Elucidating the role of P on Mn‐ and N‐doped graphene catalysts in promoting oxygen reduction: Density functional theory studies

The non‐noble Mn coordinated N, P co‐doping graphene materials were investigated theoretically in this work based on density functional theory calculation. The electronic structure is effectively tuned after the introduction of P heteroatom. The moderate d band center and density of states at Fermi energy of MnN4‐P1‐G indicate that it is of modest adsorption ability for these O‐containing intermediates. The rank of adsorption energies of O‐containing intermediates for MnN4‐P1‐G is OH* > 2OH* > OOH* > O* > O2* > H2O*, whereas the MnN4‐P1‐G favors a four‐electron process instead of two‐electron process. The doping of P on MnN4‐P1‐G can increase the kinetic activity for the rate‐determining step as well as the Ulim for MnN4‐P1‐G significantly increases from 0.38 to 0.45 V compared with MnN4‐G. The spin density and magnetic moments of Mn are effectively tuned by d, p hybridization to lower the adsorption energy of OH intermediates (rate‐determining step [RDS]) so as to improve the catalytic activity. It is concluded that the P‐doped MnN4 catalysts with excellent oxygen reduction reaction activity can be obtained and this study can provide theoretical guidance for the rational design of high‐performance Mn‐based carbon materials catalysts.


INTRODUCTION
Applying renewable and green energy technology can effectively solve the energy crisis and environmental pollution caused by the traditional application of fossil fuels. [1][2][3] Recently, the exploration of new energy conversion devices (fuel cells and zinc-air batteries) has gained wide attention. [4][5][6] Developing effective catalysts for boosting the oxygen reduction reaction (ORR) is the key solution to solving the slow kinetics of ORR, finally achieving commercialization of these devices. [7][8][9] Platinum and platinum-based alloys are regarded as high-efficient and stable electrocatalysts for ORR; however, the high cost of the noble platinum limits the large-scale application of those new energy conversion devices. 10,11 Therefore, it is both costly significant, and environmentally friendly to develop non-noble metal catalysts to achieve the extensive application of new energy devices. 12 Nowadays, transition metals, including Fe, Co, Mn, Cu, and so on, have been regarded as an alternative candidate for catalyzing ORR based on their relatively excellent performance and low cost. [13][14][15][16] Although the abundance d orbits occupied or unoccupied with electrons of transition metals are beneficial to the adsorption of O 2 , the ORR performance of these metal catalysts fails to meet the requirement of ultimate products or extensive application. 17,18 The performance of transition metal-based catalysts can be effectively improved by adjusting the electronic structure through the heteroatom doping, 19,20 whereas single-atom metal nitrogen-carbon materials have been the research focus due to their high atom-utilization efficiency compared with other materials (e.g., Metal oxides). 21,22 Among these transition metals, Fe, Co, Mn, and Cu are regarded as the promising candidate for the replacement of Pt, [23][24][25][26] in which Fenton reaction is easy to occur on Fe-N-C catalysts, which are prone to be dissolved. The side product H 2 O 2 and active oxygen-containing radicals cause a bad influence on the stability of the electrode and polymer membrane. 27,28 In contrast, the stability of Co-N-C catalysts is relatively poor and the Fenton reaction can also occur easily in acidic media. Compared with Mn-N-C catalysts, the catalytic activity of Cu-N-C catalysts can not meet the requirement of commercialization. 29 In summary, Mn-N-C catalysts gain attention widely due to the favorable stability in acidic media and low activity for the Fenton reaction. 30 It is noteworthy that the catalytic performance of Mn-N-C catalysts is still lower than that of Pt/C catalysts, but the catalytic activity of Mn-N-C catalysts can be further improved by doping of another heteroatom. For instance, Mn-based metal-organic framework was used as precursors to synthesize the O doping Mn-N-C catalysts, and the intrinsic activity was improved greatly by adjusting the electronic structure with the half-wave potential (E 1/2 ) high up to 0.86 V. 31 In contrast, doping heteroatoms (with less electronegativity than C and N) next to the Mn atom is also an effective way to lower the charge density corresponding to the d-orbital of the Mn atom. S-doping Mn-N-C catalysts were prepared through the adsorptionpyrolysis process by using ZIF-8 as precursors, whereas the E 1/2 is achieved up to 0.81 V. 32 Besides, Zhang et al. theoretically studied the influence of B doping on the catalytic activity of Mn-N-C catalysts. 33 In contrast, P atom, with relatively weak electronegativity, has been used to adjust the electronic structure and spin density of transition metals like Fe 34,35 and Co. 36 Likewise, P is regarded to have the potential to improve Mn-N-C catalytic performance. However, there is a lack of comprehensive research on P-doping Mn-N-C catalysts. [37][38][39][40] In this work, the potential structure of Mn, N, and P co-doping graphene was optimized according to density functional theory (DFT) calculations, whereas the electronic structure and possible active sites of the atomically dispersed Mn-N-C catalysts were analyzed. The adsorption energy of all ORR intermediates, including O 2 *, OOH*, 2OH*, O*, OH*, and H 2 O*, was also obtained, based on which the possible ORR reaction pathway under the influence of P-doping was proposed and all the catalysts obey the four-electron reaction pathway. The calculated results illustrated that the introduction of P can effectively tune the electronic structure so that the catalytic performance of Mn-N-C catalysts can be boosted efficiently. Among them, the MnN 4 -P1-G structure exhibited the highest ORR activity compared with other structures, which may provide theoretical guidance for the rational design of high-performance catalysts for further research.

