# Navigating Alkaline Hydrogen Evolution Reaction Descriptors for Electrocatalyst Design

Samuel Akinlolu Ogunkunle, Fabien Mortier, Assil Bouzid, Jack Jon Hinsch, Lei Zhang, Zhenzhen Wu, Samuel Bernard, Yong Zhu, Yun Wang

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Samuel Akinlolu Ogunkunle, Fabien Mortier, Assil Bouzid, Jack Jon Hinsch, Lei Zhang, et al. Navigating Alkaline Hydrogen Evolution Reaction Descriptors for Electrocatalyst Design. Catalysts, 2024, 14 (9), pp.608. 10.3390/catal14090608. [hal-04778661](https://hal HAL Id: [hal-04778661](https://cnrs.hal.science/hal-04778661v1)

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# Navigating Alkaline Hydrogen Evolution Reaction Descriptors for Electrocatalyst Design

Samuel Akinlolu Ogunkunle <fnref n="1" />, Fabien Mortier <fnref n="2" /> ID, Assil Bouzid <fnref n="2" /> ID, Jack Jon Hinsch <fnref n="1" /> ID, Lei Zhang <fnref n="1" /> ID,
Zhenzhen Wu <fnref n="1" /> ID, Samuel Bernard <fnref n="2" /> ID, Yong Zhu <fnref n="3" /> ID and Yun Wang <fnref n="1" />,* ID

**Abstract:** The quest for efficient green hydrogen production through Alkaline Water Electrolysis (AWE) is a critical aspect of the clean energy transition. The hydrogen evolution reaction (HER) in alkaline media is central to this process, with the performance of electrocatalysts being a determining factor for overall efficiency. Theoretical studies using energy-based descriptors are essential for designing high-performance alkaline HER electrocatalysts. This review summarizes various descriptors, including water adsorption energy, water dissociation barrier, and Gibbs free energy changes of hydrogen and hydroxyl adsorption. Examples of how to apply these descriptors to identify the active site of materials and better design high-performance alkaline HER electrocatalysts are provided, highlighting the previously underappreciated role of hydroxyl adsorption-free energy changes. As research progresses, integrating these descriptors with experimental data will be paramount in advancing AWE technology for sustainable hydrogen production.

**Keywords:** green hydrogen; alkaline water electrolysis; descriptor; density functional theory; electro-catalyst design

## 1. Introduction

The shift towards hydrogen gas as an alternative energy source is a significant step in combating climate change. Green hydrogen via electrocatalytic water splitting is directly competitive with fossil fuels, which decreases overall greenhouse gas emissions [1]. The intricacies of electrocatalytic water splitting involve the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) [2]. There are several types of water electrolyzers (WE): solid oxide water electrolyzer (SOWE), proton exchange membrane water electrolyzer (PEMWE), and alkaline electrolyzer (AWE) [3]. SOWE can be adapted for continuous operation in industrial areas under high temperatures. However, the technology has seen limited applications due to long start-up times, mechanical compatibility, and chemical instabilities [4,5]. PEMWE in acidic environments is the most efficient for green hydrogen production due to the abundance of the proton reactant in the solution [6]. However, the main challenge associated with PEMWE is the high cost of the electrocatalysts, which are based on platinum and platinum group metals (PGMs) to resist acid corrosion [7]. In contrast, alkaline HER in AWE offers a promising alternative allowing for the exploration of earth-abundant transition metal-based catalysts because their hydro-oxide counterparts are stable in this environment [8–10]. Shifting towards an alkaline environment will reduce reliance on expensive noble metals and reduce the hydrogen production cost. Green

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**Citation:** Ogunkunle, S.A.; Mortier, F.; Bouzid, A.; Hinsch, J.J.; Zhang, L.; Wu, Z.; Bernard, S.; Zhu, Y.; Wang, Y. Navigating Alkaline Hydrogen Evolution Reaction Descriptors for Electrocatalyst Design. *Catalysts* **2024**, *14*, 608. https://doi.org/10.3390/catal14090608

Academic Editor: Edward G. Gillan

Received: 19 July 2024

Revised: 2 September 2024

Accepted: 3 September 2024

Published: 10 September 2024

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**Copyright:** © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">¹ Centre for Clean Environment and Energy, School of Environment and Science, Griffith University, Gold Coast Campus, Southport 4222, Australia; samuelakinlolu.ogunkunle@griffithuni.edu.au (S.A.O.); jack.hinsch@griffithuni.edu.au (J.J.H.); lei.zhang@griffith.edu.au (L.Z.); zhenzhen.wu@griffith.edu.au (Z.W.)</footnote>

<footnote n="2">² Institut de Recherche sur les Céramiques (IRCER), UMR CNRS 7315-Université de Limoges, 87068 Limoges, France; fabien.mortier@unilim.fr (F.M.); assil.bouzid@unilim.fr (A.B.); samuel.bernard@unilim.fr (S.B.)</footnote>

<footnote n="3">³ School of Engineering and Built Environment, Griffith University, Gold Coast Campus, Southport 4222, Australia; y.zhu@griffith.edu.au</footnote>

<footnote>* Correspondence: yun.wang@griffith.edu.au</footnote>
hydrogen via electrocatalytic water splitting is directly competitive with fossil fuels, which decreases overall greenhouse gas emissions.

The operational principle of AWEs involves the conduction of hydroxide anions through a liquid electrolyte between two electrodes [8]. The main challenges of the current AWE are its low current densities, the inability to operate with intermittent renewable energy sources, and slow kinetics [11]. These limitations are associated with early versions of atmospheric electrolyzers designed for continuous operation at industrial sites with stable and inexpensive electricity sources. Modern pressurized high-temperature AWEs have shown the capability to reach performance and adaptability on par with PEMWEs [12]. The adaptability to various energy sources, coupled with improved design and control systems, positions pressurized AWEs as a promising solution for sustainable and flexible hydrogen generation in the evolving energy technology landscape [12].

Moreover, the anion exchange membrane water electrolyzer (AEMWE) replaces the conventional diaphragm of AWE with an anion exchange membrane [13]. A membrane reduces the gas cross-over and the need for pressure difference operation between the anode and cathode. Additionally, the thickness of the anion exchange membrane is less than the diaphragm, which leads to a lower ohmic over-voltage. The AEMWE uses an alkaline solution with low concentration. Conventional electrolyzers use concentrated potassium hydroxide electrolytes, which increase corrosion. Therefore, AEMWE has several benefits, including no leakage, ease of installation, and control. However, the low energy conversion efficiency of AWEs due to the slow kinetics remains a bottleneck, requiring high-performance electrocatalyst design.

The pursuit of an effective catalyst for AWE is multifaceted, necessitating a blend of experimental and theoretical studies to unlock the full potential of electrocatalysts [8,11,14]. The challenges for the alkaline HER electrocatalyst design are twofold: the inherently lower reaction rates of catalysts and a limited understanding of the complex kinetics involved. The HER process varies significantly depending on the electrolyte medium, which can be either acidic or alkaline. In acidic media, the HER mechanism involves the electrochemical reduction of a proton (H⁺), leading to the release of hydrogen gas (H₂) [15–17]. The HER efficiency is associated with the adsorption of hydrogen atom intermediate (H*), which consists of the Volmer/Heyrovsky or Volmer/Tafel steps as delineated below [18]:

$$ \text{Volmer reaction : } H^+ + e^- \rightarrow H^* \qquad (1) $$

$$ \text{Heyrovsky reaction : } H^* + H^+ + e^- \rightarrow H_2 \qquad (2) $$

$$ \text{Tafel reaction : } H^* + H^* \rightarrow H_2 \qquad (3) $$

Conversely, alkaline HER operates through the electrochemical reduction of water molecules, resulting in the formation of hydrogen gas and hydroxide ions (OH⁻) [19].

$$ \text{Water adsorption : } H_2O + * \rightarrow H_2O^* \qquad (4) $$

$$ \text{Volmer reaction (I) : } H_2O^* + e^- \rightarrow H^* + OH^- + e^- \rightarrow H^* + OH^- \qquad (5) $$

$$ \text{Volmer reaction (II) : } H_2O^* + e^- \rightarrow H^* + OH^- \qquad (6) $$

$$ \text{Heyrovsky reaction : } H_2O + e^- + H^* \rightarrow H_2 + OH^- \qquad (7) $$

$$ \text{Tafel reaction : } H^* + H^* \rightarrow H_2 \qquad (8) $$

The HER pathway in alkaline media involves complex Volmer-Heyrovsky or Volmer-Tafel steps, with the intermediate hydrogen formed after an initial water adsorption step (Equation (4)). Additionally, the adsorbed hydroxyl intermediate may form during the Volmer step if its binding energy with the active site is strong enough (Equation (5)). Otherwise, the solution-phase hydroxide (OH⁻) can directly form after the water dissociation
(Equation (6)) during the Volmer reaction. The H₂ product can be produced through an adsorbed H atom intermediate and water in the Heyrovsky reaction (Equation (7)) or through the combination of two adsorbed H⁺ atom intermediates in the Tafel reaction (Equation (8)). Figure 1 indicates the possible alkaline HER pathway. It shows that the performance of alkaline HER can be influenced by four main factors: (1) water adsorption strength on active sites, (2) water dissociation ability, (3) hydrogen binding energy, and (4) OH adsorption ability. To this end, the properties relevant to these four factors have been used to screen the alkaline HER electrocatalysts.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Possible hydrogen evolution reaction processes in alkaline media.</figcaption></figure>

