Uncovering the Surface and Phase Effect of Molybdenum Carbides on

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Uncovering the Surface and Phase Effect of Molybdenum Carbides on Hydrogen Evolution: A First-Principles Study Guang-Qiang Yu, Bo-Ying Huang, Xiaobo Chen, Da Wang, Feipeng Zheng, and Xi-Bo Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04461 • Publication Date (Web): 14 Aug 2019 Downloaded from pubs.acs.org on August 14, 2019

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The Journal of Physical Chemistry

Uncovering the Surface and Phase Effect of Molybdenum Carbides on Hydrogen Evolution: a First-Principles Study Guang-Qiang Yu 1, Bo-Ying Huang1, Xiaobo Chen1, Da Wang2, Feipeng Zheng1*, Xi-Bo Li1* 1

Siyuan Laboratory, Guangzhou Key Laboratory of Vacuum Coating Technologies and New Energy Materials, Department of Physics, Jinan University, Guangzhou 510632, Guangdong, PR China 2 School of Materials Science and Engineering, Shanghai University, Shanghai 200444, PR China *Corresponding Email: [email protected] (Pro. Zheng); [email protected] (Pro. Li).

Abstract Molybdenum carbides show great potential to replace platinum for electrocatalytic hydrogen evolution reaction (HER) to resolve the problem of hydrogen production, as their high reserves, stabilities, low cost, and structural diversity. However, the effect of atomic configurations of different surfaces on HER are still lacking theoretical insights. In this work, the HER activity on twenty-nine surfaces of seven phases are systematically explored by density-functional theory, taking account of water effect. The exchange current for each surface is also given. Totally, there are nine surfaces which own high exchange current (>0.1 mA/cm2), especially the hydroxylated (014)–C and (010) of TiP–MoC, (110) of β–Mo2C, and (100)–C of α–Mo2C (1.410, 0.835, 0.687, and 0.464 mA/cm2, respectively). Combing with the stabilities of the surfaces for each phase, the phases with high HER activity could be also screened out. The electronic properties, including electron transfer to adsorbed hydrogen and the shift of the electronic states coupled by oxygen and adsorbed hydrogen orbitals, are applied to uncover the termination of surface and water effect on HER. Our results are expected to contribute to the understanding of the HER on different surfaces of molybdenum carbides, and give some evidence for control synthesis of high HER activity surfaces.

1. Introduction Hydrogen is regarded as a promising candidate of clean and renewable energy in future. It could be obtained via splitting water by sunlight or electricity. Hydrogen evolution reaction (HER) is one critical step of water splitting. In order to make the HER more effective, active and stable catalysis are required. Although Pt based materials are effective catalyst for HER and related fuel cell,1-6 its low reserve and high price prohibit its commercial applications. Replacement of noble metal by earth abundant materials is desirable for the industry of hydrogen production. Recently, many kinds of no-noble transition metal compounds are explored and applied to HER catalysis. The transition-metal compounds, including transitionmetal phosphides,7-9 dichalcogenides,10-13 borides,14-15 nitrides,16-18 and carbides,19-27 and as well as other metal-free catalysis,28-31 have been greatly explored for HER. Among them, the transition metal carbides, especially the molybdenum carbides (MoxC, x = 1, 2) are widely 1

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studied as the abundant storage of the Mo, the long-term stability in both acid and alkaline environment, the convenient synthesis method, and high HER activity.20-27, 32-34 Molybdenum carbide could exist in different phases, and some experimental results show β-Mo2C exhibits higher HER activity than other phases.20 In fact, the HER activity is not only dependent on the phase and surface of a given phase, but also the different termination of the surface, such as previous work about nickel phosphides.35-36 Those factors may make the MoxC exhibit different HER activities as experimental conditions differ. Unlike the detail discussions about the HER on nickel phosphides in previous studies,35-39 seldom similar theoretical study has been carried out to elucidate the inherent relationship between the HER activities and the atomic configurations, electronic properties of the surfaces of the different phases. Thus, it’s necessary to uncover phases and surfaces dependence of MoxC on HER. Herein, first-principles calculations are carried out to explore the HER activities on surfaces of different phases of molybdenum carbides. First, atomic configurations and stabilities of seven phases of molybdenum carbides and the relative stabilities of their surfaces are discussed. Second, all possible adsorption sites for hydrogen and water effect on each surface are considered. Basing on them, we could determine whether the surface is free of *O and *OH (bare surface), or covered by *O (oxygenated surface), or *OH (hydroxylated surface), or both of *O and *OH (oxygenated/hydroxylated surface). In the following, the free energy change of hydrogen at different hydrogen coverages on the bare, oxygenated, hydroxylated, or oxygenated/hydroxylated surfaces (the later three kinds surfaces that are not bare are collectively called “covered surfaces” for simple) are explored, and the exchange current for each surface at determined hydrogen coverage is also given to reflect HER activity in real conditions. In the end, the relationship between the electronic properties and the adsorption ability of hydrogen, which also includes the electron transfer and water effect, are further uncovered. Combing with the stabilities of the surfaces for each phase, the surfaces and phases with high HER activity could be screened out. As a comprehensive study, those DFT results could benefit the control synthesis of certain surfaces of molybdenum carbide for HER electrocatalysts.