Geometry optimization of Mn-N-P-doped catalysts
Six different catalyst structures, marked as MnN 4 -G, MnN 4 -P1-G, MnN 4 -P2-G, MnN 4 -P3-G, MnN 4 -P4-G, and MnN 3 P-G, were optimized and the optimized structures are shown in Figure 1. The thermodynamic stability of these catalysts was evaluated by formation energy. 41 It can be seen from Table 1 that the formation energies for all catalysts are within −2.697 and −2.135 eV except MnN 3 P-G, illustrating that all the structures are of excellent thermodynamic stability. In contrast, the introduction of P on the MnN 3 P-G catalyst significantly reduces its stability, whose formation energy is −1.062 eV, far lower than the other five catalysts. As for other catalysts, the introduction of    Figure S1 (ESI). P hardly influences the stability although the formation energies for P-doping catalysts are relatively smaller than that of the MnN 4 -G catalyst. Bader charge was acquired to gain an insight into the possible active sites as well as the valence charge number, which was shown in Table S1 of the electronic supplementary information (ESI). 43 It can be seen from the calculated charge transfer quantities of Mn, N, and P in Table 1 that the four nitrogen atoms are negatively charged by −1.22e to −1.25e, respectively. After the introduction of heteroatom P, the charge of P atoms is relatively more positive for MnN 4 -P1-G and MnN 4 -P2-G compared with other structures, whereas the charge of adjacent N is more negative and the charge of Mn is more positive (0.034e and 0.027e higher for MnN 4 -P1-G and MnN 4 -P2-G), illustrating that the charge transfer occurred among heteroatoms P, N atom, and transition metal Mn. Likewise, the charge of Mn in MnN 4 -P2-G sees a slightly increase to 1.088e while the charge of Mn in MnN 4 -P3-G is decreased to 1.053e, respectively. The relatively low variation (−0.018e for MnN 4 -P2-G and 0.017e for MnN 4 -P3-G) indicates that the charge tunning between P atom and Mn atom in these two catalysts might be weakened by adjacent C atoms. As for MnN 3 P-G, the charge of Mn decreased while the electronegativity increased. In summary, the positively charged Mn atoms might be the active sites due to their relatively high charge, which is beneficial to the adsorption of O-containing intermediates.

