbed (−1.001 to −0.503 eV) more strongly onto N-doped graphene than did the O2 molecule (−0.280 to −0.215 eV), and the vertical distance between the Li atom and N-doped graphene (1.683–1.982 Å) was shorter than this distance between the O2 molecule and N-doped graphene (3.015–3.173 Å). Moreover, the charge transferred from the Li atom to N-doped graphene (−0.895 to −0.868 e) was larger than that transferred from the O2 molecule (−0.255 to −0.169 e). Thus, we predict that a Li atom would tend to adsorb onto N-doped graphene before an O2 molecule would do so, and that the ORR mechanism would therefore preferentially follow the Li → LiO2 → Li2O2 pathway. Because Li atom was preferentially adsorbed on N-doped graphene, it is important to figure out the diffusion of Li atom on N-doped graphene. As shown in Fig. 3, we calculated the diffusion of Li atom between site Li_B and site Li_C on N-doped graphene. The energy barrier for the diffusion of Li atom from site Li_B to site Li_C was ~ 0.10 eV (~ 0.43 eV for the opposite direction). It means that Li atom can be easily diffused toward the region which is far from the hexagonal ring containing N atom.

Fig. 2
figure 2

Optimized structures of the various configurations of Li adsorbed on N-doped graphene: a top and side views of Li_A; b top and side views of Li_B; c top and side views of Li_C. The gray, purple and blue colors denote carbon, lithium and nitrogen, respectively

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Table 2 Adsorption energy, DDEC charge distribution and vertical distance from N-doped graphene to Li for various adsorption configurations in the Li-adsorbed N-doped graphene
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Fig. 3
figure 3

Energy profile for the diffusion of Li atom along the pathway between site Li_B and site Li_C on N-doped graphene

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3.3 Adsorption of LixO2 on N-doped graphene

We next simulated the adsorption of LiO2 on N-doped graphene with a configuration in which the Li atom of LiO2 was initially positioned on the center of the hexagonal ring containing the N atom. Geometry optimization resulted in this Li atom moving farther away from the N atom, as shown in Fig. 4a. The distance between LiO2 and N-doped graphene was calculated to be 2.438 Å, and the corresponding adsorption energy was calculated to be −0.588 eV (Table 3), which is stronger than that for pristine graphene (−0.450 eV) [46].

Fig. 4
figure 4

Optimized structures of the various configurations of LixO2 adsorbed on N-doped graphene: a top and side views of LiO2_A, b top and side views of Li2O2_A, c top and side views of Li2O2_B. The gray, red, purple and blue colors denote carbon, oxygen, lithium and nitrogen, respectively

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Table 3 Adsorption energy, DDEC charge distribution and vertical distance from N-doped graphene to the Li atom of LixO2 for various adsorption configurations in the LixO2-adsorbed N-doped graphene
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We also investigated the structures consisting of Li2O2 adsorbed onto N-doped graphene. There are two possible adsorption sites based on the adsorption configuration of O2 onto N-doped mentioned above. As shown in Fig. 4b, c, the considered configurations were as follows: (1) configuration Li2O2_A, in which the two Li atoms of the Li2O2 molecule were positioned above the midpoints of opposite C–C bonds and the two O atoms in Li2O2 were, respectively, positioned above the N atom and the para C atom; and (2) configuration Li2O2_B, in which the Li2O2 of Li2O2_A was essentially rotated by 90°. Li2O2 in both configurations Li2O2_A and Li2O2_B experienced substantial structural deformations upon optimization; their structures became bent in response to a close approach of the Li2O2 of Li atoms to the graphene. Configuration Li2O2_A was calculated to have the more favorable adsorption, with an adsorption energy of −0.642 eV, which is stronger than those on pristine graphene (−0.630 to −0.611 eV) [46]. Li2O2_A also displayed the shorter distance between Li2O2 and N-doped graphene (2.607 Å) and was accompanied by substantial charge transfer (|0.241e|).

3.4 Analysis of the other electronic properties

We also investigated the electronic properties of all the systems in order to gain further insight into their adsorption behaviors. Figure 5 shows the band structure of graphene, N-doped graphene, O2-adsorbed N-doped graphene, Li-adsorbed N-doped graphene, LiO2-adsorbed N-doped graphene and Li2O2-adsorbed N-doped graphene systems. We chose the most stable configurations for each system to analyze the electronic properties. The band structure of pristine graphene featured Dirac points at the Fermi level, in which the valence and conduction bands coincide, and displays metallic characteristics with a zero band gap. Because the N atom, with its five valence electrons, has one more valence electron than does the C atom, the doping of the N atom into graphene makes it a more electron-rich system. Hence, the band structures of N-doped graphene showed energy bands that were shifted down to the Fermi level, as shown in Fig. 5b. In addition, we found that the Dirac point, which is a specific property of graphene, became blurred due to the breaking of the symmetry of the graphene sub-lattices that resulted from the inclusion of the N atom [48]. In the N-doped graphene/O2 system (Fig. 5c), the energy bands were slightly shifted up in comparison with the pristine N-doped graphene system owing to the hybridization between O2 and N-doped graphene orbitals. As compared to the case of the pristine N-doped graphene system, the N-doped graphene/Li system (Fig. 5d) showed that the energy bands were downshifted because of the electron injection from the Li atom to N-doped graphene. In the N-doped graphene/LiO2 system (Fig. 5e), the slightly more downshifted energy bands, compared to those of the N-doped graphene system, resulted from the hybridization between Li, O2 and N-doped graphene. In the N-doped graphene/Li2O2 system (Fig. 5f), we found more band shifts than for the N-doped graphene/LiO2 system because electrons from the two Li atoms of Li2O2 were injected into N-doped graphene.

