Unveiling the mechanism of high-performance hydrogen evolution reaction on noble-metal-free (113)-faceted Ni₃C: ab initio calculations

Abstract

To examine the reactivity of noble-metal-free Ni₃C towards hydrogen evolution reaction (HER), we report a comprehensive first-principles density functional theory (DFT) study on the stability, geometric structure, electronic characteristics, and catalytic activity for HER on the Ni₃C crystal (113) surfaces with different surface terminations, namely the C-rich and Ni-rich terminated surface of Ni₃C (113). The results indicate that C-rich and some stoichiometric surfaces are thermodynamically stable. The bridge-site of C-rich Ni₃C (113) is indispensable for HER because it not only displays improved electrocatalytic activity, but also possesses appropriate hydrogen adsorption energy, overpotential and robust stability. The ΔG_H (0.02 eV) and overpotential obtained by C-rich Ni₃C outperformed that obtained by Pt determined by computation (ΔG_H = −0.07 eV). Thus, the bridge-sites of C-rich Ni₃C (113) function as both excellent and stable active sites and adsorption/desorption sites. Increasing the density of active sites through doping or enlarging the surface area renders a prospective strategy to ameliorate the HER activity further. Overall, this study elucidates new insights into the surface properties of Ni₃C for HER from water splitting and opens up a fascinating avenue to optimize the performance of solar energy conversion devices by synthesizing preferentially exposed catalyst facets.

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Introduction

Energy crisis and environmental pollution have become serious problems that human society must face in the age of Anthropocene. In the war against energy security and climate change, this has attracted considerable attention to opt for renewable and clean energy sources.^1–4 Because of the environmental friendliness, recycling utilization and high-energy capacity of hydrogen (H₂) fuels, H₂ has been considered as a green and potential new energy carrier over the past few decades.⁵ To date, hydrogen evolution reaction (HER) by water splitting, including electrocatalysis⁶ and photocatalysis,^7,8 has been regarded as a pivotal technique to resolve the energy and environmental-related problems. At present, noble metals (e.g. Pt, Ag and Au) have been proven to be superior catalysts for HER. However, their high cost and scarcity severely limit their commercial applications with potential industrialization. In order to tackle these obstacles, searching for alternative catalysts composed of abundant elements for robust HER activity is actively pursued at this juncture. This includes the design of TiO₂,⁹ g-C₃N₄,¹⁰ MXenes,¹¹ transition metal chalcogenides,¹² transition metal phosphides,¹³ metal–organic frameworks (MOFs),^14,15 covalent organic frameworks (COFs)¹⁶ and so forth.

For electrochemical water splitting, utilizing carbon-based nanomaterials^17,18 and transition-metal dichalcogenides¹⁹ as electrocatalysts have spurred enormous interests due to their remarkably high catalytic activity⁶ and earth-abundance. In the recent years, nickel and its corresponding compounds have emerged as auspicious electrocatalysts,²⁰ particularly nickel phosphide (Ni_xP_y)²¹ and nickel carbides.²² Co_1−xNi_xP₃ exhibits good OER activity with the Ni participation. The electronic structure can be effectively adjusted by Ni, indicating the great potential of Ni-based catalysts in electrocatalysis.²³ Yan et al. dispersed uniform Ni₃C nanodots in ultrathin N-doped carbon nanosheets and when doped with Fe, the Ni₃C-based nanosheets exhibited outstanding electrocatalytic properties towards both HER and oxygen evolution reactions (OER).²⁴ As for HER, Ni₃C also exhibits great performance. The catalyst consisting of Ni nanoparticles with Ni₃C nanosheets showed highly efficient overall water splitting.²⁵ Moreover, combined with g-C₃N₄, the Ni₃C cocatalyst/g-C₃N₄ catalyst showed high photocatalytic HER properties under visible light.²⁶ In view of the unique traits and properties of Ni₃C, it is of timely importance to demand a relentless pursuit to bridge the fundamental aspect of Ni₃C at the molecular level towards the enhancement of functionality and HER activity.