The step-by-step process that governs HER needs to be theoretically revealed by delving into the intricate details of reaction mechanisms through atomic-scale simulation [8]. Theoretical investigations can offer insights into the energetic aspects of water adsorption, water dissociation, intermediates adsorption, and hydrogen desorption [15,20–22]. This granular view allows researchers to identify and optimize the performance of active sites that influence both catalytic efficiency and stability. Such knowledge is instrumental in recognizing the rate-determining steps and potential energy barriers, which are critical for designing catalysts with optimal performance [15]. Furthermore, theoretical models serve as a blueprint for predicting the performance of different materials under various reaction conditions. Therefore, computational studies enable the fine-tuning of working conditions to enhance the overall efficiency of the process. Additionally, these studies contribute significantly to the green hydrogen field by offering a cost-effective strategy for material screening, circumventing the need for laborious and expensive experimental procedures [20,23]. Ultimately, the insights gained from theoretical research facilitate the development of innovative solutions for alkaline hydrogen production [8].

Recent advances have highlighted the importance of atomically precise electrocatalysts, which utilize theoretical descriptors to correlate the properties of catalysts with their alkaline HER performance [8,19,24]. Since different descriptors related to the different reaction steps shown in Figure 1 have been proposed and previously utilized [25–30], it is necessary to devise guidelines for selecting descriptors that can accurately predict the performance of HER electrocatalysts in alkaline conditions. Density functional theory (DFT) calculations are essential in computing the proposed energy descriptors related to water adsorption, water dissociation, intermediates adsorption [18,31–33], and product desorption. These descriptors are crucial to understanding alkaline HER electrocatalysts and electrocatalytic processes in the alkaline electrolyzer (AEL). Additionally, identifying
important descriptors can improve computational accuracy while minimizing costs [23,34]. While several reviews on the recent progress of alkaline HER electrocatalysis have been presented [8,11,35], a summary and discussion of the most appropriate descriptors for guiding the design of efficient AEL is still rare. To fill this gap, this review will provide a framework by which the desired theoretical descriptor can be selected via DFT computations to design electrocatalysts rather than a comprehensive overview of AWEs.

## 2. Theoretical Descriptors

As indicated by Equations (4)–(8) and Figure 1, the performance of alkaline HER electrocatalysts is a complex interplay of various factors. The water adsorption strength on active sites, the ability of the catalyst to dissociate water molecules, the hydrogen binding energy, and the OH adsorption processes are all critical in determining the efficiency of the HER process. These factors are intricately linked to the intrinsic properties of the electrocatalysts and their interaction with the operational reaction environment, e.g., electrolyte. Therefore, different theoretical energy-related descriptors have been employed as indicators to screen electrocatalysts for alkaline HER [25–30,36].

### 2.1. Water Adsorption and Dissociation

The first step of the electrocatalytic water splitting in an alkaline solution is water adsorption, followed by water dissociation to provide the $H^+$ cation for hydrogen production (Equations (4)–(6)). HER performance in alkaline or neutral media is primarily determined by the equilibrium between water dissociation (Volmer step) and the subsequent chemisorption of water-splitting intermediates (OH and H) on the surface of the electrocatalysts [37]. To this end, it is critical to strengthen water adsorption at the active sites and decrease the water dissociation activation energy during the Volmer step to increase the overall HER activities of these electrocatalysts. Consequently, the adsorption energy of water ($\Delta E_{H_2O^*}$) and its dissociation energy barriers ($\Delta E_a$) have been used as descriptors to evaluate the performance of alkaline HER electrocatalysts. The $\Delta E_{H_2O^*}$ value can be calculated as shown below:

$$ \Delta E_{H_2O^*} = \frac{1}{n}(E_{H_2O^*} - E_* - E_{H_2O}) \qquad (9) $$

$E_{H_2O^*}$ and $E_*$ are the energies of the surface with and without adsorbed water, respectively. $E_{H_2O}$ and $n$ represents the energy of an isolated water molecule and the number of adsorbed water molecules in each surface cell, respectively. According to Equation (9), a more negative value of $\Delta E_{H_2O^*}$ corresponds to stronger water adsorption.

To calculate the water dissociation energy barrier on the active site, the nudged elastic band (NEB) is widely used [38,39]. The NEB method is highly effective for locating the maximum energy point between specified initial and final configurations of a given transition. The NEB approach for climbing images involves finding a transition path where the saddle point corresponds to the image with the highest energy. The image does not depict the spring forces acting on the band. The image attempts to optimize its energy along the band while minimizing it in all other directions. Once this image reaches convergence, it can be precisely located at the saddle point [40]. The climbing image NEB method enhances the possibility of finding the transition state (TS) for the reaction at the highest energy point. The $\Delta E_a$ value is the energy difference between the TS state and the surface with the adsorbed water.

### 2.2. Gibbs Free Energy Change of Hydrogen Atom Adsorption

Hydrogen atoms adsorbed at the active site are the HER intermediates. The adsorption and desorption of hydrogen atoms on the catalyst surface are commonly viewed as competing processes. During the HER process, the active catalytic site must have a strong affinity for a hydrogen atom. However, a weak adsorption between the active catalytic site and the hydrogen atom is required [41,42]. The high adsorption strength of hydrogen atoms can promote hydrogen atom intermediate formation but impede the formation of
hydrogen molecules. Comparatively, weak adsorption can benefit the formation of H₂ but hinder the formation of hydrogen atom intermediates. A balance must be achieved where the hydrogen intermediate must form but not compete with/prevent the generation and release of the hydrogen molecule. As a result, the optimal adsorption strength of the hydrogen atom intermediate is essential for improving the HER. The adsorption strength of hydrogen atom intermediates on active sites in catalysts can be evaluated using the Gibbs free energy change of hydrogen atom adsorption (ΔG<sub>H*</sub>) [43].

The ΔG<sub>H*</sub> is obtained by using the computational hydrogen electrode (CHE) method:

$$ \Delta G_{H^*} = \Delta E_{H^*} + \Delta ZPE_{H^*} - T\Delta S_{H^*} \quad (10) $$

where ΔE<sub>H*</sub> describes the binding energy, which is calculated as follows:

$$ \Delta E_{H^*} = E_{H^*} - E_* - \frac{1}{2} E_{H_2} \quad (11) $$

Here, E<sub>H*</sub> is the total energy of the system with one adsorbed H atom and E<sub>H₂</sub> represents the energy of an isolated H₂ molecule. ΔZPE<sub>H*</sub> is calculated by ΔZPE<sub>H*</sub> = ZPE<sub>H*</sub> - 1/2 ZPE<sub>H₂</sub>, where the ZPE<sub>H*</sub> denotes the vibrational energy of the adsorbed H atom on the active site and the value of ZPE<sub>H₂</sub> is 0.27 eV. Further, ΔS<sub>H*</sub> is the entropy change of H* adsorption, which is obtained by 1/2 ΔS<sub>H₂</sub>. The TΔS<sub>H*</sub> value is equal to 1/2 TΔS<sub>H₂</sub>, which is -0.20 eV at 300 K, obtained by Nørskov et al. [32]. The ideal ΔG<sub>H*</sub> value is 0 eV.

### 2.3. Gibbs Free Energy Change of Hydroxyl Adsorption

While hydrogen adsorption energy (ΔG<sub>H</sub>) primarily determines the alkaline HER activity, the Gibbs free energy change of OH adsorption energy (ΔG<sub>OH*</sub>) is found to be equally important since it is responsible for the water dissociation and the amount of hydrogen available [44]. Therefore, the adsorption and desorption of both reaction intermediates (OH* and H*, see Equation (2)) dictate the overall alkaline HER efficiency [45].

