Electrochemical Hydrogen Evolution at the Interface of Monolayer


Under typical conditions of HER, the catalyst surface is ... deteriorate the HER activity of VS2. KEYWORDS: .... fully relaxed through molecular dynam...
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Electrochemical Hydrogen Evolution at the Interface of Monolayer VS and Water Using First-Principles Calculations 2

Qiaoqiao He, Xiaobo Chen, Shiqi Chen, Lu Liu, Fangwang Zhou, Xi-Bo Li, and Guangjin Wang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b17075 • Publication Date (Web): 31 Dec 2018 Downloaded from http://pubs.acs.org on January 4, 2019

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Electrochemical Hydrogen Evolution at the Interface of Monolayer VS2 and Water Using First-Principles Calculations Qiaoqiao He,† Xiaobo Chen,*,† Shiqi Chen,† Lu Liu,† Fangwang Zhou,† Xi-Bo Li,† and Guangjin Wang‡,§ † Siyuan

Laboratory, Guangzhou Key Laboratory of Vacuum Coating Technologies and New

Energy Materials, Guangdong Provincial Engineering Technology Research Center of Vacuum Coating Technologies and New Energy Materials, Department of Physics, Jinan University, Guangzhou, Guangdong 510632, China. ‡

Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York

11973, United States. §College

of Chemistry and Materials Science, Hubei Engineering University, Xiaogan 432000,

China. KEYWORDS: hydrogen evolution, Pourbaix diagram, Vanadium disulfide, reaction mechanism, First-Principles

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ABSTRACT: Density functional theory (DFT) calculations are carried out to study the hydrogen evolution reaction (HER) at the electrochemical double-layer interface of monolayer 2H phase VS2 and water. Under typical conditions of HER, the catalyst surface is predicted to have a low hydrogen coverage of ca. 12% while the aqueous solution side features a high hydronium concentration of ca. 8.3%. As a result, the HER takes place through the Volmer-Heyrovsky route, with an overall reaction barrier of ca. 1.0 eV, much larger than that of 1T phase VS2. This result demonstrates that 2H phase VS2 is much less reactive than its 1T phase counterpart and the 1Tto-2H phase transformation induced by thickness reduction may deteriorate the HER activity of VS2.

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1. INTRODUCTION The hydrogen evolution reaction (HER) is becoming increasingly important for both the scientific community and human life because of the increasing demand of replacing fossil fuels with hydrogen as the next-generation energy.1,

2

Pt has been recognized as the most effective

catalysts towards hydrogen generation, but the commercial utilization of Pt is impeded by its low abundance and high cost.3 Among a variety of non-Pt catalysts, transition metal disulfides (TMDs), as represented by MoS2, have been studied extensively because of its low cost and diversity in both crystal phases and categories of active sites.4-8 2H phase is a common crystallographic form adopted by MoS2, which has reactive edges but is catalytically inert on its basal plane.9-11 Transformation from 2H phase to the 1T’ phase counterpart by means of chemical exfoliation induces significant enhancement in HER activity on both the edge and basal plane sites.5, 12, 13 VS2 is a group-V TMD, which also adopts the crystal structures of 2H and 1T phases like those of MoS2. However, the former has one d electron less than the latter in each of its formula unit (f.u.). As a result, VS2 presents ferromagnetic characteristic in both the semiconducting 2H phase and metallic 1T phase.14-16 Density functional theory (DFT) calculations for hydrogen adsorption free energies (ΔGH) predict that both 2H and 1T phases of VS2 are catalytically active toward HER.17-21 This is confirmed later by experiments, in which 1T-VS2 nanosheets presents ultralow overpotentials and ultrafast reaction kinetics.22,

23

The single site reaction rate even

outperforms that of Pt, which greatly stimulates the subsequent effort to reduce the thickness of 1T-VS2 nanosheets to obtain higher density of active sites.24, 25 However, the stability of 1T-VS2 decreases as the number of layers goes down, and at the few-layer or monolayer limit, the triangular prismatic 2H phase becomes more favorable, which has been theoretically predicted

