Theoretical Density Functional Theory Study of Electrocatalytic Activity of MN4-Doped (M = Cu, Ag, and Zn) Single-Walled Carbon Nanotubes in Oxygen Reduction Reactions.

The mechanism of oxygen reduction reaction (ORR) on transition metal-doped nitrogen codoped single-walled nanotubes, C114H24MN4 (MN4-CNT where M = Zn, Cu, or Ag; N = pyridinic nitrogen), has been studied with the density functional theory method at the ωB97XD/DGDZVP level of theory. The charge density analysis revealed two active sites of the catalyst toward ORR: the MN4 site and the C=C bond of the N-C=C-N metal-chelating fragment (C2 site). The structure of O-containing adsorbates (O2 *, HOO*, O*, HO*, etc.) on the two sites and the corresponding adsorption energies were determined. The analysis of the free energy diagrams allows to conclude that the 4e - mechanism of ORR is thermodynamically preferable for all the studied catalysts. The probability of the 2e - mechanism of ORR with the formation of hydrogen peroxide decreases in the order Cu > Ag > Zn. The most and the least exergonic steps of the conventional 4e - mechanism of ORR on each active site of model catalysts as well as the electrode potentials of deceleration and of maximum catalytic activity in both acidic and alkaline media are determined. The relative catalytic activity toward ORR increases in the order Zn < Ag ≪ Cu and is mainly attributed to the C2 site rather than the MN4 site, while combined catalytic activity of the two sites (AgN4/C2 sites) is predicted for the AgN4-CNT catalyst.

Introduction

The oxygen reduction reaction (ORR) is the cathode reaction in proton exchange membrane fuel cells and in metal–air batteries, resulting in the formation of water; it plays an important role in technologies using renewable energy sources. The ORR suffers from some disadvantages such as high energy barrier (sluggish kinetics) and low selectivity with respect to the target products. To overcome these shortcomings and enhance the performance of ORR, various catalysts are used.[1] Currently, most commonly used catalysts for ORR are noble-metal-based catalysts of the platinum group, like Pt/C.[2] The use of these catalysts allows to perform the ORR at room temperature and atmospheric pressure and to control the rate and selectivity of ORR by varying the applied electrode potential and/or using a proper catalyst. However, still low selectivity and durability and easy poisoning, without mentioning their high cost, persuaded the researchers to search for alternative materials, such as nonprecious metals, organometallic carcass structures, perovskites, and carbon nanomaterials.[3] So far, their catalytic properties are far from being ideal, but the results look very promising. Development of eco-friendly, cost-effective, and high-performance electrocatalysts to replace precious metal platinum for ORR has received increasing attention in past few years.[4]

The increased interest in utilization of the carbon-based structured nanomaterials (NCMs), like graphene (Gr),[5−9] and, especially, nanotubes (CNTs)[8,10−14] and so forth, led to the discovery and elaboration of a large number of new catalytically active materials and identified the optimal ways for the development in the field.[1,9,15,16] Indeed, large surface area and excellent electric and mechanical properties of NCMs determine their advantages over other ORR catalysts. However, in the pristine form, they cannot accelerate the four-electron (4e–) ORR process. The catalytic activity is created by the presence of local defects,[17] including those created by heteroatom (B, N, S, etc.) doping of NCMs.[11,16,18] Thus, one of the efficient ORR catalysts is nitrogen-doped NCMs.[8,19−25] The nitrogen atom’s covalent radius is close to the radius of the carbon atom (0.75 and 0.77 Å, respectively) resulting in minimal geometric distortion of the carbon lattice and a higher electronegativity (3.04 vs 2.55, Pauling scale). The latter effect results in charge density redistribution in the catalyst, localization of the positive charge on the carbon atoms adjacent to nitrogen, and appearance of active sites for oxygen chemisorption and, finally, facilitates the O–O bond rupture.[1]

In the carbon lattice of the N-doped carbon nanomaterials, the nitrogen atom can exist as amino N, pyridinic N, pyrrolic N, graphitic N, or N-oxides of the former two forms.[23] The question of which form is more effective in ORR catalysis is still debatable. The pyridine-N-doped nanocarbon catalysts are deemed to be most efficient in ORR catalysis,[24] although there are experimental and theoretical studies refuting this assumption.[17,26] A crucial problem in the experimental studies is the assignment of the dopant atoms to pyridinic/graphitic or both nitrogen atoms, which is complicated by possible superposition of their signals in the X-ray photoelectron spectra.[26] Thus, it is difficult to answer which form of nitrogen is more active in ORR catalysis.

If nitrogen atom doping the catalyst has a lone electron pair that is not involved in the π-system of the NCM support (like pyrrolic N or pyridinic N), it can form strong chelate complexes with transition metals of the type metal–nitrogen–carbon (M–N–C). The methods of synthesis of such catalysts are mainly based on the thermolysis of NCMs in the presence of metal-chelated heterocyclic (macrocyclic) compounds (porphyrins, phthalocyanines, etc.).[15,27] The formed nanocarbon catalysts containing single atomic non-noble-metal are comparable in activity to Pt/C and often superior in stability and price (M = Fe, Co, Mn).[23,27−30] The ORR activity of M–N–C is very sensitive to the transition metals, and the activity is predicted to decrease in the order Fe > Co > Cu > Mn > Ni.[31] A more comprehensive discussion on the synthesis and performance of M–N–C catalysts in ORR can be found in recent reviews.[27,32]

More than one and half decade ago, it has been predicted that Cu has higher activity than other transition metals (Fe, Co, Ni, etc.).[33,34] Moreover, as copper possesses the second highest electrical conductivity, which is only 6% lower than that of silver, it can promote charge transfer and energy transfer between active sites and reactants.[34−37] Thus, Cu-promoted N-doped carbon (Cu–N–C) obtained by annealing Cu@ZIF-8 in Ar/H2 atmosphere exhibits satisfactory ORR activities with an E1/2 of 0.813 V and larger limit-current density of −6.0 mA cm–2, good methanol tolerance, and better stability compared to Pt/C in the base medium.[34] The authors ascribed the increased ORR activity to the strong synergistic effect between Cu(II)–N ligands and Cu0, abundant active sites, and improved mass transfer due to porous structures. In recent experiments, the authors succeeded in the synthesis of CuN2-doped graphene, which showed superior activity in accelerating the ORR via the 4e– mechanism.[34,38] Addition of KSCN remarkably decreases catalytic activity of Cu–N–C in alkaline media because of the poisoning of Cu–N sites by the coordination of SCN– ions to the metal.[37] However, even the poisoned catalyst still showed high current density and half-wave potential, suggesting that the Cu–N sites in Cu–N–C have strong KSCN tolerance due to the dispersed Cu coordinated with several N atoms.[37,39]

