First-Principles Determination of Active Sites of Ni Metal-based

Oct 26, 2018 - First-Principles Determination of Active Sites of Ni Metal-based Electrocatalysts for Hydrogen Evolution Reaction. Yujuan Dong , Jingsh...
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Cite This: ACS Appl. Mater. Interfaces 2018, 10, 39624−39630

First-Principles Determination of Active Sites of Ni Metal-Based Electrocatalysts for Hydrogen Evolution Reaction Yujuan Dong,† Jingshuang Dang,† Wenliang Wang,*,† Shiwei Yin,*,† and Yun Wang*,‡ †

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Key Laboratory for Macromolecular Science of Shaanxi Province, School of Chemistry & Chemical Engineering, Shaanxi Normal University, Xi’an 710119, China ‡ Centre for Clean Environment and Energy, School of Environment and Science, Griffith University, Gold Coast Campus, Southport, Queensland 4222, Australia S Supporting Information *

ABSTRACT: The determination of active sites of materials is essential for the molecular design of high-performance catalysts. In this study, the first-principles method is applied to investigate the active sites of low-cost Ni metal-based electrocatalysts for hydrogen evolution reactions (HER), which is a promising alternative to expensive Pt metal-based catalysts. The adsorption of hydrogen on different sites of pristine and partially oxidized Ni(111) surface is investigated. All of the possible configurations have been systematically investigated here with the consideration of their Boltzmann distribution. Using the Gibbs free energy of intermediate H atoms (ΔGH*) as a descriptor, it is found that the ΔGH* increases with the increase of the coverage of oxygen atoms. The slightly oxidized surface Ni atoms are theoretically identified to be the best catalytic centers for the electrocatalytic HERs when the coverage of oxygen is considerably low. On the basis of the analyses of Bader charge distribution and density of states, our results reveal that the superior performance of the slightly oxidized surface Ni atoms can be ascribed to the optimal electronic properties. KEYWORDS: hydrogen evolution reaction, Ni metal electrocatalysts, partial oxidation, Boltzmann distribution, Gibbs free energy

1. INTRODUCTION Electrocatalytic hydrogen evolution reaction (HER) is a half reaction of electrolytic water splitting, whose yield is essential for the large-scale clean hydrogen fuel production.1−7 Platinum (Pt) is one of the most widely used catalysts for HER.8−11 However, the scarcity and cost of Pt seriously impede its largescale applications of electrocatalytic HERs. Therefore, searching nonprecious earth-abundant metal catalysts is of paramount importance.3 Because of the high chemical stability, excellent electrical conductivity, and low cost, nickel (Ni) metal has been considered as one of the promising candidates for HER.12−15 Moreover, the three-dimensional skeleton of Ni foam is beneficial to both the mass and the charge-transfer processes,15−17 both of which are decisive to the HER performance of electrocatalysts. Yet, previous theoretical study demonstrated that performances of pure Ni-metalbased electrocatalysts are not ideal with an overpotential around 0.3 V.8 The recent experimental study also supported that the Ni nanosheets on the Ni foam have an overpotential of ∼253 mV for HER to deliver a current density of 10 mA cm−2.17 To address this issue, the Ni-based compounds, for example, sulfides, selenides, oxides, carbides, phosphides, and pentlandites have been conducted to achieve a better HER performance.18−28 Recently, Dai and co-workers reported a nickel oxide/nickel metal heterostructure on mildly oxidized © 2018 American Chemical Society

carbon nanotube (NiO/Ni-CNT), which achieves a high HER catalytic activity compared with the commercial Pt/C because of a synergistic effect between NiO and Ni metal.10 Similarly, Wang and co-workers studied the activities of Ni atoms at different locations (bulk or interface) of Ni/NiO by using a NiOx@bamboolike CNT hybrid structure, suggesting that both the inherent high Ni0 ratio and the Ni0 on the interface of Ni/NiO play vital roles in the outstanding catalytic performance compared with that of bulk Ni0. The Ni0 at the Ni/NiO interface is the active site with an excellent catalytic performance for HER.29 Yet, the impact of NiO on the HER performance is largely unclear. Moreover, the theoretical results reveal that Ni0 atoms in the Ni(111) surface have considerably low reactivity to HER,8 which has a conflict to the experimental observation. To address these issues, the systematic investigation on the physicochemical properties and the corresponding HER performance of oxidized Ni metalbased electrocatalysts are urgently required to uncover the insights of the HER process, which can further provide theoretical guidelines to design feasible catalysts with an improved electrocatalytic HER performance. Received: July 25, 2018 Accepted: October 26, 2018 Published: October 26, 2018 39624