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and experimentally observed.26, 27 Compared with the increasing reports of 1T-VS2, however, the knowledge on the catalytic activity of 2H-VS2 is extremely lacking, leaving the underlying effect of phase transformation during size reduction untouched. This brings about large uncertainties in experimental exploration of the HER activity of VS2 nanosheets by thickness engineering. Recent progress in theoretical simulation of HER using an electrochemical double-layer (EDL) interfacial model enables us to accurately predict the HER activity of a catalyst by combining thermodynamic analysis and accurate kinetic calculations.28, 29 In this work, we used this model to study the HER process at the interface of monolayer 2H phase VS2 (denoted as H-VS2 thereafter) and water. By constructing the Pourbaix diagram of the H-VS2/H2O interface, the surface hydrogen coverage is determined to be only ca. 12%, much lower than those of 1T-VS2 and MoS2. Kinetic barrier calculations show that the HER goes through the Volmer-Heyrovsky route, with a total reaction barrier of as high as 1.0 eV. We demonstrate that 2H-VS2 is much less reactive than its 1T phase counterpart and meanwhile indicates the possible loss of HER activity induced by phase transformation during thickness reduction. 2. MODELS AND METHODS 2.1. Structural Models. We constructed a Helmholtz double-layer (HDL) model to simulate the H-VS2/H2O interface, which consisted of a monolayer H-VS2 and two layers of water molecules (Figure 1a). In the normal direction, a vacuum layer of ca. 15 Å was used to prevent the electrostatic interaction of neighboring structural images. A rectangular supercell of 8 VS2 f.u. with 12 water molecules covered on the surface was adopted for calculations, as shown in Figure 1b. Proton number in this system could be engineered by changing the number of hydrogen atoms involved in the HDL. Hydrogen atoms are either solvated in the solution to form protons or adsorbed on the catalyst surface. Water network was fully relaxed through molecular

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dynamic modelling and geometry optimization. This interfacial model simulates the realistic scenario of a HDL in an acid electrolyte, in which only hydroniums are involved.

Figure 1. Helmholtz double-layer (HDL) model of the H-VS2/H2O interface. (a) is the side view and (b) is the top view. The 2×2 supper cell within the black box in (b), which includes 8 VS2 formula units and 12 water molecules, is selected for calculations.

2.2. Calculation Methods. Spin-polarized DFT calculations were performed on the interfacial system using the Vienna Ab-initio Simulation Package (VASP) with the Projector Augment Wave (PAW) potential.30-32 To describe the weak van der Waals (vdW) interactions involved in the interfacial system, we employed the optB86b scheme for the exchange-correlation functional.33-35 A high cutoff energy of 500 eV was set for the plane wave expansion, and a dense 4×8 Monkhorst-Pack k mesh was used for the selected supercell. All structures were relaxed to ensure that forces acting on atoms were not larger than 0.02 eV/Å. Dipole correction was introduced in all calculations. The Climbing-Image Nudged Elastic Band method (CI-NEB) was used to determine the transition states of all fundamental reactions.36 Zero point energies and entropies were obtained following the methods described in Supporting Information (SI).

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2.3. Electrochemical Free Energies. A reasonable interfacial model that well simulates the realistic HDL should represent the lowest total chemical potential of protons and electrons (i.e. the electrochemical potential 𝜇H + + e ― ) at given electrode potential USHE and pH.29 𝜇H + + e ― = ―e𝑈SHE ―2.3𝑘𝑇PH (1) Here USHE is the electrode potential relative to the standard hydrogen electrode (SHE), which is determined by calculating the work function Φ of the interfacial model. 𝑈SHE = (𝛷 ― 𝛷SHE)/e

(2)

ΦSHE is experimentally determined to be 4.44 eV.37 At the electrochemical equilibrium condition (i.e. 𝜇H + + e ― = 0), it is more convenient to calculate the electrochemical free energy (𝐺H + + e ― ) of protons and electrons than to evaluate 𝜇H + + e ― , 𝐺H + + e ― (𝜇H ― + e ― = 0) =

