Heterometallic cluster-based organic frameworks as highly active electrocatalysts for oxygen reduction and oxygen evolution reaction: a density functional theory study

Abstract

Recently, metal–organic frameworks are one of the potential catalytic materials for electrocatalytic applications. The oxygen reduction reaction and oxygen evolution reaction catalytic activities of heterometallic cluster-based organic frameworks are investigated using density functional theory. Firstly, the catalytic activities of heterometallic clusters are investigated. Among all heterometallic clusters, Fe₂Mn–Mn has a minimum overpotential of 0.35 V for oxygen reduction reaction, and Fe₂Co–Co possesses the smallest overpotential of 0.32 V for oxygen evolution reaction, respectively 100 and 50 mV lower than those of Pt(111) and RuO₂(110) catalysts. The analysis of the potential gap of Fe₂M clusters indicates that Fe₂Mn, Fe₂Co, and Fe₂Ni clusters possess good bifunctional catalytic activity. Additionally, the catalytic activity of Fe₂Mn and Fe₂Co connected through 3,3′,5,5′-azobenzenetetracarboxylate linker to form Fe₂M–PCN–Fe₂M is explored. Compared with Fe₂Mn–PCN–Fe₂Mn, Fe₂Co–PCN–Fe₂Co, and isolated Fe₂M clusters, the mixed-metal Fe₂Co–PCN–Fe₂Mn possesses excellent bifunctional catalytic activity, and the values of potential gap on the Mn and Co sites of Fe₂Co–PCN–Fe₂Mn are 0.69 and 0.70 V, respectively. Furthermore, the analysis of the electron structure indicates that constructing a mixed-metal cluster can efficiently enhance the electronic properties of the catalyst. In conclusion, the mixed-metal cluster strategy provides a new approach to further design and synthesize high-efficiency bifunctional electrocatalysts.

Key words： bimetallic metal–organic frameworks; bifunctional electrocatalyst; density functional theory; oxygen reduction reaction; oxygen evolution reaction

1 Introduction

The oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) play essential roles in several energy conversion technologies [1–3]. Because of the slow multistep proton-coupled electron transfer process, ORR and OER need efficient electrocatalysts to overcome these kinetic barriers and accelerate the reaction rate [4,5]. Although Pt- and Ru-based catalysts are efficient electrocatalysts for ORR and OER, respectively, their uses are limited due to high costs, natural scarcity, and poor resistance to poisoning [6,7]. Therefore, it becomes very urgent for researchers to develop non-noble metal catalysts for low cost as well as high activity and stability to replace the typical Pt- and Ru-based catalysts.

Recently, more and more non-precious metal materials have been studied, including metal-free carbon-based materials [8,9], metal–nitrogen–carbon materials [10,11], and metal–organic frameworks (MOFs) [12,13]. Among them, MOFs stand out as a type of porous and crystalline materials with structural tunability, high specific surface area, and other beneficial intrinsic physicochemical features [14–17]. Various modification strategies have been investigated, including changing the morphology of MOFs (different organic linkers) [18] or forming heterostructures (bimetallic or multi-metallic MOFs) to develop high-performance MOFs [19–21]. Compared with monometallic materials, bimetallic MOFs materials show more excellent ORR/OER catalytic activity, which can be attributed to the synergistic effect between different metals [22–24]. For instance, Wang et al. [25] have synthesized a series of stable MOFs based on trinuclear metal carboxylate clusters and tridentate carboxylate ligands (BPTC). The results reveal that the OER catalytic activities of bimetallic Fe₂Co−BPTC, Fe₂Zn−BPTC, and Fe₂Ni-BPTC are improved compared with monometallic Fe₃-BPTC. Additionally, 3,3′,5,5′-azobenzenetetracarboxylate (ABTC), as a type of bridging aromatic tetracarboxylate organic ligand, possesses many advantages to be designed as catalytically-active MOFs [26,27]. For example, the exposed azo bond is from a well-known Lewis base group, which is expected to modulate the catalytic performance. Furthermore, the rigid ABTC ligand has four carboxyl groups, then it is easily deprotonated to form different geometries. In these geometries, several strong metal−oxygen coordination bonds can greatly enhance the thermal stability and rigidity of the framework [28,29]. Recently, Dong et al. [30] have synthesized a series of nanocomposite MOFs materials with porous coordination network structure (Fe₂M−PCN−Fe₂M) composed of the ABTC linker and trinuclear metal cluster, which can construct a mixed-metal-cluster structure with multiple active centers. These findings indicate that Fe₂Ni−PCN−Fe₂Co possesses better OER catalytic activity than Fe₂Ni−PCN−Fe₂Ni and Fe₂Co−PCN−Fe₂Co. Based on these previous studies, it is worthwhile to investigate the potential bifunctional catalytic performance of heterometallic Fe₂M clusters formed using 3d transition metals other than Ni and Co, as well as the effect of mixed heterometallic clusters connected by an ABTC linker on catalytic activity.

