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Probing the activity of transition metal M and heteroatom N4 co-doped in vacancy fullerene (M–N4–C64, M = Fe, Co, and Ni) towards the oxygen reduction reaction by density functional theory

In this study, a novel type oxygen reduction reaction (ORR) electrocatalyst is explored using density functional theory (DFT); the catalyst consists of transition metal M and heteroatom N4 co-doped in vacancy fullerene (M–N4–C64, M = Fe, Co, and Ni). Mulliken charge analysis shows that the metal center is the reaction site of ORR. PDOS analysis indicates that in M–N4–C64, the interaction between Fe–N4–C64 and the adsorbate is the strongest, followed by Co–N4–C64 and Ni–N4–C64. This is consistent with the calculated adsorption energies. By analyzing and comparing the adsorption energies of ORR intermediates and activation energies and reaction energies of all elemental reactions in M–N4–C64 (M = Fe, Co, and Ni), two favorable ORR electrocatalysts, Fe–N4–C64 and Co–N4–C64, are selected. Both exhibited conduction through the more efficient 4e− reduction pathway. Moreover, PES diagrams indicate that the whole reaction energy variation in the favorable ORR pathways of Fe–N4–C64 and Co–N4–C64 is degressive, which is conducive to positive-going reactions. This study offers worthwhile information for the improvement of cathode materials for fuel cells.


Introduction
With the expansion of industrialization and urbanization, environmental pollution and energy consumption are being increasingly aggravated. Fuel cells (FCs) have become the most promising power generation technology, with the characteristics of sustainable, pollution-free and wide-ranging fuel sources. [1][2][3][4] The oxygen reduction reaction (ORR) is carried out in the cathode through 2e À and 4e À pathways. 5,6 The 4e À pathway directly reduces O 2 to H 2 O and has high energy conversion efficiency; hence, it is the preferred pathway for FCs. 7,8 However, the 2e À pathway (the less efficient pathway involving the formation of H 2 O 2 as an intermediate) and slow kinetics on the cathode hinder the power generation efficiency of FCs. [9][10][11] In addition, Pt-based catalysts, which are considered to be highly efficient, 12,13 have limited commercial applications in FCs due to their high cost. 14,15 Therefore, it is urgent to exploit highperformance and inexpensive ORR electrocatalysts to substitute the expensive Pt-based catalysts on the market.
Because single-atom catalysts (SACs) have different activity, selectivity and stability from traditional nanocatalysts, 16,17 they are proposed to exhibit remarkable behavior in various energy transformation reactions, such as HER, 18,19 CO 2 RR 20,21 and ORR. 22,23 Moreover, the realization of single-atom dispersion of SACs usually requires a suitable substrate and dopant. 24 Fullerenes are cage structures in which carbon atoms form a conjugated system through sp 2 hybridization. 25 As nonmetallic materials with a wide range of sources, fullerenes have demonstrated excellent performance including biological applications, 26 energy storage, 27 thermoelectric materials, 28 and optoelectronic devices. 29 In addition, as a result of the curvature and pentagon defects of fullerenes, 30,31 they can be used as promising candidates for electrocatalytic reactions. Vinu et al. investigated a polymeric mesoporous fullerene C 60 material prepared at 130 C (MFC 60 -130), which showed effective ORR behavior beneting from its specic surface area of 680 m 2 g À1 and steady and conductive C 60 reticulation. 32 Subsequently, Vinu et al. continued to report mesoporous fullerene C 70 materials, which were endowed with good mesoporous framework, excellent conductivity and connectivity; further, materials exhibited good ORR performance. 33 However, it is necessary to improve their electrocatalytic properties for practical applications.
Heteroatom doping is an effectual way to regulate the electronic and conductive properties of fullerenes and enhance their electrocatalytic behavior. 34, 35 Chen et al. discovered that nitrogen-doped fullerenes showed higher ORR properties than pure fullerenes. 36 Wang et al. also reported that nitrogen-doped C 60 cages (C 59 N) exhibited superior ORR electrocatalytic activity to other heteroatom-doped C 60 cages, 37 which was further experimentally proved by Gao et al. 35 Furthermore, to facilitate the embedding of metal atoms, introducing vacancies in the substrate can change the coordination environment and electronic structure around the vacancies; thus, under-coordinated sites can act as bait and vacancies can act as traps to trap metal atoms. 38,39 The codoping of transition metal atoms and heteroatoms on vacant carbon materials has been widely studied both experimentally and theoretically. Fe-porphyrin-like carbon nanotubes synthesized by Lee et al. showed excellent oxygen reduction activity due to the characteristics of the Fe-N 4 structure. 40 Fei et al. found that the composite material obtained by embedding individual Ni atoms into the double vacancies of an N-doped graphene lattice displayed higher oxygen evolution reaction (OER) activity and stability. 41 Chen et al. embedded individual iron atoms into N-pore carbon through the thermolysis approach of cage-encapsulated precursors, and the composite exhibited remarkable ORR properties and satisfactory methanol tolerance. 42 Recently, Wang et al. reported synthesized Feanchored graphite carbonitride, which was used in CO 2 RR to improve the selectivity of CO and realize the high-efficiency transformation of CO 2 due to the Fe-N 4 sites in the composite. 43 Theoretically, many studies have illuminated that metal-N 4 -vacancy carbon materials have attractive performance as cathode materials for FCs. [44][45][46][47] Signicantly, Brindaban Modak et al. found that transition metal-modied porous fullerene C 24 N 24 can serve as an oxygen reduction electrocatalyst and carry out a more effectual 4e À reduction mechanism. 48 These reports led us to wonder whether transition metal and heteroatom N could be co-doped in vacancy fullerenes as effective electrocatalysts for ORR. However, related reports are rare. Therefore, we systematically studied all possible intermediate steps involved in the ORR process of co-doping transition metal M and heteroatom N 4 in vacancy fullerene (M-N 4 -C 64 , M ¼ Fe, Co, and Ni). The promising ORR electrocatalysts were selected and the corresponding favorable ORR pathways were determined. This work offers worthwhile information for the improvement of cathode materials for FCs.