𝐺(𝑁,𝑛) ― 𝐺(𝑁,0) 𝑁

𝑛

― 2𝑁𝐺H2 (3)

where 𝐺H2 refers to the free energy of a hydrogen molecule at 298.15 K and 1 atm. G(N, n) is the free energy of a HDL system containing n protons, while G(N, 0) is that of the reference system without protons. N gives the number of H2O molecules. For conditions away from the electrochemical equilibrium, 𝐺H + + e ― changes with USHE and pH following a linear dependence,38 𝑛 𝐺H + + e ― (𝜇H + + e ― ) = 𝐺H + + e ― (𝜇H + + e ― = 0) ― 𝜇H + + e ― (4) 𝑁 Using eq. (1) – (4), one can obtain the electrochemical free energy of an interfacial system at any condition of electrode potential and pH. A set of interfacial structures have been considered, which are different from each other in proton concentration (n/N), proton distribution and water molecular orientation. By screening the HDL structures with the lowest free energies at different

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potentials and pH’s, one can plot the Pourbaix diagram that is important to determine the reaction barriers of all the fundamental reactions. 3. RESULTS AND DISCUSSION 3.1. Pourbaix Diagram. Figure 2a, b show the calculated 𝐺H + + e ― at different USHE for interfacial structures of different proton concentrations. The scenarios for pH = 0 and 14 are presented, while that for pH = 7 is shown as Figure S1. Data for different proton concentrations are indicated by different colors, while those for different proton distributions are differentiated by different symbol shapes. Overall, protons are solvated in solution in the form of hydroniums at negative potentials but are adsorbed on the catalyst surface at relatively positive potentials. Because the overall orientation of water layers also influences the free energy and electrode potential of a system, the number ratio of H-up water molecules (↑) to those of H-down ones (↓) is included for consideration by means of symbols’ size.

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Figure 2. Linear dependence of 𝐺H + + e ― (𝜇H + + e ― ) on USHE for the H-VS2/H2O interfacial system of different proton concentrations at (a) PH=0 and (b) PH=14. (c) Pourbaix diagram for the H-VS2/H2O interface at different USHE and PH. Structural characteristics on proton concentration (n/N), proton distribution and water molecular orientation are included. Data for different proton concentrations are indicated by the color bar. A negative proton concentration denotes the concentration of hydroxyls in the HDL. (d) Information on proton distribution and water molecular orientation. Hydroniums and adsorbed protons are indicated by Psol and Pad, respectively. Slashes used in the latter two cases of proton distribution in (d) indicate possible adsorbates on the catalyst surface.

When pH = 0, the whole potential range is divided into four regions, each of which is dominated by one proton concentration. When pH increases, all these regions move to the negative side. By linearly interpolating the structural characteristics from pH = 0 to pH =14, a

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Pourbaix diagram that includes the interfacial structural information on protonic concentration and distribution and water molecular orientation is plotted in Figure 2c. Consistent with Figure 2a and b, the Pourbaix diagram presents four phase regions. In region IV, the catalyst surface is covered by hydroxyls, with a ratio of 1/8. When USHE decreases, all hydroxyls disappear gradually, and instead, protons appear in the HDL. Meanwhile, the overall water orientation transforms gradually from H-up water molecules to H-down ones. For each of the phase regions, decrease of USHE leads to transfer of protons from the catalyst surface to the solution. In region II, the shaded area represents the experimental HER conditions, where USHE lies in between -0.3 and 0 V and pH ranges from 0 to 1. Within this region, the HDL features a high hydronium concentration of 8.3% (one hydronium in a supercell) while the catalyst surface has a relatively low proton coverage of 12.5%. This is in large contrast to the simulated HDL of 1T’MoS2, where the hydronium concentration is no more than 1.8% while the catalyst surface coverage reaches as high as 37%.29 Considering the low surface proton coverage of H-VS2, the proton desorption process is not likely to go through the Tafel manner. Instead, the Heyrovsky process probably dominates. In the section 4 of SI, we discussed the possible influence when more water molecules are added in the simulated super cell. In the following, we will use the most stable interfacial structures represented by the Pourbaix diagram to calculate the kinetics of the fundamental reaction steps of HER.

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Figure 3. Top: Structures of the initial state (IS), transition state (TS) and final state (FS) of a Volmer reaction at an electrode potential of -0.03V. The proton transferring from the solution to the catalyst surface is indicated by a blue ball. Bottom: (a) Black dots: DFT-calculated reaction path of the Volmer reaction. Red stars: reaction path corrected by the charge-extrapolation scheme. ν indicates the only imaginary frequency of the TS structure. (b) Work function (red stars) and interfacial dipole moments (blue dots) along the reaction path.