This study systematically investigates heterometallic cluster-based organic frameworks’ ORR and OER catalytic activities using density functional theory (DFT) methods. First, the structures of heterometallic clusters (Fe₂M, M = Ti, V, Cr, Mn, Co, Ni, Cu, Zn) are constructed. Next, the bifunctional catalytic activity of Fe₂M clusters is investigated, and the Fe₂Mn and Fe₂Co clusters with the most superior catalytic activity are screened. Finally, the Fe₂Mn and Fe₂Co are connected through an ABTC linker to form Fe₂M−PCN−Fe₂M, and the catalytic activity of Fe₂M−PCN−Fe₂M is determined by calculating the binding energy of the reaction intermediate and the Gibbs free energy change of each elementary step.

2 Computational detail

All calculations in this work were employed with a spin-polarized DFT framework and implemented by the DMol³ module in Materials Studio software [31]. The generalized gradient approximation with the Perdew–Burke–Ernzerhof functional was adopted to describe the electron exchange and correlation effect [32]. The effective core potentials were used to deal with the related relativistic effect, and the basis set of atomic orbitals was described by double numerical polarization. The convergences of energy, maximum force, and maximum displacement were set as 2 × 10⁻⁵ Ha, 0.004 Ha∙Å⁻¹, and 0.005 Å, respectively.

The stability of the catalyst is evaluated by calculating the substitution energy, which is the energy of M atom replace Ni atom in Fe₂Ni, due to the good stability of synthesized Fe₂Ni cluster according to the experiment [30,33]. The substitution energy (E_sub) is calculated as follows:

(1)E_{\mathrm{s}\mathrm{u}\mathrm{b}}=E_{\mathrm{F}{\mathrm{e}}_2\mathrm{M}}+E_{\mathrm{N}\mathrm{i}}-E_{\mathrm{F}{\mathrm{e}}_2\mathrm{N}\mathrm{i}}-E_{\mathrm{M}},

where E_{\mathrm{F}{\mathrm{e}}_2\mathrm{M}}, E_Ni, E_{\mathrm{F}{\mathrm{e}}_2\mathrm{N}\mathrm{i}}, and E_M are the energies of Fe₂M clusters, isolated Ni atom in bulk phase, Fe₂Ni cluster, and isolated M atom of Fe₂M clusters in bulk phase, respectively. When the calculated value of E_sub is negative, it means that the replacement of Ni by other M atoms is energetically favorable, that is, the structure of Fe₂M is more stable than that of Fe₂Ni.

It is well known that ORR has two different reaction pathways, namely two-electron and four-electron pathways. In this paper, only the four-electron pathway with higher power output has been investigated [34,35]. The specific reaction steps of the four-electron pathway are as follows (The asterisk represents the active site of catalysts):

(2)\text{*}+{\mathrm{O}}_2+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to \text{*}\mathrm{O}\mathrm{O}\mathrm{H}

(3)\text{*}\mathrm{O}\mathrm{O}\mathrm{H}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to \text{*}\mathrm{O}+{\mathrm{H}}_2\mathrm{O}

(4)\text{*}\mathrm{O}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to \text{*}\mathrm{O}\mathrm{H}

(5)\text{*}\mathrm{O}\mathrm{H}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to \text{*}+{\mathrm{H}}_2\mathrm{O}

The binding energies of reaction intermediates (∆E_species) are calculated by the following equations:

(6)\mathrm{\Delta }{E}_{\text{*}\mathrm{O}\mathrm{O}\mathrm{H}}=E_{\text{*}\mathrm{O}\mathrm{O}\mathrm{H}}-E_{\text{*}}-(2E_{{\mathrm{H}}_2\mathrm{O}}-3/2E_{{\mathrm{H}}_2}),

(7)\mathrm{\Delta }{E}_{\text{*}\mathrm{O}}=E_{\text{*}\mathrm{O}}-E_{\text{*}}-(E_{{\mathrm{H}}_2\mathrm{O}}-E_{{\mathrm{H}}_2}),

(8)\mathrm{\Delta }{E}_{\text{*}\mathrm{O}\mathrm{H}}=E_{\text{*}\mathrm{O}\mathrm{H}}-E_{\text{*}}-(E_{{\mathrm{H}}_2\mathrm{O}}-1/2E_{{\mathrm{H}}_2}),

where the E_*OOH, E_*O, and E_*OH are the total energies of the catalyst combined with *OOH, *O, and *OH, respectively. The E_* is the energy of the isolated catalyst. The E_{{\mathrm{H}}_2\mathrm{O}} and E_{{\mathrm{H}}_2} are the total energies of H₂O and H₂ molecules, respectively.