Electronic structure of Mn-N-P-doped catalysts
The density of states (DOS), as well as the d-band center, is widely used to analyze the electronic structure to provide support for the catalytic activity of ORR. [42][43][44] The introduction of P atoms in Mn-N-C catalysts results that the electronic structure changed according to the partial and total DOS (Figure 2 and Figure S2). It can be seen from Figure 2 that strong hybridization occurred between the 3p orbital of P atom and the 3d orbital of Mn atom. The DOS near the Fermi level indicates that there is overlap between the 3d orbital of Mn atom (3d z2 and 3d yz ) and 3p z orbital of P atom for MnN 4 -P1-G and MnN 4 -P2-G catalysts, whereas 3d xz and 3d z2 orbital of Mn atom have large electronic overlap with 3p z orbital of P atom for MnN 4 -P3-G catalysts. Likewise, the electronic overlap existed among 3d yz , 3d z2 of Mn atom, and p z of P atom for MnN 4 -P4-G. In contrast, p y and p z of P atom have overlap with d orbital of Mn atom for MnN 3 P-G. Besides, the MnN 4 -G exhibits the lowest DOS (0.002) near the Fermi energy compared with those catalysts doped with the P atom. Among these P-doped catalysts, MnN 4 -P2-G and MnN 4 -P3-G exhibit the high-est DOS (2.571 and 2.891, respectively); however, over high DOS near the Fermi energy will result in stronger adsorption of O-containing intermediates, which may bring a bad influence on the catalytic activity due to higher energy barrier. 45 In contrast, the DOS of the other three catalysts, namely, MnN 4 -P1-G, MnN 4 -P4-G, and MnN 3 P-G, are relatively moderate (ranging from 0.2317 to 0.9465), which is beneficial to the ORR.
Furthermore, it can also be concluded that the introduction of the P atom would result that the d-band center shifting positively. Likewise, the P atom doping of MnN 4 -P2-G, MnN 4 -P3-G, and MnN 4 -P4-G would further increase the unoccupied d band center (−0.355, −0.324, and −0.366 eV, respectively), closer to the Fermi level (Ef) compared with MnN 4 -G catalysts. According to the d-band theory, antibonding states are pulled above the Fermi level when the d-band center is close to Ef, thereby intensifying the adsorption of the intermediates and increasing the energy barrier of intermediates. 45,46 In contrast, the d-band centers of MnN 4 -P1-G and MnN 3 P-G are comparably moderate, illustrating that these two structures are conducive to improving the activity of ORR. The above analysis demonstrates that different coordinated P atoms have a significant influence on the d electronic states and activity of Mn and the difference in terms of electronegativity of P atom and N atom could tune the interface electronic structure to display excellent ORR performance compared with traditional MnN 4 -G catalysts.
Meanwhile, the frontier molecular orbits of these studied catalysts were calculated to provide information about the adsorption between O-containing intermediates and catalysts, including the highest occupied crystal orbital (HOCO) and the lowest unoccupied crystal orbital (LUCO), the calculated results of frontier molecular orbitals are shown in Figures S3 and S4. Usually, relatively high HOCO and low LUCO can benefit the adsorption of intermediates as it is easier for high HOCO to donate the electron to the absorbates and for low LUCO to accept electrons from O-containing intermediates. As a result, relatively low ΔE (E LUCO − E HOCO ) indicates that catalysts are of good adsorption. 47 It can be seen from Figure 2 of the schematic diagrams of the frontier crystal orbitals of these catalysts that the energy of HOCO saw an increase with the doping of P, indicating that the doping of P is beneficial to the donation of electrons. In contrast, the energy of LUCO saw a decline with the doping of heteroatom P except for MnN 4 -P3-G and MnN 3 P3-G, which is conducive to the desorption of O-containing intermediates. Figures  S3 and S4 display that the crystal orbitals occur preferentially around Mn atoms, illustrating that the Mn atom is the preferential adsorption site. Meanwhile, the rank of ΔE is MnN 4 -P3-G < MnN 4 -P4-G < MnN 4 -P2-G < MnN 3 P-G < MnN 4 -P1-G < MnN 4 -G, as shown in Figure 3. As for these catalysts, the ΔE of the MnN 4 -P1-G and MnN 3 P-G is moderate compared with other catalysts, which is consistent with the d band center analysis and DOS analysis discussed above.  Tables 2  and 3, respectively.

The adsorption of the O-contained intermediates
The adsorption energies of different absorbates on these six catalysts were summarized in Figure 3g. It can be seen that the rank of adsorption energies is OH* > 2OH* (representing co-adsorption of two OH) > OOH* > O* > O 2 * > H 2 O* except for MnN 3 P-G, in which the adsorption energy of O* is larger than OOH*. It should be noted that the H 2 O 2 molecular dissociated into two OH* and no stable H 2 O 2 could exist on the Mn atom active sites, illustrating that ORR obeys a four-electron process for these catalysts. The adsorption of O 2 (the first step in ORR) is important for the whole ORR reaction. It is hard to undergo ORR since there is little O 2 absorbed on catalysts if the adsorption energy of O 2 is low. It can be seen that the adsorption energies for MnN 4 -G, MnN 4 -P1-G, MnN 4 -P2-G, MnN 4 -P4-G, and MnN 3 P-G are similar, ranging from −0.75 to −0.9 eV. Those relatively large O 2 adsorption energy demonstrates that O 2 can effectively absorb on these catalysts, which is beneficial to the ORR process. However, it should be noted that the adsorption energy of O 2 on MnN 4 -P3-G is too large, and it might harm the following process of ORR. The next step is the formation of OOH* and the corresponding adsorption energies are relatively low for these catalysts, which is beneficial to the hydrogenation of O 2 *. As for the 2OH*, the adsorption energies of 2OH* on MnN 4 -P3-G and MnN 3 P-G are far larger than others, meaning that the hydrogenation of OOH* is more easily happen. In contrast, the adsorption energies of O* are within −1.     49 For the further process of OOH*, there are also two possible ways, one of which is the dissociation into O* + H 2 O, TA B L E 4 Gibbs free energies (eV) for the elementary reaction steps.