3.2. Reaction Mechanism. We first examine the Volmer reaction, in which a proton in solution is transferred onto the top site of an S atom of the catalyst surface. An interfacial structure with its electrode potential close to the equilibrium potential (USHE = -0.03 V) is selected as the initial state (IS). In this structure, a hydronium is solvated in solution and a proton is adsorbed on the catalyst surface. This manner of proton distribution typically represents the most stable configuration under the experimental HER conditions. The IS, transition state (TS) and final state (FS) structures along the reaction pathway are displayed on the upper panel of Figure 3. The reaction minimum energy pathway (MEP) is shown in Figure 3a (black line), while the changes of work function and interfacial dipole moment along the MEP are plotted in

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Figure 3b. In Figure S2, we also show the charges transferred across the interface along the reaction route. Obviously, the change of work function follows that of interfacial dipole moment, indicating that the electrode potential of the interfacial system is actually set up by the interfacial dipole moment. Since the work function deviates from the IS by more than 1 eV induced by the small supercell size, the MEP is corrected by the charge-extrapolation scheme.28 The corrected result is displayed by the red line in Figure 3a, which differs from the uncorrected one primarily in the last half of the reaction route due to the large change of work function. After correction, the Volmer reaction exhibits an exothermic nature, with a reaction energy Er = EFS - EIS = -0.27 eV. The corrected reaction barrier Ea = ETS – EIS = 0.21 eV, indicating that the Volmer reaction is quite easy to go under HER conditions. This is consistent with the scenario of MoS2, where a facile Volmer process is also found.29, 39 The Heyrovsky reaction is then examined, in which a hydronium in water reacts with a proton adsorbed on H-VS2 to form a H2 molecule. The interfacial structure used to model the Volmer reaction is utilized again as the IS of the Heyrovsky reaction. The reaction MEP, together with the charge-extrapolation corrected result, is plotted in Figure 4a, while the changes of work function and interfacial dipole moment are displayed in Figure 4b. Similar to the Volmer reaction, the Heyrovsky process is exothermic, with an Er of -0.75 eV. However, the calculated reaction barrier is as large as 1.45 eV. Even with the zero point energy and entropy corrected, the free energy barrier of room temperature (ΔGRT) is still 1.05 eV, not small enough for efficient formation of H2 molecules.

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Figure4. Top: IS, TS and FS structures of the Heyrovsky reaction at USHE = -0.03V. The protons reacting to form a H2 molecule are indicated by blue balls. Bottom: (a) Black dots: DFT-calculated reaction path of the Heyrovsky reaction. Red stars: reaction path corrected by the charge-extrapolation scheme. ν indicates the only imaginary frequency of the TS structure. (b) Work function (red stars) and interfacial dipole moments (blue dots) along the reaction path.

We also examine the possibility of the Tafel reaction, in which two protons adsorbed on neighboring surface sites combine to form a H2 molecule. The selected IS structure has an electrode potential of -0.65 V, which contains four adsorbed protons on the catalyst surface and no hydroniums in water. This structure represents the most stable interfacial configuration in the region indicated by green lower triangles (Figure 2c). The MEP for this reaction is shown in Figure 5a, in which the DFT calculated energies are nearly identical to those corrected by the charge-extrapolation scheme. This is because there is no charge transferred across the interface during the reaction. The reaction barrier is calculated to be 1.37 eV, which becomes 1.20 eV when the zero point energy and entropy are corrected.

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In a similar way, ΔGRT for the Tafel reactions at several different potentials are obtained, which are plotted in Figure 5b. Through a linear extrapolation, the free energy barrier at USHE = 0 V is determined to be 1.34 eV, much higher than that of the Heyrovsky reaction. This demonstrates that the proton desorption process occurs through the Heyrovsky manner. The reason for this could be ascribed to the unique H-VS2/H2O interfacial configuration, which has a low proton coverage of 12.5% on the catalyst surface and a high hydronium concentration of 8.3% in solution.

Figure5. Top: IS, TS and FS structures of the Tafel reaction at USHE = -0.65 V. The adsorbed protons reacting to form a H2 molecule are indicated by blue balls. (a) Black dots: DFT-calculated reaction path of the Tafel reaction. Red stars: reaction path corrected by the charge-extrapolation scheme. ν indicates the only imaginary frequency of the TS structure. (b) Tafel reaction barrier as a function of electrode potential.

