Computational Design of Ni6@Pt1M31 Clusters for Multifunctional Electrocatalysts

Abstract

High-efficiency and low-cost multifunctional electrocatalysts for hydrogen evolution reaction (HERs), oxygen evolution reaction (OERs) and oxygen reduction reaction (ORRs) are important for the practical applications of regenerative fuel cells. The activity trends of core–shell Ni₆@M₃₂ and Ni₆@Pt1M31 (M = Pt, Pd, Cu, Ag, Au) were investigated using the density functional theory (DFT). Rate constant calculations indicated that Ni₆@Pt₁Ag₃₁ was an efficient HER catalyst. The Volmer–Tafel process was the kinetically favorable reaction pathway for Ni₆@Pt₁M₃₁. The Volmer–Heyrovsky reaction mechanism was preferred for Ni₆@M₃₂. The Pt active site reduced the energy barrier and changed the reaction mechanism. The ORR and OER overpotentials of Ni₆@Pt₁Ag₃₁ were calculated to be 0.12 and 0.33 V, indicating that Ni₆@Pt₁Ag₃₁ could be a promising multifunctional electrocatalyst. Ni₆@Pt₁M₃₁ core–shell clusters present abundant active sites with a moderate adsorption strength for *H, *O, *OH and *OOH. The present study shows that embedding a single Pt atom onto a Ni@M core–shell cluster is a rational strategy for designing an effective multifunctional electrocatalyst.

1. Introduction

Reversible fuel cells or unitized regenerative fuel cells (URFCs) combine the functions of fuel cells and electrolyzers, which attract increasing attention because of their high levels of efficiency and environmentally friendly merits [1]. The key challenge is to develop highly active and stable multifunctional electrocatalysts for hydrogen and oxygen electrode reactions [2,3]. The cathodic hydrogen evolution reaction (HER) and the anodic oxygen evolution reaction (OER) have sluggish kinetics due to large overpotentials. Pt/C and noble metal oxides of RuO₂ and IrO₂ demonstrated advanced activity with reduced overpotentials in ORR/HER/OER processes [4,5,6]. However, the wider applications of noble-metal materials have been limited by their high price and scarcity [7,8]. Thus, efforts are mainly devoted to the design of efficient and cheap catalysts whose catalytic performances are comparable to noble metals in accelerating the ORR, OER and HER [9,10,11,12,13].

Recently, electrocatalysts with core–shell structures were prepared to be applicable for catalyzing the ORR/OER/HER efficiently [14,15]. The electronic structure of a core–shell cluster can be regulated through the electronic interaction between the core and shell [16]. Many core–shell nanoclusters have been explored theoretically and experimentally for the ORR process [17,18,19]. A novel Pt core–shell catalyst for the ORR was reported with an impressive improvement, producing 3.7 times greater results relative to a Pt/C material [20]. Chen and colleagues reported that Ni-Pd alloys with Pd-enriched surfaces exhibited significantly enhanced ORR activities and improved CH₃OH tolerances compared to Pd/C catalysts [21]. Lin et al. reported the synthesis of snap-bean-like, multi-dimensional core/shell Ni/NiCoP nano-heterojunctions (NHs), presenting improved stability and activity for both hydrogen evolution reactions (HERs) and oxygen evolution reactions (OERs) [22]. Ma et al. demonstrated a core–shell-structured non-noble-metal, Ni@In, loaded on silicon nanowire arrays (SiNWs) for the efficient reduction of CO₂ to formate [23]. Park’s group synthesized a Ni-based core–shell material (Ni@Ni-NC) which displayed excellent electrocatalytic OER performance with over- and onset potentials of 371 mV and 1.51 V, respectively, which are superior to those of commercial IrO₂ [24], and Yu’s group found that Ni@Pd core–shell nanoparticles exhibited robust ORR activity and stability in both acidic and alkaline electrolytes, comparable to commercially available Pt/C catalysts [25]. In addition, Lang’s group prepared binary core–shell Ni@Pt NPs [26] with good ORR performance and durability. A Ni₁₉@Pt₇₀ cluster exhibited better catalytic activity and stability for the ORR than Pt₇₉ [27].