2. Computational Methods All calculations were conducted with the Vienna ab initio simulation (VASP)40-41 package. The exchange–correlation potential was described by the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof (PBE).42 And the van der Waals interactions were not considered in this work. The plane-wave cut-off energy was chosen to be 400 eV. A k-point distance of 0.02/Å in reciprocal space based on the Monkhorst-Pack43 scheme was applied for all structural relaxations, and the structural optimization process was performed until the final force on each atom was less than 0.02 eV/Å. In order to prevent the interaction between the periodic images ， a vacuum space of 15 Å was added in each slab model. The slab models contain 4~9 atomic layers with the bottom 2~4 ones fixed. In order to access the stability of the bulk in each phase, the bulk cohesive energy is defined as following: Ecoh = (nMoEMo + nCEC – Ebulk)/NMoxC (1) where the Ecoh stands for the cohesive or binding energy of the molybdenum carbide, the Ebulk stands for the energy of relaxed bulk, the EMo and EC stands for the energy of isolated Mo atom 2


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and C atom, respectively. The nMo, nC and NMoxC stands for the number of Mo atoms, C atoms, and formula units, respectively. In order to explore the stabilities of surfaces, the surface energy is calculated as following: Esur = (Eslab – mEbulk)/A (2) where the Esur, Eslab and Ebulk denote the surface energy of the relaxed surface, the energy of slab model of a relaxed surface, and the energy of the relaxed bulk, respectively. m stands for the number of bulk units that a given surface contains, and A is the area of the given slab. The more accurate and systematic discussions about the stability of surfaces should consider the local chemical of Mo or C, just as the previous work about nickel phosphides. 44 However, the access of relative stabilities of surfaces by Eq.2 in this work is still reliable in some extent. The total HER can be expressed in two steps, adsorption step and desorption step. In the adsorption step, an electron transfers to a proton at the catalyst surface and provides an intermediate state of an adsorption hydrogen atom at an active site (the Volmer reaction): H+ + e− → Had. The free energy change of the adsorption hydrogen atom could be obtained by ΔGmH= ΔEmH + ΔEZPE – TΔS, ΔEmH = E[mH] – E[(m – 1)H] – 1/2 E[H2]. The ΔEZPE and TΔS are zero-point energy and entropy corrections, respectively. For all the surfaces, ΔEZPE – TΔS is determined to be ca. 0.24 eV at Mo site and ca. 0.31 eV at C site, respectively. E[mH] is the total energy of a surface with m hydrogen atoms adsorbed, while E[H2] is the energy of a hydrogen molecule. The corresponding value at Mo site is the same as that on metal surface2. The different values on the two kinds sites are mainly caused by the different bonding type while H adsorbs at corresponding site. The corresponding chemical bonding type for Mo-H and C-H is metallic and covalent bonding, respectively, which could be seen from the transferred electron as shown in Figure 6 (0.36~0.70 e for H at Mo site, and -0.08~0.17 e for H at C site). The less transferred electron indicates more degree of freedom, or larger vibrational motion, which lead to larger zero-point energy. This why the ΔEZPE – TΔS at C site is larger than that at Mo site. As a good catalysis for HER, the ΔGmH should be close to 0 eV. In this work, we mainly focus on the surfaces which own |ΔGmH| < 0.20 eV. The exchange current is used to evaluate the HER activity of a catalyst,2 i0= −ek0/(1+exp(|G|/kT) (3) G is the reaction free energy of the rate-limiting step. The rate constant k0 is taken as 200s1site-1.2 In addition, our calculated data are in standard condition, U=0 V, pH = 0 and T = 298.15 K.

3. Results and Discussions 3.1 Bulk Properties and Surfaces of MoxC (x =1, 2) Totally, five different MoC phases and two different Mo2C phases are explored in this work, and the detail atomic configurations of the corresponding unit cells are shown in Figure 1. It should be noted that the notation is defined by the Joint Committee on Power Diﬀraction Standards (JCPDS) data files as previous work.45 The five MoC phases are δ-MoC,46-47 αMoC,45, 48 G-MoC,49 η-MoC20, 50-51 and TiP-MoC48, 50(it is called as γ' in ref. 42 and 44), as shown in Figure 1c, d, e, f and g, respectively. The two Mo2C phases are β-Mo2C21, 45, 52-55 and α-Mo2C,53-54, 56 as shown in Figure 1a and b, respectively. The structural parameters of different MoxC(x =1, 2) phases, which contains space group, number of formula units, lattice parameters, cohesive energy, as well as theoretical and experimental data from previous literature are listed 3



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in Table S1. The larger the cohesive energy, the more stable the corresponding MoxC. Thus, the stability of the seven MoxC is order of β-Mo2C, α-Mo2C, α-MoC, G-MoC, TiP-MoC, ηMoC, δ-MoC (Table S1), which is consistent with previous work45. Noticeably, all calculated lattice parameters are in good agreement with previous results (within 2% error).