Under the condition of USHE = 0 V and pH = 0.3, the exchange current density of 1T-VS2 nanosheets is experimentally measured to be 0.955 mA·cm-2,22 which corresponds to a turnover frequency (TOF) of 4.96 s-1site-1. With the expression of reaction rate,

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𝑘=

𝑘𝐵𝑇 ℎ

𝑒𝑥𝑝 (

―∆𝐺𝑅𝑇 𝑘𝐵𝑇

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) (5)

the corresponding reaction barrier is estimated to be 0.72 eV, much lower than that of 0.87 eV experimentally estimated for 1T’-MoS2 in a similar manner.5, 29 Since the experimental condition of 1T’-MoS2 is the same with that of 1T-VS2, this comparison indicates that the HER activity of 1T-VS2 is much higher than that of 1T’-MoS2. In fact, we also predicted a reaction barrier of 0.91 eV for the HER on 1T’-MoS2 in our previous work, which is in good agreement with the experimentally estimated result of 0.87 eV.29 Considering that the calculation accuracy of 1T’-MoS2 is also consistent with that of H-VS2 in this work, we can compare the HER activity of 1T’-MoS2 and H-VS2 from their DFT calculated barriers. By regulating the chemical potential of protons to the case of pH = 0.3, ΔGRT of the HER on H-VS2 is calculated to be 1.0 eV under the experimental condition, which is higher than that of 1T’-MoS2 (0.91 eV). This demonstrates a descending HER activity order of 1T-VS2 > 1T’-MoS2 > H-VS2. In other words, once a phase transformation occurs upon thickness engineering of 1T-VS2 nanosheets, the HER activity will be greatly deteriorated. 4. CONCLUSIONS In summary, the HER activity of monolayer H-VS2 is studied by modelling the H-VS2/H2O interfacial structure and calculating the fundamental reaction steps of HER. By screening the HDL structures with the lowest chemical potential of protons and electrons, we find that the interfacial system has a low surface proton coverage of ca. 12% and a high hydronium concentration of ca. 8.3% under the experimental HER condition. As a result, the HER takes place preferentially through the Volmer-Heyrovsky route and the proton desorption process is the rate-limiting step. The overall reaction barrier is determined to be 1.0 eV, much higher than that experimentally estimated for 1T-VS2. Our results demonstrate that 2H phase VS2 is much

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less reactive than its 1T phase counterpart and indicate possible loss of HER activity due to the 1T-to-2H phase transformation induced by thickness reduction.

ASSOCIATED CONTENT Supporting Information. Supplementary figures and tables, calculation details for zero-point energies and entropies, adsorption of water layers onto the catalyst surface, Pourbaix diagram for supercells with more water molecules included. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *[email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENT The high-performance computing platform of Jinan University and the Guangzhou Key Research Center of Public Opinion and Big Data are thanked for providing computational support. This work is supported by the National Natural Science Foundation of China (NO. 21303237, 21703081 and 21802037), the Natural Science Foundation of Guangdong Province (NO. 2018A030313386), the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (No. U1501501), the Fundamental Research Foundation for the