With nearly 100% atom utilization, a unique local coordination environment and electronic configuration, noble-metal single-atom catalysts (SACs) exhibit unique properties [28,29,30,31,32]. Li’s group predicted that the Pt₁/PMA (phosphomolybdic acid cluster) catalyst is a promising multifunctional electrocatalyst for use in water splitting (η^HER = 0.02 V and η^OER = 0.49 V) and a metal–air battery (η^ORR = 0.79 V) [33]. Zhao et al. reported a single-atom Ru catalyst for the OER with the overpotential of 118 mV [34]. Zhang et al. proposed a single-atom Au electrocatalyst supported by NiFe-LDH with high activity for the OER [35].

A multifunctional electrocatalyst should have abundant active sites which remarkably facilitate the adsorption/desorption of *H, *O, *OH and *OOH intermediates and products or two reactions simultaneously. The adsorption and desorption energies of the reaction species should be moderate, according to the Sabatier’s principle [36].

We systematically investigated the stability and multifunctional catalytic behavior of Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, Au) and Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au) for the ORR, OER and HER using DFT calculations. The OER overpotential of Ni₆@Pt₁Ag₃₁ (η^OER = 0.33 V) is lower than RuO₂ (η^OER = 0.37 V) [34] and IrO₂ (η^OER = 0.56 V) [37]. Rate constant calculations indicated that Ni₆@Pt₁Ag₃₁ is an efficient HER catalyst. The Volmer–Tafel process was a kinetically favorable reaction pathway for Ni₆@Pt₁M₃₁, while the Volmer–Heyrovsky process was the major pathway for Ni₆@M₃₂. The present study shows that embedding a single Pt atom onto core–shell Ni@PtM cluster is a rational strategy for designing a multifunctional electrocatalyst.

2. Results and Discussion

2.1. Structure and Stability Analysis

A core–shell Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, Au) cluster (Figure 1) was used as a catalyst model to understand the activity trends of the HER, OER and ORR. The average bond lengths were calculated and are shown in Table S2. The average bond lengths of the Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, Au) clusters were shorter than those of pure M₃₂ clusters arising from a lattice mismatch between the core and shell atoms. The average bond length of the shell decreases in the following order: Ni₆@Au₃₂ ≈ Ni₆@Ag₃₂ > Ni₆@Pd₃₂ > Ni₆@Pt₃₂ > Ni₆@Cu₃₂.

The formation energies of the Ni₆@Pt₁M₃₁ structures were calculated according to Equation (S1) and are presented in Table 1. The negative values indicate that it is thermodynamically favorable for the formation of Ni₆@Pt₁M₃₁ from Ni₆@M₃₂ and a Pt atom. The thermodynamic trend is Ni₆@Pt₁Pd₃₁ (−0.56 eV) > Ni₆@Pt₁Ag₃₁ (−0.51 eV) > Ni₆@Pt₁Cu₃₁ (−0.08 eV) > Ni₆@Pt₁Au₃₁ (0.33 eV).

The average binding energy was calculated according to Equation (S2) and is presented in Figure 2a. The average binding energy decreases in the following order: Ni₆@Pt₃₂ (4.53 eV) > Ni₆@Pd₃₂ (4.36 eV), Ni₆@Pt₁Pd₃₁ (4.40 eV) > Ni₆@Pt₁Au₃₁ (3.02 eV), Ni₆@Au₃₂ (2.96 eV) > Ni₆@Pt₁Ag₃₁ (2.63 eV), Ni₆@Ag₃₂ (2.53 eV) > Ni₆@Pt₁Cu₃₁ (0.42 eV), Ni₆@Cu₃₂ (0.25 eV). Ni₆@Pt₃₂ has the highest binding energy (4.53 eV) and is the most stable catalyst.

A Bader charge analysis was carried out to investigate the electronic properties of the Ni₆@M₃₂ and Ni₆@Pt₁M₃₁. The electronegativities (Pauling scale) of Ni, Pt, Pd, Au, Ag and Cu are 1.91, 2.28, 2.20, 2.54, 1.93 and 1.90, respectively. As presented in Figure 2b, the charge transfer amount changes in the following order: Ni₆@Pt₃₂ > Ni₆@Pd₃₂, and Ni₆@Au₃₂ > Ni₆@Ag₃₂ > Ni₆@Cu₃₂. The charge transfer amount increases with the increased difference in the electronegativity between the core and shell elements. It is closely related to the average binding energy, as shown in Figure S1. The average binding energy increases with an increased amount of charge transferred between the core and shell.