The ΔG<sub>OH*</sub> is calculated by using the computational hydrogen electrode (CHE) method:

$$ \Delta G_{OH^*} = \Delta E_{OH^*} + \Delta ZPE - T\Delta S \quad (12) $$

where ΔE<sub>OH*</sub> describes the binding energy of an OH group at the active site, which is calculated as follows:

$$ \Delta E_{OH^*} = \left( E_{OH^*} - E_* - E_{H20} + \frac{1}{2} E_{H_2} \right) \quad (13) $$

where E<sub>OH*</sub> is the total energy of the system with one adsorbed OH intermediate, the ΔZPE - TΔS value is 0.35 eV at 300 K, obtained by Nørskov et al. The ideal ΔG<sub>OH*</sub> value is -0.3 eV for the alkaline HER [46].

## 3. Applications of Descriptors

### 3.1. Water Adsorption and Dissociation

Figure 1 shows that water adsorption is the first step in generating hydrogen atom intermediates for alkaline HER. The H₂O dissociation becomes a rate-determining step that regulates the catalytic HER activity in alkaline media [47,48]. To this end, the adsorption energy of water and its dissociation energy barriers have been used as descriptors in some research to explain the performance of alkaline HER electrocatalysts.

For example, Chen et al. experimentally synthesized a Ni-doped Pt catalyst on carbon support at 500 °C (termed as NiPt-C-500), which has a low overpotential of 14.0 mV at 10 mA/cm² in the alkaline media [49], using the adsorption energy of water molecules and their dissociation energy barriers as descriptors through DFT computations at the PBE-GGA level to identify the active sites of the NiPt-C-500 catalyst. Figure 2a shows that H₂O can be adsorbed on the Ni sites with an adsorption energy of -0.48 eV. As a
comparison, the water adsorption energy on Pt is +0.37 eV. The positive value suggests that the adsorption on Pt is energetically unfavorable. Moreover, a lower H₂O-dissociation barrier on Ni-doped Pt (111) of 0.17 eV was theoretically revealed compared to that on Pt(111), as illustrated in Figure 2b. This suggests a rapid dissociation of H₂O catalyzed by surface Ni atoms on the Pt surface in NiPt-C-500 electrocatalysts, which can increase the rate of H\* generation for alkaline HER. Using the same descriptors, Yao et al. resorted to DFT computations to explain the high performance of Cr-doped Co₄N nanorods on carbon cloth (Cr-Co₄N) for alkaline HER [50]. Figure 2c shows that the calculated H₂O adsorption energy on the top of the Cr dopant within Cr-Co₄N is -0.63 eV, which is much lower than that on the surface Co of Co₄N (-0.18 eV). Therefore, the water adsorption on Cr dopants is substantially stronger than on undoped Co₄N. This is because the oxygen atom of water carries a negative Bader charge of -1.13 |e|. As a result, Cr atoms with a higher positive charge (0.72 |e|) than surface Co (0.21 |e|) can more strongly adsorb water molecules via higher electrostatic interactions. The enhanced adsorption strength of water can further facilitate the dissociation of the adsorbed water and lower the dissociation barrier, as illustrated in Figure 2d. It explains the experimental observation that introducing Cr dopants can boost the alkaline HER activity.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** (a) DFT-calculated water adsorption energies (ΔE<sub>H₂O*</sub>) and (b) water dissociation energy barriers (ΔE<sub>a</sub>) on Pt (1 1 1) and Pt (1 1 1)-Ni surfaces. Reprinted with permission from Ref. [49]. Copyright 2023 Elsevier. (c) DFT-calculated water adsorption energies (ΔE<sub>H₂O*</sub>) and (d) water dissociation energy barriers (ΔE<sub>a</sub>) on Co₄N Cr-Co₄N. Reprinted with permission from Ref. [50]. Copyright 2019 Wiley.</figcaption></figure>

More examples of studies using the ΔE<sub>H₂O*</sub> to identify the active sites of the alkaline HER electrocatalysts can be found in Table 1. Similarly, some examples of using the ΔE<sub>a</sub> as the descriptor to explain the performance of alkaline HER electrocatalysts are listed in Table 2.
<table><caption>**Table 1.** Water adsorption energies as descriptors to identify the active site of the alkaline HER electrocatalyst.</caption><thead><tr><th>Catalysts</th><th>DFT Method</th><th>Adsorption Site</th><th>ΔE<sub>H<sub>2</sub>O</sub>(eV)</th><th>Overpotential@<br>Current Density of<br>10 mA cm<sup>-2</sup></th><th>Conclusion</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="3">Co-doped<br>WO<sub>2</sub>/Amorphous<br>Co<sub>x</sub>W</td><td rowspan="3">PBE</td><td>Co<br>WO<sub>2</sub> (001)</td><td>0.12<br>-0.66</td><td>-<br>49</td><td rowspan="3">Amorphous CoxW is an active<br>site for water adsorption.</td><td rowspan="3">ACS Appl. Mater. Interfaces (2019), 11,<br>38771 [51]</td></tr><tr><td>Co<sub>x</sub>W</td><td>-0.88</td><td>25.0</td></tr><tr><td>Ni(111)<br>Cr-doped Ni(111)</td><td>-0.21<br>-0.58</td><td>322.0<br>203.0</td></tr><tr><td rowspan="4">CuCoMo-doped<br>Ni(111)</td><td rowspan="4">PBE</td><td>Ni-top</td><td>-0.23</td><td>-</td><td rowspan="4">Water is mainly adsorbed on Mo<br>dopants.</td><td rowspan="4">J. Am. Chem. Soc. (2019), 839, 224 [53]</td></tr><tr><td>Co-top</td><td>-0.25</td><td>-</td></tr><tr><td>Cu-top</td><td>-0.15</td><td>-</td></tr><tr><td>Mo-top</td><td>-0.67</td><td>-</td></tr><tr><td rowspan="2">N-doped Ni</td><td rowspan="2">PBE</td><td>Surface Ni</td><td>-0.30</td><td>-</td><td rowspan="2">N dopants can strengthen the<br>water adsorption on their<br>neighboring Ni atoms.</td><td rowspan="2">J. Am. Chem. Soc. (2017), 139, 12283<br>[54]</td></tr><tr><td>Surface Ni next to N<br>dopants</td><td>-0.41</td><td>64.0</td></tr><tr><td rowspan="2">Cu-Ru/RuSe<sub>2</sub></td><td rowspan="2">PBE</td><td>Cu-RuSe<sub>2</sub></td><td>-0.40</td><td>61.0</td><td rowspan="2">Cu-doped Ru/RuSe<sub>2</sub> displays a<br>much stronger affinity to water.</td><td rowspan="2">Adv. Mater. (2023),<br>35, 2300980 [55]</td></tr><tr><td>Cu-Ru/RuSe<sub>2</sub></td><td>-1.28</td><td>23.0</td></tr><tr><td rowspan="2">Ru<sub>SA</sub>@Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td rowspan="2">PBE</td><td>Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td>-0.18</td><td>-</td><td rowspan="2">Enhanced H<sub>2</sub>O adsorption by<br>single Ru atom (Ru<sub>SA</sub>) on MXenes.</td><td rowspan="2">EcoMat (2023), 5,<br>12274 [56]</td></tr><tr><td>Ru<sub>SA</sub>@Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td>-1.47</td><td>40.3</td></tr></tbody></table>

The overpotential values are reported based on the experimental results in the corresponding reference.