Computational methods
All calculations were carried out using the spin-polarized DFT implemented in Materials Studio DMol 3 code. 36,49 The generalized gradient approximation of the Perdew-Burke-Ernzerhof functional (GGA + PBE), 48,50 together with all electrons and the double numerical basis set (DNP), was adopted throughout all calculations. To improve computational performance, the selfconsistent eld (SCF) was converged to 10 À6 Ha and the smearing was set to 0.005 Ha. The convergence tolerance was 2 Â 10 À5 Ha for the energy change, 0.004 HaÅ À1 for the max force and 0.005Å for the max displacement. The Grimme method for DFT-D correction was used to describe the van der Waals interactions. The energy difference between the transition state and the reactant was the activation barrier (E act ).
The formation energy (E f ) of M-N 4 co-doped in vacancy fullerene was calculated as follows: where E M-N 4 -C 64 and E fullerene are the energies of the optimized M-N 4 -C 64 and perfect fullerene C 70 , correspondingly. m C and m N are the chemical potentials of carbon and nitrogen atoms, which were obtained by the total energy per C atom in perfect fullerene C 70 and one half of an N 2 gas molecule, correspondingly. E M is the energy of the individual metal atom.
The adsorption energy (E ads ) was calculated as follows:

Conguration and properties of M-N 4 -C 64
To embed M-N 4 in fullerene, as Fig. 1a shows, the no. 1 and 2 carbon atoms in the optimized fullerene C 70 were removed. Then, four nitrogen atoms were utilized to substitute the no. 3, 4, 5 and 6 carbon atoms, which had insufficient coordination. Finally, the metal atom was incorporated in the center of the vacancy. We calculated the different multiplicities of M-N 4 -C 64 (M ¼ Fe, Co, and Ni) to obtain the most stable energies. The results show that the most stable states for Fe-N 4 -C 64 , Co-N 4 - C 64 , and Ni-N 4 -C 64 are triplet, doublet, and singlet, correspondingly. The oxygen molecule is a triplet in our research system. The stable congurations of Fe-N 4 -C 64 , Co-N 4 -C 64 and Ni-N 4 -C 64 were optimized (see Fig. 1b-d), and the formation energies (E f ) of the three congurations were calculated as À3.82, À4.11, and À3.43 eV, correspondingly. This nding demonstrates that Fe-N 4 -C 64 , Co-N 4 -C 64 and Ni-N 4 -C 64 are thermodynamically stable. In addition, as can be seen from the Mulliken charges in Fig. 1e-g, nitrogen atoms in M-N 4 -C 64 (M ¼ Fe, Co, and Ni) show negative charge density, while the adjacent carbon atoms show positive charge density. This is caused by the fact that the electronegativity of N atoms is greater than that of C atoms. This porphyrin-like structure can stably x M-N 4 embedded on C 64 . The Mulliken charges of the Fe, Co and Ni atoms were calculated as 0.664, 0.483 and 0.540|e|, correspondingly. Because a positively charged site is more advantageous for O 2 adsorption, the metal center was chosen as the reaction site for ORR. On the other hand, it was found that in the Fe-N 4 -C 64 system, the electron transfer from the metal center to N 4 -C 64 is the largest.