DOI: 10.1021/acsami.8b12573 ACS Appl. Mater. Interfaces 2018, 10, 39624−39630

Research Article

ACS Applied Materials & Interfaces

respectively. The * means the active sites of the surface. The vibrational entropy was calculated by TΔSH* = TSH* − 1/2TS0 H2. TSH* presents the vibrational entropy of adsorbed H atom, which is 0.026 eV at 300 K.34 S0 H2 represents the entropy of H2 in the gas phase at standard conditions. TS0 H2 is 0.41 eV based on previous studies.8 ΔEZPE was calculated to be 0.05 eV for H/Ni(111). This suggests that ΔGH* = ΔEH* + 0.229, which was used for all calculations in this study. Exchange current density is the rate of hydrogen evolution per surface area at the electrode potential. The catalytic descriptor ΔGH* can be used to predict trends in the hydrogen evolution exchange current density based on Nørskov’s assumption.8 For the exothermic hydrogen adsorption (ΔGH* ≤ 0), the following expression for the exchange current at pH = 0 was used 1 i0 = −ek 0 1 + exp( −ΔG H */k bT ) (4)

In the present work, first-principles density functional theory (DFT) calculations were carried out to explore the HER on pristine and partially oxidized Ni(111) surface. The (111) surface was selected because of its highest stability among all low-index surfaces of the fcc metals.30 According to previous studies by Nørskov and his co-workers, the high-performance electrocatalysts need to have the optimal Gibbs free energy of H adsorption (ΔGH*) close to 0.0 eV on their surface, which indicates that all of the reaction steps of HER are nearly thermoneutral.8 Herein, using ΔGH* as a key descriptor, our results demonstrate that the slightly partial oxidized Ni atoms are active sites for the Ni metal-based electrocatalysts.

2. METHODOLOGY AND CALCULATION MODEL The spin-polarized first-principles DFT calculations were performed by using Vienna Ab initio Program package (VASP).31 The exchange and correlation effects of the electrons were described by using the Perdew−Burke− Ernzerhof functional of a generalized gradient approximation method.32 The projector augmented wave33 method was used to describe the electron−ion interaction. The valence electron structures for Ni, O, and H are 3d84s2, 2s22p4, and 1s1, respectively. The cutoff energy of the plane wave was set at 520 eV. All calculations were carried out on the thermodynamically stable (111) surface using a (2 × 4) five-layer slab model with the periodic boundary condition. A vacuum region of 15 Å was used to avoid the interaction between slabs. The (6 × 3 × 1) kpoint mesh was used for the k-space integration in our structure relaxations and density of state calculations. During the optimization of atomic structures, the bottom two Ni layers were fixed at the bulk position, whereas the top three metal layers and the adsorbents were fully relaxed with the energy and force convergences less than 1 × 10−5 eV and 1 × 10−2 eV Å−1, respectively. To select thermodynamically stable configurations of partially oxidized Ni(111) surface, all possible structures were optimized and analyzed based on the Gibbs free energy. The most stable configurations were selected according to the Boltzmann distribution, whose percentage was greater than 10%. The Boltzmann distribution was defined below Q i(Relat) e−ΔEi / RT Pi = = −ΔEj / RT Q (Relat) ∑j e (1)

It has been fitted to the experimental data for the exchangecurrent density of the elemental metals. For the endothermic adsorption (ΔGH* > 0), the model predicts that a high barrier for H* formation from solvated protons gives rise to a low-exchange current density.18 The exchange current was calculated by i0 = −ek 0

where kb is the Boltzmann constant, T is the temperature, which is 300 K here, and k0 is the rate constant, which is set to 1 as there is no experimental data available.36 For ΔGH* ≈ 0, the reaction is approximately balanced, and a maximum in the exchange-current density can be predicted.