The Gibbs free energy change is one of the important parameters used to evaluate the catalytic activity of a catalyst, and the specific calculation equations are as follows:

(9)\mathrm{\Delta }{G}_1=\mathrm{\Delta }{G}_{\text{*}\mathrm{O}\mathrm{O}\mathrm{H}}-4.92,

(10)\mathrm{\Delta }{G}_2=\mathrm{\Delta }{G}_{\text{*}\mathrm{O}}-\mathrm{\Delta }{G}_{\text{*}\mathrm{O}\mathrm{O}\mathrm{H}},

(11)\mathrm{\Delta }{G}_3=\mathrm{\Delta }{G}_{\text{*}\mathrm{O}\mathrm{H}}-\mathrm{\Delta }{G}_{\text{*O}},

(12)\mathrm{\Delta }{G}_4=-\mathrm{\Delta }{G}_{\text{*}\mathrm{O}\mathrm{H}},

where the ΔG₁, ΔG₂, ΔG₃, and ΔG₄ represent the Gibbs free energy change of each step of ORR. The ΔG_*OOH, ΔG_*O, and ΔG_*OH are the adsorption free energies of *OOH, *O, and *OH, respectively. The adsorption free energies of reaction intermediates (ΔG_*species) are calculated by the equation of ΔG_*species = ∆E_species + ∆ZPE − T∆S. Based on the previous work, the zero-point energies and entropies of intermediates adsorbed on different catalysts are similar [36]. Therefore, the ΔG_*species can be described by ΔG_*OOH = ∆E_*OOH + 0.40, ΔG_*O = ∆E_*O + 0.05, and ΔG_*OH = ∆E_*OH + 0.35. The overpotential of ORR can be calculated by the following equation:

(13){\eta }^{\mathrm{O}\mathrm{R}\mathrm{R}}=max(\mathrm{\Delta }{G}_1,\mathrm{\Delta }{G}_2,\mathrm{\Delta }{G}_3,\mathrm{\Delta }{G}_4)/\mathrm{e}+\mathrm{1.23.}

For OER, as is well known that it is the reverse reaction of ORR [37,38]. The Gibbs free energy of each elementary reaction step of OER is the opposite value of the Gibbs free energy of the corresponding ORR step, ΔG_OER = −ΔG_ORR. The overpotential of OER is calculated by the following equation:

(14){\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}=max(-\mathrm{\Delta }{G}_4,-\mathrm{\Delta }{G}_3,-\mathrm{\Delta }{G}_2,-\mathrm{\Delta }{G}_1)/\mathrm{e}-\mathrm{1.23.}

Based on the previous works [39,40], the potential gap (ΔE) is defined to reflect the bifunctional catalytic activity, and the specific equation is as follows:

(15)\mathrm{\Delta }E={\eta }^{\mathrm{O}\mathrm{R}\mathrm{R}}+{\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}.

3 Results and discussion

3.1 Structure and catalytic activity of Fe₂M clusters

In this work, the constructed Fe₃ cluster structure, the considered transition metals, and the established Fe₂Ti cluster (which is one of the heterometallic Fe₂M clusters, M = Ti, V, Cr, Mn, Co, Ni, Cu, Zn) are shown in Fig.1. Firstly, the MIL-88 (Materials of Institute Lavoisier) [41], namely, the Fe₃ cluster, is constructed, as shown in Fig.1(a). It can be observed that the three Fe sites are joined by a central μ₃-O atom and connected by the carboxylate linkers. Subsequently, a Fe atom in the Fe₃ cluster is replaced with a 3d transition metal atom to examine the catalytic performance of bimetallic MOF catalysts, and the considered transition metals are shown in Fig.1(b). The optimized configurations of Fe₂M clusters are expressed in Fig. S1 (cf. Electronic Supplementary Material, ESM). It can be clearly observed that all Fe₂M clusters have not undergone deformation compared to Fe₃ cluster. In order to accurately appraise the stability of Fe₂M, the E_sub values are calculated and plotted in Table S1 (cf. ESM). It can be found that all E_sub values are negative, demonstrating that the substitution of M atom to Ni atom is energetically favorable. Compared with Fe₂Ni, all the Fe₂M being studied possess satisfactory thermodynamical stability. Moreover, the first-principles molecular dynamics calculations are also performed during a period of 1 ps at 300 and 500 K temperatures, respectively. After dynamics calculations, the final structures and the M–O bond lengths of Fe₂M clusters are shown in Fig. S2 (cf. ESM). It is clearly observed that all Fe₂M clusters have no obvious deformation, and the change in bond length is insignificant (no more than 0.15 Å), indicating that they are stable. In each Fe₂M clusters, both the Fe and doped M are considered as active sites. Taking the Fe₂Ti cluster as an example (Fig.1(c)), Fe₂Ti–Ti and Fe₂Ti–Fe represent the Ti and Fe sites of the Fe₂Ti cluster, respectively. Likewise, naming the active sites of other Fe₂M clusters also follows this rule.