<table><caption>**Table 2.** The dissociation energy barrier of the adsorption water as descriptors to identify the active site of the alkaline HER electrocatalyst.</caption><thead><tr><th>Catalyst</th><th>DFT<br>Method</th><th>Active Site</th><th>ΔE<sub>a</sub>(eV)</th><th>Overpotential<br>(mV@ Current<br>Density of<br>10 mA cm<sup>-2</sup>)</th><th>Conclusion</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="3">Co-doped WO<sub>2</sub><br>/Amorphous<br>Co<sub>x</sub>W</td><td rowspan="3">PBE</td><td>Co-WO<sub>2</sub></td><td>1.25</td><td rowspan="3">49<br>25</td><td rowspan="3">Amorphous CoxW is an active site for water<br>dissociation.</td><td rowspan="3">ACS Appl. Mater. & Interface. (2019),<br>11, 38771 [51]</td></tr><tr><td>WO<sub>2</sub> (001)</td><td>1.03</td></tr><tr><td>Co<sub>x</sub>W</td><td>0.46</td></tr><tr><td rowspan="3">W/WO<sub>2</sub></td><td rowspan="3">PBE-D3</td><td>W</td><td>0.84</td><td>183</td><td rowspan="3">W/WO<sub>2</sub> interface is the active site that allows water<br>dissociation.</td><td rowspan="3">Nat. Commun. (2023), 14, 5363 [57]</td></tr><tr><td>WO<sub>2</sub></td><td>0.06</td><td>106</td></tr><tr><td>W/WO<sub>2</sub></td><td>0.02</td><td>35</td></tr><tr><td rowspan="2">F-Ni<sub>3</sub>S<sub>4</sub></td><td rowspan="2">PBE + U</td><td>Ni<sub>3</sub>S<sub>4</sub></td><td>1.05</td><td>112</td><td rowspan="2">F-Ni<sub>3</sub>S<sub>4</sub> allows a better H<sub>2</sub>O adsorption.</td><td rowspan="2">Adv. Funct. Mater. (2021), 31, 2008578<br>[58]</td></tr><tr><td>F-Ni<sub>3</sub>S<sub>4</sub></td><td>0.55</td><td>29</td></tr><tr><td rowspan="2">Co<sub>2</sub>P/O-Co<sub>2</sub>P</td><td rowspan="2">PBE</td><td>Co<sub>2</sub>P</td><td>0.88</td><td>247</td><td rowspan="2">Oxygen incorporation may induce a higher positive<br>charge state Co, which could benefit water adsorption<br>and weaken the O-H bond in adsorbed H<sub>2</sub>O.</td><td rowspan="2">Adv. Mater. (2017),<br>29, 1606980 [59]</td></tr><tr><td>O-Co<sub>2</sub>P</td><td>0.51</td><td>160</td></tr><tr><td rowspan="2">Cr-doped Ni(111)</td><td rowspan="2">-</td><td>Ni(111)</td><td>0.78</td><td>322</td><td rowspan="2">Co-dopant can facilitate water dissociation.</td><td rowspan="2">J. Am. Chem. Soc. (2020), 143, 1399<br>[52]</td></tr><tr><td>Cr-doped Ni(111)</td><td>0.43</td><td>203</td></tr><tr><td rowspan="2">Bimetallic<br>Nickel-Based<br>Alloys</td><td rowspan="2">PBE</td><td>NiCu</td><td>1.02</td><td>85</td><td rowspan="2">Partial oxidization of CuNi alloy can facilitate water<br>dissociation.</td><td rowspan="2">Angew. Chem. Int. Ed. (2022), 61,<br>202202518 [60]</td></tr><tr><td>O-NiCu</td><td>0.65</td><td>23</td></tr><tr><td rowspan="2">N-modified Ni</td><td rowspan="2">PBE</td><td>Ni</td><td>0.84</td><td>-</td><td rowspan="2">N dopant can greatly facilitate water dissociation on<br>its neighbouring active site.</td><td rowspan="2">J. Am. Chem. Soc. (2017), 139, 12283<br>[54]</td></tr><tr><td>N-Ni</td><td>0.42</td><td>64</td></tr><tr><td rowspan="2">Cu-Ru/RuSe<sub>2</sub></td><td rowspan="2">PBE</td><td>Cu-RuSe<sub>2</sub></td><td>0.31</td><td>61</td><td rowspan="2">Cu-dopant can promote water dissociation on<br>Ru/RuSe<sub>2</sub></td><td rowspan="2">Adv. Mater. (2023),<br>35, 2300980 [55]</td></tr><tr><td>Cu-Ru/RuSe<sub>2</sub></td><td>0.10</td><td>23</td></tr></tbody></table>
<table><caption>**Table 2.** *Cont.*</caption><thead><tr><th>Catalyst</th><th>DFT Method</th><th>Active Site</th><th>ΔE<sub>a</sub>(eV)</th><th>Overpotential (mV@ Current Density of 10 mA cm<sup>-2</sup>)</th><th>Conclusion</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="5">NiP<sub>2</sub>-FeP<sub>2</sub>/Cu</td><td rowspan="5">PBE</td><td>NiP<sub>2</sub></td><td>0.52</td><td>37</td><td rowspan="5">The coupling between interface-rich NiP<sub>2</sub>-FeP<sub>2</sub> and metallic Cu can synergistically accelerate water dissociation.</td><td rowspan="5">ACS Energy Lett. (2021), 6, 354 [61]</td></tr><tr><td>FeP<sub>2</sub></td><td>0.49</td><td>-</td></tr><tr><td>NiP<sub>2</sub>-FeP<sub>2</sub></td><td>0.40</td><td>-</td></tr><tr><td>NiP<sub>2</sub>-FeP<sub>2</sub>/Cu</td><td>0.16</td><td>23.6</td></tr><tr><td>F-Ni<sub>3</sub>S<sub>4</sub></td><td>0.55</td><td>-</td></tr><tr><td>High-entropy alloys (HEAs)<br>Pt<sub>18</sub>Ni<sub>26</sub>Fe<sub>15</sub>Co<sub>14</sub>Cu<sub>27</sub></td><td>PBE</td><td>Fe</td><td>0.11</td><td>11</td><td>Adsorption of H<sub>2</sub>O located on the Fe sites, which activates the dissociation of water molecules.</td><td>Nat. Commun. (2020), 11, 5437 [62]</td></tr><tr><td rowspan="4">2D transition-metal dichalcogenide</td><td rowspan="4">PBE</td><td>MoS<sub>2</sub></td><td>0.62</td><td>-</td><td rowspan="4">MoS<sub>2</sub> and WS<sub>2</sub> have similar activation energy.</td><td rowspan="4">J. Phys. Chem. C. (2022), 126, 5151 [63]</td></tr><tr><td>MoSe<sub>2</sub></td><td>0.74</td><td>-</td></tr><tr><td>WS<sub>2</sub></td><td>0.60</td><td>-</td></tr><tr><td>WSe<sub>2</sub></td><td>0.84</td><td>-</td></tr></tbody></table>

The overpotential values are reported based on the experimental results in the corresponding reference.

## 3.2. *Hydrogen Atom Adsorption*

The Gibbs free energy change of the intermediate H atom adsorption (ΔG<sub>H*</sub>) was proposed as a descriptor for HER by Nørskov and his co-workers. This descriptor has successfully identified the active site of acidic HER electrocatalysts and the relevant reaction mechanism [32]. A volcano plot is a valuable tool for understanding and optimizing catalyst performance in acidic HER. It is usually a plot of ΔG<sub>H*</sub> against activities (such as overpotential, specific current density, and turnover frequency) [64,65]. The highest point on the volcano map is the ideal ΔG<sub>H*</sub> value at which the catalytic activity is maximized. Catalysts located on the left side of the volcano plot exhibit excessive hydrogen binding (very strong), while those on the right side have insufficient hydrogen binding (very weak). According to the Sabatier principle, an optimum catalyst should exhibit adsorption energies that are neither too strong nor too weak. In the alkaline HER, the adsorption of H atoms at the active site is also important since it is related to the water dissociation, Volmer, Heyrovsky, and Tafel steps, as suggested by Equations (5)–(8) and Figure 1. To this end, the ΔG<sub>H*</sub> was also widely used in the analysis of the performance of the alkaline HER electrocatalysts [66].

For example, Chen et al. adopted a dual approach to simultaneously promote water dissociation and hydrogen desorption kinetics with Co-doped WO<sub>2</sub>/amorphous Co<sub>x</sub>W hybrid catalysts using DFT [51]. As shown in Figure 3a, the ΔG<sub>H*</sub> on amorphous Co<sub>x</sub>W is -1.88 eV, indicating a strong hydrogen-binding interaction that prevents H<sub>2</sub> production and desorption (Figure 4a). The most catalytically active site on Co-WO<sub>2</sub>(011) has a ΔG<sub>H*</sub> of -0.06 eV, closer to thermoneutral than Pt's -0.09 eV, indicating significant hydrogen adsorption capability. According to DFT calculations, the HER on Co-doped WO<sub>2</sub>/amorphous CO<sub>x</sub>W hybrid catalyst follows the Volmer-Tafel step, where water molecules are activated and cleaved to form H<sub>2</sub> atoms on the surface of amorphous CO<sub>x</sub>W. These H<sub>2</sub> atoms then rapidly combine to form H<sub>2</sub> on the surface of Co-doped WO<sub>2</sub>. He et al. incorporated a single Ru atom into Ni<sub>5</sub>P<sub>4</sub> to achieve an effective electrocatalyst for alkaline HER [67]. The DFT calculations were conducted to comprehend the impact of single-atomic Ru incorporation into Ni<sub>5</sub>P<sub>4</sub> on its catalytic and structural properties. The structures of Ni<sub>5</sub>P<sub>4</sub> were determined, both with and without Ru incorporation, and they revealed several potential catalytic sites. Experimental analysis and the established model structural parameters were remarkably congruent. In the case of Ni<sub>5</sub>P<sub>4</sub>-Ru, the computed ΔG<sub>H*</sub> value at the Ru-doped sites was -0.30 eV, which was comparatively higher than the value of -0.42 eV observed at the site of P of pristine Ni<sub>5</sub>P<sub>4</sub> (see Figure 3b). This finding indicated that the Ru dopant exhibited favorable energetics for the desorption of absorbed H<sub>2</sub> atoms to form the H<sub>2</sub> gas.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** (a) DFT-calculated Gibbs free energy change of the intermediate H atom adsorption (ΔG<sub>H+</sub>) on WO<sub>2</sub>, Co-WO<sub>2</sub>, CoxW, and Pt. Reprinted with permission from Ref. [51]. Copyright 2019 American Chemical Society. (b) DFT-calculated Gibbs free energy change of the intermediate H atom adsorption (ΔG<sub>H+</sub>) on Ni<sub>5</sub>P<sub>4</sub> and Ni<sub>5</sub>P<sub>4</sub>: Ru. Reprinted with permission from Ref. [67]. Copyright 2020 Wiley.</figcaption></figure>

Table 3 lists more examples of using ΔG<sub>H+</sub> as the descriptor to identify the active site of the alkaline HER electrocatalysts and evaluate their performance.