Herein, we investigate the electronic characteristics and reactivity of Ni₃C for the application in HER from the theoretical insight via first-principles density functional theory (DFT) calculations. Previous experiments have demonstrated that Ni₃C exposed with the (113) facet is a highly stable surface.²⁷ Sparked by the flourishing finding, we unveil the HER activity of (113)-faceted Ni₃C by calculating the Gibbs free energy and adsorption energy of different active sites on the surface of Ni₃C (113). Importantly, insights into the C-rich and Ni-rich terminated surface of Ni₃C (113) for HER will be thoroughly unravelled. As a whole, this work casts favorable prospects for the potential utilization of earth-abundant Ni₃C in the field of electrochemical water splitting, which will pave a new frontier in the materials science to engineer precious-metal-free electrocatalysts in experiments.

Computational methods

The CASTEP²⁸ of the Materials Studio software (Accelrys Inc.) was employed for the quantum chemistry calculations. During the calculations, self-consistent periodic DFT was adopted to explore the electronic structure and catalytic activities on the facets. Ionic cores were represented by an ultrasoft pseudopotential. Perdew–Burke–Ernzerhof (PBE)²⁹ approximation was selected as the generalized gradient approximation (GGA)³⁰ method to calculate the exchange–correlation energy. The Broyden–Fletcher–Goldfarb–Shanno (BFGS)³¹ scheme was selected as the minimization algorithm. DFT-D3 correction was used for dispersion corrections. The energy cut-off was 380 eV and the SCF tolerance was 1.0 × 10⁻⁶ eV per atom. The optimization was completed when the energy, maximum force, maximum stress and maximum displacement were smaller than 5.0 × 10⁻⁶ eV per atom, 0.01 eV Å⁻¹, 0.02 GPa and 5.0 × 10⁻⁴ Å, respectively.³² The gamma points only were set as k-point samplings during the calculations because there were no significant changes in the calculated energies for larger k-point mesh such as 2 × 2 × 1 and 3 × 3 × 1. Furthermore, at least four Ni layers were selected to reduce the dispersive error. The (113) surfaces with Ni rich and C rich terminations were built from the optimized Ni₃C (space group 167, a = b = 4.553 Å, c = 12.920 Å) with a vacuum region of 15 Å (in Fig. S1, ESI†). The Gibbs free energy of the adsorption atomic hydrogen (ΔG_H) is obtained by eqn (1):

ΔG_H = ΔE_H + ΔE_ZPE − TΔS_H (1)

where ΔE_ZPE is the zero-point energy of the system and is simplified as 0.05 eV. The term −TΔS_H is the contribution from entropy at temperature K (0.20 eV at 298 K).³³ ΔE_H is the energy needed to increase the coverage by one hydrogen atom, which is calculated as eqn (2):

ΔE_H = E[Ni₃C + H] − E[Ni₃C] − ½E[H₂] (2)

where E[Ni₃C + H] is the total energy of the system, including the adsorbed molecules and the Ni₃C facet, E[Ni₃C] is the energy of the Ni₃C facet, and E(H₂) is the total energy of a gas phase H₂ molecule.

The exchange current at pH 0 can be calculated by eqn (3) and (4):³⁴

where k₀ is the rate constant and equal to 200 s per site; k is the Boltzmann constant and T is the temperature, set at 298 K in the current work.

Furthermore, ab initio molecular dynamics (AIMD) simulations via the Vienna ab initio simulation package (VASP)³⁵ were performed within the NVT ensemble at 400 K with a time step Δt = 1 fs and an overall time scale of 10 ps to assess the thermal stability of the Ni₃C (113) structure.

Results and discussion

Ni₃C (113) has been demonstrated as a stable surface in the experiment.²⁷ With the same crystal surface index, the stable surface can be divided into two different terminations. One of the surfaces has carbon ratios larger than the other one, which is denoted as C-rich Ni₃C (113). On the contrary, the higher surface nickel ratio represents Ni-rich Ni₃C (113). The scaling factor is applied for the searching of optimised lattice parameters. The curve of the electronic energy vs. scaling factor is shown in Fig. S1.† Fig. 1 displays the top and side views of C-rich Ni₃C (113) and Ni-rich Ni₃C (113).