Fig.1 (a) Optimized configuration of Fe₃ cluster. The orange circle represents the location of the metal to be replaced. (b) Transition metals considered in this work. (c) Active sites of Fe₂Ti cluster. The blue dotted circle represents the active site.

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The ∆E_species on all possible active sites of Fe₂M clusters are calculated to examine the catalytic activity of Fe₂M clusters, as listed in Tab.1. For comparison, the values of ∆E_species on the Pt(111) [42] and RuO₂(110) [43] surfaces are used as a benchmark for ORR and OER, respectively. The smaller the value of ∆E_species, the stronger the binding strength. As is known to us, compared with the ideal ORR catalyst, the Pt(111) surface binds *OOH relatively weak and binds *O and *OH relatively strong. Meanwhile, compared with the ideal OER catalyst, the RuO₂(110) surface binds *O slightly weak. The ∆E_species values on Fe₂Ti, Fe₂V, and Fe₂Cr clusters are significantly smaller than Pt(111) or RuO₂(110), implying that the binding strength of reaction intermediates on them is excessively strong. In contrast, the values of ∆E_species on Fe₂Cu and Fe₂Zn clusters are significantly larger than that on Pt(111) or RuO₂(110), showing their weak binding strength of reaction intermediates. Therefore, the OER and ORR catalytic activities of the above catalysts may be unsatisfactory. Surprisingly, for Fe₂Mn and Fe₂Co clusters, the ∆E_species values of reaction intermediates are all relatively close to that on the Pt(111) and RuO₂(110) surfaces, proving that they may have excellent ORR and OER activities. It is worth noting that the binding strength of reaction intermediates on the M site of Fe₂M clusters (M = Ti, V, Cr, Mn) is almost stronger than that on the Fe site.

Tab.1 ∆E_species values of reaction intermediates on all possible active sites of Fe₂M clusters

Active site	∆E*OOH/eV	∆E*O/eV	∆E*OH/eV
Fe2Ti–Ti	1.66	−0.44	−1.72
Fe2Ti–Fe	3.20	0.86	−1.01
Fe2V–V	2.07	−0.48	−1.14
Fe2V–Fe	3.00	1.60	0.02
Fe2Cr–Cr	2.22	0.56	−0.85
Fe2Cr–Fe	2.52	1.33	−0.31
Fe2Mn–Mn	3.71	2.69	0.70
Fe2Mn–Fe	4.06	2.67	1.04
Fe2Co–Co	4.04	2.84	1.02
Fe2Co–Fe	3.97	3.00	1.00
Fe2Ni–Ni	3.76	2.80	0.57
Fe2Ni–Fe	3.20	2.32	0.26
Fe2Cu–Cu	4.27	4.49	1.93
Fe2Cu–Fe	4.29	3.28	1.19
Fe2Zn–Zn	4.38	4.60	1.85
Fe2Zn–Fe	4.28	3.28	1.19
Pt(111)	3.66	1.65	0.88
RuO2(110)	3.91	2.66	0.97

The ΔG_*species values of the reaction intermediates on Fe₂M clusters are calculated and depicted in Fig.2. It can be detected that there are significant linear relationships of ∆G_*OOH and ∆G_*O with ∆G_*OH on Fe₂M clusters. Generally, *O forms a double bond with the catalyst surface, and *OH forms a single bond with the catalyst surface. The O atom of *OOH forms a single bond with the metal atom. Consequently, the slope between ∆G_*O and ∆G_*OH is greater than 1, and the slope of ∆G_*OOH vs. ∆G_*OH is close to 1 [44]. The correlation between ∆G_*OOH and ∆G_*OH can be explained by ∆G_*OOH = 0.76∆G_*OH + 3.27 with the coefficients of determination (R²) of 0.88. The slope and intercept are similar to those reported in previous studies [45,46]. Furthermore, the ∆G_*O and ∆G_*OH display a linear correlation of ∆G_*O = 1.36∆G_*OH + 1.29, and they have a stronger linear relationship due to a higher R² value of 0.96. Based on the above analysis, it can be predicted that when Fe₂M clusters have a strong binding ability of *OH, they also interact strongly with *O and *OOH.