<table><caption>**Table 3.** Gibbs free energy change of H intermediate adsorption as descriptors to identify the active site of the alkaline HER electrocatalyst.</caption><thead><tr><th>Catalyst</th><th>DFT Method</th><th>Active Site</th><th>ΔG<sub>H+</sub>(eV)</th><th>Overpotentials (mV@ Current Density of -10 mA cm<sup>-2</sup>)</th><th>Conclusion</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="3">W/WO<sub>2</sub></td><td rowspan="3">DFT-D3</td><td>W</td><td>-0.51</td><td>183.0</td><td rowspan="3">W/WO<sub>2</sub> interface is the active site for HER.</td><td rowspan="3">Nat. Commun. (2023) 14, 5363 [57]</td></tr><tr><td>WO<sub>2</sub></td><td>-1.24</td><td>106.0</td></tr><tr><td>W/WO<sub>2</sub> interface</td><td>-0.41</td><td>35.0</td></tr><tr><td rowspan="3">Co-doped WO<sub>2</sub>/Amorphous Co<sub>x</sub>W</td><td rowspan="3">PBE</td><td>Co-WO<sub>2</sub></td><td>-0.06</td><td>-</td><td rowspan="3">Co-WO<sub>2</sub> is the active site for H<sub>2</sub> formation.</td><td rowspan="3">ACS Appl. Mater. &amp; Interface (2019), 11, 38771 [51]</td></tr><tr><td>WO<sub>2</sub> (001)</td><td>-0.30</td><td>49.0</td></tr><tr><td>Co<sub>x</sub>W</td><td>-1.88</td><td>-</td></tr><tr><td rowspan="2">Cr-doped Ni(111)</td><td rowspan="2">-</td><td>Ni(111)</td><td>-0.23</td><td>322.0</td><td rowspan="2">Co-dopant can reduce the hydrogen desorption rate.</td><td rowspan="2">J. Am. Chem. Soc. (2020), 143, 1399 [52]</td></tr><tr><td>Cr-doped Ni(111)</td><td>-0.38</td><td>203.0</td></tr><tr><td rowspan="4">CuCoMo-doped Ni(111)</td><td rowspan="4">PBE</td><td>Ni<sub>3</sub>-fcc</td><td>-2.76 *</td><td>-</td><td rowspan="4">The preferential adsorption site is a Mo-coordinated fcc site.</td><td rowspan="4">Electroanal. Chem. (2019), 839, 224 [53]</td></tr><tr><td>Cu<sub>2</sub>Co-fcc</td><td>-2.51 *</td><td>-</td></tr><tr><td>Co<sub>2</sub>Cu-fcc</td><td>-2.67 *</td><td>-</td></tr><tr><td>CuCoMo-fcc</td><td>-2.78 *</td><td>-</td></tr><tr><td rowspan="3">Ni/NiCu/O-NiCu</td><td rowspan="3">PBE</td><td>Ni</td><td>-0.31</td><td>-</td><td rowspan="3">Cu can weaken the adsorption strength of hydrogen to benefit the H<sub>2</sub> production.</td><td rowspan="3">Angew. Chem. Int. Ed. (2022), 61, 202202518 [60]</td></tr><tr><td>NiCu</td><td>-0.11</td><td>85.0</td></tr><tr><td>O-NiCu</td><td>-0.035</td><td>23.0</td></tr><tr><td rowspan="2">Cu-Ru/RuSe<sub>2</sub></td><td rowspan="2">PBE</td><td>Cu-RuSe<sub>2</sub></td><td>0.50</td><td>61.0</td><td rowspan="2">Cu can weaken the adsorption strength of hydrogen to benefit the H<sub>2</sub> production.</td><td rowspan="2">Adv. Mater. (2023), 35, 2300980 [55]</td></tr><tr><td>Cu-Ru/RuSe<sub>2</sub></td><td>0.19</td><td>23.0</td></tr></tbody></table>
<table><caption>**Table 3. Cont.**</caption><thead><tr><th>Catalyst</th><th>DFT Method</th><th>Active Site</th><th>ΔG<sub>H*</sub>(eV)</th><th>Overpotentials (mV@ Current Density of -10 mA cm<sup>-2</sup>)</th><th>Conclusion</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="4">NiP-FeP<sub>2</sub>/Cu</td><td rowspan="4">PBE</td><td>NiP<sub>2</sub></td><td>-0.358</td><td>37.0</td><td rowspan="4">NiP-FeP<sub>2</sub>/Cu interface effectively adsorbs generated H intermediate.</td><td rowspan="4">ACS Energy Lett. (2021), 6, 354. [61]</td></tr><tr><td>FeP<sub>2</sub></td><td>-0.203</td><td>-</td></tr><tr><td>NiP-FeP<sub>2</sub></td><td>-0.043</td><td>-</td></tr><tr><td>NiP-FeP<sub>2</sub>/Cu</td><td>-0.03</td><td>23.6</td></tr><tr><td rowspan="2">O-Co<sub>2</sub>P</td><td rowspan="2">PBE</td><td>Co<sub>2</sub>P</td><td>0.70</td><td>247.0</td><td rowspan="2">Oxygen incorporation may induce a higher positive charge state Co to benefit water adsorption and weaken the O-H bond in adsorbed H<sub>2</sub>O.</td><td rowspan="2">Adv. Mater. (2017), 29, 1606980 [59]</td></tr><tr><td>O-Co<sub>2</sub>P</td><td>0.19</td><td>160.0</td></tr><tr><td rowspan="2">Ru<sub>S</sub>A @ Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td rowspan="2">PBE</td><td>Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td>-0.33</td><td>-</td><td rowspan="2">Ru<sub>S</sub>A favours H<sub>2</sub> formation.</td><td rowspan="2">EcoMat (2023), 5, 12274 [56]</td></tr><tr><td>Ru<sub>S</sub>A @ Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td>-0.07</td><td>40.3</td></tr><tr><td rowspan="2">F-Ni<sub>3</sub>S<sub>4</sub></td><td rowspan="2">PBE</td><td>Ni<sub>3</sub>S<sub>4</sub></td><td>0.12</td><td>112.0</td><td rowspan="2">F-doping can promote water dissociation to increase the rate of Hads formation.</td><td rowspan="2">Adv. Funct. Mater. (2021), 31, 2008578 [58]</td></tr><tr><td>F-Ni<sub>3</sub>S<sub>4</sub></td><td>-0.034</td><td>29</td></tr><tr><td rowspan="10">Metal-modified transition metal carbides</td><td rowspan="10">PW91</td><td>Pt/Mo<sub>2</sub>C interface</td><td>0.01</td><td>-</td><td rowspan="10">The ΔG<sub>H*</sub> has a strong correlation with the alkaline HER performance.</td><td rowspan="10">ACS Catal. (2019), 9, 2415 [29]</td></tr><tr><td>Pt/NbC</td><td>-0.28</td><td>-</td></tr><tr><td>Pt/TaC</td><td>-0.07</td><td>-</td></tr><tr><td>Pt/TiC</td><td>-0.03</td><td>-</td></tr><tr><td>Mo<sub>2</sub>C(0001)</td><td>-0.75</td><td>-</td></tr><tr><td>NbC</td><td>-0.90</td><td>-</td></tr><tr><td>TaC</td><td>-0.99</td><td>-</td></tr><tr><td>TiC</td><td>-0.96</td><td>-</td></tr><tr><td>VC</td><td>-0.84</td><td>-</td></tr><tr><td>W<sub>2</sub>C(0001)</td><td>-0.60</td><td>-</td></tr><tr><td>WC(0001)</td><td>-0.81</td><td>-</td></tr><tr><td rowspan="3">Ni/Co-modified MoSe<sub>2</sub></td><td rowspan="3">PBE</td><td>MoSe<sub>2</sub></td><td>1.49</td><td>301</td><td rowspan="3">Partial substitution of Ni or Co atoms for Mo atoms can optimize the ΔG<sub>H*</sub> value.</td><td rowspan="3">Angew. Chem. (2020), 132, 15344 [27]</td></tr><tr><td>Ni-MoSe<sub>2</sub></td><td>-0.43</td><td>98</td></tr><tr><td>Co-MoSe<sub>2</sub></td><td>-0.20</td><td>183</td></tr><tr><td rowspan="5">FeCoNiCu<sub>0.5</sub></td><td rowspan="5">PBE</td><td>Ni</td><td>-0.08</td><td>436</td><td rowspan="5">ΔG<sub>H*</sub> value of -0.08 eV, close to that of the Pt catalyst.</td><td rowspan="5">J. Alloys Compd. (2024), 175356 [68]</td></tr><tr><td>Fe</td><td>0.17</td><td>509</td></tr><tr><td>Co</td><td>-0.18</td><td>361</td></tr><tr><td>Cu</td><td>0.23</td><td>252</td></tr><tr><td>FeCoNiCu<sub>0.5</sub></td><td>-0.08</td><td>71</td></tr><tr><td rowspan="4">2D transition-metal dichalcogenides</td><td rowspan="4">PBE</td><td>MoS<sub>2</sub></td><td>0.03</td><td>-</td><td rowspan="4">Except for WSe<sub>2</sub>, the calculated ΔG<sub>H*</sub> of the rest is close to zero.</td><td rowspan="4">J. Phys. Chem. C. (2022), 126, 5151 [63]</td></tr><tr><td>MoSe<sub>2</sub></td><td>0.09</td><td>-</td></tr><tr><td>WS<sub>2</sub></td><td>-0.03</td><td>-</td></tr><tr><td>WSe<sub>2</sub></td><td>0.24</td><td>-</td></tr></tbody></table>