Fig. 1 Model of Ni₃C (113): (a) the terminated position of different surfaces. The side view of (b) C-rich Ni₃C (113) and (c) Ni-rich Ni₃C (113).

In order to reveal the underlying mechanism of the HER activity of Ni₃C and to investigate the electronic properties of Ni₃C (113), the total and partial density of states (DOS) of C-rich Ni₃C (113) and Ni-rich Ni₃C (113) are depicted in Fig. 2. It is evident that the carrier density of C-rich Ni₃C (113) and Ni-rich Ni₃C (113) is continuous at the Fermi level, which is not equal to zero. This confirms that the two different terminated surfaces are metallic. Furthermore, the main contributions in the range from −3.75 to 1.25 eV originated from Ni 3d, and a minority from Ni 4p and C 2p orbitals. A broad and strong signal of the peak is observed from −3.75 to −0.5 eV for the Ni 3d orbital both in C-rich Ni₃C (113) and Ni-rich Ni₃C (113), but the intensity of the peak decreases rapidly near the Fermi level in which the free carrier density of Ni₃C (113) under the Fermi level is reduced. In addition, owing to the interaction between Ni 3d and C 2p orbitals, a significant overlap of states appears from −7.5 to −5 eV, which indicates that the formation of Ni–C bonds is close and stable. In general, the difference between the DOS of C-rich Ni₃C (113) and Ni-rich Ni₃C (113) is not apparent.

Fig. 2 The calculated electronic characteristics of the Ni₃C (113) surface with different terminations. (a) C-rich Ni₃C (113) surface and (b) Ni-rich Ni₃C (113) surface.

Moreover, the work function of C-rich Ni₃C (113) and Ni-rich Ni₃C (113) is calculated to uncover the mechanism for HER (Fig. 3). The work function of two different terminated surfaces is calculated to be around 4.85 eV, which is relatively higher than the standard hydrogen electrode energy of 4.5 eV. Interestingly, the Fermi level of Ni₃C is lower than the standard hydrogen electrode potential, rendering Ni₃C (113) an appealing catalyst for HER.

Fig. 3 Work function of the Ni₃C surface with different terminations. (a) Ni-rich Ni₃C (113) surface and (b) C-rich Ni₃C (113) surface.

To clarify the origin of the HER catalytic activity of different facets, Gibbs free energies of hydrogen adsorption are calculated via DFT calculations. The Gibbs free energy of hydrogen adsorption (ΔG_H) is one of the important criteria for evaluating the catalytic properties of HER. As a matter of fact, the optimal value for HER is ΔG_H = 0. Alternatively, smaller |ΔG_H| signifies better HER performance of the designed catalyst.

Fig. 4 illustrates the calculated free energy diagram for H₂ evolution on different active surface sites. As shown in Fig. 4(a), the free energies of H₂ evolution for Ni (111) and Pt (111) surfaces are labelled, and the values of ΔG_H for Ni (111) and Pt (111) are consistent with the previous experiments and calculations.^34,36 It is worth noting that although the Gibbs free energies of some active sites are close to zero, and their hydrogen adsorption energies (E_ads) are greater than zero, inferring that the active site is not necessarily the stable adsorption site. Most of these stable adsorption sites are not catalytically active because they require a high energy for desorption of the adsorbed H*.

Fig. 4 Free energy profiles for the H₂ generation on different active sites of surfaces. (a and b) C-rich Ni₃C (113) surface with Pt (111) and Ni (111) surfaces for comparison; (c and d) Ni-rich Ni₃C (113) surface. White, grey and blue spheres represent H, C and Ni atoms, respectively. More details about the adsorption sites are described in Tables S1 and S2 (ESI†).

