Model and stability
As stated in section 2, the different C pairs make MN4C60 structure different. Therefore, the calculated Esub values are plotted in Fig. 2a, and the optimized MN4C60 structure are shown in Fig. 2b and c (taking CoN4C60-I and CoN4C60-II as example). It can be seen that all type I structures are more stable and show more generation tendency than that of type II MN4C60, suggesting that the energetically more favorable configuration of MN4C60 is type I. Hence, the MN4C60-II structures will no longer be considered in following discussion.
To evaluate the difficulty for encapsulating M4 clusters in C60, the Eenc values are calculated and displayed in Fig. 3a. All Eenc values are as high as ~10 eV, which indicates the thermodynamic instability of M4@MN4C60. Meanwhile, this also intrinsically explains why few successfully experimental synesis of EMFs have been reported. The optimized M4@MN4C60 structure are shown in Fig. 3b−d. Clearly, the metal cluster is encapsulated in the C60 shell in the form of triangular pyramid, with the shell showing barely extension, indicating that the M4@MN4C60 can exist stably.
Thermodynamics of ORR on M4@MN4C60
According to Sabatier principle [47], to design a catalyst with promising performance, the appropriate intermediates biding is necessary. Therefore, we explored the binding behaviors of the ORR intermediates on M4@MN4C60, as shown in Fig. 4. For FeN4C60, the negative ΔG*OH value indicates the extremely *OH binding, which may hinder the last proton-electron transfer step, thus lowering the catalytic activity. After encapsulation, the over-strong *OH binding is significantly improved, making ΔG*OH as high as 0.90 eV and close to the ideal ΔG*OH value 1.23 eV. In addition, the ΔG*O slightly decreased, which may attribute to the slightly collapsed MN4 sites. Contrarily, the ΔGads values on Co4@CoN4C60 and Ni4@NiN4C60 are decreased to various degrees compared to corresponding MN4C60, with the bulge MN4 sites not collapsing obviously. Aiming at ideal ΔGads values (ΔG*OOH = 3.69 eV, ΔG*O = 2.46 eV, ΔG*OH = 1.23 eV), the Fe4@FeN4C60 possesses the closest ΔGads values among all studied catalysts, suggesting the great potential for ORR applying.
Previous work reported that ΔG*OH and (ΔG*OH − ΔG*O) can be recognized as two independent descriptors to descript the ORR activity of catalysts [48−50], the volcano map of ηORR as the function of these two descriptors are therefore plotted and shown in Fig. 5. It can be seen that the CoN4C60 data point located at the edge of dark blue region which represents the promising activity with ηORR below 0.43 V. Meanwhile, the Fe4@FeN4C60 also falls on the blue high-activity region, which contrast obviously with FeN4C60 in undesirable red region. For Ni4@NiN4C60, it shows relatively strong *OH binding compared to original NiN4C60, which makes it left shift from the narrow transition area between blue high-activity region and red poor-activity region to the loose transition area, and it shows higher activity than NiN4C60.
For deeply investigating the ORR mechanism, the Gibbs free energy diagram are plotted in Fig. 6. It is clearly seen that all studied MN4C60 and M4@MN4C60 can catalyze ORR process spontaneously except for FeN4C60. Meanwhile, after encapsulated Fe4 cluster, the Fe4@FeN4C60 possesses sharply reduced ηORR of 0.58 V, which benefiting from the tuned *OH binding and thereby enhanced last patron-electron step of *OH reduction, and the rate-determining step (RDS, step with the highest ΔG) even changed to the third step of *OH generation. For Co-metallofullerenes, the origin CoN4C60 possesses a low ηORR of 0.43 V, which is lower than the theoretical model of commercial Pt catalysts (0.45 V) [44]. After encapsulation, the binding of ORR intermediates on Co4@CoN4C60 are all became stronger, leading to a hinderance in *OH reduction step. For Ni-metallofullerenes, the over-weak binding of ORR intermediates, especially *OOH, is the main block of the ORR process. Fortunately, it is significantly improved as the encapsulation of Ni4 cluster. In summary, the binding of ORR intermediates is generally getting tuned after the cluster encapsulation, and the ORR mechanism may also be changed according to the change in RDS.
Activity origin
The electronic structure calculations are performed to unveil the origin of ORR activity for M4@MN4C60, and the FeN4C60 and Fe4@FeN4C60 are selected as representative. The charge deformation density of these two catalysts is calculated and displayed respectively in Fig. 7a and b, and the inserts are the profile chart across Fe atom along XY plane. It can be seen that the electron-depletion region obviously reduces after the encapsulation of Fe4 cluster, while contrarily strengthening for the electron-accumulation region. This indicating that the Fe4 cluster plays a role of “electron donor”, which can donate electrons to the outer-layer exposed Fe atom, and the enriched electrons of Fe in Fe4@FeN4C60 lead to the weakened binding of *OH. This can also be reflected by the lifted highest occupied molecular orbital (HOMO) level and the barely changed lowest unoccupied molecular orbital (LUMO) level (Fig. 7c). The density of states analysis of *OH binding system further confirm the above conclusion, as shown in Fig. 7d. It can be seen that the energy level of σ bonding orbital of O atom in *OH on FeN4C60 is clearly lower than that on Fe4@FeN4C60, and the d-states of Fe in Fe4 cluster hybrids with the Fe in active center, thereby making upshifted σ bonding orbital of O atom in *OH on Fe4@FeN4C60 and weaking the *OH binding.