### 3.3. Hydrogen and Hydroxyl Adsorption

In recent studies, the volcano plot has been adopted to describe HER activities in alkaline media by plotting ΔG<sub>OH*</sub> against activities. In contrast to the volcano-shaped association observed with ΔG<sub>H*</sub>, Zhang et al. demonstrated that ΔG<sub>OH*</sub> exhibits a significantly weaker correlation with alkaline HER activity than the volcano-shaped relationship established with ΔG<sub>H*</sub> [29]. Au-modified TMCs exhibit OHBEs comparable to those of Pt and Pt-modified TMCs; however, the alkaline exchange current densities of Au/TMCs are two to three orders of magnitude lower than those of their Pt counterparts. Furthermore, carbides modified with Ag and Cu exhibit a broad spectrum of ΔG<sub>OH*</sub>, but there is no discernible HER trend within this spectrum. According to the research of Zhang et al., ΔG<sub>OH*</sub> is not an appropriate descriptor for alkaline HER on TMCs and metal-modified TMCs. It also implies that the adsorbed hydroxyl group does not directly participate in the rate-determining step of alkaline HER kinetics on these surfaces [29].

Markovic et al. were the first to study the impact of adsorbed OH on Pt-based electrocatalysts, emphasizing its poisoning effect on surface sites and its influence on the kinetics of the alkaline HER [69]. The hydrogen binding energy (HBE) and hydroxyl binding energy (OHBE) values for pure Ru and various Mo-Ru compounds were computed (Figure 4a) by Zhao et al. Through DFT, the optimal H and OH adsorption sites on distinct catalysts for alkaline HER were identified [70]. In the Mo-Ru-1 structure, one of the Ru

<footnote>* The authors calculated the adsorption energy of the H atoms here. The overpotential values are reported based on the experimental results in the corresponding reference.</footnote>
atoms is doped with Mo, while Mo-Ru-2 and Mo-Ru-3 are doped with two and four atoms of Mo, respectively. Figure 4a displays the HBE ($\Delta G_H^\ominus$) values of Ru, Mo-Ru-1, Mo-Ru-2, and Mo-Ru-3, which are -0.64, -0.69, -0.67, and -0.76 eV, respectively. These results indicate that the adsorption energy of H is similar for all catalysts and nearly identical to experimental values [25,71,72]. The OHBE ($\Delta G_{OH^\ominus}$) values of Mo-Ru-1 (-0.53 eV), Mo-Ru-2 (-0.68 eV), and Mo-Ru-3 (-0.97 eV) exhibited a substantial increase after Mo-doping, in comparison to native Ru (-0.31 eV). Consequently, the OHBE progressively rose as the Mo atom content increased. Furthermore, the increased OHBE after Mo-doping can be ascribed to the augmented HOR/HER activity of Mo-Ru.

Zhang et al. designed high-efficiency alkaline HER electrocatalysts using a unique dual descriptor of optimal free energies ($\Delta G_H^\ominus$ and $\Delta G_{OH^\ominus}$). Ni₃N surface reactivity was tailored using theory to balance the adsorption energies of hydrogen and hydroxyl species. Nickel-based materials are highly promising non-noble metal electrocatalysts for the hydrogen evolution reaction (HER) [73,74]. In this study, the metallic Ni₃N was considered a case study to illustrate the application of dual-descriptor-driven design. Ni₃N has been regarded as a suitable electrocatalyst for cleaving OH-H bonds in the Volmer phase. According to Figure 4b, the DFT calculations demonstrate that the Ni₃N (111) surface exhibits a facile hydroxyl adsorption free energy of 0.03 eV. This characteristic is advantageous for the energetics of water dissociation and subsequent hydroxyl desorption [75]. Such findings align with prior studies indicating that Ni₃N can function as a promoter of water dissociation [76]. Nevertheless, the DFT calculations indicate that the average $G_H^\ominus$ value observed on the surface of Ni₃N (111) is approximately -0.31 eV, which surpasses the ideal value of $\Delta G_H^\ominus$ = 0 eV by a wide margin. The excessive reactivity of the surface results in unfavorable desorption of hydrogen and subsequent formation of H₂. This approach has successfully enhanced the hydrogen evolution reaction (HER) performance by incorporating various transition-metal dopants into Ni₃N, including Mo-Ni₃N, W-Ni₃N, and V-Ni₃N [30]. The hydrogen and hydroxyl binding energy results on Mo-Ni₃N effectively balance the dual descriptors.

<figure><img src="image_7.png" /><figcaption>**Figure 4.** (a) DFT-calculated Gibbs free energy change of the intermediate H atom adsorption ($\Delta G_H^\ominus$, HBE) and the Gibbs free energy change of OH adsorption energy ($\Delta G_{OH^\ominus}$, OHBE) on Ru, Mo-Ru-1, Mo-Ru-2, Mo-Ru-3. Reprinted with permission from Ref. [70]. Copyright 2022 American Chemical Society. (b) DFT-calculated Gibbs free energy change of the intermediate H atom adsorption ($\Delta G_H^\ominus$) and the Gibbs free energy change of OH adsorption energy ($\Delta G_{OH^\ominus}$) on Ni₃N, Mo-Ni₃N, W-Ni₃N, and V-Ni₃N. Reprinted with permission from Ref. [30]. Copyright 2019 American Chemical Society.</figcaption></figure>