Figure. 1 Atomic configurations of the molybdenum carbides in different phases. (a) β-Mo2C, (b) α-Mo2C, (c) δ-MoC, (d) α-MoC, (e) G-MoC, (f) η-MoC, and (h) TiP-MoC. The red upward and rightward arrows indicate the z directions for (a)-(e) and (f)-(g), respectively. The blue and grey balls indicate the Mo and C atoms, respectively. The dashed lines indicate the unit cell.

The δ-MoC (Figure 1c) displays a NaCl like FCC arrangement with each Mo atom bonds six C atoms, the α-MoC (Figure 1d) forms a hexagonal close packed (HCP) structure with alternating Mo and C layers, the G-MoC (Figure 1e) has staggered Mo atom in two layers along the xy plane and one more C layer between two adjacent Mo layers, η-MoC is a hexagonal structure with ABCABC stacking, the TiP-MoC (Figure 1g) also forms HCP structure with alternating two Mo and two C layers. In β-Mo2C (Figure 1a), the atoms form an orthorhombic structure in which C atoms occupy half octahedral interstitial sites available in one layer, and the remaining octahedral sites in the next carbon layer. α-Mo2C (Figure 1b) is obtained from in a way of moving half of C in a 2 × 2 × 2 supercell of α-MoC. In sum, the MoC phase displays as each Mo (C) atom has six nearest chemical bonds with C(Mo) atoms, whereas the Mo2C phase displays as each Mo (C) atom has three (six) chemical bonds with C(Mo) atoms. One could turn to “CIF-FILE” which contains atomic configurations for more detail information. Table. 1 Surface energies of different surfaces of each MoxC (x =1, 2) phase. The “mnk–Mo” and “mnk– C” and “mnk” denote (mnk) surface is only terminated by Mo, C, and Mo and C atoms, respectively. The Mom(Cm) indicates the Mo(C) in the top layer has m chemical bonds, e.g., the C5 indicates it has five chemical bonds with Mo atoms, or one broken bond comparing with that in bulk of MoC (as each C atom has six chemical bonds with Mo atoms in bulk of MoC). According to this definition, we could clearly show how the atom in one surface differ from that in bulk one, and that in the other surfaces. The corresponding C5 and C3 atoms are as shown in Figure S1a and S1d, respectively. The bold ones indicate the most favored surface for given phase. Phase Surface

δ–MoC 001

110

α–MoC

111–Mo

111–C

001–Mo/C

100–C

G–MoC 110

001–

110

010

C4, Mo4

C4, Mo4

Mo/C Term.

C5, Mo5

C4, Mo4

Mo3

C3

Mo3/C3

C4

4


C4, Mo4

Mo3/C3

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Es(J/m2)

2.17

6.75

Phase

6.17

13.88

10.66/8.99

η–MoC

4.65

7.26

001–Mo

001–C

110

0-14

010

110

014

Term.

Mo3

C3

C4, Mo4

C4, Mo4,

C4, C5,

C4, Mo4

C4, Mo4,

C5, Mo5

Mo5

4.71

3.82

Es

6.93

6.13

6.79

5.58

TiP–MoC

Surface

(J/m2)

9.08/7.88

5.69

Phase

C5, Mo5 5.41

5.02

β–Mo2C

α–Mo2C

Surface

100–Mo

100–C

001–C

110–C

110–Mo

111-C

001–C

001–Mo

100–C

011-C

Term.

Mo1,

Mo3, C3,

C3

C4, C5,

Mo2

C3,

C3

Mo1,

C3

C4, C5

Mo2 Es

(J/m2)

7.19

Mo3 6.43

6.80

8.91

C4,Mo3, 8.71

3.27

Mo2 6.62

6.91

Mo3 6.71

6.22

According to the seven MoxC phases above, 29 kinds of surfaces are constructed and their corresponding atomic configurations are shown in Figure S1-S7. Once the surface is cleaved from the bulk above, the number of the chemical bonds of atoms in top layer will be reduced, leading to the difference of the chemical properties from that of bulk. In order to explore the stability of the surfaces, the surface energies are calculated and listed in Table 1. It clearly shows that the stability of surface (surface energy) has an approximately positive (negative) relationship with the number of the chemical bonds of atoms in top layer of the surface for a given MoxC. The more the chemical bonds, or less broken bonds for atoms in top layers, the more stable the surface. For example, the (001) (2.17 J/m2) which is terminated by C5 and Mo5 is the most stable surface of δ-MoC, while the (111)-C (13.88 J/m2) which is terminated by C3 is the most unstable one. Furthermore, the stability may differ a lot as the different termination for the same surface index, e.g., the formation energies for (111)-C and (111)-Mo of δ-MoC are 13.88, 6.17J/m2, respectively. The most stable surface for each MoxC is labelled in bold characters in Table 1. In addition, the (001) and (111)-C is the most stable surface of δ-MoC and β-Mo2C discussed in this work, respectively, which is in accord with previous results in literature and indicates the reasonability of our results. 45 3.2 Hydrogen Adsorption on Surfaces of MoxC (x =1, 2) The possible adsorption sites for hydrogen are classified into four kinds, top, bridge, hcp and fcc site on considered surfaces of each MoxC as shown in Figure S1-S7. The adsorption ability of H (ΔGH) on different sites of considered surfaces are calculated and listed in Table S2-S8. The adsorption ability of H is dependent on the number of chemical bonds of the adsorption site, as shown in Figure 2. It clearly shows the H adsorption ability has a strongly positive relationship with the number of broken bonds of Mo or C atom in surface. While the H adorbs on C site of MoC phase related surfaces, the ΔGH have a decreased trend from C5 with one broken bond to C3 with three broken bonds. The corresponding values of ΔGH are in range of 0.50~-0.25 eV, -0.24~-0.75 eV and -0.75~1.25 eV on top of C5, C4 and C3, respectively, as shown in Figure 2a. The similar trends also appear on Mo site of MoC phases, Mo and C site of Mo2C phases. Those trends could give us guidance to determine the active site of MoxC surfaces, e.g., the possible active sites are Mo4, top of Mo3, and top of C5 on MoC surfaces, and Mo3 and C4 site on Mo2C surfaces, respectively, as indicated in grids part of Figure 2. In addition, there are only top site for the C atoms, as the larger distance between C atoms. The 5