The density of the states projected onto the d states of the Ni₆@M₃₂ clusters and Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au) clusters is shown in the Figure S2. The introduction of a Pt atom narrows the distribution of the d states. Its influence is smaller on the Ni₆@Pd₃₂ cluster than on the other three clusters. The Ni₆@Pt₁Ag₃₁ cluster shows the most significant change in its PDOS compared to the Ni₆@Ag₃₂ cluster, with the population of high-energy states decreasing and the population of low-energy states increasing. This feature may present active sites with a moderate adsorption strength for *H, *O, *OH and *OOH.

2.2. Hydrogen Evolution Reaction (HER) Catalytic Activity

Mechanistically, the HER involves three possible principal steps in acidic media which occur via either the Volmer–Heyrovsky or Volmer–Tafel process as presented in Text S1. The Volmer reaction refers to the initial adsorption of protons from the acid solution to form adsorbed H and is usually considered to be fast. The Heyrovsky reaction refers to the reaction of a proton in the water layer with an adsorbed hydrogen to form H₂. Two adsorbed H atoms react to form H₂, which is Tafel reaction process.

2.2.1. The Hydrogen-Adsorption Gibbs Free Energies of Ni₆@M₃₂ and Ni₆@Pt₁M₃₁

To assess the Volmer performance of the Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, Au) and Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au), we calculated the differential hydrogen-adsorption Gibbs free energy (d−ΔG_H*) and average-hydrogen-adsorption Gibbs free energy (a−ΔG_H*) values (Equations (S3)–(S5) in Text S1) as functions of the hydrogen coverage (θ_H*). Here, θ_H* was defined as n/6, where n is the number of adsorbed H atoms. The exchange current density value i₀ was calculated as a function of d−ΔG_H* according to the Equations (S6) and (S7) in Text S1. The d−ΔG_H* and a−ΔG_H* values of Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au) from θ_H* = 1/6 to 6/6 are presented in Figure 3a,b,d,e,g,h,j,k. A volcano relation formed between d−ΔG_H* and the exchange current density. The volcano plot of i₀ as a function of d−ΔG_*H is presented in Figure 3c,f,i,l. For comparison, data regarding Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, Au), including the d−ΔG_H*, a−ΔG_H* and i₀ values, are presented in Figure S3.

For Ni₆@M₃₂ and Ni₆@Pt₁M₃₁ (M = Pd, Pt), the high hydrogen coverage value (θ_H* = 6/6) corresponds to the optimal d−ΔG_H* and i₀ values. For example, for Ni₆@Pt₁Pd₃₁, the d−ΔG_H* values were calculated to be −0.28, −0.23, −0.25, −0.12, −0.33 and 0.10 eV at a H coverage ranging from 1/6 to 6/6, and the volcano plot indicates that the high θ_H* = 6/6 corresponds to the low d−ΔG_H* and high i₀ values. Compared with the Ni₆@Pd₃₂ cluster (Figure S3), the d−ΔG_H* and a−ΔG_H* values of Ni₆@Pt₁Pd₃₁ are closer to zero, demonstrating the benefit of the introduction of single-site Pt. For Ni₆@M₃₂ (M = Cu, Ag, Au) and Ni₆@Pt₁M₃₁ (M = Ag, Au), the low hydrogen coverage (θ_H* = 1/6) value corresponds to the optimal d−ΔG_H* and high i₀ values.

The repulsion interaction between neighboring negatively charged, adsorbed *H atoms possibly improves the desorption. At low H coverage, Ni₆@M₃₂ (M = Cu, Ag, Au) present d−ΔG_H* and i₀ values which are comparable to Ni₆@Pt₃₂. The optimal |d−ΔG_H*|, |a−ΔG_H*| and i₀ values and the Bader charges of the hydrogen atoms in the Ni₆@M₃₂ and Ni₆@Pt₁M₃₁ systems are presented in Table S3. These results show the complex influence of the hydrogen coverage on the interaction between the adsorbate and the adsorption site. An analysis of the projected density of states (PDOS, Figure S4) shows that high coverage can broaden the distribution of the d-DOS of the adsorption sites for the Ni₆@Pd₃₂ and Ni₆@Pt₁Pd₃₁ clusters. This weakens the adsorption strength of the adsorbates at the adsorption site.