Among the closest neighbors of Cu in the periodic table, that is, Ag and Zn, silver deserves special attention as a relatively cheap and auspicious Ag–N–C ORR catalyst.[32,40−42] Moreover, Ag is an excellent catalyst for hydrogen peroxide reduction, oxidation, or disproportionation,[41] so it is able to reduce O2 to water via the 4e– mechanism within the whole ORR potential window. Note that Zn is deemed to be inactive when used alone; however, being combined with another active metals, it imparts desirable features to the catalyst, such as higher surface area and N fixation.[27,43,44] On the other hand, recent experiments on codoping of CNTs with melamine and Co and Zn nitrates revealed a decisive role of ZnN centers in acceleration of ORR on the Co–N–C catalyst via the 4e– mechanism.[45]

It is assumed that ORR proceeds on metal–nitrogen codoped NCMs (M–N–C) with direct participation of the metal atom; however, apart from the 4e– mechanism, the 2e– process is accelerated that decreases the experimentally measured efficiency of the catalyst to <3.3e–.[30] The computationally studied common ORR mechanism on CuN-doped graphene model catalysts (x = 2 and 4) predicts strong interaction between Cu (as an active site) and oxygen-containing intermediates.[46] Further mechanistic studies showed HO* intermediates (* denotes the support, CuN2-doped graphene) to be a low-lying one (ca. −1 eV) on the free energy diagram at 0.8 V electrode potential[38] and, hence, did not allow to expect good catalytic properties of Cu–N–C in ORR experiments. The authors believe that the free energy of dioxygen molecule adsorption on the active site of the catalyst depends on the electrode potential. This statement, however, is wrong. According to the Nørskov equation,[33] the free energy ΔG, indeed, depends on the electrode potential U but occurs only in the case of electron transfer. Since the number of electrons transferred upon dioxygen molecule adsorption on the catalyst is zero, the free energy ΔG of the process does not depend on U.

With all the aforesaid in mind, the experimental observations of excellent catalytic activity of CuN-co-doped graphene in ORR, as well as scarce data on the mechanistic studies of ORR catalysis with participation of other carbon lattices and the absence of theoretical studies on the mechanism and thermodynamic aspects of ORR on Ag–N–C and Zn–N–C, prompted us to investigate the mechanism of ORR with the participation of the model MN4-doped single-walled carbon nanotube catalysts (M = Cu, Ag, and Zn) since nanotubes are structurally more congested than graphene. Recently, we reported on the effect of Si-doped nanotube diameters on oxygen electroreduction thermodynamics.[47]

Carbon nanotubes are unique among other forms of carbon as they can be exploited as an alternative material for the catalyst support in heterogeneous catalysis and in fuel cells due to the high surface area, microporous nature, excellent electronic conductivity, and high chemical stability.[10] The higher activity of CNT-supported catalysts with respect to other carbons is associated with (i) the crystalline nature of CNTs and (ii) the hollow cavity and graphitic layer interspaces, and so forth.

Another goal of the present work was to assess the effects of the metal nature upon the replacement of the copper atom by the atoms of its closest neighbors in the periodic table—silver and zinc, on which the thermodynamic properties of the ORR process have virtually not been studied.[40]

Results and Discussion

Preliminary Studies

First, we have constructed a model (6,6)armchair single-walled carbon nanotube (structure 1) of the molecular formula C120H24, Figure a. Then, two adjacent carbon atoms equidistant from the ends of the nanotube were removed from the model structure, and the neighboring atoms to the four carbon atoms were replaced by pyridinic nitrogen atoms to create a potentially four-coordinate cavity (N4-CNT, structure 2, Figure c) and to fix the metal atom by the type M–N4–C, Figure .

Figure 1

Structure of model single-walled (6,6)armchair carbon nanotube C120H241 (a), CDD plot for the first excited state of 1 (b); structure of the N4-doped derivative N4-CNT 2 (c), and CDD plot for the first excited state of 2 (d). Isocontour values are ±0.001 e Å–3. Red color corresponds to charge accumulation and blue color—to charge depletion.

Figure 2

Structure of model metal–nitrogen codoped carbon nanotubes: CuN4-CNT 3 (a), AgN4-CNT 4 (c), and ZnN4-CNT 5 (e) along with respective CDD plot for the first excited states of 3–5 (b,d,f). Isocontour values are ±0.001 e Å–3. Red color corresponds to charge accumulation and blue color—to charge depletion.

The charge distribution in structure 1 is characterized by localization of the negative charge on the belt of carbon atoms at the edge of the nanotube, whereas the positive charge is delocalized over the second belt of carbon atoms. The carbon atoms in the middle part of the nanotube bear a charge close to zero in accordance with the results obtained from the charge model 5 (CM5) analysis.[45] The charge density difference (CDD) analysis of the pristine nanotube shows negligible charge accumulation/depletion variations occurring on the internal middle part of model CNT 1. According to eq (see Computational Details section), the frontier highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/LUMO) energy gap (Egap) is as high as 4.44 eV. The formation of defects by removing the >C=C< fragment from the structure CNT 1 and replacing the neighboring carbon atoms by pyridinic nitrogen atoms results in a substantial charge redistribution in the structure N4-CNT 2, Figures c and S1. Thus, the charges on the nitrogen atoms vary from −0.337 to −0.304|e|, whereas the carbon atoms bearing the highest positive charge (from +0.122 to +0.144|e|) are those directly bonded to the nitrogen atoms, while the whole charge of the structure N4-CNT 2 was assumed to be −2|e|. The CDD map of N4-CNT 2 shows numerous alternating centers of charge accumulation/depletion as depicted in Figure d. The energy gap (Egap) in N4-CNT 2 (2.91 eV) is smaller as compared to that in CNT 1. The distances between the opposite nitrogen atoms forming the N4 quadrangle in N4-CNT 2 (Figure c) are equal to 3.798 and 4.016 Å.