d [Å] MnN 4 -G MnN 4 -P1-G MnN 4 -P2-G MnN 4 -P3-G MnN 4 -P4-G MnN 3 P-G
Step  Figure 3h,i. To verify which pathway the ORR process obeys in these six different catalysts, the reaction free energy for different ORR process was calculated, as shown in Table 4. As for the adsorption of O 2 on active sites of catalysts, the free energies were all lower than −0.75 eV, illustrating that all catalysts are beneficial to the formation of O 2 *. Then, the absorbates O 2 * are hydrogenated to form OOH*. Likewise, the free energies on different catalysts were larger than −0.55 eV. As for the next step, the reaction free energy for both pathways were calculated, in which the free energies of pathway one for MnN 4 -G, MnN 4 -P1-G, MnN 4 -P2-G, and MnN 4 -P4-G are lower than those of pathway two, illustrating that OOH* obeys the pathway one process for these catalysts. In contrast, the free energies of pathway two for MnN 4 -P3-G and MnN 3 P-G are lower than that of pathway one. As a result, the OOH* is prone to dissociate into two OH* for MnN 4 -P3-G and MnN 3 P-G. Afterward, O* would be further hydrogenated to form OH* for catalysts obeying pathway one, as well as the free energies of O* hydrogenation were larger than −0.78 eV, whereas one of OH* is hydrogenated to form H 2 O product as for catalysts undergoing pathway two. The final step for both pathways is OH* hydrogenation and the production of H 2 O, and the relevant free energies of these catalysts are larger than

Comparison of the catalytic activity with thermodynamics
According to the above analysis, the four-electron pathway was confirmed for all these designed catalysts. To evaluate the performance of these different catalysts, the standard hydrogen electrode model was accepted to study the influence of electrode potential (U) on the free energy of each step. 41 The values of relevant energy changes for six different catalysts were listed in Tables S2-S7 of the ESI, whereas the Gibbs free energy for each step was summarized in Figure 4.
It can be seen from Figure 4 that the free energy for the ORR process goes downhill for each catalyst, indicating that each step is exothermic. At the open circuit potential, the minima (0.38 eV) of free energy are the OH* transformation into the product (H 2 O) without P doping, which is the rate-determining step. Likewise, the minima of free energy for P-doped catalysts are also the last step. However, it can be concluded that the rate-determining step for other catalysts is also the last step, whereas it should be noted that for MnN 4 -P1-G and MnN 3 P-G the free energy of the rate-determining step is increased, meaning that these two structures can effectively improve the catalytic activity of Mn atom. When the electrode potential is 1.23 V, some of the ORR steps are downhill and the other steps are uphill, meaning that there is a need for energy to surmount the positive free energy change. The applied potential keeping all ORR steps exothermic is the limiting potential (U lim ). Generally, the higher the limiting potential, the lower the overpotential. As a result, the limiting potential (0.45 and 0.41 V) of P-doping MnN 4 -P1-G and MnN 3 P-G was higher than that (0.38 V) of MnN 4 -G, meaning that the catalytic activity was improved by P doping, whereas the limiting potential revealed a decline as for other structures, especially for MnN 4 -P2-G and MnN 4 -P3-G (0.19 and 0.12 V, respectively), which might be influenced by the over stronger adsorption of OH* intermediates (RDS) to decrease the catalytic performance.
In summary, these two structures of P-doping MnN 4 -P1-G and MnN 3 P-G can effectively improve the catalytic