Fig.2 Scaling relationships of (a) ∆G_*OOH vs. ∆G_*OH and (b) ∆G_*O vs. ∆G_*OH on Fe₂M clusters.

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According to the linear relationships of ∆G_*OOH and ∆G_*O with ∆G_*OH, ∆G_*OH can be determined as the descriptor to explore the catalytic activity of Fe₂M clusters. In addition, by introducing the linear relationships into the Eqs. (8)−(11), the equations can be expressed as ∆G₁ = 0.76∆G_*OH − 1.65, ∆G₂ = 0.60∆G_*OH − 1.98, ∆G₃ = −0.36∆G_*OH − 1.29, and ∆G₄ = −∆G_*OH. Therefore, the volcano plot between overpotential and ∆G_*OH is established, as shown in Fig.3. In addition, the potential-determining step (PDS) is determined by the step with the maximum ΔG value.

Fig.3 Volcano plot of η^ORR and −η^OER as a function of ∆G_*OH (the square and circle symbols represent η^ORR and −η^OER, respectively). Taking ORR as an example, blue line: η^ORR = 0.76∆G_*OH − 0.42; orange line: η^ORR = 0.60∆G_*OH − 0.75; purple line: η^ORR = −0.36∆G_*OH − 0.06; green line: η^ORR = −∆G_*OH + 1.23.

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For ORR, the top of the volcano appears (inverted) when ∆G_*OH value reaches 0.94 eV, and the minimum theoretical ƞ^ORR value of this kind of catalyst is 0.29 V. For Fe₂M clusters with the strong binding strength of *OH (∆G_*OH < 0.94 eV), the *OH reduction step is determined as the PDS. As the ∆G_*OH values on Fe₂M clusters increase, the data points fall near the blue line, indicating that the PDS becomes the step of *OOH formation. Additionally, it can be clearly observed that the values of ∆G_*OH on Fe₂Mn–Mn and Fe₂Ni–Ni are close to 0.94 eV, manifesting that these catalysts possess good catalytic activity. Notably, the ƞ^ORR value of Fe₂Mn–Mn is the minimum (0.42 V), which is smaller than the corresponding value of the Pt(111) surface (ƞ^ORR = 0.45 V) [42], showing that the catalytic activity of Fe₂Mn−Mn is comparable to that on the Pt(111) surface.

For OER, the volcanic top appears when ∆G_*OH value is equal to 0.72 eV, and the minimum theoretical ƞ^OER value is calculated as 0.32 V. When ∆G_*OH value is less than 0.72 eV, the PDS of Fe₂M clusters is the third proton-coupled electron transfer step (*O → *OOH). As the binding strength of *OH on Fe₂M clusters weakens, the PDS is calculated as the step of *OH → *O or H₂O → *OH. Apparently, Fe₂Co−Co possesses the smallest ƞ^OER value of 0.32 V, which is smaller than the corresponding value on the RuO₂(110) surface (ƞ^OER = 0.37 V) [43], manifesting that it has excellent catalytic activity toward OER.

3.2 Bifunctional catalytic activity of Fe₂M clusters

To further examine the bifunctional catalytic activity of this material, the values of ΔE on Fe₂M clusters are calculated and shown in Fig.4. The smaller the values of ΔE, the better the bifunctional catalytic performance of Fe₂M clusters. Among all Fe₂M clusters, it can be clearly noticed that Fe₂Mn, Fe₂Co, and Fe₂Ni clusters possess better bifunctional catalytic activity due to their smaller ΔE values. Furthermore, the energy gap (E_gap) values between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of Fe₂M clusters are calculated to investigate their electronic property, as shown in Tab.2. As is well known, a relatively small E_gap value implies high chemical reactivity and low dynamic stability [47]. In addition, our previous work has pointed out that an appropriate HOMO value is conducive to the transfer of electrons from the catalyst to O₂, which can weaken the O−O bond and further promote the subsequent reaction process [48]. Compared with other Fe₂M clusters, Fe₂Mn, Fe₂Co, and Fe₂Ni have moderate E_gap and HOMO values. This may explain why they possess good bifunctional activity.