Incorporation of the metal atom into the vacant cavity of N4-doped CNT 2 results in a notable energy decrease of the metal–nitrogen codoped CNT (MN4-CNTs 3–5), and, in accordance with the reaction equation N4-CNT2– + M2+ = MN4-CNT, ΔE is −30.3, −29.7, and −27.8 eV for MN4-CNTs with M = Cu, Ag, and Zn (structures 3–5), respectively. The structures of the catalysts and the M–N distances are shown in Figure . Note, that due to the increase of the covalent radius of the metal atom in the order Zn < Cu < Ag, the altitude drawn from the vertex M to the opposite side N–N becomes longer and amounts to 0.225 (Zn), 0.530 (Cu), and 1.233 Å (Ag). The atomic charges on the metal in MN4-CNT 3–5 are +0.569 (Cu), +0.654 (Ag), and +0.788|e| (Zn), Figure S1, respectively. The HOMO/LUMO energy gap Egap in MN4-CNT 3–5 is slightly larger than that of the model nitrogen-doped N4-CNT 2, being equal to 3.13 (Cu), 3.08 (Ag), and 3.03 eV (Zn), respectively.

The analysis of the CDD isocontour map for catalysts 3–5 (Figure b,d,f) showed only small variations of the charge density on the metal atom; however, its incorporation results in accumulation of positive charge density on the carbon atoms in one-half of the nanotube and of negative charge density on the other one, as shown in Figure b,d,f, respectively. The comparison of the CDD isocontour maps for nitrogen-doped CNTs (N4-CNT, Figure d) and metal–nitrogen-codoped CNTs (MN4-CNT, Figure b,d,f) allows us to conclude not only on the synergistic effect of the metal in the N4 cage of N4-CNTs, but also on its promoting (activating) effect on the charge density distribution in the catalyst. Indeed, as evident from Figure , the carbon atoms marked as C1 and C2 (forming C2 site) in Figure a,c,e demonstrate positive CDD and, hence, can also be considered as an active site for oxygen adsorption. Moreover, these carbon atoms are positively charged, the charge varying from +0.113 to +0.144|e| which also favors the adsorption of molecular oxygen. It is assumed that it is the charge and/or charge density accumulation on an atom or group of atoms in the catalyst that determines the ability of the catalytic site to effectively adsorb molecular oxygen as the first step of ORR.[48,50,51] With this in mind, in addition to the metal atoms (MN4 site) in the catalysts MN4-CNT 3–5, we have also considered the carbon atoms of the C2 site as potential active in ORR.

Structure and Adsorption Energy of ORR Intermediates

The structures of all O2* adsorbates and some interatomic distances are summarized in Figure S2 and Table . In all cases, the dioxygen molecule coordinates to the metal in the MN4 site by one of the oxygen atoms (the Pauling model). In the case of the C2 site, the oxygen molecule is attached by both ends to the C1 and C2 carbon atoms (the Yeager model), except for the catalyst CuN4-CNT 3, in which the dioxygen molecule is attached by only one atom to the C1 carbon, Figure S2. Note that the C1–O distance in the latter is substantially longer than in other O2* adsorbates on the C2 site. The adsorption of the O2 molecule on both MN4 and C2 sites of all studied MN4-CNT catalysts was found to be exothermic as shown in Table . Note that neither the M–O nor O–O bond length in the O2* adsorbates on the MN4 site correlates with their Eads (Tables and 2); the same is true for the C2 site. The adsorption energy Eads of O2* adsorbates increases in the order Cu < Ag < Zn for the MN4 site and Zn < Cu < Ag for the C2 site. Besides, the adsorption of the dioxygen molecule on the MN4 site with M = Cu and Ag is favorable over the C2 site by 0.13 and 1.03 eV, respectively, whereas for M = Zn, the opposite dependence is observed and the oxygen absorption on the MN4 site is by 1.24 eV less favorable as compared to the C2 site. The lowest lying O2* adsorbate is the one on the C2 site of ZnN4-CNT (−2.26 eV), while the smallest Eads value is that of the same site of AgN4-CNT (−0.48 eV).

Table 1

Distances (Å) in O2*, HOO*, O*, HO*HO*, and HO* Adsorbates

		MN4 site		C2 site
MN4-CNT		M–O	O–O	C1–O	C2–O	O–O
Cu (3)	O2*	1.975	1.268	1.544		1.305
	HOO*	1.913	1.453	1.459		1.430
	O*	1.830		1.354
	HO*HO*	2.251a		1.411	1.453
	HO*	1.880		1.437
Ag (4)	O2*	2.223	1.337	1.484	1.487	1.458
	HOO*	2.174	1.467	1.471		1.430
	O*	2.123		1.356
	HO*HO*	2.568a		1.433	1.448
	HO*	2.128		1.449
Zn (5)	O2*	1.961	1.312	1.473	1.458	1.463
	HOO*	1.899	1.461	1.460		1.429
	O*	1.916		1.318
	HO*HO*	2.222a		1.419	1.444
	HO*	1.858		1.438

Spontaneous formation of H2O2* occurs. Refer to Figure S4 for the structures.

Table 2

Adsorption Energies (Eads, eV) and Free Energies (ΔGa, eV) of the Oxygen-Containing Species Involved in ORR on Different Sites of MN4-CNT (*) Model Catalysts; M = Cu, Ag, and Zn

	CuN4-CNT				AgN4-CNT				ZnN4-CNT
	CuN4 site		C2 site		AgN4 site		C2 site		ZnN4 site		C2 site
adsorbate	Eads	ΔGa	Eads	ΔGa	Eads	ΔGa	Eads	ΔGa	Eads	ΔGa	Eads	ΔGa
*		0.00		0.00		0.00		0.00		0.00		0.00
O2*	–1.73	–0.21	–1.60	–0.11	–1.51	–0.44	–0.48	1.01	–1.02	0.19	–2.26	–0.86
HOO*	–1.05	0.41	–1.37	0.18	–0.98	0.41	–1.43	0.11	–2.11	–0.95	–1.61	–0.32
HO*HO*	–0.56b	1.00b	–3.85	0.09	–0.50b	1.01b	–3.57	0.30	–0.84b	0.58b	–5.25	–1.58
O*	–4.38	0.57	–5.02	0.03	–4.23	0.72	–5.29	–0.24	–5.07	–0.18	–5.49	–0.64
HO*	–1.98	–0.20	–2.43	–0.48	–1.90	–0.09	–2.48	–0.52	–3.22	–1.68	–2.70	–1.01

ΔG refers to the electrode potential U = 1.23 V in acidic medium corresponding to the 4[H+ + e–] + O2 = 2H2O equilibrium.

Adsorption and free energies refer to the formation of H2O2 molecules adsorbed on the support (H2O2*), as proved by spontaneous HO–OH bond formation.

Spontaneous formation of H2O2* ocn class="Chemical">curs. Refer to Figure S4 for the structures.

ΔG refers to the electrode potential U = 1.23 V in acidic medium n class="Chemical">corresponding to the 4[H+ + e–] + O2 = 2H2O equilibrium.