Magnetic effect of catalysts on ORR performance
The magnetic moments of Mn in different catalyst structures with and without O-containing intermediates were investigated as is shown in Table S8. It can be seen that the magnetic moments of Mn changed after different O-containing intermediates are absorbed on active sites (Mn atom) except for H 2 O. To gain an insight into the influence of O-containing intermediates, the partial DOSs of Mn d orbits of different catalysts and O-containing intermediates were calculated respectively, as is shown in Figures S16-S21. Figure S16 shows that strong hybridization between 2p orbits of O 2 absorbates and 3d orbits of Mn occurred and results in the change in magnetic moment of Mn atom. Likewise, a similar orbital overlap occurred among p orbits of OOH*, O*, 2OH*, and OH* and d orbits of Mn atom of different catalysts in Figures S17-S20 and these strong hybridizations tune the electronic structures to change the magnetic moments of Mn. However, the orbital overlap between 2p orbits of H 2 O and 3d orbits of Mn did not occur due to the relatively weak adsorption of H 2 O on all kinds of catalysts. As a result, H 2 O absorbate has little influence on magnetic moments.
Besides, the influence of OH absorbate on magnetic moments of Mn and catalytic performance should be further studied since the rate-determining step (RDS) for all six catalysts are the last step of ORR, namely, the desorption of OH absorbates. The partial DOS for p orbits of O and d orbits of Mn is obtained for these six different catalysts, as is shown in Figure 5. The hybridization between d yz orbits of Mn and p y orbits of OH occurred and tune the spin density to increase the magnetic moments for MnN 4 -G and MnN 4 -P3-G. In contrast, the hybridization between d z2 of Mn and p z of O leads to the decline of magnetic moments of Mn, whereas the spin density is also changed by strong orbital overlap among d xz , d yz , d xy , and d z2 orbits of Mn and p y orbits of O, which lower the magnetic moments of Mn for MnN 3 P-G. As for MnN 4 -P1-G, the hybridization between d yz , d z2 of Mn and p y , p z of O push the magnetic moments closer to 0. In summary, the d, p hybridization that occurred between Mn and OH effectively change the spin density, as is shown in Figure S22.
The relationship between the adsorption energies of OH intermediates and the magnetic moment of Mn is further investigated to study the influence of magnetic moments on catalytic performance. Figure 5h indicates that the relationship is a volcano diagram. The adsorption energy of OH intermediates is lowered with the magnetic moment of Mn shifting closer to the 0 µ B , which is beneficial to the desorption of the following species. Figure 5i shows the linear relationship between U lim and adsorption energies of OH intermediates, illustrating that the OH intermediate adsorption intensity of the RDS is related to the catalytic performance. There is an increasing trend in terms of catalytic activity with the declining of OH adsorption energy. As a result, the d, p hybridization of MnN 4 -P1-G adjusted the magnetic moments of Mn closer to 0 µ B to lower the adsorption energy of OH intermediates (RDS), which have a positive side on the desorption of OH absorbates and improvement of catalytic performance.

CONCLUSION
The ORR mechanism of P-doped MnN x -G was investigated theoretically and comprehensively.

MODELS AND METHODS
All the theoretical calculations in this work were carried out based on the DFT according to Vienna Ab Initio Simulation Package. 50,51 The general gradient approximation parameterized by Perdew, Burke, and Ernzerhof was applied to solve the exchange-correlation functional in structural relaxations, 52 whereas the ion-electron interactions were studied based on the projected augmented wave pseudopotentials with the plane-wave basis set cut off at 500 eV. All these six MnN x -G catalysts structures with or without P doping were relaxed through conjugate gradient method until the force component on each atom was less than 0.02 eV Å −1 , whereas the convergence criterion of total energy within the self-consistent field method was set as 10 −5 eV. The spin polarization is considered throughout the calculations. The DFT + U method was used to calculate the electronic properties of Mn with U of 5 eV. 53 The monolayer graphene doped with Mn, N, and P was used as catalysts in this work with the vacuum space above the graphene layer of 20 Å. The different doping sites of P on MnN 4 catalysts were calculated and marked as MnN 4 -G, MnN 4 -P1-G, MnN 4 -P2-G, MnN 4 -P3-G, MnN 4 -P4-G, and MnN 3 P-G, respectively, as shown in Figure 1. In order to evaluate the stability of different structures, the formation energy was calculated according to the following equation: In which, E M/slab and E slab represent the energy of optimized catalysts doped with and without metal atom, E bulkperAtom is the energy of the single metal atom calculated from the energy of bulk metal divided by the number of bulk metal atoms. The adsorption energy was obtained to compare the adsorption properties of different O-containing intermediates on these six catalytic structures according to the following equation 54 56 The free energy of the intermediates was acquired by the following equation: In which, E DFT is the total energy, ZPE represents the zero-point energy, T is the temperature (K) and S is the entropy, G u is the influence of electrode potential. G u can be calculated according to −neU, where n is the number of transferred electrons, U is the applied electrode potential.

A C K N O W L E D G M E N T S Supports of the State Key Laboratory of Urban Water
Resource and Environment, Harbin Institute of Technology, China (No. 2021TS07) and Harbin Advanced Computing Center for this work are gratefully acknowledged.

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors declare no conflict of interest. Gang Wu is an Associate Editor of SusMat and a co-author of this article. To minimize bias, he was excluded from all editorial decision-making related to the acceptance of this article for publication.