More examples of using $\Delta G_H^\ominus$ and $\Delta G_{OH^\ominus}$ as the descriptor to identify the active site of the alkaline HER electrocatalysts and evaluate their performance are listed in Table 4.
<table><caption>**Table 4.** Gibbs free energy change of OH intermediate adsorption as descriptors to identify the active site of the alkaline HER electrocatalyst.</caption><thead><tr><th>Catalyst</th><th>DFT Method</th><th>Active Site</th><th>ΔG<sub>OH*</sub></th><th>Overpotentials (mV@ Current Density of -10 mA cm<sup>-2</sup>)</th><th>Conclusion</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="2">Cr-doped Ni(111)</td><td rowspan="2"></td><td>Ni(111)</td><td>-3.23 *</td><td>322</td><td rowspan="2">Co-doping allows for a balance between facilitating the dissociation of water and preventing the poisoning effect.</td><td rowspan="2">J. Am. Chem. Soc., (2021), 143, 1399 [52]</td></tr><tr><td>Cr-doped Ni(111)</td><td>-3.83 *</td><td>203</td></tr><tr><td rowspan="2">Ru<sub>5</sub>A@Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub>/Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td rowspan="2">PBE</td><td>Ru<sub>5</sub>A@Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td>-0.49</td><td>40.3</td><td rowspan="2">Ru improved adsorption ability of Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub> toward HO<sup>*</sup>.</td><td rowspan="2">EcoMat (2023), 5, 12274 [56]</td></tr><tr><td>Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td>2.00</td><td>-</td></tr><tr><td rowspan="3">Ni/Co-modified MoSe<sub>2</sub></td><td rowspan="3">PBE</td><td>Mo-MoSe<sub>2</sub></td><td>-1.74</td><td>301</td><td rowspan="3">Co-MoSe<sub>2</sub> is favorable for OH<sup>-</sup> desorption in alkaline HER.</td><td rowspan="3">Angew. Chem. (2020), 132, 315344 [27]</td></tr><tr><td>Co-MoSe<sub>2</sub></td><td>0.67</td><td>183</td></tr><tr><td>Ni-MoSe<sub>2</sub></td><td>1.22</td><td>98</td></tr><tr><td rowspan="14">Metal-modified transition metal carbides</td><td rowspan="14">PW91</td><td>Pt</td><td>-2.39</td><td>-</td><td rowspan="14">The ΔG<sub>OH*</sub> does not show a strong correlation with the alkaline HER performance.</td><td rowspan="14">ACS Catal. (2019), 9, 2415 [29]</td></tr><tr><td>Nb</td><td>-2.41</td><td>-</td></tr><tr><td>Ta</td><td>-2.51</td><td>-</td></tr><tr><td>Mo</td><td>-4.6</td><td>-</td></tr><tr><td>Nb</td><td>-4.85</td><td>-</td></tr><tr><td>Ta</td><td>-4.6</td><td>-</td></tr><tr><td>Ti</td><td>-4.85</td><td>-</td></tr><tr><td>V</td><td>-4.96</td><td>-</td></tr><tr><td>W</td><td>-4.91</td><td>-</td></tr><tr><td>W</td><td>-4.19</td><td>-</td></tr><tr><td>Ru<sub>5</sub>A@Ti<sub>3</sub>C<sub>2</sub>O<sub>2</sub></td><td>-0.49</td><td>-</td></tr><tr><td>Ni</td><td>0.17</td><td>-</td></tr><tr><td rowspan="2">Ni-modified Pt (111)</td><td rowspan="2">PBE</td><td>Pt</td><td>1.05</td><td>28.9</td><td rowspan="2">The strong adsorption of OH on Ni indicates a fast H<sub>2</sub>O dissociation.</td><td rowspan="2">J. Colloid Interface Sci. (2023) 650, 1715 [49]</td></tr><tr><td>Ni-Pt</td><td>-0.51</td><td>14</td></tr></tbody></table>

## 4. Discussion

The selection of the right descriptor for screening alkaline HER electrocatalysts is a long-standing debate, especially using the ΔG<sub>OH*</sub> descriptor. For example, Zhang et al. demonstrated that ΔG<sub>OH*</sub> exhibits a significantly weaker correlation with alkaline HER activity than the volcano-shaped relationship established with ΔG<sub>H*</sub> (Figure 5a), which implies that the adsorbed hydroxyl group does not directly participate in the rate-determining step of alkaline HER kinetics on these surfaces [29]. Contrastingly, McCrum et al. found that the performance of alkaline HER electrocatalysts shows a volcano relationship between the natural logarithm of the experimentally measured rate of hydrogen evolution and the DFT-calculated ΔG<sub>OH*</sub> [19]. The reaction is bifunctional as it involves both ΔG<sub>H*</sub> and ΔG<sub>OH*</sub> on the too-strong OH binding side of the volcano. On the too-weak OH binding side of the volcano, ΔG<sub>H*</sub> is only apparently bifunctional; ΔG<sub>OH*</sub> is not a useful descriptor for evaluating the performance of catalysts. The different conclusions of these two studies may be ascribed to the scopes of ΔG<sub>OH*</sub> values. All the ΔG<sub>OH*</sub> values from Zhang et al. shown in Figure 5a are less than -1.0 eV, which belong to the too-strong OH binding side suggested in Figure 5b. As a result, no volcanic relationship can be identified in Figure 5a. Since all ΔG<sub>OH*</sub> values are far from the optimal value of -0.3 eV, the performance of these metal-modified transition metal carbides is more affected by the ΔG<sub>H*</sub> value, as suggested by Zhang et al. [29].

<footnote>* The authors calculate the adsorption energy of the OH radical at the active site. The overpotential values are reported based on the experimental results in the corresponding reference.</footnote>
<figure><img src="image_8.png" /><figcaption>**Figure 5.** (a) The logarithm of the experimentally measured rate of hydrogen evolution of metal-modified transition metal carbides in 0.1 M KOH and the corresponding DFT-calculated $\Delta G_{OH^*}$. Reprinted with permission from Ref. [29]. Copyright 2019 American Chemical Society. (b) The natural logarithm of the experimentally measured rate of hydrogen evolution of Pt (553), Pt(553) with $Mo^*$, $Re^*$, $Ru^*$, $Rh^*$, and $Ag^*$ adsorbed at the step, and Pt(111) in 0.1 M NaOH and the corresponding DFT-calculated $\Delta G_{OH^*}$. Reprinted with permission from Ref. [19]. Copyright 2020 Springer Nature.</figcaption></figure>

To better screen the alkaline HER electrocatalysts, McCrum et al. adopted a three-dimensional (3D) volcano plot depicting the rate of hydrogen evolution in relation to the $\Delta G_{OH^*}$ and $\Delta G_{H^*}$, as illustrated in Figure 6a. Catalysts exhibiting minimal hydrogen and hydroxide binding energies yield the lowest rates, as indicated by the purple area on the upper right of Figure 6a. The catalysts show the highest performances when they bind hydrogen at an intermediate strength at 0 $V_{RHE}$ (near 0 eV) and hydroxide strongly (near -0.3 eV) (yellow in the middle of Figure 6a). The too-strong H and OH binding leads the $H_2$ or $OH^*$ desorption to become the rate-determining step. Consequently, Figure 6a qualitatively represents trends in alkaline HER kinetics and provides design guidelines for efficient catalysts. For example, to improve the hydrogen evolution rate of the well-studied Pt(111) electrocatalysts in an alkaline solution, the $\Delta G_{H^*}$ must be increased by approximately 0.2 eV. In comparison, the $\Delta G_{OH^*}$ must be significantly reduced by approximately 0.9 eV through appropriate manipulation strategies such as doping, surface engineering, and defect engineering [19].

Following these guidelines, we employed both $\Delta G_{H^*}$ and $\Delta G_{OH^*}$ descriptors to investigate the catalytic HER performance of 1T' transition metal dichalcogenides (TMDs such as $MoSe_2$, $MoS_2$, $WSe_2$, and $WS_2$) in an alkaline solution using DFT [77]. Our findings indicate that the pristine sulfides exhibited superior alkaline HER performance compared to their selenide counterparts. Nevertheless, the activities of all pristine 1T' TMDs are insufficient to dissociate water (See Figure 6b). Defect engineering techniques were employed to improve the reactivity of TMD-based electrocatalysts. Our DFT results indicate that the reactivities of TMD materials can be enhanced by introducing single S/Se vacancy defects, as shown in Figure 6c. However, the rate-determining phase is the desorption of OH. The reactivities of active sites were further regulated to achieve optimal OH desorption by doping defective $MoS_2$ with late 3d transition metal (TM) atoms, particularly Cu, Ni, and Co, as illustrated in Figure 6d. Consequently, the TM-doped defective 1T' $MoS_2$ can substantially improve the alkaline HER performance, which matches the recently reported experimental observations.
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 6.** (a) Logarithm of the rate of hydrogen evolution (contours) as a function of DFT-calculated $\Delta G_{H^+}$ and $\Delta G_{OH^+}$ on Pt(111), Pt(553), Ru* adsorbed at the step of Pt(553), PtRu(111) alloy and Ru* clusters on Pt(111). Reprinted with permission from Ref. [19]. Copyright 2020 Springer Nature. (b) Plot of $\Delta G_{OH^+}$ against $\Delta G_{H^+}$ of pristine MX$_2$ TMDs (M = Mo, W and X = S, Se), (c) plot of $\Delta G_{OH^+}$ against $\Delta G_{H^+}$ of MX$_2$ TMDs with a single X vacancy; and (d) plot of $\Delta G_{OH^+}$ against $\Delta G_{H^+}$ of MX$_2$ TMDs with 3d TM dopant next to the single X vacancy. Reprinted with permission from Ref. [77]. Copyright 2024 IOPscience.</figcaption></figure>

It is crucial to remember that each descriptor has limitations and challenges when studying alkaline HER in alkaline media. Descriptors such as water adsorption energy and water dissociation energy barriers serve as indicators of material reactivity. They are closely linked to the Volmer step, which encompasses the adsorption of water molecules and their subsequent dissociation into adsorbed hydrogen ($H^+$) and hydroxide ions ($OH^-$). These steps are fundamental to the overall HER process, yet they do not provide a complete picture of the catalytic site's capabilities, especially concerning the Heyrovsky and Tafel steps. The Heyrovsky step involves the electrochemical desorption of $H^+$ to form hydrogen gas.