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bond length between H and atoms in top layer could be applied to distinct its adsorption site: the values for H on top of C, top of Mo, bridge of Mo, fcc or hcp of Mo are about 1.12 Å, 1.74 Å, 1.84~1.97 Å, 2.00~2.27 Å, respectively. Those results could give some theoretical guidance in HER experiments. In addition, the water effect is not considered in this part.

Figure. 2 The free energy of adsorbed H (ΔG) on different sites of (a) MoC and (b) Mo2C surfaces. The “Mo5” and “C4” indicate that the adsorbed sites of Mo and C have five and four chemical bonds with C and Mo, respectively. The “T”, “Bri”, “HCP”, and “FCC” indicate the top, bridge, hcp and fcc site, respectively. The grids area indicates the ΔG is range of -0.25~0.25 eV. The blue solid circles in (a) denote the adsorbed C site will change their bonding behavior after H adsorption, e.g., the ones in the “C5”, “C5” and ““C3, C2”” part will change from the C5, C4 and C4 into C4, C3 and C2, respectively. Those data are in Table S1-S7.

3.3 Water effects on Surfaces of MoxC (x =1, 2) Before exploring the HER activity on different H coverages, the problem whether the adsorbed O (*O) or OH (*OH) are formed on surface once the adsorption and dissociation of water in real electrocatalytic experiment, 57 is explored. In order to solve this problem, we have carried out DFT calculations to explore effect of molecular water on adsorption. The water could form adsorbed O and OH on surfaces in the following two reactions H2O + * → *OH + 1/2H2

(4)

H2O + * →

(5)

and *O + H2

Table. 2 The stabilities of different surfaces of each MoxC (x =1, 2) phase in water. The “*”, “*O”, and “*OH” represent the surface will be covered by neither O or OH, O, and OH, respectively in water. The results are obtained from Table S2-S15

*

δ–MoC

α–MoC

G–MoC

η–MoC

TiP–MoC

β–Mo2C

α–Mo2C

(111)–C

(001)–C

(001)–C

(001)–C

(010)

(100)–C

(001)–C

(001)

(100)–C

(001)–Mo

(001)–C

(100)–C

(110)–C

(011)–C

(111)–C *O *OH

(111)–Mo

(001)–Mo

(110)

(001)–Mo

---

(0-14) (110)

(110)

(010)

(110)

(100)–Mo

(001)–Mo

(110)–Mo (110)

6


---

---

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(014)

By calculating the free energy changes (ΔGOH, ΔGO) for the two reactions, we could estimate whether the reactions could happen. If the free energy change of the first (second) reaction is more negative than that of adsorption of H (ΔGH), then the surface will be covered by OH or O. In this situation, the HER will not happens on the bare surfaces but the corresponding oxygenated, hydroxylated, or oxygenated/hydroxylated one in experiment. Furthermore, if ΔGOH is larger than ΔGO, the surface will be covered by O, and vice versa. The corresponding results are as shown in Table 2. It clearly shows all the surfaces only terminated by C atoms are free of O and OH adsorption, and most of the surface only terminated by Mo are covered by O except (001)–Mo of G-MoC without O or OH. Those surfaces, each of them is terminated by both Mo and C, are more complicated. The (001) of δ–MoC and (010) of TiP– MoC are free of O and OH, the (110) of G–MoC, (0-14) of η–MoC are covered by O, and the rest of them are covered by OH. In general, the Mo atom has stronger chemical interaction with O or OH than that of C atom. That is why the Mo terminated surfaces prefer to be oxidized and the C terminated ones are still bare (free of O and OH). In order to explore real HER performance on oxygenated, hydroxylated, or oxygenated/hydroxylated surfaces considered, the corresponding coverage is also explored. In all the fourteen kinds covered surfaces, only six surfaces covered by more than one O or OH on the slab models according to DFT calculated ΔGH, ΔGOH, and ΔGO as above discussions. For example, the (111)–Mo of δ–MoC will be covered by two O and two OH on the fcc sites, the ΔGO of the first and second adsorbed O, ΔGOH of the third and fourth adsorbed OH are 1.40, -0.76, -0.72 and -0.08 eV, respectively. And the total coverage of the O and OH will reach 1 ML. And also, there are two O (1/2 ML), two OH (1 ML), four OH (4/3 ML), two OH (1 ML) and two OH (1 ML) on (001)–Mo of η–MoC, (110) of δ–MoC, (110) of η–MoC, and (110) and (014) of TiP–MoC according our DFT calculations, respectively. The corresponding values of ΔGOH and ΔGO are as shown in Table S16. For the rest of the eight covered surfaces, only one O or OH in the slab models are considered to simulate the water effect in the DFT results, as the further O and OH will not be stable by estimating whether the two reactions (eq.4 and 5) could happen. The corresponding slab models are applied for further study on HER. 3.4 Hydrogen Evolution on Surfaces of MoxC (x =1, 2) and Exchange Current In order to explore the dependence of HER activity on H coverage, the differential free energy changes of adsorbed H (ΔGH) on the two types of MoxC surfaces, bare ones and covered (*O ,*OH, or *OH and *O) ones in water environment, are explored. For each of two type surfaces, ΔGH has positive relationship with H coverage, which is mainly induced by the different adsorption sites for H and the interaction between them. In additional, the H coverage is defined as the ratio of the number of adsorbed H and that of all atoms in top layer (including Mo and C). It should be noted that, it will be more accurate if we consider the Poubaix diagrams by considering real water environment and pH effect as in previous work,58 several surfaces are also considered as shown in SI part. However, the results by comparing ΔGOH, ΔGO, ΔGH in this work are reliable, as similar method has done in previous work2. The detail discussions are as follows.