3. RESULTS AND DISCUSSION 3.1. H Adsorption on the Ni(111). The adsorption properties of H atoms on the Ni(111) surface were first investigated, which are listed in Table 1. As illustrated in Table 1. Calculated Average Distance between H and Surface Ni Atoms, r(H−Ni), Binding Energy, ΔEH*, and Gibbs Free Energy, ΔGH*, on Top, fcc and hcp Sites of the Ni(111) Surface adsorption sites

r(H−Ni) (Å)

ΔEH* (eV)

ΔGH* (eV)

top Fcc Hcp

1.47 1.71 1.71

0.05 −0.53 −0.51

0.28 −0.30 −0.29

Figure 1, four different adsorption sites: top, bridge, fcc (hollow), and hcp (hollow) were considered here to examine the regioselectivity of H atoms. The ΔGH* at the fcc (ΔGH* = −0.30 eV) and hcp (ΔGH* = −0.29 eV) sites are much more negative than others, indicating the hollow sites are thermodynamically preferred for the hydrogen adsorption. On the contrary, the ΔGH* is 0.28 eV when H adsorbs on the top site. The positive ΔGH* value suggests that the activity of the top site is considerably low. We found that the adsorption on the bridge site is not preferred because the H atom migrates to the fcc site after structural optimization. Additionally, our results are consistent with previous works.37−39

(2)

where n is the number of adsorbed H atoms. Esurf and Esurf+H* are the total energy of surfaces without and with adsorbed H atoms, respectively. The Gibbs free energy for the adsorption of H atoms was calculated by the following expression8 ΔG H * = ΔE H *+ΔEZPE − T ΔSH *

(5) 35

where Pi and ΔEi represent the proportion and energy difference of the ith configuration in terms of the lowest energy of all configurations, respectively. T presents temperature, which is set at 300 K in our study. R is the ideal gas constant. Qi(Relat) is the partition function of the ith configuration, and Q(Relat) represents the partition function of the total relative energy of all configurations. In addition, the binding energy of H atoms with the surface was introduced to evaluate the activity of HER according to following equation8 ΔE H * = 1/n(Esurf + H * − Esurf − n/2E H2)

exp( −ΔG H */k bT ) 1 + exp( −ΔG H */k bT )

(3)

where ΔEZPE and ΔSH* represent the changes of zero-point energy and entropy between the adsorbed H and the gas phase, 39625

DOI: 10.1021/acsami.8b12573 ACS Appl. Mater. Interfaces 2018, 10, 39624−39630

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ACS Applied Materials & Interfaces

Table 2. Binding Energy and Gibbs Free Energy of H Adsorption at Surface Ni Hollow Sites Adjacent to O* (ΔEH*−O*) and (ΔGH*−O*) or Adjacent to OH* (ΔEH*−OH*) and (ΔGH*−OH*) at Different O Coverages from 1/8 to 4/8 ML

Figure 1. Illustration of top, bridge, fcc, and hcp adsorption sites for H or O atoms on the Ni(111) surface. Blue, Ni in the first surface layer; pale grey, Ni in the subsurface layer; and red dashed circles, adsorption sites.

Θ (ML)

ΔEH*−O* (eV)

ΔGH*−O* (eV)

ΔEH*−OH* (eV)

ΔGH*−OH* (eV)

1/8 2/8 3/8 4/8

−0.42 −0.37 −0.28 −0.10

−0.19 −0.14 −0.05 0.12

−0.44 −0.40 −0.26 −0.02

−0.22 −0.17 −0.03 0.09

interaction between H atoms and surface Ni atoms. Therefore, we shall focus only on the O-covered Ni surface in the following sections. 3.2.2. H Adsorption on the Surface Ni Atoms. A partially oxidized Ni(111) surface with the Θ of 1/8 ML was employed to explore the impact of O* on the HER performance of surface Ni atoms. As evidenced by Figure 3, the ΔGH*

3.2. H Adsorption on the Partially Oxidized Ni(111). Next, the impact of partial oxidation on the HER performance was investigated. On the basis of the Boltzmann distribution analysis, oxygen atoms prefer to reside on the hollow sites of Ni(111), (Table S1 of Supporting Information), which is in agreement with the previous results.40−42 Therefore, oxygen atoms are adsorbed at the fcc and hcp hollow sites of Ni(111) in the following calculations. Herein, both the surface O and Ni atoms can act as the adsorption sites. As such, adsorption properties of H atoms both on O and Ni atoms were considered. 3.2.1. H Adsorption on the Surface O Atoms. When the H atoms interact with the surface O atoms, the ΔGH* becomes much lower than that on the pristine Ni(111) surface with the high O coverages. Figure 2 reveals that H atoms can strongly