2.2.2. The Energy Barriers of the Tafel and Heyrovsky Processes

From the point of the adsorption free energy, at a low H coverage, Ni₆@M₃₂ (M = Cu, Ag, Au) present Volmer activity comparable to Pt-based Ni₆@Pt₃₂. We further investigated the kinetic properties of all candidates. Considering the water environment, the energy barriers of the Tafel and Heyrovsky processes were calculated for Ni₆@M₃₂ and Ni₆@Pt₁M₃₁, with a d−ΔG_*H value close to zero. Figure 4 displays the structures of the adsorption state, transition state and product species and the energy barriers. The energy barriers of the Tafel process for Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au) are 0.33, 0.21, 0.10 and 0.55 eV, respectively. We employed the H₃O species to consider the H₃O⁺ + e⁻ approximately for the simulation of the Heyrovsky step. The energy barriers of the Heyrovsky process were calculated to be, respectively, 0.89, 0.88, 0.45 and 0.77 eV. For Ni₆@Pt₁M₃₁ (M = Pd, Cu, Au), the Heyrovsky process needs to overcome a relatively higher energy barrier to form H₂ by H₃O reacting with an adsorbed H*. The Volmer–Tafel reaction mechanism is main pathway for Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au) by combining two adsorbed hydrogens to form H₂. The energy barriers of the Tafel process for Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag) are 0.55, 0.66, 0.78 and 1.06 eV, respectively, as presented in Figure S6. The energy barriers of the Heyrovsky process for Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag) are 0.43, 0.54, 0.14 and 0.70 eV, respectively. The Volmer–Heyrovsky reaction pathway is favorable for Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag).

The rate constants (k/s) of the Tafel and Heyrovsky processes in the HER were calculated according to Equation (S8), based on the Eyring transition state theory with Wigner correction [38], as presented in Table 2. By comparing the rate constants, the Volmer–Heyrovsky reaction mechanism was determined to be favorable for Ni₆@M₃₂, and the Volmer–Tafel process was determined to be a kinetically advantageous reaction pathway for Ni₆@Pt₁M₃₁. The Pt active site decreases the energy barrier and modulates the reaction mechanism.

Platinum metal catalysts have been known as the most efficient catalysts for the HER due to their optimum Gibbs free energy for atomic hydrogen adsorption (ΔG_H*). Ni₆@Cu₃₂ has comparable HER activity to Ni₆@Pt₃₂, and at θ_H* = 2/6, Ni₆@Pt₁Ag₃₁ is the most efficient catalyst of Ni₆@M₃₂ and Ni₆@Pt₁M₃₁. These results indicate the H coverage is an important factor in the kinetic activity of the HER.