7



Figure. 3 The free energy change (ΔGmH) of H adsorption on different bare surfaces of (a) MoC and (b) Mo2C. The dashed horizontal line represents the 0 eV. The grey area indicates the ΔG is range of -0.20~0.20 eV.

Above of all, the ΔGH on bare surfaces (MoC and Mo2C) at different H coverage are calculated and shown in Figure 3, and that on bare MoC surfaces are explored firstly. Prior to explore the HER activity on bare surfaces of MoC, we subdivide them into five classes by the terminations, C5 [δ–(001)], C5 and C4[TiP–(010)], C4[α–(100)–C], C3[δ–(111)–C, α–(001)–C, G–(001)–C and η–(001)–C], and Mo3 ones [G–(001)–Mo], respectively. Those terminations could be seen in Table 1. The HER activities show different behaviours for the five bare MoC surfaces (Figure 3a). a), For the C5 terminated δ–(001), it clearly shows the ΔGH has a relatively suitable value (-0.18~0.17 eV from 1/8~1/2 ML) on C5 site, which indicates the relative high HER activity of C5 site. This could also be seen from Figure S8. b), If the termination turns into C4, such as α–(100)–C, the HER performance will be worse. As the first H adsorption on C4 is too stronger (-0.67 eV) and the second one is too weak (0.74 eV). c), The termination of TiP–(010) includes both C4 and C5, only the C5 show high activity. When the first H adsorption on C4 site of TiP–(010) is as stronger as C4 of the α–(100)–C (-0.71 eV vs -0.67 eV), whereas the further two H adsorption on C5 site will make the ΔGH more close to 0 eV (0.06 and -0.01 eV at 2/6 and 3/6 H ML, respectively), indicating the corresponding high HER activity at 2/6 and 3/6 H ML. The fourth and fifth H atoms prefer to the bridge and top site of Mo, but the adsorption abilities are too weak (0.44 and 0.60 eV at 4/6 and 5/6 H ML, respectively). d) The fourth type surfaces which are terminated by C3, may show high HER activity when the second H adsorbs on one C3 site. For example, the first, second, and third H atoms (1, 2, and 3 H ML) on top of one C3 of α–(001)–C will be -0.76,-0.15, and 0.97 eV, respectively. This could also be seen from Figure S9. It also happens to δ–(111)–C, G–(001)–C and η–(001)–C, as they show suitable ΔGH (-0.20~0.20 eV) at 5/4~6/4, 4/7~8/4, and 7/4~8/4 H ML, respectively. e) The Mo3 terminated surface, G–(001)–Mo, will not be good for HER. As the ΔGH will in range from -0.59~-0.44 eV (fcc and bridge sites of Mo3) at 1/4 ~1 H ML, but further H adsorption will be much hard as the saturated of Mo3, e.g., the ΔG5H of bridge site and ΔG6H at top site will be as high as 0.51 and 0.54 eV, respectively. Thus, only C5 (first H adsorption) and C3 (second H adsorption) of bare MoC surfaces will be good catalytic site for HER, especially the former one. 8