Figure 3. ΔGH* (eV) and Bader charge (QNi3) as a function of the distance between H* and O* (dO*−H*) with 1/8 ML of oxygen. The configurations of close and further of the distance between H* and O* are displayed. Blue, Ni in the first surface layer; pale grey, Ni in the subsurface layer; red, oxygen; and white, hydrogen.

decreases with the increase of the O*−H* distance, suggesting that the existence of O* can weaken the binding strength of the H atoms with the surface Ni atoms. However, when the O*−H* distance is increased to 4.98 Å, the ΔGH* is almost identical to that on the clean Ni(111) surface. It indicates that the influence of O* on the adsorption properties of H atoms is only semilocalized. To understand the influence of O* on the HER performance, the sum of Bader charge of three surface Ni atoms (QNi3), which are associated with H*, was calculated to rationalize the variance of ΔGH* in the presence of O*. As shown in Figure 3, the QNi3 values are positive when the O*− H* distance is small because of the partial oxidation of the surface Ni atoms by O*. As such, the electron-donating capability of the surface Ni atoms is reduced after their partial oxidization. On the basis of our computational result, the negative ΔGH* values on Ni(111) indicate that the surface Ni atoms are too active, which can limit the desorption of H* to produce H2. The reduced electron-donating capability of surface Ni atoms via partial oxidation can weaken their binding strength with the H atom, which is beneficial for their

Figure 2. Calculated ΔGH* along the O coverage. The H atoms adsorb on the top of the surface O atoms.

bind with the surface O atoms. Moreover, the ΔGH* further decreases with the increase of the coverage of surface O atoms (Θ). Herein, the Θ is defined as the surface O/Ni ratio.43 To this end, H atoms prefer to adsorb on the surface O sites to form OH*. To understand the impact of preadsorbed H on O* on the interaction between H atom and surface Ni atoms, the Gibbs free energies of H adsorption were calculated with Θ from 1/8 to 4/8 ML. Here, two types of surface Ni, which is adjacent to either OH* or O*, were considered as the adsorption sites (detailed structures are shown in Table S9). From Table 2, the difference between ΔGH*\−OH* and ΔGH*−O* is less than 0.03 eV, which suggests that the preadsorption of H on O* has a small impact on the 39626

DOI: 10.1021/acsami.8b12573 ACS Appl. Mater. Interfaces 2018, 10, 39624−39630

Research Article

ACS Applied Materials & Interfaces electrocatalytic HER. Similar to the change in trend of ΔGH*, the QNi3 values decrease with the increase of the dO*−H*. When the dO*−H* is 4.98 Å, the calculated QNi3 (−0.08 e) is almost the same as that of the pristine Ni surface, confirming the semilocalized influence of O* on the electronic properties of surface Ni atoms. 3.3. Coverage Effect of O*. To understand the impact of partial oxidation on the HER reactivity, a series models with different coverages of O* (with the Θ from 1/8 to 8/8 ML) were investigated. All possible configurations were optimized, which are listed in Tables S10−S15. In addition, the low-lying O* structures with great Boltzmann distribution (>10%) were selected (Tables S1−S8) for H adsorption. The number of possible adsorption active sites of H atoms on the hollow sites of Ni is listed in Table 3. Here, the active site for H adsorption

Figure 4. Most stable configuration with the corresponding ΔGH* on the Ni(111) surface with (a) Θ = 1/8, (b) Θ = 2/8, (c) Θ = 3/8, (d) Θ = 4/8, (e) Θ = 5/8, and (f) Θ = 7/8. Blue, Ni in the first surface layer; pale grey, Ni in the subsurface layer; red, oxygen; and white, hydrogen.

Table 3. Number of Active Sites for O Adsorption (NO*) and the Active Sites for H Adsorption (NH*) Which Are Bonded with O*−Ni on the Ni(1 1 1) Surface at Different Oxygen Coverages (Θ) Based on the Boltzmann Distribution Analyses Θ (ML) NO* NH*