Adsorption and free energies refer to the formation of n class="Chemical">H2O2 molecules adsorbed on the support (H2O2*), as proved by spontaneous HO–OH bond formation.

Protonation of intermediates O2* leads to the formation of peroxide intermediates HOO*, whose structures are given in Figure S3. The reduction results in a substantial shortening of the M–O and C1–O bonds in HOO* on average by ∼0.058 and 0.013 Å respectively, except the C1–O bond in HOO* adsorbed on the C2 site of CuN4-CNT, which shortens by 0.085 Å, Table . The length of the O–O bond in HOO* also increases to 1.429–1.467 Å relative to that of O2* but still is substantially shorter than that of the H2O2 molecule (1.49 Å). Noteworthy, the O–O distance in HOO* adsorbed on the C2 site is by ∼0.03 Å shorter than that on the MN4 site, Table . In spite of a stronger interaction between the active site of MN4-CNT and HOO, the adsorption energies Eads of peroxide adsorbates HOO*, though still negative, are less negative than those of the corresponding O2* adsorbates, except HOO adsorbed on the C1 carbon of the C2 site of the AgN4-CNT or the ZnN4 site of ZnN4-CNT, Table . The adsorption energy Eads of HOO* adsorbates increases in the order Zn ≪ Cu ≈ Ag for the MN4 site and Zn < Ag ≈ Cu for the C2 site of MN4-CNTs. The Cu- and AgN4-CNTs catalysts are characterized by more negative Eads values for HOO absorbed on the C2 site, while for the ZnN4-CNT catalyst, vice versa, the adsorption on the ZnN4 site is preferable, Table .

The high values of Eads of molecular O2, radical OH, or atomic O (−1.73, −1.98, or −4.38 eV on the CuN4-CNT site) in Table seem to be inconsistent with the Sabatier’s principle that both too strong and too weak interaction between the catalyst and the adsorbate is unfavorable for heterogeneous catalysis. However, the free energy change ΔG is more relevant for the description of the catalytic activity or selectivity of the electrocatalysts than gas-phase Eads values[52] because of instability of the corresponding radical species. Indeed, the corresponding values of ΔG in Table are much less negative (−0.21 and −0.20 eV) or even positive (0.57 eV).

The commonly adopted 4e– mechanism of ORR suggests further protonation of the HOO* adsorbate leading to the formation of atomic oxygen O* adsorbates and release of the first H2O molecule (eqs and 16a); however, an alternative route is possible consisting of protonation of HOO* with the rupture of the O–O bond with the formation of two hydroxyls 2HO* bonded to the active site of the catalyst (eqs and 16b), as described recently.[51,53] Thus, the formation of the 2HO* adsorbate is observed only on the C2 site of MN4-CNTs, Figure S4b,d,f, whereas in the case of the MN4 site, spontaneous formation of the hydrogen peroxide molecule adsorbed on the active site, H2O2*, was observed, Figure S4a,c,e. The energy of adsorption Eads of H2O2* on the MN4 site of MN4-CNT is negative, being ca. −0.5 eV for M = Cu and Ag and −0.84 eV for M = Zn, Table . Much larger adsorption energy gain is observed for the 2HO* adsorbate on the C2 site of MN4-CNT, which is 6–7 times more than that of H2O2*, Table .

The atomic oxygen adsorbate O* on both active sites of the MN4-CNT catalyst, expectedly, has large negative adsorption energy Eads, Table . Thus, the adsorption of atomic oxygen on the MN4 site of MN4-CNT weakens in the order Zn (−5.07 eV) ≪ Cu (−4.38 eV) < Ag (−4.23 eV), but most effectively atomic oxygen interacts with the carbon active site C2, on which the adsorption becomes stronger by 0.42 (Zn), 0.64 (Cu), and 1.06 eV (Ag). Note an interesting structural feature of the O* adsorbates on the C2 site of MN4-CNT, Figure S5b,d,f, for which the possibility of interaction of oxygen atoms with the metal atom remained. The performed fuzzy bond order (FBO) analysis,[54] as implemented in Multiwfn 3.7 program,[55] showed negligible interaction between Zn and O in the O* adsorbate, Figure S5f, while bond orders of Cu···O and Ag···O amount to 0.21 and 0.66, respectively. Evidently, the largest covalent radius of Ag [1.45 vs 1.22 (Zn) or 1.32 Å (Cu)] favors more efficient interaction between the Ag metal and atomic oxygen O* adsorbed on the C2 site of MN4-CNT, Figure S5d. Another interesting structural feature observed for the O* adsorbate on the ZnN4 site of ZnN4-CNT, Figure S5e, is the interaction of the adsorbed atomic oxygen not only with the Zn metal but also with the adjacent nitrogen atom in the metal coordination sphere to form a three-membered ring ZnON with the O···N distance as low as 1.451 Å. The FBO analysis predicts bond orders of 0.55, 1.14, and 1.10 for Zn–N, O–N, and Zn–O, respectively. Hence, the Zn–N bond is weakened, and the O···N interaction strengthened up to the formation of the covalent N–O bond in the O* adsorbate on the ZnN4 site of ZnN4-CNT, Figure S5e, leading ultimately to a deep energy drop upon the adsorption of atomic oxygen on the MN4 site of MN4-CNTs, Table .

Formation of hydroxyl HO* adsorbates (Figure S6) shows a smaller decrease of the adsorption energy Eads as compared to the respective atomic oxygen O* adsorbate, albeit the Eads values are ∼1 eV below than those for the peroxide HOO* adsorbates, Table . Substantially more negative values of Eads for the HO* and O* adsorbates, which are formed exclusively in the 4e– mechanism of ORR, as compared to those of the HOO* adsorbates (formed both along the 2e– and 4e– pathway), are one of the evidence of ORR to follow the 4e– pathway on both active sites of the studied MN4-CNTs. This is in agreement with the statement that the selectivity of the catalyst toward the formation of H2O2 or H2O is determined by its propensity to break the O–O bond, which, in turn, depends on the binding strengths of the intermediates along the 4e– pathway, namely, O* and HO*.[56] It deserves to mention that the energy of the hydroxyl adsorption increases in the order Zn ≪ Cu ≈ Ag on both the MN4 and C2 sites of MN4-CNT, the C2 site being ∼0.5 eV preferable over the MN4 site for M = Cu or Ag.