Electronic structure of M-N 4 -C 64
The calculated DOS (see Fig. 2a) display that the band gaps of Fe-N 4 -C 64 , Co-N 4 -C 64 and Ni-N 4 -C 64 are all zero, which reveals that they have the potential to be ORR electrocatalysts due to their excellent electrical conductivity. The calculated PDOS (see Fig. 2b-d) display that the C-2p and N-2p orbitals in M-N 4 -C 64 (M ¼ Fe, Co, and Ni) exhibit strong resonance regions below the Fermi level, which indicates that the interaction between C and N is very strong. Meanwhile, the PDOS display that in M-N 4 -C 64 , the Co-3d orbital contribution is the most average below the Fermi level, followed by Fe-3d and nally Ni-3d, which is consistent with stability of the calculated E f for M-N 4 -C 64 . In addition, the calculated d-band centers in the range of À8.0 eV-4 eV are À1.24 eV for Fe-N 4 -C 64 , À1.33 eV for Co-N 4 -C 64 and À1.61 eV for Ni-N 4 -C 64 , which demonstrates that the interaction between Fe-N 4 -C 64 and the adsorbate is the strongest among the three, followed by Co-N 4 -C 64 and nally Ni-N 4 -C 64 . This is attributable to the fact that the upward shi of the d-band center to the Fermi level will arouse the upward shi of the antibonding orbitals; thus, they are   Table 1 Activation barriers (E act ), reaction energies (DE) and virtual frequencies (V freq ) of the basic reaction steps for the ORR on M-N 4 -C 64 (M ¼ Fe, Co, and Ni)

Catalysts
Reaction steps harder to ll, and in turn, the interaction between the catalyst and adsorbates is stronger.