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The bare Mo2C surfaces are also subdivided into three classes by termination, C4[α2– (011)–C, β2–(110)–C], C4 and C3[β2–(111)–C], and C3 ones[β2–(100)–C, β2–(001)–C, α2– (001)–C, α2–(100)–C], for further discussions of the effects of H coverage on HER. Besides, The C5 terminated one is not considered for HER as the larger ΔGH (>0.50 eV, Figure 2a). Here, the α2 and β2 denote α–Mo2C and β–Mo2C for short. a), The two surfaces terminated by C4 show different HER activities on different sites. The β2–(110)–C has suitable differential ΔGH (-0.17~-0.01 eV, 1/8~1/2 H ML) on the four C4 top layer, and the fifth H could only adsorption on bridge of Mo with larger ΔGH (0.22 eV at 5/8 H ML). Whereas, the C4 are not active site on α2–(011)–C, as the ΔGH on first two C4 and last four Mo3 top site are -0.29,-0.31, 0.17, 0.35, 0.54 and 0.58 eV, respectively. Only the third H adsorption Mo3 shows suitable ΔGH. b) The β2–(111)–C, ΔGH are -0.51 (C3+1H), -0.56(C3+1H), -0.27 eV(C4+1H), 0.09(C3+2H), and 0.27 eV (C3+2H) at 1/4~5/4 H ML, respectively. In addition, the “C3+2H” indicates the given C3 site adsorbs the second H atom. It clearly shows that ΔGH owns smaller values (0.09 eV) only when the second H atom adsorbs on the same C3 sites, indicating the narrow H coverage for high HER activity. c), As the C3 site of C3 terminated surface is just similar to that of C4 and C3 terminated surfaces above. Thus, the ΔGH will be much negative on C3 and it may increase to the value larger than 0.20 eV after all C3 site are covered by one H atom. For example, the ΔGH on β2–(100)–C are -0.45 (C3+1H), -0.34(C3+1H), -0.15 eV(Mo3+1H), -0.14(Mo3+1H), 0.15 eV (C3+2H) and 0.22 eV (C3+2H) at 1/2~6/2H ML, respectively. Obviously, β2–(100)–C shows high HER activity on moderate coverage, 3/2~5/2 H ML at Mo3 related and part of C3 sites. The other three surfaces, including β2–(001)–C, α2– (001)–C, α2–(100)–C, has nearly the same trend as β2–(100)–C. The dependence of H coverage on ΔGH for all Mo2C bare surfaces are shown in Figure 3b. Thus, only Mo3 (first H adsorption) and C3 (second H adsorption) of bare MoC surfaces will be good catalytic sites for HER. Basing on oxide or hydroxyl coverage on MoC and Mo2C surfaces in the section above, the ΔGH at possible site is calculated and shown in Figure 4a. It clearly shows that almost all ΔGH are either too negative (0.20 eV), except the that (0.14 eV) on top of O of oxide δ–(111)–Mo, top of C (-0.17 eV) of hydroxyl G–(110) and hcp site (-0.20 eV) of oxide η–(001)–Mo. In addition, as there are possibly suitable sites for HER on η–(0-14) and TiP-(014) while the water condition is not considered, as in Section 3.2. it may also exhibit higher HER activity if there are oxide or hydroxyl. Thus, we pick four typical covered surfaces to explore the H coverage effect on ΔGH, and the corresponding results are shown in Figure 4b. The ΔGH on hydroxyl δ–(110) are either too negative (-0.38 eV at 1/4 H ML) or too positive (0.96 eV at 2/4 H ML) at all H coverage, indicating it poor HER performance. The ΔGH on oxide G–(110) are -0.17, -0.33, and 0.41 eV at 1/4, 2/4, and 3/4 H ML, indicating its poor HER activity at high H coverage (>2/4 H ML). Once the oxidization is considered on the η–(0-14), the HER activity will be greatly reduced and close to the real case. While considering the bare η–(0-14), the ΔGH on the C5 sites are in rang of -0.07 ~0.16 eV. However, if considering oxide case, the ΔGH will become -0.63(C3), -0.12(C4), -0.23(C5), 0. 44(C5), and 0.19 eV (C5) at 1/10 ~5/10 H ML. Those results show the C5 site will not be active site when considering the oxide case and the H coverage, and only the C4 at 2/10 H ML could be. Interestingly, hydroxyl G– (110) could inherit the suitable adsorption ability of C5. In detail, the ΔGH is -0.58(C4), 0.08(C5), 0.04(C5), 0.17(on *OH) at 1/10~4/10 H ML, indicating its higher HER activity at 9



2/10~4/10 H ML. The different HER performances on oxide η–(0-14) and hydroxyl G–(110) may be induced by the electronegativity of O and OH, and the C3 in η–(0-14). In additional, in order to compare the surfaces covered by *O or *OH in this paragraph, the ΔGH on the corresponding bare surfaces (water effect is not considered) are shown given as shown in Figure S10.

Figure. 4 (a) The free energy change of adsorbed H (ΔGH) on different sites of *O and *OH surfaces and (b) the differential (ΔGH) free energy of H adsorption on four selected *O and *OH ones at different H coverages. The grey area indicates the ΔG is range of -0.20~0.20 eV. The “α2” and “β2” indicate α-MoC and α-Mo2C, respectively. In (a), α–(001)–Mo, G–(110), η–(001) and β2–(110)–Mo are oxygenated surfaces, δ–(110), α–(110), G–(010), η–(110), TiP–(110), α2–(001)–Mo are hydroxylated surfaces, and δ– (111)–Mo is covered by both oxygen and hydroxyl.