2.3. The Oxygen Reduction Reaction (ORR)/Oxygen Evolution Reaction (OER): Catalytic Activity

The activity of the ORR and OER under acidic conditions were investigated for Ni₆@M₃₂ and Ni₆@Pt₁M₃₁. It was given that the oxygen reduction reaction pathway occurs via an associative mechanism, with four protonation reaction steps. The adsorption free energies of the oxygenated intermediates were calculated as presented in Table S4 via the computational hydrogen electrode (CHE) model, using hydrogen and water as references, according to Equations (S18)–(S21). The free energy diagram of the four-electron reaction is presented in Figure 5. The OER/ORR overpotential was obtained by Equations (S22) and (S23). As shown in Figure 4, the ORR’s potential-limiting step is the proton-coupled electron transfer step *OH → H₂O for Pt₃₈, Pt (111), Ni₆@Pt₁Cu₃₁ and Ni₆@M₃₂ (M = Pd, Cu, Ag, Au). The potential-limiting step of the ORR’s elementary reactions for Ni₆@Pt₁M₃₁ (M = Pd, Au) is O₂ + H⁺ + e⁻ → *OOH. For Ni₆@Pt₃₂ and Ni₆@Pt₁Ag₃₁, *O → *OH is the potential-limiting step. The ORR overpotentials are presented in Table S5. The overpotential (η^ORR) values of the Pt (111) and Pt₃₈ clusters were calculated to be 0.73 and 0.81 V. For Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au), the overpotentials were calculated to be 0.77, 0.83, 0.12 and 1.06 V, respectively. Ni₆@Pt₁Ag₃₁ showed the best activity, with η^ORR = 0.12 V. In the OER process, the potential-limiting step is the *O → *OOH step for Pt₃₈, Pt (111), Ni₆@M₃₂ (M = Pt, Pd) and Ni₆@Pt₁M₃₁ (M = Pd, Cu, Au). For Ni₆@Cu₃₂ and Ni₆@Pt₁Ag₃₁, the OER’s potential-limiting step is the *OOH → O₂ process. The second deprotonation process (*OH → *O) is the OER’s potential-limiting step for Ni₆@M₃₂ (M = Ag, Au). The OER overpotentials for Pt₃₈ and Pt (111) are 1.34 and 0.74 V. The OER overpotentials for the Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, and Au) clusters are 1.17, 0.81, 0.92, 0.93 and 1.08 V, respectively. The calculated OER overpotentials for Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au) are respective 1.36, 1.61, 0.33 and 0.61 V. The OER overpotential for a Ni₆@Pt₁Ag₃₁ (η^OER = 0.33 V) single-atom catalyst is lower than those of RuO₂ (η^OER = 0.37V) [37] and IrO₂ (η^OER = 0.56V) [37].

The adsorption strength of the three intermediates, *OOH, *O and *OH, was analyzed to explore the activity trend of the Ni₆@M₃₂ and Ni₆@Pt₁M₃₂ (M = Pd, Cu, Ag, Au). As shown in Figure 6a,b, there is a linear relationship between the adsorption free energy values of *OOH and *OH. The inverted volcano curve was obtained by plotting the adsorption free energy of *OH and the corresponding ORR overpotential, as presented in Figure 6c. On the left leg, the rate-limiting step is the *OH → H₂O process due to the strong *OH adsorption strength. On the right-side, because of the weak adsorption for *OOH, the process of generating *OOH intermediates from oxygen becomes the limiting step. A similar volcano curve can be obtained by plotting the adsorption free energy of the *OOH and the ORR overpotential, and the details are presented in Figure S7.

The d-band centers (ε_d) were calculated to explain the interaction of the adsorbates with the adsorption sites because the O* adsorption strength of a metal is closely correlated with its d-orbital levels [39]. The d-band centers of the adsorption sites of Ni₆@M₃₂ and Ni₆@Pt₁M₃₁ were calculated to explain the interaction of the *O intermediate with the adsorption sites. As shown in Figure 7a, there is no linear relationship between the adsorption energy of the *O intermediate and the d-band center of the adsorption site. A small deformation of the geometry of the metal cluster was caused by O adsorption. The adsorption energy was thought to be the superposition of the metal cluster’s geometry deformation energy and the binding energy between the metal cluster and the O. The adsorption energy was decomposed as follows: ΔE_ads = ΔE_deformation + ΔE_binding, where ΔE_deformation is the difference in the energy of the metal cluster before and after the O adsorption; ΔE_binding is the binding energy of the O on the metal cluster. A linear relationship between the binding energy and the d-band center is presented in Figure 7b. The adsorption strength of the adsorbed oxygen intermediate decreases with the downshift in ε_d to the Fermi energy level due to the d-p anti-bond orbital occupancy [39].