1/8 1 3

2/8 1 8

3/8 2 5

4/8 6 2

5/8 5 1

7/8 2 1

is defined as the fcc/hcp site next to O* or OH* when the oxygen coverage is low, only limited surface fcc/hcp sites next to O* become active sites (Θ = 1/8 ML). With the increase of the oxygen coverage, more surface sites become active to H adsorption, as evidenced by the increased NH* value when the coverage increases to 2/8 and 3/8 ML. On the other hand, the increased O* will occupy more fcc/hcp sites, which will further prohibit the adsorption of H. Consequently, NH* decreases when the oxygen coverage was higher than 3/8 ML, as collected in Table 3. The result implies that the availability of active sites for HER on the partially oxidized Ni(111) surface can be greatly improved when the Θ is between 2/8 and 3/8 ML. Moreover, H atoms cannot adsorb on the surface via the Ni−H interaction with the Θ of 6/8 and 8/8 ML because the H shifts to bond with O* after structural optimizations. Therefore, the adsorption configurations with the Θ of 6/8 and 8/8 ML are not discussed here. Figure 4 shows the most stable configuration with a specific Θ and its corresponding ΔGH*. The increased ΔGH* with an elevated Θ is revealed. This is because a larger Θ represents a denser oxygen distribution on the surface. As revealed by Figure 3, a shorter O*−H* distance leads to a weaker adsorption energy of the H atom. With the increase of Θ on the Ni(111) surface, the ΔGH*ave is more positive, which is up to 0.50 eV with the Θ of 7/8 ML, implying that the HER performance decreases in cases of highly oxidative Ni(111) surface. The ΔGH*ave is the average ΔGH* values of all possible configurations with a specific Θ. According to Nørskov’s work, the performance of catalysts with the ΔGH* around zero is on the top of the volcano curve for HER.8 In our study, the ΔGH*ave values are −0.06 and 0.01 eV for the Θ of 2/8 and 3/8 ML, respectively, which indicates that the Ni(111) surface with a small coverage of O* may possess the best HER performance. The exchange current i0 along with the calculated ΔGH*ave is plotted to a volcano shape, as shown in Figure 5. The catalyst performance can be quantitatively evaluated by the i0 and the

Figure 5. Volcanic curve of the exchange current (i0) as a function of the average ΔGH*ave. The red dots present clean Ni(111) surface and different oxygen coverage (Θ = 0/8, 1/8, 2/8, 3/8, 4/8, 5/8, and 7/8 ML).

average ΔGH*ave values relative to the volcano peak (the catalyst has better performance when its log i0 is closer the peak).44 The much higher exchange current is favorable for the HER with the Θ of 2/8 and 3/8 ML. Therefore, the exchange current density plot confirms that the slightly oxidized Ni(111) surface with a lower oxygen coverage around 2/8−3/8 ML can possess the superior HER performance. 3.4. Mechanistic Insights. Recent studies on the electrocatalytic oxygen evolution reactions using perovskite oxides as catalysts demonstrated that the electronic configurations on the frontier crystal orbitals of the catalysts play an essential role to their performance.45 To this end, the Bader charge analysis was first performed to clarify the charge distribution of active sites.46 To rationalize the alternation of charge in the presence of O* and H*, the Bader QNi3, and the average charge of O* and H*, which are termed as QO and QH, respectively, were calculated. As shown in Figure 6, the QH atom is −0.30 (e) on the pristine Ni(111) surface, and the corresponding QNi3 is 39627

DOI: 10.1021/acsami.8b12573 ACS Appl. Mater. Interfaces 2018, 10, 39624−39630

Research Article

ACS Applied Materials & Interfaces

(∼0.0 eV), and antibonding (E − EFermi > 0.0 eV) contributions, respectively. Because the electronic configuration of the H atom is 1s1, the adsorption strength of the H atoms is mainly determined by the densities of the nonbonding states. Thus, the intensity of nonbonding states directly reflects the activity of surface Ni atoms. As shown in Figure 7, it can be found that the nonbonding states of Ni 3d decrease with the increase of the Θ. As a comparison, both bonding and antibonding states of Ni 3d and O 2p increase with the strengthened hybridization between O 2p and Ni 3d states when the Θ increases. This trend agrees with the change of the corresponding atoms, as shown in Figure 6. It suggests that the strong interaction between the surface Ni and O atoms weakens the activity of Ni atoms in the vicinity as suggested by the fewer nonbonding states. The change of the activities of the oxidized surface Ni atoms explain the increased ΔGH* values with the increase of the Θ, as observed in Figure 4.

Figure 6. Bader charge of Q (e) of surface atoms with different oxygen coverages (Θ = 0/8, 1/8, 2/8, 3/8, 4/8, 5/8, and 7/8 ML). QNi3, the sum of Bader charge of three surface Ni atoms; QO, the average Bader charge of O atoms; and QH, the Bader charge of H atom.