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Central Universities (NO. 21617330), and the Natural Science Foundation of Hubei Province (NO. 2018CFB669). REFERENCES (1) Turner, J. A. Sustainable Hydrogen Production. Science. 2004, 305, 972-974. (2) Hou, Y.; Abrams, B. L.; Vesborg, P. C.; Bjorketun, M. E.; Herbst, K.; Bech, L.; Setti, A. M.; Damsgaard, C. D.; Pedersen, T.; Hansen, O.; Rossmeisl, J.; Dahl, S.; Norskov, J. K.; Chorkendorff, I. Bioinspired Molecular Co-Catalysts Bonded to a Silicon Photocathode for Solar Hydrogen Evolution. Nat. Mater. 2011, 10, 434-438. (3) Faber, M. S.; Jin, S. Earth-Abundant Inorganic Electrocatalysts and Their Nanostructures for Energy Conversion Applications. Energy Environ. Sci. 2014, 7, 3519-3542. (4) Merki, D.; Hu, X. Recent Developments of Molybdenum and Tungsten Sulfides as Hydrogen Evolution Catalysts. Energy Environ. Sci. 2011, 4, 3878-3888. (5) Yin, Y.; Han, J.; Zhang, Y.; Zhang, X.; Xu, P.; Yuan, Q.; Samad, L.; Wang, X.; Wang, Y.; Zhang, Z.; Zhang, P.; Cao, X.; Song, B.; Jin, S. Contributions of Phase, Sulfur Vacancies, and Edges to the Hydrogen Evolution Reaction Catalytic Activity of Porous Molybdenum Disulfide Nanosheets. J. Am. Chem. Soc. 2016, 138, 7965-7972. (6) Hinnemann, B.; Moses, P. G.; Bonde, J.; Jørgensen, K. P.; Nielsen, J. H.; Horch, S.; Chorkendorff, I.; Nørskov, J. K. Biomimetic Hydrogen Evolution,  MoS2 Nanoparticles as Catalyst for Hydrogen Evolution. J. Am. Chem. Soc. 2005, 127, 5308-5309. (7) Karunadasa, H. I.; Montalvo, E.; Sun, Y.; Majda, M.; Long, J. R.; Chang, C. J. A Molecular MoS2 Edge Site Mimic for Catalytic Hydrogen Generation. Science. 2012, 335, 698-702.

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(25) Qu, Y.; Shao, M.; Shao, Y.; Yang, M.; Xu, J.; Kwok, C. T.; Shi, X.; Lu, Z.; Pan, H. UltraHigh Electrocatalytic Activity of VS2 Nanoflowers for Efficient Hydrogen Evolution Reaction. J. Mater. Chem. A. 2017, 5, 15080-15086. (26) Zhang, H.; Liu, L.-M.; Lau, W.-M. Dimension-Dependent Phase Transition and Magnetic Properties of VS2. J. Mater. Chem. A. 2013, 1, 10821-10828. (27) Zhou, J.; Wang, L.; Yang, M.; Wu, J.; Chen, F.; Huang, W.; Han, N.; Ye, H.; Zhao, F.; Li, Y.; Li, Y. Hierarchical VS2 Nanosheet Assemblies: A Universal Host Material for the Reversible Storage of Alkali Metal Ions. Adv. Mater. 2017, 29, 1702061. (28) Chan, K.; Nørskov, J. K. Electrochemical Barriers Made Simple. J. Phys. Chem. Lett. 2015, 6, 2663-2668. (29) Chen, S.; Chen, X.; Wang, G.; Liu, L.; He, Q.; Li, X.-B.; Cui, N. Reaction Mechanism with Thermodynamic Structural Screening for Electrochemical Hydrogen Evolution on Monolayer 1T ′ Phase MoS2. Chem. Mater. 2018, 30, 5404-5411. (30) Kresse, G. F., J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B. 1996, 54, 11169-11186. (31) Kresse.G , J. D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B. 1999, 59, 1758-1775. (32) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B. 1994, 50, 17953-17979. (33) Dion, M.; Rydberg, H.; Schroder, E.; Langreth, D. C.; Lundqvist, B. I. Van Der Waals Density Functional for General Geometries. Phys. Rev. Lett. 2004, 92, 246401. (34) Roman-Perez, G.; Soler, J. M. Efficient Implementation of a Van Der Waals Density Functional: Application to Double-Wall Carbon Nanotubes. Phys. Rev. Lett. 2009, 103, 096102.

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(35) Klimeš, J.; Bowler, D. R.; Michaelides, A. Van Der Waals Density Functionals Applied to Solids. Phys. Rev. B. 2011, 83, 195131. (36) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 99019904. (37) Randles, J. E. B. The Real Hydration Energies of Ions. Trans. Faraday Soc. 1956, 52, 15731581. (38) Rossmeisl, J.; Chan, K.; Ahmed, R.; Tripkovic, V.; Bjorketun, M. E. PH in Atomic Scale Simulations of Electrochemical Interfaces. Phys. Chem. Chem. Phys. 2013, 15, 10321-10325. (39) Tang, Q.; Jiang, D. Mechanism of Hydrogen Evolution Reaction on 1T-MoS2 from First Principles. ACS Catal. 2016, 6, 4953-4961.

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