The PDOS was analyzed to explore the interaction between O* and the active site, as presented in Figure 7c. The blue and green colors represent the d state distributions of the adsorption sites, and the red part represents the p-orbital distribution of the adsorbed oxygen atom. In the PDOS diagrams of Ni₆@M₃₂ (M = Au, Ag) and Ni₆@Pt₁M₃₁ (M = Au, Ag), the antibonding orbitals are occupied, resulting in weakened adsorption strength. On the contrary, the PDOS diagrams of Ni₆@M₃₂ (M = Pt, Pd) and Ni₆@Pt₁M₃₁ (M = Pt, Pd) show that the antibonding orbital energy levels shift up over the Fermi energy level, leading to a relatively stronger d-p interaction. Comparing Ni₆@M₃₂ and Ni₆@Pt₁M₃₁, the single Pt atom causes the d-band centers to up-shift to the Fermi energy level, resulting in a slightly stronger adsorption strength. Combined with the d-band center and PDOS analyses, a moderate O adsorption interaction significantly improved the potential-limiting step *O → *OH, with a reduced overpotential of η^ORR = 0.12 V. Among all the candidates, Ni₆@Pt₁Ag₃₁ is a promising multifunctional electrocatalyst for splitting water (∆G_TS^Heyrovsky = 0.10 eV and η^OER = 0.33 V) and has a low overpotential of η^ORR = 0.21 V.

In summary, the electronic properties of the adsorption sites can be manipulated by changing the chemical composition of the core and shell. The free energies and electronic structures of the core–shell Ni₆@Pt₁M₃₂ nanoclusters can be modulated to offer improved performance in the electrocatalysis of the ORR, HER and OER. In the ORR, Ni₆@Pt₁Pd₃₁ and Ni₆@Pt₁Ag₃₁ exhibit lower overpotentials than Pt (111). In the HER, Ni₆@Cu₃₂ (0.14 eV), Ni₆@Pt₁Cu₃₁ (0.21 eV), Ni₆@Pt₁Pd₃₁ (0.33 eV) and Ni₆@Pt₁Ag₃₁ (0.10 eV) are promising efficient electrocatalysts. In the OER, the overpotentials of Ni₆@Pt₁Ag₃₁ and Ni₆@Pt₁Au₃₁ are lowered compared to that of Pt (111).

3. Computational Details

3.1. Computational Methods

Spin-polarized DFT methods were implemented in the Vienna Ab initio Simulation Package (VASP) [40,41,42] to carry out energy calculations and a geometry optimization. The interaction between valence and core electrons was described using the projector-augmented wave (PAW) pseudopotential [43,44], with an energy cutoff for the plane waves of 400 eV. A generalized gradient approximation (GGA) with the PW91 functional was used to calculate the exchange–correlation energies [45,46]. The clusters were placed at the center of a 20 × 20 × 20 ų cubic box, 65% of which was vacuum space to avoid interaction between the clusters and their images. A Pt (111) slab was modeled using a five-layer, periodically repeated √3 × √2 super cell with 35 Å of vacuum space. A Gamma (1 × 1 × 1) point mesh was used during the geometric optimization of clusters. A threshold for self-consistent calculations of 1 × 10⁻⁵ eV was used, and 0.02 eV/Å was used for ionic optimization. The transition state (TS) was determined via the Dimer method [47]. A Bader charge analysis was conducted to analyze the charge transfer [48].

3.2. Models

A truncated octahedral (TO) structure was employed as the theoretical model. The shell of the TO structure consists of eight (111) planes and six (100) planes. There are eight non-equivalent adsorption sites (two top sites, three bridge sites, two face sites and one hollow site) on the Pt₃₈ and Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, Au) clusters. The structures are shown in Figure 1.

4. Conclusions

A high-efficiency and low-cost multifunctional electrocatalyst for splitting water and reducing oxygen is required for the practical applications of regenerative fuel cells. The HER, OER and ORR activity trends were investigated for core–shell Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, Au) and Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au) via first-principles calculations. The core–shell Ni₆@Pt₁M₃₁ clusters present abundant active sites with moderate adsorption strengths for *H, *O, *OH and *OOH. The HER reaction energy barriers and rate constants indicated that Ni₆@Pt₁Ag₃₁ was the most efficient catalyst of all the Ni₆@M₃₂ (M = Pt, Pd) and Ni₆@Pt₁M₃₁ clusters at an H coverage of θ_H* = 2/6. The Pt active site decreased the energy barrier and changed the reaction mechanism. The Volmer–Heyrovsky reaction mechanism was favorable for Ni₆@M₃₂, and the Volmer–Tafel process was a kinetically advantageous reaction pathway for Ni₆@Pt₁M₃₁. The ORR and OER overpotentials of Ni₆@Pt₁Ag₃₁ were calculated to be 0.12 and 0.33 V, and the OER overpotential was lower than that of RuO₂ and IrO₂, which proves that Ni₆@Pt₁Ag₃₁ is a promising multifunctional electrocatalyst for the OER, HER and ORR. The present work provides significant insights for further searches for a high-efficiency and low-cost multifunctional electrocatalyst for regenerative fuel cells.