Tab.2 HOMO, LUMO, and E_gap values of Fe₂M clusters

Item	Fe2Ti	Fe2V	Fe2Cr	Fe2Mn	Fe2Co	Fe2Ni	Fe2Cu	Fe2Zn
HOMO/eV	−4.749	−4.724	−4.708	−5.859	−5.792	−5.269	−5.985	−6.146
LUMO/eV	−3.829	−4.311	−4.087	−5.049	−4.978	−4.672	−5.041	−4.995
Egap/eV	0.920	0.413	0.621	0.810	0.814	0.597	0.944	1.151

Fig.4 Values of ∆E on Fe₂M clusters.

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3.3 Structure and catalytic activity of Fe₂M–PCN–Fe₂M

Although Fe₂Mn–Mn and Fe₂Co–Co have the highest ORR and OER catalytic activity, respectively, their bifunctional catalytic activities are not ideal. Compared with some reported bifunctional catalysts, including carbon nanotube-supported trimetallic (Mn–Ni–Fe) oxide catalyst (ΔE = 0.73 V) [49], Ni₃Fe nanoparticles embedded in porous nitrogen-doped carbon sheets catalyst (ΔE = 0.84 V) [50], and commercial carbon-supported iridium metal nanoparticles catalyst (ΔE = 0.92 V) [51], the ΔE values of Fe₂Mn and Fe₂Co clusters are relatively larger. To further promote their bifunctional catalytic activity, Fe₂–PCN–Fe₂M is constructed, in which Fe₂Mn and Fe₂Co clusters are connected through the organic linker ABTC. Instead of interacting with the metal element, the carboxylate linker in the heterometallic cluster interacts with the ABTC linker. The optimal configurations of Fe₂Mn–PCN–Fe₂Mn, Fe₂Co–PCN–Fe₂Co, and Fe₂Co–PCN–Fe₂Mn are shown in Fig.5. Additionally, only Mn and Co sites are considered active sites for the corresponding catalysts due to the fact that Fe₂Mn–Mn and Fe₂Co–Co, respectively, have the best ORR and OER catalytic activity, as well as relatively small ΔE values.

Fig.5 Optimal configurations of (a) Fe₂Mn–PCN–Fe₂Mn, (b) Fe₂Co–PCN–Fe₂Co, and (c) Fe₂Co–PCN–Fe₂Mn.

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The optimal configurations of the reaction intermediates on Fe₂M–PCN–Fe₂M are calculated, as shown in Fig. S3 (cf. ESM). Meanwhile, the corresponding ∆E_species on Fe₂M–PCN–Fe₂M are calculated, as presented in Tab.3. For ORR, the ∆E_*OOH values on almost all Fe₂M–PCN–Fe₂M are smaller than those on Fe₂Mn–Mn and Fe₂Co–Co, suggesting the binding strength of *OOH is enhanced on almost all Fe₂M–PCN–Fe₂M. The findings show that the catalytic activities of Fe₂M–PCN–Fe₂M may be improved. Moreover, except for Fe₂Co–PCN–Fe₂Co, the values of ∆E_*O and ∆E_*OH on Fe₂M–PCN–Fe₂M do not change significantly compared with those on Fe₂Mn–Mn and Fe₂Co–Co. Specifically, Fe₂Co–PCN–Fe₂Co possesses the ∆E_*O value of 3.15 eV, which is much larger than the corresponding values on Fe₂Co–Co (2.84 eV) and Pt(111) (1.65 eV), indicating that such weak *O binding strength may cause the ORR process restricted by the formation of *O.

Tab.3 ∆E_species values on Fe₂M–PCN–Fe₂M

Catalyst	Site	∆E*OOH/eV	∆E*O/eV	∆E*OH/eV
Fe2Mn–PCN–Fe2Mn	Mn site	3.71	2.56	0.61
Fe2Co–PCN–Fe2Co	Co site	3.61	3.15	0.82
Fe2Co–PCN–Fe2Mn	Mn site	3.68	2.55	0.72
	Co site	3.68	2.82	0.98

For OER, the PDS of Fe₂Mn–Mn and Fe₂Co–Co is the step of *OH → *O, which is attributed to the weak binding strength of *O. Fortunately, the values of ∆E_*O on almost all Fe₂M–PCN–Fe₂M are smaller than that on Fe₂Mn–Mn and Fe₂Co–Co, implying stronger *O binding. Therefore, their OER catalytic activity may be improved by the strong binding strength of *O. As is well known, the ∆E_*OOH, ∆E_*O, or ∆E_*OH alone is insufficient to predicate catalytic activity. Hence, the detailed catalytic process and overpotential are further discussed.