In order to compare the HER activity of different surfaces in real case, the exchange current at a given surface H coverage is discussed. The determined H coverage of a surface is obtained according to hydrogen adsorption ability: H atom is much easier to desorb than to adsorb.59 The exchange current obtained at the determined H coverage will represent the HER activity of the surface. Our results for each surface can be illustrated by the volcano curve, as shown in Figure 5. Among all the surfaces, nine surfaces own the exchange current larger than 0.1 mA/cm2, and the hydroxyl TiP–(014)–C [1.410 mA/cm2] has the best HER activity followed by TiP–(010) [0.835 mA/cm2], β2–(110) [0.687 mA/cm2], α2–(100)–C [0.464 mA/cm2], G– (001)–C[0.279 mA/cm2], β2–(111) [0.203 mA/cm2], δ–(001) [0.159 mA/cm2], δ–(111)–C [0.145 mA/cm2], and α–(001)–C [0.130 mA/cm2]. Obviously, the termination of all the nine surfaces include C atoms, and all of them are not covered by neither oxygen or hydroxyl except TiP–(014)–C. This indicates that both of C termination and inert with water of molybdenum 10


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carbide have positive effect on HER activity. In additional, in order to compare the surfaces covered by *O or *OH in this paragraph, the ΔGH on the corresponding bare surfaces (water effect is not considered) are shown given as shown in Figure S10. Although the larger exchange currents for the nine surfaces indicates their high HER activity, the HER activity for the corresponding molybdenum carbide phase may be low in experiment. As the most stable surface dominates explosed surfaces in real case, the HER activity of it surface represents that of the molybdenum carbide phase. As seen in Figure S1, (001), (100)–C, (010), (0-14), (010), (111), and (100)–C are the most stable surface of δ–MoC, α–MoC, G–MoC, η–MoC, TiP–MoC, β–Mo2C, and α–Mo2C, respectively. Thus, only δ–MoC, TiP–MoC, and β–Mo2C show high HER activity as their most stable surfaces with the larger exchange current 0.159, 0.835 and 0.203 mA/cm2, respectively. The rest of four phases, α– MoC, G–MoC, η–MoC and α–Mo2C show poor HER activity, and their exchange currents (most stable surfaces) are about 10-9, 10-7, 10-6, 0.045 mA/cm2, respectively. Our results is consist with previous works, e.g., β–Mo2C shows better HER performance than η–MoC, α– MoC and δ–MoC1-x,19 and the δ–MoC shows better HER activity.20, 60 In addition, exchange current β–Mo2C in this work is larger than previous DFT results (0.01 mA/cm2), as it considered nanoparticles (most of the nanoparticles contains (011) surface in their work, but we didn’t consider this facet in this work).61 Both the experimental and theoretical works verify the accuracy of our results. In other words, each molybdenum carbide phase could modify their HER activities if proper surface with larger exchange current could be fabricated by control in experiment.

Figure. 5 The exchange current densities as a function of the hydrogen adsorbed free energy are shown for MoC and Mo2C surfaces. The grey area indicates the corresponding surfaces own larger exchange current (> 0.1 mA/cm2). The “α2” and “β2” indicate the α-Mo2C and β-Mo2C, respectively.

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3.5 Electronic Properties and Hydrogen Adsorption Ability In order to explore the electronic properties effect on hydrogen adsorption ability, the electron transferred between the adsorbed of one hydrogen atom and the molybdenum carbide slab are discussed firstly. Here, the water is not considered. The transferred electron is classified into two types according to different adsorption sites, on Mo and C related site, respectively, as seen in Figure 6a and b, respectively. When a H adsorbs on the Mo related sites, the electron transfers from slab to adsorbed H (0.35~0.68 e). Contrarily, the electron transfers from H to the slab in most case while H adsorbs on C related sites. The exception could be explained by the formation of chemical bond of H with Mo, e.g., the bond lengths of H and C, and H and Mo are 1.14 and 2.23 Å on TiP–(014), as seen Figure 6b. The bond length indicates the H forms both chemical bond with C and Mo, and electron transfers from Mo to H is larger than that from H to C, leading to the electron transfer from slab to H (0.053 e) in the end. This is different from that H atom only form chemical bonds with C in most of other surfaces, such as electron transfer of H on MoC(hkl)-C, which will be shown in next paragraph. Furthermore, it clearly shows that ΔGH has a negative relationship with the transferred electron, e.g., the H adsorbed on Mo related site of MoC and Mo2C slab (Figure 6a), C related site of MoC(hkl), C related site of Mo2C(hkl)-C, and C related site of Mo2C(hkl)-C(Figure 6b), respectively. This is similar to hydrogen on metal surfaces3. Thus, the transferred electron could be applied as standard to access the hydrogen adsorption ability on molybdenum carbide surfaces: the |ΔGH| will be smaller than 0.20 eV when the transferred electron is 0.425~0.510 e (from slab to H) on Mo related sites, -0.020~0.080 e (from H to slab) on C related site, respectively.

Figure. 6 The hydrogen adsorption ability (ΔGH) as a function of (a) electron transfers from slab to H on Mo site, and (b) electron transfers from H to slab on C site for bare molybdenum carbide surfaces.