The $\Delta G_{H^+}$ has been the most prevalent descriptor for assessing HER performance at the Heyrovsky and Tafel steps. It offers a measure of the free energy change when $H^+$ is adsorbed on the catalyst surface, which is a critical factor in determining the rate of the HER. However, $\Delta G_{H^+}$ alone is insufficient for evaluating the Volmer step or the desorption efficiency of adsorbed OH, which are also essential for a complete understanding of the HER mechanism.

The Gibbs free energy of hydroxide adsorption ($\Delta G_{OH^+}$) can be used to evaluate the desorption efficiency of adsorbed OH, providing insights into the potential for water dissociation, as suggested by the Bronsted-Evans-Polanyi (BEP) relationship [19]. This relationship posits a linear correlation between the activation energy of a reaction and the reaction enthalpy, allowing for the prediction of reaction barriers based on thermodynamic
parameters. However, it does not offer information on the catalyst’s performance during
the Heyrovsky or Tafel steps. Therefore, relying solely on $\Delta G_{OH*}$ would give an incomplete
assessment of a catalyst’s overall activity and efficiency.

Given these considerations, it is evident that no single descriptor can fully encapsulate
the complexities of the HER process. Researchers must carefully select and combine
multiple descriptors to gain a comprehensive understanding of the catalytic activity and
to design more efficient catalysts. This approach allows for the evaluation of catalysts
across all steps of the HER, ensuring a more accurate prediction of their performance in
real-world applications.

It is also worth noting that different descriptors may be required to understand the
performance of alkaline HER composite electrocatalysts. For example, Chen et al. designed
a complicated composite electrocatalyst including a Co dopant on WO₂/amorphous CoₓW
hybrid materials [51]. Using the water adsorption energy and dissociation energy barrier
energy as the descriptor, they found that the amorphous CoxW is the active site. However,
the analysis of the $\Delta G_{H*}$ descriptor indicates that Co-doped WO₂ is the active site for H₂ for-
mation. The DFT calculations then suggest that the individual component of this composite
electrocatalyst has a different function. The synergy between them enables the high alkaline
HER performance of this Co-Doped WO₂/amorphous CoₓW hybrid electrocatalyst.

**5. Conclusions and Outlook**

The hydrogen evolution reaction (HER) in alkaline media is a prominent method for large-scale hydrogen production from an electrolyzer. Alkaline Water Electrolysis (AWE) has demonstrated superior cost-effectiveness to acidic proton exchange membrane (PEM). One of the biggest challenges of AWE is ascribed to the relatively low energy conversion efficiency of their electrocatalysts. To address this issue, selecting the right computational tools for theoretical studies is essential in designing high-performance alkaline HER electrocatalysts. The descriptors used to evaluate the energy conversion efficiency of electrocatalysts include water adsorption energy, water dissociation barrier, Gibbs free energy change of hydrogen adsorption, and Gibbs free energy change of hydroxyl adsorption from DFT calculations. In the review, some of the latest examples have been used to illustrate the applications of different descriptors. It reveals that the hydroxyl ($\Delta G_{OH*}$) adsorption process is one of the important parameters often ignored in many previous theoretical studies. When the adsorption strength of hydroxyl is weak, it suggests a high water dissociation energy barrier due to the BEP relationship [19]. The water cannot effectively interact with the active site to provide an H atom intermediate. At the same time, the weak adsorption of OH also indicates that the dissolved hydroxide is via the Volmer (II) mechanism (Equation (6)), as shown in Figure 1. In this case, the $\Delta G_{H*}$ becomes a more important descriptor to analyze and predict the efficiency of an active site. It explains the great matches between some experimental measurements and the trend of the $\Delta G_{H*}$ descriptor in some combined studies.

The CHE model has evolved to include previously overlooked factors such as sol-
vent and electrolyte effects, reflecting its adaptability [18]. Despite these advancements,
a knowledge gap persists, particularly in the dynamic aspects of water splitting. A sig-
nificant hurdle remains in developing a more accurate model of the electrode–electrolyte
interface, which is crucial for pinpointing active sites in HER and connecting microscopic
interactions with macroscopic observations. The electrified solid–liquid interface in alkaline
HERs largely determines the charge transfer rate of electrochemical redox reactions [78].
Innovative approaches, such as engineering a localized acid-like environment within an
alkaline medium, have significantly boosted HER performance significantly [79]. This
is achieved by tailoring the local reaction conditions, which are critical for the process.
Moreover, understanding the impact of variables like electrolyte concentration on HER
allows for further refinement of reaction conditions [16]. The descriptors described in this
review can only provide limited dynamic information about the electrochemical processes
at the electrode–electrolyte interface [15,21,22]. This is because the atomistic models used
in most of these studies make it difficult to comprehend the thermodynamic state and dynamic properties of interfacial processes [21]. The interaction between water molecules and the electrified surface must be investigated by examining scenarios in which water molecules are introduced to the catalyst surface in various configurations [80]. Insights into the hydrogen bonding network and structural characteristics of the water layer can be derived from the average dipole orientation of water molecules relative to the surface normal [80]. Furthermore, the complex relationship among adsorbed hydrogen, water molecules, and the electrochemical environment, which influences the behaviors of adsorption and the overall characteristics of the interface between solid and water, needs to be investigated [81]. To comprehend the activities of HER intermediates in alkaline media, it is critical to know the potential and pH-dependent adsorption energies of these intermediates [82]. To this end, it is clear that theoretical studies on alkaline HER are still an area ripe for further research.

The intersection of machine learning (ML) with density functional theory and multiscale modeling is a burgeoning field that holds great promise for advancing materials science and chemistry [83–86]. By leveraging ML’s ability to analyze vast datasets and identify patterns, researchers can significantly reduce the computational resources required for DFT calculations. This synergy enables the prediction of complex chemical behaviors and the design of new materials with tailored properties. However, the success of the ML methods hinges on the quality and consistency of the data fed into the ML models [84]. As such, creating comprehensive and reliable databases is crucial for training algorithms that can accurately predict electrochemical behaviors and guide the development of efficient alkaline HER electrocatalysts. This integrated approach is set to transform the landscape of computational chemistry, offering a more streamlined and precise method for exploring the vast potential of chemical space. They can predict the performance of electrocatalysts, thereby informing the design of next-generation materials with enhanced catalytic properties. These concerted efforts in theoretical research are essential for the progression of clean energy technologies.

In sum, the exploration of electrocatalytic mechanisms in alkaline HER is a complex field that necessitates a comprehensive approach. Advancements beyond the DFT-calculated descriptors are critical for a deeper understanding. Operando simulations offer a dynamic perspective by considering actual working conditions, providing insights into the real-time structural and chemical changes during the reaction process. Meanwhile, ML-based force fields for classical molecular dynamics and Monte Carlo simulations represent a significant leap in mesoscale modeling, enabling simulations that capture the nuanced interactions within molecular systems. These ML models can bridge the gap between classical and quantum mechanical accuracy, offering a more detailed view of the catalytic processes. Lastly, ML-driven high-throughput screening is revolutionizing the way electrocatalysts are discovered and optimized. By analyzing vast datasets, ML algorithms can predict performance, stability, and efficiency, thereby accelerating the development of new materials for HER. Together, these methodologies form a multi-faceted approach that could significantly advance the field of electrocatalysis.

**Author Contributions:** Methodology, Formal analysis, Writing—original draft, S.A.O.; Writing—review & editing, F.M.; Writing—review & editing, Funding Request, A.B.; Writing—review & editing, J.J.H.; Writing—review & editing, L.Z.; Writing—review & editing, Z.W.; Writing—review & editing, S.B.; Writing—review & editing, Y.Z.; Project administration, Funding Request, Supervision, Conceptualization, Resources, Writing—review & editing, Y.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors acknowledge financial support from the Australian Research Council Discovery Project (Grant No. DP210103266, DP210104010). This research was conducted on the supercomputers in 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. Calculations were performed by using resources from Grand Equipement National de Calcul Intensif (GENCI,
grant no. A0120913426). Computational resources provided by the computing facilities Mésocentre de Calcul Intensif Aquitain (MCIA) of the Université de Bordeaux and of the Université de Pau et des Pays de l'Adour. We acknowledge funding from CNRS Institute of Chemistry through the "International Emerging Actions 2022" mobility grant (2DH2 project) and from Agence national de recherche under the RECIFE ANR-DFG project (Grant Number ANR-21-CE08-0036-01).

**Data Availability Statement:** The data presented in this study are available on request from the
corresponding author.

**Conflicts of Interest:** The authors declare no conflicts of interest.

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