The Gibbs free energy change in each reaction step of ORR and OER on Fe₂M–PCN–Fe₂M is calculated, as shown in Fig.6. For ORR, it can be found that the free energy curves of each ORR step on all Fe₂M–PCN–Fe₂M being studied are downhill, showing that ORR can occur spontaneously on them. Except for Fe₂Co–PCN–Fe₂Co, the PDS of all Fe₂M–PCN–Fe₂M is the first proton–electron transfer step (the formation of *OOH). The PDS of Fe₂Co–PCN–Fe₂Co is the step of *OOH → *O, which is attributed to its weak binding strength to *O. The corresponding η^ORR values on Fe₂Mn–PCN–Fe₂Mn, Fe₂Co–PCN–Fe₂Co, as well as the Mn and Co sites of Fe₂Co–PCN–Fe₂Mn are 0.42, 0.41, 0.39, and 0.39 V, respectively, demonstrating that they have remarkable catalytic activity, even better than the Pt(111) surface (η^ORR = 0.45 V) [42]. For OER, the PDS of all Fe₂M–PCN–Fe₂M being studied is the step of *OH → *O. It is noteworthy that the Mn and Co sites of Fe₂Co–PCN–Fe₂Mn have small η^OER values of 0.30 and 0.31 V, respectively. These values are even less than that on the RuO₂(110) surface (0.37 V) [43], indicating that Fe₂Co–PCN–Fe₂Mn possesses excellent OER catalytic activity. Furthermore, some experimental studies have shown that the Fe₂Co cluster-based organic frameworks exhibit excellent OER performance, including Fe₂Co–MOF (0.34 V) [17] and Fe₂Co-BPTC (0.38 V) [25].

Fig.6 Free energy diagrams of ORR and OER on (a) Fe₂Mn–PCN–Fe₂Mn, (b) Fe₂Co–PCN–Fe₂Co, (c) Mn site of Fe₂Co–PCN–Fe₂Mn, and (d) Co site of Fe₂Co–PCN–Fe₂Mn. The PDS of ORR and OER are denoted by blue and green lines, respectively.

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Additionally, the bifunctional catalytic activity of Fe₂M–PCN–Fe₂M is also investigated. For Fe₂Co–PCN–Fe₂Co, its ΔE value (1.17 V) is larger than that for Fe₂Co–Co (1.07 V), implying its inferior bifunctional catalytic activity. For Fe₂Mn–PCN–Fe₂Mn, its ΔE value only becomes 0.05 V smaller than Fe₂Mn–Mn (0.89 to 0.84 V). Following the above analysis, forming Fe₂M–PCN–Fe₂M by the same Fe₂M clusters cannot significantly improve the bifunctional catalytic activity. Encouragingly, when forming mixed-metal Fe₂Co–PCN–Fe₂Mn, the ΔE values on the Mn and Co sites on it are 0.69 and 0.70 V, respectively, significantly smaller than the corresponding values on Fe₂Co–Co, Fe₂Mn–Mn, and other previously reported catalysts [49–51]. All in all, forming mixed-metal Fe₂Co–PCN–Fe₂Mn is an effective strategy to improve the bifunctional catalytic performance of the original Fe₂M clusters.

3.4 Origin of the activity

The number of electrons in the 3d orbital of Mn or Co active atoms of Fe₂Co–PCN–Fe₂Mn, Fe₂Co, and Fe₂Mn is calculated to investigate the origin of catalytic activity of Fe₂Co–PCN–Fe₂Mn. A previous study has found that a greater number of electrons in the 3d orbital of an active metal atom is more conducive to the binding of *OOH [52]. As shown in Fig.7, the profiles of density of states (DOS) are integrated to calculate the accurate number of electrons in 3d orbital metal atom. The number of electrons under the Fermi level in 3d orbitals of the Mn and Co sites of Fe₂Co–PCN–Fe₂Mn is 8.75e and 10.72e, which are respectively larger than that of the Mn site of Fe₂Mn (8.44e) and Co site of Fe₂Co (9.59e). The greater number of electrons in the 3d orbital makes the Mn and Co sites of Fe₂Co–PCN–Fe₂Mn have stronger *OOH binding strength than that on the Mn site of Fe₂Mn and Co site of Fe₂Co, respectively, which is proven by the calculated values of ∆E_*OOH (Tab.1 and Tab.3). Additionally, taking Fe₂Mn and Fe₂Co–PCN–Fe₂Mn as examples, the corresponding DOS is calculated to reflect the electronic properties of catalysts before and after forming a mixed-metal cluster, as shown in Fig.8. It can be observed that the Mn-d orbitals of the catalysts overlap with O-p orbitals of *OOH near the Fermi level, implying that the specific interaction between the catalyst and *OOH. Compared with the case of Fe₂Mn, the peak of O-p orbitals of *OOH on Fe₂Co–PCN–Fe₂Mn is split into several peaks and shifted to a lower energy level, indicating the stronger orbital hybridization between Mn-d and O-p orbitals. Therefore, the results reveal that the strategy of constructing a mixed-metal cluster can effectively tune the electronic property of the active site, increasing the catalytic activity of the catalyst.