Electrode Potential Effect

As the energy of adsorption of the oxygen-containing species on an active site of the catalyst tells only about the internal energy changes in the system, all Eads are negative (Table ); to obtain the information on the proceeding of ORR and the influence of the electrode potential on each elementary step, we have constructed free energy diagrams in both acidic and alkaline media of oxygen electroreduction on both MN4 and C2 sites of MN4-CNT (M = Cu, Ag, and Zn) using eqs –19 in accordance with the method proposed by Nørskov et al.[33]

CuN4 Site of CuN4-CNT

The adsorption of molecular oxygen on the CuN4 site of CuN4-CNT with the formation of O2* (eqs , 7, and 14) proceeds spontaneously with small free energy decrease (ΔΔG0, eq ) by 0.21 eV irrespective of the medium and electrode potential U, Figure a,b. Further protonation of O2* by [H+ + e–] in acidic medium (eq ) leading to the formation of HOO* is downhill in terms of free energy (exergonic) up to U ≈ 0.6 V at which ΔΔG1 = 0 (eq ), Figure a. For U ≈ 0.6 V, all elementary steps of the conventional 4e– pathway of ORR on the CuN4 site of CuN4-CNT in acidic medium are exergonic; therefore, the range of U ≤ 0.6 V can be considered as a window of spontaneous proceeding of oxygen electroreduction in acidic medium. With increasing U to 0.8 V, the overall reaction is still exergonic but the second step (O2* → HOO*) becomes endergonic. We call this potential as deceleration potential of ORR (Ud) since for U > Ud, the overall ORR must overcome a barrier, as clearly seen in Figure a for U = 1.23 V (the equilibrium potential in acidic medium). Taking into account the value of ΔΔG1, the transfer of the first electron on the CuN4 site must be the least exergonic step. As already mentioned, the transfer of the second of four possible electrons by [H+ + e–] protonation of the HOO* adsorbate can result in the formation of either the adsorbed hydrogen peroxide H2O2* (calculated in accordance with eq ) or atomic oxygen O* (eq ). The latter wins in the competing reaction since the difference in the free energy of its formation is lower than that of H2O2* by 0.43 eV, also indicating the thermodynamic instability of the 2e– mechanism of ORR (the inset in Figure a). The reaction HOO* → O* + H2O (eq ) proceeds spontaneously at U < 1.1 V, whereas at the equilibrium potential (U = 1.23 V), it is uphill by only 0.16 eV (ΔΔG3, eq ). The transfer of the third electron by the reaction O* → HO* (eq ) is the steepest-descending step within all electrode potential windows and, according to the Bell–Evans–Polanyi principle stating a direct relationship between the activation and reaction energies,[57] can be considered as the most exergonic step of ORR on this active site. The final protonation of the HO* adsorbate resulting in the second H2O molecule release is slightly uphill only at U > 1 V (while at U = 1.23 V, ΔΔG4 is 0.2 eV, eq ). As evident from Figure a and Table , the absolute maximum on the free energy plot for the 4e– course of ORR on the CuN4 site in acidic medium at the equilibrium potential U = 1.23 V corresponds to O* adsorbates lying only by 0.57 eV above in ΔG with respect to the product (2H2O), while the most low-lying adsorbates are O2* and HO* (ca. −0.2 eV).

Figure 3

Free energy diagrams of ORR on CuN4 (top row) and C2 sites (bottom row) of Cu,N-codoped CNT, CuN4-CNT, at different electrode potential U in acidic (a,c) and alkaline (b,d) media.

Free energy diagrams of ORR on n class="Chemical">CuN4 (top row) and C2 sites (bottom row) of Cu,N-codoped CNT, CuN4-CNT, at different electrode potential U in acidic (a,c) and alkaline (b,d) media.

In an alkaline medium, the whole 4e– process O2 → O2* → HOO* → O* + H2O → HO* + H2O → 2H2O on the CuN4 site becomes downhill in free energy at U < −0.2 V, Figure b, suggesting good electrochemical ORR performance. The least and the most exergonic steps are the same as in acidic medium, namely, O2* → HOO* and O* → HO*, respectively. Nevertheless, the catalytic activity of ORR catalysts in alkaline medium is substantially higher than in acidic medium. This is due to the less corrosive effect on the catalyst in the alkaline medium favoring the kinetics of ORR.[58]

The free energy change (ΔΔG0) obtained by us in the reaction O2 → O2* on the CuN4 site of the CuN4-CNT catalyst is in agreement with that obtained by Wang et al.[38] at U = 0 V for CuN2-doped graphene. However, to our surprise, in the plot,[38] ΔΔG0 decreases with U, which is wrong because the free energy change upon the oxygen adsorption on a catalyst is a constant value and does not depend on U since according to eqs , 7, 14, and 21, the term ΔG = 0 (see also above in the Introduction section). Most relevant to our study are the results from Li et al.[46] who obtained ΔΔG0 ≈ 0.9 eV for CuN4-doped graphene. The ΔΔG0 value obtained by us is ca. 1.1 eV lower than that in ref (46) and is downhill in free energy, which is indicative of a positive effect of the nanotube support on the ORR performance as compared to graphene. Although ΔG = 0, the adsorption of oxygen may depend on the electrode potential because, for example, for AgN4-CNT, the adsorption of O2 on the Ag site increases the dipole moment by 9.8 D (from 4.3 to 14.1 D) and on the C2 site—by 4 D. Hence, O2* species should be also stabilized by the electric field in the double layer, which is proportional to the absolute electrode potential.a

C2 Site of CuN4-CNT

The second active site for oxygen electroreduction on the CuN4-CNT catalyst is the C2 site according to CDD analysis of the catalyst. The adsorption of dioxygen molecule O2 on it is only 0.1 eV less effective than on the CuN4 site, Table , Figure c. The [H+ + e–] reduction of the O2* adsorbate in acidic medium (O2* → HOO* transformation) is downhill at U ≤ 0.94 V, although further increase of the electrode potential to the equilibrium (U = 1.23 V) results in a small increase of ΔΔG1 to 0.29 eV. Next two steps of the 4e– process, that is, HOO* → O* → HO* transformation, are downhill within the whole electrode potential window, Figure c. The 2e– ORR via the formation of H2O2 on the C2 site is unfavorable since the free energy gap between the O* adsorbate and H2O2 is as large as 1.04 eV (U = 0) in favor of the former and increases with U. Therefore, the probability of the H2O2 formation and proceeding of the ORR by the energetically less favorable 2e– mechanism on the C2 site of the CuN4-CNT catalyst is lower than that on the CuN4 site. Note that apart from the reaction HOO* → O* + H2O, protonation of the HOO* adsorbate is possible with simultaneous rupture of the O–O bond in it and formation of the HO*HO* adsorbate, in which each hydroxyl is covalently bonded to the C1 and C2 carbon atoms of the C2 site. The free energy of HO*HO* is slightly higher than that of O*, by 0.06 eV. The third electron transfer on the C2 site proceeds by the reaction O* → HO* or HO*HO* → HO*, similar to that on the CuN4 site. The catalytic cycle along the 4e– pathway of ORR on the C2 site is closed by the fourth electron transfer HO* + H* → H2O*, which affords two H2O molecules and is uphill in free energy at U > 0.75 eV. The ΔΔG4 value is 0.48 eV at the equilibrium electrode potential U = 1.23 V. The electrode potential window, within which the 4e– ORR proceeds in acidic medium on the C2 site with the free energy decrease at each step and, hence, the ORR can proceed spontaneously, is U < 0.75 eV, whereas for the CuN4 site, the window is somewhat smaller (U ≤ 0.6 V), Figure a,c. Consequently, the C2 site is catalytically more reactive than the CuN4 site of the CuN4-CNT catalyst. Thus, in the alkaline medium, all steps of the catalytic cycle on the C2 site are downhill at U < +0.12 V, whereas for the CuN4 site, the corresponding potential U is <−0.2 V, Figure b,d.