Author Contributions

Conceptualization, D.T.; methodology, D.T. and J.J.; software, D.T. and J.J.; validation, D.T. and J.J.; formal analysis, D.T. and J.J.; investigation, J.J.; resources, D.T.; data curation, D.T. and J.J.; writing—original draft preparation, J.J.; writing—review and editing, D.T. and J.J.; visualization, J.J.; supervision, D.T.; project administration, D.T.; funding acquisition, D.T. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Data Availability Statement

Data are contained within the article and Supplementary Materials.

Acknowledgments

The authors acknowledge the Supercomputer Center of Dalian University of Technology for providing computation resources.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures and Tables

Figure 1. The structures of Pt38, Pt (111), core–shell Ni6@M32 (M = Pt, Pd, Cu, Ag, Au) and Ni6@Pt1M31 (M = Pd, Cu, Ag, Au) clusters. T, b, f and hollow represent the top, bridge, face and hollow site, respectively.

Figure 2. (a) Average binding energies for core–shell clusters. (b) Bader charge transfer amounts between the cores and shells of clusters.

Figure 3. The differential Gibbs free energy profiles (d−ΔGH*) over the Ni6@Pt1M31 (M = Pd, Cu, Ag, Au) clusters (a,d,g,j); the average Gibbs free energy profiles (a−ΔGH*) (b,e,h,k); the volcano plot of i0 as a function of d−ΔGH* at the best H coverage (c,f,i,l); the highlight in blue denotes the free energy window of ±0.25 eV.

Figure 4. The potential energy profiles of the HER via the Tafel process and the Heyrovsky process at the optimal H coverage. 6H-Ni6@Pt1Pd31 (a,b), 4H-Ni6@Pt1Cu31 (c,d), 2H-Ni6@Pt1Ag31 (e,f) and 2H-Ni6@Pt1Au31 (g,h). White, red, blue, coppery, grey and golden ball represent H, O, Ni, Cu, Ag and Au, respectively.

Figure 5. The Gibbs energy diagrams for the ORR and OER for (a) Pt38, Pt (111), (b) Ni6@M32 (M = Pt, Pd) and Ni6@Pt1Pd31, (c) Ni6@M32 (M = Cu, Ag, Au), (d) Ni6@Pt1Pd31 (M = Cu, Ag, Au) at U = 0 V (RHE).

Figure 6. (a) Scaling relationships between the Gibbs free energy (ΔG) of *OOH and *OH for Ni6@M32 and (b) for Ni6@Pt1M31. (c) The linear relationship between the ORR overpotential and *OH adsorption free energy.

Figure 7. (a) Plot of the adsorption free energy of *O on Ni6@M32 and Ni6@Pt1M31 against the d-band center of the adsorption site. (b) Plot of the binding energy of *O on Ni6@M32 and Ni6@Pt1M31 against the d-band center of adsorption site. (c) Density of states projected onto the d states of adsorption site on *O of Ni6@M32 (blue), adsorption site on *O of Ni6@Pt1M31 (green), and the p states of adsorbed oxygen atoms, respectively (pink).

Table 1

The formation energies of the Ni₆@Pt₁M₃₁ structures.

Reaction Coordination	Ef/eV
Ni6@Pd32 + Pt1 → Ni6@Pt1Pd31 + Pd1	−0.56
Ni6@Cu32 + Pt1 → Ni6@Pt1Cu31 + Cu1	−0.08
Ni6@Ag32 + Pt1 → Ni6@Pt1Ag31 + Ag1	−0.51
Ni6@Au32 + Pt1 → Ni6@Pt1Au31 + Au1	0.33

Table 2

Rate constants (k/s) and energy barriers of the Tafel and Heyrovsky processes in the HER on Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag) and Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au).