Fig.7 (a) The number of electrons in the 3d orbital of Mn active atoms of Fe₂Co–PCN–Fe₂Mn and Fe₂Mn; (b) the number of electrons in the 3d orbital of Co active atoms of Fe₂Co–PCN–Fe₂Mn and Fe₂Co. The Fermi level is set to zero. Inset is the magnified pattern near the Fermi level.

Full size|PPT slide

Fig.8 DOS of d orbitals for Fe₂Mn and Fe₂Co–PCN–Fe₂Mn. The O-p refers to the p orbital of the oxygen atom of *OOH.

Full size|PPT slide

4 Conclusions

The ORR and OER catalytic activities of heterometallic cluster-based organic frameworks are systematically explored by DFT methods in this work. Firstly, the binding strength of the reaction intermediates on Fe₂M clusters is studied. It can be found that Fe₂Mn and Fe₂Co clusters may have excellent ORR and OER catalytic activities due to the ∆E_species values on them are close to that on the Pt(111) and RuO₂(110) surfaces. Subsequently, the scaling relationships of ∆G_*OOH and ∆G_*O with ∆G_*OH on Fe₂M clusters are established, and the volcano plot between the overpotential and ∆G_*OH is constructed. Fe₂Mn–Mn possesses the highest ORR activity (η^ORR = 0.42 V), which is better than the Pt(111) surface (η^ORR = 0.45 V). Fe₂Co−Co has the smallest ƞ^OER value of 0.32 V, which is smaller than that on the RuO₂(110) surface (ƞ^OER = 0.37 V). Additionally, the potential gap on Fe₂M clusters is calculated to assess the bifunctional catalytic activity. Among them, Fe₂Mn, Fe₂Co, and Fe₂Ni clusters have better bifunctional catalytic activity due to the ΔE values on them being relatively small. Furthermore, Fe₂M–PCN–Fe₂M formed by Fe₂Mn and Fe₂Co clusters is constructed, and the bifunctional catalytic activity is investigated. For ORR, except for Fe₂Co–PCN–Fe₂Co (*OOH → *O), the PDS of all Fe₂M–PCN–Fe₂M is the formation of *OOH. Compared with the Pt(111) surface, the η^ORR values on all Fe₂M–PCN–Fe₂M being studied are smaller, indicating that they have excellent ORR catalytic activity. For OER, the PDS of all Fe₂M–PCN–Fe₂M under study is the step of *OH → *O. Fe₂Co–PCN–Fe₂Mn possesses excellent OER catalytic activity due to the small η^OER values on the Mn and Co sites of the catalyst. Encouragingly, it can be found that both the Mn and Co sites of Fe₂Co–PCN–Fe₂Mn have excellent bifunctional catalytic activity, which is attributed to their potential gap of 0.69 and 0.70 V, respectively. Moreover, the analysis of the number of electrons in the 3d orbital of an active metal atom indicates that formed mixed-metal Fe₂Co–PCN–Fe₂Mn can effectively tune the electronic properties of the active site. These results demonstrate that mixing Fe₂Co and Fe₂Mn clusters to construct mixed-metal Fe₂Co–PCN–Fe₂Mn is an effective strategy to improve the catalytic activity of the original Fe₂M clusters.

Acknowledgements

This work was supported by the Science and Technology Project of Sichuan Province (Grant No. 2022YFS0447), the Local Science and Technology Development Fund Projects Guided by the Central Government of China (Grant No. 2021ZYD0060), the Science and Technology Project of Southwest Petroleum University (Grant No. 2021JBGS03), the Special Project of Science and Technology Strategic Cooperation between Nanchong City and Southwest Petroleum University (Grant No. SXQHJH064), and the Postgraduate Research and Innovation Fund of Southwest Petroleum University (Grant No. 2021CXYB14). We acknowledge the National Supercomputing Center in Shenzhen for providing the computational resources and Materials Studio.

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://dx.doi.org/10.1007/s11705-022-2247-y and is accessible for authorized users.

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