The above thermodynamic analysis indicates that the MN4-doped CNT-catalyzed ORR is thermodynamically possible but it gives no information about the kinetics of the process. The analysis of transition states for molecular systems of about 140 atoms including heavy metals is very time-consuming, so it is usually performed without thermochemistry calculations (e.g. ref (38)), if at all. We performed full calculations of the pre-reaction complexes and transition states for all elementary steps of ORR on the C2 site of the most efficient CuN4-CNT catalyst (Table , Figures S7–S11). The free energy plot of the catalytic turnover including pre-reaction complexes and transition states is shown in Figure S12.

Table 3

Reaction Energies (ΔE and ΔG, eV) and Activation Barriers (ΔE⧧ and ΔG⧧, eV) with Respect to the Pre-reaction Complexes for the Elementary Steps of ORR on the C2 Site of the CuN4-CNT Catalyst

reaction step	ΔE⧧	ΔE	ΔG⧧	ΔG
<keep-together>O2* + H* → HOO*</keep-together>	0.04	–0.34	0.07	–0.34
<keep-together>HOO* + H* → H2O2*</keep-together>	2.26	0.23	1.90	–0.59
HOO* + H* → O* + H2O	0.90	–0.71	1.19	–1.47
O* + H* → HO*	0.68	–2.97	0.51	–3.01
HO* + H* → H2O*	1.19	–0.05	0.87	–0.91

The first evident result of Table is that the 2e– pathway (entry 2) is less favorable than the 4e– pathway (entry 3) not only thermodynamically (ΔE 0.23 vs −0.71 eV, ΔG −0.59 vs −1.47 eV) but also kinetically (ΔE⧧ 2.26 vs 0.90 eV, ΔG⧧ 1.90 vs 1.19 eV). Most important, however, is the question whether the thermodynamically favorable processes can be restrained kinetically by high barriers. The free energy barriers fall in the range 0.07–1.19 eV, except for the extremely high barrier for the formation of H2O2 of 1.9 eV, making the process impossible under the conditions of ORR. Note that ΔG⧧ = 1.19 eV (entry 3) is the upper limit of ΔG⧧ because the solvation of the eliminating water molecule must facilitate the reaction and, hence, further decrease ΔG⧧.

AgN4 Site of AgN4-CNT

The AgN4 site of the AgN4-CNT catalyst showed a higher adsorption activity toward molecular oxygen and formation of the O2* adsorbate as compared to its lighter homologue Cu, ΔΔG0 = −0.44 eV, Table , Figure a. Further protonation/electron transfer (O2* → HOO*) is downhill in free energy (ΔΔG1) at U < 0.4 V, which is substantially less than that for the CuN4 site, as described above. At U < 0.4 V, the whole catalytic cycle proceeds spontaneously. O2* → HOO* transformation on the AgN4 site is the least exergonic step along the 4e– ORR pathway, the maximum value of ΔΔG1 = 0.84 eV at U = 1.23 V in acidic medium. At U = 0.92 V, the HOO* and O* adsorbates are in equilibrium (ΔΔG2 = 0). The free energy separation between the O* and H2O2* adsorbates on the AgN4 site, as on the CuN4 site, is small and amounts to 0.29 eV in favor of the former, which seems to disagree with the experimentally found ability of the Ag,N-codoped reduced graphene catalyst, Ag/N-rGO, to produce very little peroxide amount.[41,42] However, assuming switching of the active center during the electroreduction from AgN4 to the C2 site (see below) by HOO* adsorbates, the free energy separation between the O* adsorbate and the H2O2 molecule can increase up to 1.31 eV, in agreement with the experiment.

Figure 4

Free energy diagrams of ORR on AgN4 (top row), C2 site (middle row), and combined AgN4/C2 sites (bottom row) of Ag,N-codoped CNT, AgN4-CNT, at different electrode potential U in acidic (a,c,e) and alkaline (b,d,f) medium.

Free energy diagrams of ORR on n class="Chemical">AgN4 (top row), C2 site (middle row), and combined AgN4/C2 sites (bottom row) of Ag,N-codoped CNT, AgN4-CNT, at different electrode potential U in acidic (a,c,e) and alkaline (b,d,f) medium.

C2 Site of AgN4-CNT

The molecular oxygen chemisorption on the C2 site is characterized by a large positive free energy change of ΔΔG0 = 1.1 eV and is the least exergonic step for oxygen reduction on the C2 site, Figure c. However, this is only an apparent problem since the real catalyst is a dynamic system, so the oxygen molecule can be initially adsorbed to form O2* on the adjacent AgN4 site (as described above) with lowering the free energy. A large covalent radius of Ag makes the formed HOO* adsorbate on AgN4 “slide aside” to the adjacent C2 site to give C2-adsorbed HOO* by lowering the free energy by 0.3 eV, Figure e,f. The assumed mechanism of oxygen electroreduction on the combined AgN4/C2 sites of AgN4-CNT is somewhat energetically favorable over the process occurring only on AgN4 or on the C2 site since it allows us to avoid the formation of the two unfavorable intermediate adsorbates O* on AgN4 and O2* on C2 sites (cf. Figure a,c). Note, however, that such characteristics as the least exergonic and the overall exergonic catalytic cycle on the combined active site in both acidic and alkaline medium are the same as on the AgN4 site, Table , except that the most exergonic step is the chemisorption of O2 on the AgN4 site of AgN4-CNT.