The adsorption of ORR species on M-N 4 -C 64
The adsorption of ORR species plays a formative role in the study of the ORR mechanism and electrocatalytic activity. For comparison, Fig. 3 Fig. 4, where the red line pathway represents the optimal summarized ORR mechanism for Fe-N 4 -C 64 . The details of the ORR on Fe-N 4 -C 64 will be discussed next.
For  Fig. 5a. Conversely, the hydrogenation of *O 2 to *OOH is more feasible because for *O 2 + *H / *OOH, this reaction has an exothermic reaction energy of 0.97 eV. Moreover, this process is accompanied by an extremely low E act of 0.06 eV, which is obviously lower than the E ads of *O 2 (À0.73 eV) on Fe-N 4 -C 64 . The virtual frequency (V freq ) of i1514 cm À1 in the transition state TS2 exactly shows the formation of the intermediate *OOH. The hydrogenation details (see Fig. 5b Fig. 5c. Conversely, the reaction *OOH + *H / *O + *H 2 O releases 1.21 eV of energy with a low E act of 0.32 eV, which is more feasible under the support of thermodynamics and kinetics. Moreover, the energy required for this stage is notably lower than the E ads of *OOH (À1.87 eV) on Fe-N 4 -C 64 . The V freq of i1355 cm À1 in TS4 exactly exhibits the formation of *H 2 O, and the formed *H 2 O can be effortlessly detached from the Fe-N 4 -C 64 surface, which only requires a very low energy of 0.27 eV. The hydrogenation details (see Fig. 5d Fig. 6 The conceivable ORR pathways on Co-N 4 -C 64 . The value on the left in parentheses is the activation energy and the value on the right is the reaction energy (in eV). * means adsorbed species. this process is accompanied by a low E act of 0.47 eV, which is signicantly lower than the E ads of *OH (À2.87 eV) on Fe-N 4 -C 64 . The hydrogenation details (see Fig. 5f) indicate that the d Fe-O lengthens from 1.816Å in IS6 to 2.010Å in FS6, which indicates that the interaction between Fe-O is weakened, and the formed *H 2 O can be easily detached from the Fe-N 4 -C 64 surface due to its low E ads of À0.75 eV. V freq is i1298 cm À1 for TS5 and i1426 cm À1 for TS6, respectively. This describes the formation of *OH and the second *H 2 O.
3.4.2 ORR mechanisms on Co-N 4 -C 64 . The ORR mechanisms on Co-N 4 -C 64 were studied, and all conceivable pathways are shown in Fig. 6, where the red and blue lines represent the two pathways that facilitate the ORR on Co-N 4 -C 64 . The details of the ORR on Co-N 4 -C 64 will be discussed next.
For  Fig. 7a. Conversely, the hydrogenation of *O 2 to *OOH is more feasible because for *O 2 + *H / *OOH, this reaction has an exothermic reaction energy of 0.69 eV. Moreover, this process is accompanied by a very low E act of 0.13 eV, which is evidently lower than the E ads of *O 2 (À0.57 eV) on Co-N 4 -C 64 . The V freq of TS8 is i981 cm À1 . The hydrogenation details (see Fig. 7b For *OOH + *H / H 2 O 2 , this reaction has an exothermic reaction energy of 0.46 eV. Moreover, this process is accompanied by an E act of 0.80 eV, which is obviously lower than the E ads of *OOH (À1.54 eV) on Co-N 4 -C 64 . The hydrogenation details (see Fig. 7c) indicate that *H attacks the O atom that bonds to Co, and d O-H decreases from 2.345Å in IS9 to 0.980Å in FS9. Moreover, d Co-O increases from 1.846Å in IS9 to 2.180Å in FS9. The generated H 2 O 2 is adsorbed on Co-N 4 -C 64 with an E ads of À0.70 eV. Then, *H 2 O 2 is instantly decomposed to *O + *H 2 O because the reaction of *H 2 O 2 / *O + *H 2 O has an exothermic energy of 0.23 eV with a very low E act of 0.33 eV, which means that the stage of *H 2 O 2 / *O + *H 2 O on Co-N 4 -C 64 is advantageous both thermodynamically and kinetically. Moreover, the energy required for this stage is lower than the E ads of *H 2 O 2 (À0.70 eV) on Co-N 4 -C 64 . It can be seen that although the *H 2 O 2 on Co-N 4 -C 64 is formed by the 2e À path, both thermodynamics and kinetics character enable its decomposition reaction to pass through the favorable 4e À path again. The decomposition details (see Fig. 7d) indicate that the *H on the O atom that bonds to Co is transferred to the adjacent hydroxyl oxygen to generate the rst *H 2 O, and the generated *H 2 O can be effortlessly separated from the Co-N 4 -C 64 surface, which only requires 0.43 eV. Meanwhile, d Co-O shortens from 2.180Å in IS10/FS9 to 1.720Å in FS10 and d O-O increases from 1.479Å in IS10 to 2.750Å in FS10, which implies that the interaction between Co-O is strengthened and the O-O bond is broken. The V freq of i1469 cm À1 for TS9 and i627 cm À1 for TS10 respectively describe the formation and the decomposition of *H 2 O 2 .
For *OOH + *H / *O + *H 2 O, this reaction has an exothermic reaction energy of 0.41 eV. Moreover, this process is accompanied by an E act of 0.78 eV, which is obviously lower than the E ads of *OOH (À1.54 eV) on Co-N 4 -C 64 . The V freq of i768 cm À1 in TS11 exactly exhibits the formation of *H 2 O, and the formed *H 2 O can easily detach from the Co-N 4 -C 64 surface, which only requires 0.26 eV. The hydrogenation details (see Fig. 7e Moreover, this process is accompanied by a very low E act of 0.04 eV, which is signicantly lower than the E ads of *O (À2.62 eV) on Co-N 4 -C 64 . The hydrogenation details (see Fig. 7f) indicate that d O-H diminishes from 2.134Å in IS12 to 0.976Å in FS12. d Co-O lengthens from 1.724Å in IS12 to 1.821Å in FS12, which manifests that the interaction between Co-O is weakened with the formation of *OH. Then, the *OH remaining on Co experiences the succeeding hydrogenation: *OH + *H / *H 2 O. This stage has an exothermic reaction energy of 0.86 eV. Moreover, this process is accompanied by a very low E act of 0.22 eV, which is evidently lower than the E ads of *OH (À2.54 eV) on Co-N 4 -C 64 . The hydrogenation details (see Fig. 7g) indicate that d Co-O lengthens from 1.848Å in IS13 to 2.098Å in FS13; this indicates that the interaction between Co-O is weakened and the formed *H 2 O can be effortlessly detached from the Co-N 4 -C 64 surface due to the low E ads of À0.60 eV. The V freq values of i918 cm À1 for TS12 and i1467 cm À1 for TS13 respectively describe the formation of *OH and the second *H 2 O.
3.4.3 ORR mechanisms on Ni-N 4 -C 64 . The ORR mechanisms on Ni-N 4 -C 64 are also discussed. Firstly, the positive E ads of 0.33 eV for *O 2 on Ni-N 4 -C 64 demonstrates that the ORR activity of Ni-N 4 -C 64 is unsatisfactory. Fig. 8 shows the 4e À pathway through which the *O 2 on the Ni-N 4 -C 64 is hydrogenated to *OOH, then to *O + *H 2 O; nally, the atomic O remaining on Ni is continuously hydrogenated. As can be viewed in Fig. 8, the stage of *OOH + *H / *O + *H 2 O requires an endothermic reaction energy of 0.21 eV to complete. Moreover, the two stages for *O + *H / *OH and *OH + *H / *H 2 O have extremely high energy barriers (3.25 eV and 2.97 eV). In conclusion, Ni-N 4 -C 64 is unfavorable as an ORR electrocatalyst.