Besides, how the water affects the hydrogen adsorption ability through electron transfer and bonding behavior is also unveiled. The ΔGH will be much weaker once the surface is covered by O or OH according to our DFT results. The δ–MoC(110) and η–MoC(001)–Mo, which will be covered by OH and O in water environment, are taken as an example. Once the OH and O are considered, The ΔGH will increase from -0.65 and -0.65 eV(bare surfaces) to -0.37 and 0.20 eV (*O or *OH surfaces) at top of C site of δ–MoC(110) and bridge of Mo site of η– MoC(001)–Mo, respectively. While considering *OH (Figure 7a vs b) and *O (Figure 7c vs d), it clearly shows that the coupling of O and adsorbed H leading to upward shift of adsorbed 12


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H state, which in turn leads to the increase of ΔGH. In fact, the coupling of O and the adsorbed H are related through Mo and C atoms. Because of the interaction between *OH or *O and Mo, there will be less electron on Mo and less electron transfer to C while comparing bare surfaces. Thus, there will be less electron transferring to adsorbed H at Mo related site (η–MoC(001)– Mo, 0.617 vs 0.525e), or more electron transferring from adsorbed H at C related site to slab(δ– MoC(110), 0.074 vs 0.146 e). In sum, *OH or *OH could tune the electronic properties of the surfaces, and modify the HER activity of those molybdenum carbide surfaces. And more, the dense states near the fermi level indicates the surfaces exhibit their good conducting properties, which could benefit the electron transport during HER.

Figure. 7 The DOS (density of state) of one H adsorption on top of C of (a) δ–MoC(110), (b) δ–MoC(110) with 2*OH, bridge site of Mo of (c)η–MoC(001)–Mo, and (d) η–MoC(001)–Mo with 2*O. The energy levels are relative to the vacuum level, and the solid lines indicate the fermi level, and the dashed lines and dashed circles indicate the shift of the adsorbate H states. The states of adsorbate H are timed by 10. The energy difference from the fermi level (solid line) to vacuum level (0 eV) is the work function, which is obtained from DFT calculations.

4

Conclusions Molybdenum carbides have been widely explored for HER in experiments for their excellent performances. Here, theoretical studies are carried out to uncover the HER on twentynine surfaces of seven phases of molybdenum carbides. The DFT results show that the surfaces with less broken bonds are more favored in general, and has weak adsorption ability of hydrogen in the trend. In fact, the strength of the hydrogen adsorption ability is related with the electron transfer between adsorbed hydrogen and surfaces. In order to explore the HER on each surface in real condition, the electrochemical water environment is considered through adsorbed oxygen and hydroxyl. In general, the surfaces only with the carbon terminated are 13



favored as bare ones, and those with molybdenum terminated are prone to covered ones. The free energy change of hydrogen is explored on those surfaces at different hydrogen coverages. According to the free energy change of hydrogen, the exchange current for each surface is calculated, and nine surfaces which own high exchange current (>0.1 mA/cm2) are screened out, and all of them are bare surfaces except the hydroxyl TiP–(014)–C. In detail, the largest exchange current reaches 1.410 (hydroxyl (014)–C), 0.687((110)), 0.464((100)–C), 0.279((001)–C), 0.159((001)), and 0.130 mA/cm2((001)–C) on TiP–MoC, β–Mo2C, α–Mo2C, G–MoC, δ–MoC, and α–MoC related surfaces, respectively. Instead of the surface with the highest HER activity, the most stable surface is more favored in experiment for each phase of molybdenum carbide, which explain why one phase of molybdenum carbide may show low HER activity although one surface of it owns high one. At last, the electron transfer and the shift of the coupling states between adsorbed hydrogen and oxygen could explain why *O and *OH weaken the hydrogen adsorption ability. Those DFT results could give theoretical guidance for enhancing HER activity on molybdenum carbides through further control synthesis of HER active surfaces.

ASSOCIATED CONTENT Supporting Information vdW Effect and Ideal Binding Site for H, lattice parameters and cohesive energies of molybdenum carbide(Table S1), free energies of hydrogen at different sites on different surfaces of molybdenum carbides (Table S2-S8), free energies change of *O or *OH on surfaces different surfaces of molybdenum carbides (Table S9-S16), zero-point energy (ZPE) corrections and entropy corrections to the free energies (Table S17), transformation of H Coverage (Table S18), atomic configuration for possible adsorption site on different surfaces of molybdenum carbides (Figure S1-S7), H adsorption process (Figure S8-S9), free energy on bare surface (Figure S10), bulk phase diagram and surface stability (Figure S11-12)

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (Feipeng Zheng) *E-mail: [email protected] (Xi-Bo Li) Notes The authors declare no competing ﬁnancial interest. ACKNOWLEGEMENTS This work was supported by the National Natural Science Foundation of China (No. 21703081, 11804118, and 51802187), the Fundamental Research Funds for the Central Universities (No.21617330), the Natural Science Foundation of Guangdong Province (No. 2018A030313386), and the Shanghai Sailing Program (18YF1408700). We gratefully acknowledge the computational support by High-performance Super Computing Platform of Jinan University.

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Uncovering the Surface and Phase Effect of Molybdenum Carbides on

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