Table 4

Least and Most Exergonic Steps, Deceleration Ud, and Exergonic Reaction Ue Potentials (V) vs Standard Hydrogen Electrode of 4e– ORR on the Active Sites of MN4-CNTs, M = Cu, Ag, and Zn

				acidic medium		alkaline medium
catalyst	active site	least exergonic step	most exergonic step	Ue	Ud	Ue	Ud
CuN4-CNT	CuN4 site	<keep-together>O2* → HOO*</keep-together>	O* → HO*	U ≤ 0.6	0.82	U < −0.2	0
	C2 site	HO* → H2O	O* → HO* or HO*HO* → HO*	U ≤ 0.75	1.05	U < +0.12	+0.22
AgN4-CNT	AgN4 site	<keep-together>O2* → HOO*</keep-together>	O* → HO*	U < 0.4	0.82	U ≤ −0.45	0
	C2 site	<keep-together>O2 → O2*</keep-together>	<keep-together>O2* → HOO*</keep-together>
	mixed AgN4/C2 sites	<keep-together>O2* → HOO*</keep-together>	<keep-together>O2 → O2*</keep-together>	U < 0.4	0.82	U ≤ −0.45	0
ZnN4-CNT	ZnN4 site	HO* → H2O and <keep-together>O2 → O2*</keep-together>	O* → HO*			U ≤ −1.05	–1.05
	C2 site	HO* → H2O	HOO* → HO*HO*	U ≤ 0.2	0.2	U ≤ −0.14	–0.14

ZnN4 Site of ZnN4-CNT

The Zn,N-codoped catalyst demonstrates poor catalytic activity toward ORR, Figure a,b. The first step of the catalytic cycle—the adsorption of O2 to the metal—is slightly uphill in free energy, ΔΔG0 = 0.19 eV. This low barrier is easily outbalanced by the subsequent protonation/electron transfer since the O2* → HOO* transformation is exergonic within the whole electrode potential window. Yet, in acidic medium, there is another much steeper rise in free energy corresponding to the transfer of the last (fourth) electron by the conventional 4e– mechanism of ORR, namely HO* → H2O transformation, the HO* adsorbate being the global minimum on the reaction coordinate. For the zero electrode potential U, ΔΔG4 is 0.45 eV but increases to 1.68 eV when U rises to the equilibrium value, Figure a. Therefore, for the catalytic center ZnN4 site, there is no such potential U at which the ORR could proceed spontaneously in the acidic medium. In the alkaline medium, the catalytic center may still show some activity toward ORR at highly negative potentials U < −1.05 V, Figure b.

Figure 5

Free energy diagrams of ORR on ZnN4 (top row), C2 site (bottom row) of Zn,N-codoped CNT, ZnN4-CNT, at different electrode potential U in acidic (a,c) and alkaline (b,d) media.

Free energy diagrams of ORR on n class="Chemical">ZnN4 (top row), C2 site (bottom row) of Zn,N-codoped CNT, ZnN4-CNT, at different electrode potential U in acidic (a,c) and alkaline (b,d) media.

C2 Site of ZnN4-CNT

Zinc, as the dopant, also has a negative effect on the catalytic activity of the C2 site in acidic medium. Thus, at U ≤ 0.2 V, all steps of the catalytic cycle are downhill, Figure c. A further increase of U results in HO* → H2O to be uphill in free energy, which is also the least exergonic step. As distinct from the above-discussed catalytic centers of MN4-CNTs, more probable for the C2 site is the formation of HO*HO* rather than the atomic oxygen O* adsorbate because the free energy of the former is 0.94 eV lower than of the latter, Table . Note that in the case of poisoning of the catalyst by too strong binding of oxygen-containing adsorbates to the active site, the possibility for adsorption of the second more weakly bound the O2 molecule still remains, making the catalysis possible, although less efficient.

The formation of HO*HO* by protonation/electron transfer of the HOO* adsorbate is also the most exergonic step along the ORR pathway that also indicates a highly improbable 2e– pathway of ORR. In alkaline medium, the 4e– ORR is exergonic at U ≤ −0.14 V, Figure d. Therefore, the C2 site of ZnN4-CNT is moderately active in alkaline medium as compared to being limited ORR active in acidic medium and with respect to the practically inactive ZnN4 site. The made theoretical conclusion is consistent with the recent experimental results on the activity of the catalytic centers Zn–N in the increasing ORR activity of double metal Co–Zn N-doped carbon nanotubes.[45] The comparison of the free energies in Figure c also suggests a low probability of H2O2 formation on the C2 site of the ZnN4-CNT catalyst from the values of ΔG for HO*HO* (0.88 eV on the main diagram at U = 0) and H2O2 (3.53 eV on the inset), which amount to 2.65 eV.

The catalytic efficiency of the studied MN4-CNT catalysts is estimated from the free energy diagrams in Figures –5. As a criterion of the catalytic efficiency, the shape of the lines can be used: in the absence of the onset potential, the free energy should decrease on each step, whereas at the equilibrium potential, the closer to the zero line are the intermediates, the higher is the catalytic activity of the MN4-CNT complex. By this criterion, the C2 site in the copper catalyst is more efficient than that in the silver catalyst, the zinc catalyst being least effective. Note that neither the Eads itself nor even the absolute value of free energy ΔG can be considered as a reliable measure of the catalytic efficiency.

Since the ORR intermediates can act as hydrogen bond donors and/or acceptors and the process is performed in the presence of water, the role of the solvent can be very important and crucial for understanding the energetics of the ORR. Thus, for HO* adsorbed on a Pt support, solvent stabilization was calculated to be from 0.1 to 0.3 eV.[33,59] The HO* and HOO* intermediates adsorbed on the IrO2 catalyst were shown to be stabilized by the solvent, whereas O* or HO* coadsorbates demonstrated only small changes in the energetics of the reaction by explicit inclusion of water molecules.[60] For molecular oxygen adsorbed on the N-doped graphene and solvated with five water molecules, the solvation effect was calculated to be ca. 0.2 eV.[61] However, detailed analysis of the solvent effects deserves special analysis and goes beyond the scope of the present work.