For instance, the most stable adsorption position of C-rich Ni₃C (113) is “Top C1” with an adsorption energy of −0.97 eV, while the |ΔG_H| of “Top C1” is much higher than zero. Furthermore, by putting the focus on the “Bridge site of “Ni₄Ni₅”” (“Bridge Ni₄Ni₅”), the |ΔG_H| of the “Bridge Ni₄Ni₅” site is 0.02 eV (very close to zero), highlighting that the “Bridge Ni₄Ni₅” site is an active site for HER. The hydrogen adsorption energies of the “Bridge Ni₄Ni₅” site is less than zero, manifesting that it is facile to capture protons and bond with hydrogen ions (H⁺) with the relative ease of desorbing H₂. As for Ni-rich Ni₃C (113), the most active site for HER is the “Top C1” site, and its Gibbs free energy is 0.18 eV.

However, the hydrogen adsorption energy of the “Top C1” site is greater than zero, revealing its difficulty for the adsorption of H⁺ ion in the “Top C1” site. As for the other sites on Ni-rich Ni₃C (113), their E_ads values are far less than zero, so it is hard for them to desorb the adsorbed H*. All in all, if the active site is a stable adsorption site, H* will continuously adsorb on the active sites, hence substantially boosting the H₂ production rate. Nevertheless, when the stable adsorption site is not the active site, H* will first adsorb at the stable adsorption sites and then on the active sites, thus requiring a longer reaction pathway.

A plot of exchange current densities against ΔG_H has a volcano shape in Fig. 5. As indicated in Fig. 5, there is a clear disparity between the exchange current densities on different Ni₃C surfaces for H₂ evolution. Compared to the Ni-rich Ni₃C, the C-rich Ni₃C (113) has much higher exchange current density and lower overpotential. Also, more than this, the plot of C-rich Ni₃C (113) is much closer to the summit, which markedly outperforms the theoretically simulated Pt (111) and Ni (111).^34,36 As such, the C-rich Ni₃C (113) is an appropriate catalytic surface for HER.

Fig. 5 The exchange current for H₂ evolution over different Ni₃C surfaces, Pt (111) and Ni (111) plotted as a function of the calculated hydrogen chemisorption energy. The experimental and calculated data for Ni and Pt are also added.^34,36,37

To further illustrate the stability of the structures in our calculations, AIMD simulations are performed at 400 K for 10 ps to test the stability of Ni₃C. As shown in Fig. 6(a and b), the total energy and temperature oscillate near the initial condition and the geometric structures of Ni₃C are preserved well within 10 ps.

Fig. 6 Variations of energy and temperature versus the AIMD simulation time for (a) C-rich Ni₃C (113) and (b) Ni-rich Ni₃C (113). The AIMD simulation lasts for 10 ps at 400 K.

Conclusions

In summary, we have calculated the electronic properties and HER catalytic activity for both C-rich Ni₃C (113) and Ni-rich Ni₃C (113). Through calculation and analysis, C-rich Ni₃C (113) endows excellent adsorption and active sites, and importantly, the Gibbs free energy of the “Bridge Ni₄Ni₅” site records a value of 0.02 eV, which is closer to zero than Pt (111). In addition, the overpotential of C-rich Ni₃C (113) is smaller than that of Pt (111), which demonstrates that C-rich Ni₃C (113) is an ideal surface for superior HER. However, the catalytic activity is not only related to these conditions, and further considerations on the number of active sites of the catalytic surface will be examined in the future.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Natural Science Fund for Distinguished Young Scholars of Hubei Province (No. 2020CFA087); the Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (No. 161008); the Basic Research Program of Shenzhen (No. JCYJ20190809120015163); the Central Government Guided Local Science and Technology Development Special Fund Project (2021Szvup106); the Overseas Expertise Introduction Project for Discipline Innovation of China (No. B18038), and Fundamental Research Funds for the Central Universities (2022WUT). We gratefully acknowledge HZWTECH for providing computation facilities.

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Footnotes

† Electronic supplementary information (ESI) available: Stable adsorption structures of H on the C-rich and Ni-rich Ni₃C (113) surface. See DOI: 10.1039/d1ra07448b

‡ Equal contribution on this work.

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