4. CONCLUSIONS In this study, the first-principles DFT method was employed to identify the active sites of Ni metal-based electrocatalysts for the HERs. Our results agree with the previous conclusion that the Ni atoms in the pristine Ni(111) surface can bind with the adsorbed H atoms too tightly, which limits the formation and desorption of H2 gas. Consequently, the pristine Ni metal electrocatalysts possess a considerably large overpotential. After the oxidation of the Ni(111) surface, the activity of the surface Ni atoms can be reduced by the strong Ni−O* interaction. However, the activity of highly oxidized Ni(111) surface, for example, the NiO surface, is too low as evidenced by the positive ΔGH*ave values, which is unfavorable to the formation of the intermediate of H atoms. Using the ΔGH* values as the descriptor, our results reveal that only slightly oxidized Ni atoms with the relatively low oxygen coverage of 2/8−3/8 ML can have the superior HER performance. To this end, slightly oxidized Ni atoms, not Ni0 atoms, are responsible for the superior HER performance at the Ni/NiO interface, as observed in previous experiments.29 Because it is experimentally challenging to control the extent of the oxidation on the metal surface, the heterostructures with Ni metal and other oxides or oxidation of Ni metal surfaces using other heteroatoms with relatively low electronegativity, for example, S, Se, C, and P, can be promising approaches to manipulate the

+0.21 (e), which reveals that the charge-transfer process from the Ni(111) surface to H* occurs. On the partially oxidized Ni(111) surface, QNi3 increases with the increase of Θ, which demonstrates that more electrons are transferred from the surface Ni atoms to O*. There are still some electrons that are transferred to H* because the QH values are negative in all considered systems. Yet, the absolute amplitude of the transferred charge to H* is reduced with the increase of the Θ, as evidenced by Figure 6. The result indicates that the weaker interaction between the surface Ni atoms and H* leads to the gradually increased average ΔGH* with the increase of Θ. To understand the variation of the binding strength between the surface Ni and H* atom, the local density of states (LDOS) profiles of the surface Ni and O atoms with different Θs were calculated.47 As depicted in Figure 7, the LDOS images always cross the Fermi level for all systems with a pronounced spin-splitting feature of Ni and O atoms, which clearly reveals their metallic character. As such, the partially oxidized Ni metal still possess high electrical conductivity, which is beneficial to the electrocatalytic HERs. Moreover, the LDOS around the Fermi energy level are dominated by the Ni 3d and O 2p with bonding (E − EFermi < 0.0 eV), nonbonding

Figure 7. LDOS profiles of surface Ni 4s (green), Ni 3d (red), O 2s (pink), and O 2p (blue) at (a) pristine Ni(111) surface and (b−g) partially oxidized Ni(111) surface with Θ of 1/8, 2/8, 3/8, 4/8, 5/8, and 7/8 ML, respectively. The Fermi energy is set as zero, whose location is indicated by the dashed line. 39628

DOI: 10.1021/acsami.8b12573 ACS Appl. Mater. Interfaces 2018, 10, 39624−39630

Research Article

ACS Applied Materials & Interfaces

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activity of surface Ni atoms, as already observed in previous studies.18−24,29 This work, therefore, provides a fundamental understanding on the impact of the electronic structures of Ni atoms on their electrocatalytic efficiency of HERs, which is important for the molecular design of other low-cost earthabundant catalysts with the high production of hydrogen fuels in practice.



ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.8b12573.



Adsorption site of O atoms or H atoms, their adsorption configurations on the Ni(111) surface, energy differences in terms of the most stable configuration (ΔEi), partition function (Qi) and population (Pi) based on the Boltzmann distribution with different oxygen coverages, and binding energy (ΔEH*) and Gibbs free energy (ΔGH*) of H* with partially oxidized Ni(111) surface (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (W.W.). *E-mail: [email protected] (S.Y.). *E-mail: yun.wang@griffith.edu.au (Y.W.). ORCID

Shiwei Yin: 0000-0002-4389-9509 Yun Wang: 0000-0001-8619-0455 Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (21636006 and 21473108), National Key R&D program of China (grant no. 2017YFB0203404), National Natural Science Foundation of China (grant no. 21173138), the 111 Project (grant no. B14041), and the Australian Research Council (DP 170104834). This research was undertaken on supercomputers in the National Computational Infrastructure (NCI) in Canberra, Australia, which is supported by the Australian Commonwealth Government, and Pawsey Supercomputing Centre in Perth with the funding from the Australian government and the Government of Western Australia.



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