Fig. 5
figure 5

Band structures of a graphene, b N-doped graphene, c N-doped graphene/O2, d N-doped graphene/Li, e N-doped graphene/LiO2 and f N-doped graphene/Li2O2

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To gain a deep understanding of the electronic structures in each system, we examined the density of states (DOS) and local density of states (LDOS), as shown in Fig. 6. The DOS of pristine graphene and N-doped graphene are shown in Fig. 6a, b, respectively. The DOS of pristine graphene featured a zero DOS at the Fermi level, and that of N-doped graphene was downshifted to below the Fermi level due to its electron-rich character resulting from the doping of the N atom. In the N-doped graphene/O2 system (Fig. 6c), the adsorption of O2 on N-doped graphene introduced the appearance of spin polarization, which was caused by a new spin-up O p peak around the Fermi level. In the N-doped graphene/Li system (Fig. 6d), the overall DOS was downshifted, as compared with the DOS of N-doped graphene system, and the DOS peak around the Fermi level was increased. The DOS of the Li s orbital was found to partially contribute to the total DOS according to the LDOS analysis. In the case of the N-doped graphene/LiO2 and N-doped graphene/Li2O2 systems (Fig. 6e, f), the total DOS were observed to be shifted down and the hybridization of the O p, Li s, C p and N p orbitals contributed to the introduction of spin polarization of the total DOS. Furthermore, we calculated the charge density difference of lithium oxides (LiO2 and Li2O2) adsorbed on the N-doped graphene system, ∆ρ, which was defined as follows.

$$\Delta \rho = \rho_{\text{total}} - (\rho_{n - {\text{graphene}}} + \rho_{\text{adsorbate}} )$$
(2)

where ρ total , ρ n – graphene and ρ adsorbate denoted the charge distributions of the total system, of an N-doped graphene surface and of an isolated adsorbate species in vacuum, respectively. Figure 7a, b shows the charge density difference of lithium oxides (LiO2 and Li2O2) adsorbed onto N-doped graphene. The yellow-colored region represents charge accumulation, and the blue-colored region represents charge depletion. The calculations for both systems found a net gain of most charges between the Li atom of the lithium oxides and N-doped graphene. In addition, the gain of electron charge remained in the regions between the oxygen atoms of lithium oxides because of the strong electronegativity of the O atom. These results showed that the most charge was transferred from the Li of lithium oxides (LixO2) to N-doped graphene due to the tendency of Li to easily lose electrons, and therefore a substantial interaction between N-doped graphene and lithium oxides in the intermediate region was observed. Moreover, in our calculations, Li2O2 adsorbed more strongly onto N-doped graphene than did LiO2 because the Li2O2-adsorbed N-doped system had a wider charge accumulation region than did the LiO2-adsorbed N-doped system.

Fig. 6
figure 6

Density of states (DOS) and local density of states (LDOS) of a graphene, b N-doped graphene, c N-doped graphene/O2, d N-doped graphene/Li, e N-doped graphene/LiO2 and f N-doped graphene/Li2O2

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Fig. 7
figure 7

Plots of charge density difference a for N-doped graphene/LiO2 and b for N-doped graphene/Li2O2

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4 Conclusions

We performed DFT calculations to elucidate the adsorption mechanisms of lithium oxides (LixO2) onto N-doped graphene. We considered O2 → LiO2 → Li2O2 and Li → LiO2 → Li2O2 ORR pathways and modeled adsorption properties of the ORR reactants O2 and Li and of the ORR products LiO2 and Li2O2. Our results showed that in the case of N-doped graphene, the adsorption energies of the O2 molecule ranged from −0.280 to −0.215 eV, which were stronger than the adsorption energies (−0.111 to −0.089 eV) on pristine graphene. Moreover, the amount of charge transferred between the adsorbed O2 molecule and N-doped graphene was calculated to be greater than that for O2 adsorbed on pristine graphene, and the vertical distance between O2 and N-doped graphene was less than that between O2 and pristine graphene. Meanwhile, the N-doped graphene achieved in our calculations lowers adsorption energies of Li (−1.001 to −0.503 eV) with less charge transfer (−0.895 to −0.868 e) than did the pristine graphene (−1.079 to −0.768 eV). In addition, the calculated adsorption energies clearly tended to increase as the O2 molecule was moved closer to the substituted N atom, and as the Li atom was moved away from the N atom, results that can be explained by the doping of the N atom making graphene an electron-rich system. Hence, the electron-donating Li atom preferred to be adsorbed onto a site of graphene far away from the electron-rich N-substituted hexagonal ring, whereas electronegative O2 favored this ring as the adsorption site. However, because the adsorption of Li onto graphene was still found to be stronger than the adsorption of O2 onto graphene, we conclude that the Li atom may be adsorbed by graphene before O2 is adsorbed, and therefore the ORR may preferentially follow the Li → LiO2 → Li2O2 pathway. For all of the LiO2 and Li2O2 adsorption configurations, the N-doped graphene bound LiO2 and Li2O2 more strongly than did pristine graphene in our calculations. The band energies and DOS in the N-doped graphene/LiO2 and N-doped graphene/Li2O2 systems were shifted down compared to those of the bare N-doped graphene system due to electron injection of the Li atom of lithium oxides. In addition, according to the electronic charge density distribution analysis, much of the transferred charges were accumulated in the region between the Li atoms of the lithium oxides and the N-doped graphene. These results indicate an enhancement of the adsorption of lithium oxides (LixO2) with significant charge transfer by N doping of graphene.