PES and relative energy
The relative energy curve can be utilised as an effective method to assess the ORR properties of M-N 4 -C 64 (M ¼ Fe, Co, and Ni). Fig. 9a-c exhibit the potential energy surface (PES) diagrams of Fe-N 4 -C 64 , Co-N 4 -C 64 , and Ni-N 4 -C 64 , correspondingly. In Fig. 9a Fig. 9a), the rst stage is to hydrogenate *O 2 to *OOH; *OOH is then hydrogenated to *O + *H 2 O, and nally the atomic O remaining on Fe is continuously hydrogenated. The rate-limiting step (RLS) for the favorable red line path on Fe-N 4 -C 64 is *OH + *H / *H 2 O with an E act of 0.47 eV. Moreover, the entire reaction energy variation of the red line path on Fe-N 4 -C 64 is degressive, which is conducive to positive-going reactions. Co-N 4 -C 64 can facilitate the ORR via two different paths (see Fig. 9b). One of the two paths is consistent with the aforementioned favorable ORR red line path on Fe-N 4 -C 64 . The RLS for this advantageous red line path on Co-N 4 -C 64 is *OOH + *H / *O + *H 2 O with an E act of 0.78 eV. For the other path, the difference from the red line path is that the intermediate *OOH in this path is hydrogenated to *H 2 O 2 . The generated *H 2 O 2 is immediately decomposed into *O + *H 2 O to continue the 4e À path because this stage has an exothermic reaction energy of 0.23 eV with a much lower E act (0.33 eV) than the E ads of *H 2 O 2 (À0.70 eV); nally, the atomic O remaining on Co is continuously hydrogenated. Moreover, the RLS for this feasible path on Co-N 4 -C 64 is *OOH + *H / *H 2 O 2 with an E act of 0.80 eV. The entire reaction energy variation of the two favorable ORR paths on Co-N 4 -C 64 is degressive, which is conducive to positivegoing reactions. Meanwhile, Fig. 9c intuitively shows that Ni-N 4 -C 64 as an ORR electrocatalyst is an unfavorable choice because the two stages for *O + *H / *OH and *OH + *H / *H 2 O possess high energy barriers.

Conclusions
In this work, the density functional method was utilized to systematically study the co-doping of transition metal M and heteroatom N 4 in vacancy fullerene (M-N 4 -C 64 , M ¼ Fe, Co, and Ni) as a novel type of non-precious ORR electrocatalyst. The calculated formation energies indicated that Fe-N 4 -C 64 , Co-N 4 -C 64 and Ni-N 4 -C 64 are thermodynamically stable. Mulliken charge studies manifested that the metal center is the reaction site of the ORR and that the electron transfer from the metal center to N 4 -C 64 is the largest in the Fe-N 4 -C 64 system. PDOS revealed that the interaction between Fe-N 4 -C 64 and the adsorbate is the strongest among the three, followed by Co-N 4 -C 64 and nally Ni-N 4 -C 64 . The results of the calculated adsorption energies are consistent with the PDOS analysis. By analyzing and comparing the adsorption energies of the ORR species and the activation energies and reaction energies of all the basic ORR reaction steps involved in M-N 4 -C 64 , two favorable ORR electrocatalysts, Fe-N 4 -C 64 and Co-N 4 -C 64 , were selected. Meanwhile, favorable ORR paths on Fe-N 4 -C 64 and Co-N 4 -C 64 were determined, and both catalysts used 4e À mechanisms to facilitate ORR. This study demonstrates that Fe-N 4 -C 64 and Co-N 4 -C 64 are high-efficiency ORR electrocatalysts. We expect that the proposed transition metal and heteroatom N 4 co-doped in vacancy fullerene can contribute to the development of cathode materials for FCs.

Conflicts of interest
There are no conicts to declare.