Returning to the analysis of Table and the literature data on the activity of metal–nitrogen codoped M–N–C catalysts (M = Cu and Ag), it can be concluded that the performed theoretical analysis adequately describes experimental current/voltage curves of the corresponding catalysts. In spite of the difference between the supports, for Ag,N-codoped reduced graphene, Ag/N-rGO, the catalytic cycle in acidic medium starts at ∼0.85 V (current drop) and reaches a limiting plateau at ∼0.4 V.[41] In alkaline medium, the catalyst becomes active at an onset potential of ∼0 V relative to the standard hydrogen electrode, that is, at a lower one than that predicted by us (−0.45 V), apparently suggesting the existence of catalytic centers other than those considered in the present study. Nevertheless, the potential fixed by the authors as the beginning of the mixed control region gives good agreement with the one calculated by us.[42] In the experiments on the catalytic activity of the Cu–N–C catalyst, it was found to become active at ∼0.92 and 0.85 V,[38,46] and the CV curve reaches a plateau at 0.75 V measured relative to the reversible hydrogen electrode, which excellently coincides with our theoretical results obtained for CuN4-CNT in acidic medium.

Conclusions

The mechanism of oxygen electroreduction reaction (ORR) on the transition metal and nitrogen codoped single-walled nanotube, MN4-CNT, where M = Zn, Cu, and Ag; N = pyridinic nitrogen, has been studied by density functional theory at the ωB97XD/DGDZVP level of theory. The CDD analysis revealed two possible active sites: (i) the transition metal atom in the MN4 moiety, and (ii) the C=C bond of the N–C=C–N metal-chelating segment of the nanotube. The activity of the latter site in the conventional mechanism of ORR is higher than that of the former, and it is this site which is more effective in the catalysis of ORR, as distinct from the processes which were considered in the earlier theoretical studies. The nature of the metal in MN4 also plays an important role and not only has a synergistic effect on the catalysis of ORR, but also acts as an activator of the nanotube carbons. All theoretically studied catalytic centers demonstrate high propensity of ORR to proceeding via the 4e– pathway, which increases in the order Zn < Ag < Cu. Search for the least exergonic step of the mechanism of electroreduction in alkaline medium revealed that zinc codoping of the nitrogen-doped CNT leads to appearance of slightly expressed activity of the formed catalyst, all steps of the ORR mechanism being downhill in free energy at the electrode potential U ≤ −0.14 V. In contrast, the silver doped nitrogen-doped CNT was predicted to show good catalytic activity toward ORR at U ≤ −0.45 V due to mixed activity of both catalytic centers as a result of thermodynamically driven migration of peroxide HOO* adsorbates between the two. However, the highest catalytic activity in alkaline medium was proved for the copper-doped nitrogen-doped CNT, for which the potential for the exergonic ORR is U < 0.12 V, and at U = 0.22 V, the reaction slows down. In acidic medium, only the copper-doped nitrogen-doped CNT demonstrates advanced activity in ORR; the reaction is downhill in free energy at U ≤ 0.75 V, whereas the slowing down potential is 1.05 V, and the free energy plot of 4e– ORR at the equilibrium potential is close to that of the ideal catalyst. The revealed thermodynamic features of the oxygen electroreduction mechanism on Cu, Ag, and Zn codoped nitrogen-doped CNTs are consistent with the known experimental current–voltage characteristics of real catalysts and allow us to conclude on the adequacy of predictions based on the used computational method, ωB97XD/DGDZVP, and reliability of the statements made.

Computational Details

All calculations were performed with full geometry optimization using the long-range corrected density functional with atom–atom dispersion correction, ωB97XD.[62] The reason is that dispersion-corrected functionals give the smallest errors in predicting both chemisorption and dispersion energies.[63] Moreover, ωB97XD was shown to give small deviations from the X-ray for the overall structure or selected distances for a large number of transition metal Ru-based catalysts.[64] Since the calculations include Ag from the fifth row of the periodic table and due to the size of CNTs under consideration, for all the atoms, the all-electron double-ζ basis set DGDZVP[65] was chosen to achieve an optimal accuracy/cost ratio. For thermochemistry calculations, the same level of theory, ωB97XD/DGDZVP, was applied. All calculations were performed using Gaussian 09 suite of programs.[66] For structure visualization, ChemCraft 1.8 was employed.[67] CM5[49] charges and CDD analysis were obtained using Multiwfn 3.7.[55] To assess the charge injection ability, the HOMO/LUMO gap (Egap) was used.[48]

To investigate the stability of various n class="Chemical">O2 adsorbates along with the reduced oxygen-containing species involved in ORR on MN4-doped CNTs (M = Cu, Ag, and Zn) as the catalyst, the adsorption energy (Eads) was evaluated by eq where Eadsorbate*catalyst, Eadsorbate, and Ecatalyst are gas phase total energies of the adsorbate together with the catalyst, isolated adsorbate, and catalyst, respectively. The negative value of Eads indicates the exothermic adsorption process.

The 2e– and 4e–-mechanisms of ORR on the MN4-doped CNT (M = Cu, Ag, and Zn) were investigated. In acidic medium, the following ORR steps should be considered (* denotes the catalyst support).

For 2e– ORR

For 4e– ORRor

In alkaline medium, each step for 4e– ORR is defined as followsor

Finally, the free energy diagrams of 2e– and 4e– ORR pathways on MN4-doped CNTs (M = Cu, Ag, and Zn) were estimated in accordance with the method proposed by Nørskov et al.[33] by eq where ΔEads is the total energy difference between the products and reactants (eqs –18); ΔZPE and ΔS are the zero-point energy correction to the total energy and entropy; T is the temperature (298.15 K); ΔG = −neU, where n, e, and U denote the number of electrons in the reaction, the electron charge, and the electrode potential with respect to the standard hydrogen electrode, respectively; ΔGpH = kBTln10×pH, where kB is the Boltzmann constant. In this study, pH = 0 (ΔGpH = 0 eV) and pH = 13 (ΔGpH = 0.77 eV) were assumed for the acid and alkaline media, respectively. The total energy and entropy of H2O in bulk water were calculated in the gas phase under a pressure of 0.035 bar (the equilibrium vapor pressure of H2O at 298.15 K). The free energy of O2 was obtained as the free energy of the reaction O2 + 4[H+ + e–] → 2H2O equals to −4.92 eV, and the free energy of H2O2 was taken from the reaction O2 + 2[H+ + e–] → H2O2 to be −1.39 eV. The free energy of [H+ + e–] in solution, according to the computational hydrogen electrode model, was taken as half of the energy of the H2 molecule. The free energy of HO– was obtained from the equilibrium reaction in water solution, H+ + HO– = H2O, which equals to −0.03 eV, all under standard conditions. The entropies and vibrational frequencies of the molecules in the gas phase were taken from the NIST database.[68] The ZPE correction to the total energies and entropies of the species excluding those with MN4-doped CNTs were calculated from the vibrational frequencies.

To analyze the equilibria between the adsorbates and the effect of the electrode potential U, the following relative free energies were used for convenience.