System	ΔGTafel≠/eV	Tafel (k/s)	ΔGHeyrovsky≠/eV	Heyrovsky (k/s)
6H-Ni6@Pt32	0.55	4.35 × 103	0.43	3.92 × 105
6H-Ni6@Pd32	0.66	54.4	0.54	4.78 × 103
2H-Ni6@Cu32	0.78	0.72	0.14	3.17 × 1010
3H-Ni6@Ag32	1.06	1.84 × 10−5	0.70	9.84
6H-Ni6@Pt1Pd31	0.33	1.76 × 107	0.89	6.17 × 103
4H-Ni6@Pt1Cu31	0.21	1.84 × 109	0.88	9.25 × 10−3
2H-Ni6@Pt1Ag31	0.10	1.83 × 1011	0.45	1.69 × 105
2H-Ni6@Pt1Au31	0.55	3.27 × 103	0.77	0.64

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/molecules28227563/s1, Figure S1: The relationship between the calculated average binding energy of catalysts and the amount of charge transfer between the core and shell (red represents the amount of Bader charge transfer, blue represents the average binding energy); Figure S2: Density of states projected onto the d states of Ni₆@M₃₂ clusters (left) and Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au) clusters (right); Figure S3: The differential Gibbs free energy profiles (d−ΔG_H*) over the Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, Au) clusters (a,d,g,j,m), the average Gibbs free energy profiles (a−ΔG_H*) (b,e,h,k,n), and the volcano plot of i₀ as a function of d−ΔG_H* at the best H coverage (c,f,i,l,o) and the highlight in blue denotes the free energy window of ±0.25 eV; Figure S4: Density of states projected onto the d states of adsorption sites of Ni₆@Pd₃₂ clusters (left) and Ni₆@Pt₁Pd₃₁ clusters (right) under different hydrogen coverages; Figure S5: Insight into the electron density disparity at the solid-liquid interface in the initial state (Heyrovsky) is presented for the catalysts (a) 6H-Ni₆@Pt₁Pd₃₁, (b) 4H-Ni₆@Pt₁Cu₃₁, (c) 2H-Ni₆@Pt₁Ag₃₁ and (d) 2H-Ni₆@Pt₁Au₃₁. Regions of electron depletion and electron accumulation are depicted in cyan and light yellow, respectively; Figure S6: The potential energy profiles of the HER by Volmer–Tafel process and Volmer–Heyrovsky process at the optimal coverage of H. (a,b) Ni₆@Pt₃₂, (c,d) Ni₆@Pd₃₂, (e,f) Ni₆@Cu₃₂, (g,h) Ni₆@Ag₃₂, respectively; Figure S7: The linear relationship between ORR overpotential and *OOH adsorption free energy of catalysts according to four-electron step mechanism (ORR volcano plot); Table S1: The models by doping a Pt atom at the core (Ni₅Pt₁@M₃₂), the center or the hexagonal (Ni₆@Pt₁M₃₁) site of the surface in the core-shell nanocluster Ni₆@M₃₂ (M = Pd, Cu, Ag, and Au); Table S2: Structural parameters of core-shell cluster catalysts; Table S3: The optimal |d−ΔG_H*| and |a−ΔG_H*| and log(i₀) values of Ni₆@M₃₂ (M = Pt, Pd, Cu, Ag, Au) and Ni₆@Pt₁M₃₁ (M = Pd, Cu, Ag, Au) and corresponding Bader charge of hydrogen atom; Table S4: The most stable adsorption sites and corresponding adsorption free energies of O, OH and OOH intermediates on the catalysts; Table S5: The reaction free energy corresponding to the four-electron step of the ORR reaction on the catalyst and the overpotential of the ORR and OER reactions; Table S6: The average binding energy of Ni₆@M₃₂ (M = Ni, Pt, Pd, Cu, Ag, Au); Table S7: The formation energy of Ni₆@Pt₁M₃₁ (M = Ni, Pd, Cu, Ag, Au); Table S8: Alteration in energy accompanying the migration of two hydrogen atoms from distinct adsorption sites (either on the same or different facets) on Ni₆@Cu₃₂ to a unified adsorption configuration; Text S1: Supplementary information for computational design of Ni6@Pt1M31 clusters for multifunctional electrocatalysts. References [37,49,50,51,52,53] are cited in the supplementary materials.

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