Modulation of Hydrogen Evolution Catalytic Activity of Basal Plane in Monolayer Platinum and Palladium Dichalcogenides.

With an appropriate catalyst, hydrogen evolution reaction (HER) by water splitting can be used to produce hydrogen gas. Recently, layered transition-metal dichalcogenides have been proposed as alternative HER catalysts. However, a significant challenge is how to obtain the high-density active sites. With first-principle calculations, we explore the possibility of defect engineering to trigger the HER catalytic activity of basal plane by analyzing monolayer PdSe2, PtSe2, PdTe2, and PtTe2. It is found that the double-vacancy DVSe (DVTe) and B-doping can modulate appropriately the interaction between H and basal plane and improve the HER activity of these transition-metal dichalcogenides. Especially, the B-doping with high concentration can increase enormously the density of active sites on basal plane.

Introduction

Hydrogen as an energy carrier can be used to produce clean electricity in hydrogen fuel cells.[1] Among different hydrogen production methods, electrolytic water as a sustainable one has been concerned.[2−5] The hydrogen evolution reaction (HER), as the cathodic half-reaction of water splitting, is vital for the production of hydrogen gas. In acidic condition, the total HER includes two processes.[6] The first step is hydrogen adsorption onto a catalyst by Volmer reaction with H+ + e– → H*, where the prefix of * represents the adsorption site of the catalyst. The second step is releasing of molecular hydrogen through two different mechanisms, Heyrovsky reaction H* + H+ + e– → H2+* and Tafel reaction 2H* → H2 + 2*. To decrease the overpotential and thus accelerate the reaction rate, searching for high-efficiency electric catalysts to reduce the reaction barrier becomes important in this filed. Platinum is the most electrochemically stable catalyst and exerts excellent HER electrocatalytic performance.[7−9] However, the high cost and earth-scarcity have hindered its widespread use. It is urgent to find new efficient and abundant electrocatalyst for HER.

The two-dimensional materials, such as layered transition metal dichalcogenides (TMDs), have been reported to exhibit superior catalytic properties for the electrocatalytic applications and emerged as alternative to Pt.[10−25] As a prototype, MoS2 with different phase structures (such as 1T′ and 2H) has been widely studied.[26−29] It has been found that the basal plane of MoS2 is catalytically inert and the catalytic activity originates from the sulfur-terminated Mo-edge and S-edge state for 2H phase.[29−31] To enhance the catalytic performance of MoS2 catalysts, it is considered critical to be make a substantial fraction of exposed edge sites. Synthesizing the nanostructures, such as nanoflakes,[32] nanoparticles,[11] and nanowires,[33] has been the typical method at present. Because of the thermodynamic stability of basal plane and the dominant exposed surface of monolayer TMDs, another strategy is to activate the basal plane of TMDs through defect engineering and/or phase engineering.[34−39] For example, with 1T′ phase, MoS2 exhibits metallic characteristic. Phase transition from 2H to 1T′ has been investigated as a method of tuning electronic properties to improve the HER activity. Defect engineering is also expected to activate the inert basal plane. It have been found that introducing the S vacancies and strain could activate the basal plane of monolayer 2H-MoS2 for HER.[40] The doping with transition metal and light element has been proposed to improve the catalytic activity of inert basal plane.[41−44] In fact, various structural defects, such as point defects and grain boundaries, have been observed in two-dimensional (2D) materials, and were proposed to bring additional active sites for monolayer TMDs to improve the HER ratio.[35]

Recently, platinum- and palladium-based dichalcogenides were synthesized and proposed to be as the catalysts for HER.[45] In this work, we explored the way of defect engineering to activate the basal plane of PdSe2, PtSe2, PdTe2, and PtTe2 for HER by first-principle calculations combined with the basic theory about HER. We mainly investigated the HER activity of basal plane by introducing different kinds of vacancies and the B-doping in monolayer. First, we analyzed the formation of different vacancies and the possibility of B-doping. Then, we simulated the different configurations of H-adsorption around the defects. By the analysis of electronic properties of defect structures, the atomic mechanism of interaction between H and defects was explored. Finally, with the relative free energy of H at the absorption state as the indicator and Sabatier principle, we analyzed the effect of different defects in four materials on HER catalytic activity. These results indicate that defect engineering, especially the B-doping, is an effective method to activate the basal plane of PdSe2, PtSe2, PdTe2, and PtTe2 and make them excellent HER catalysts.

Calculation Methods and Theoretical Models

We carried out the density functional theory calculations by using the Vienna ab initio simulation package.[46] The generalized gradient approximation (GGA) of the parameterization of Perdew–Burke–Ernzerhof (PBE) was used as the exchange–correlation functional.[47] The kinetic energy cutoff was set to 500 eV. The k-point grid was generated with the spacing of 0.02 Å–1 under Monkhorst–Pack scheme.[48] The criterion of energy convergence was set to be 10–5 eV. All the atomic relaxation was terminated until the Hellmann–Feynman forces were smaller than 0.01 eV/Å. The vacuum layer was set to be larger than 18 Å, enough to separate the neighboring layers.

The primitive cells of monolayer PdSe2, PtSe2, PdTe2, and PtTe2 are relaxed to the equilibrium structures. All the calculated structural parameters and electronic properties are shown in Table . The calculated lattice constants are consistent with the experimental values.[45] The bond length of Pt–Se is similar to that of Pd–Se, and the bond length of Pt–Te is similar to that of Pd–Te. All the four monolayers are semiconductors.

Table 1

Structural Parameters Including Lattice Constant a (Angstrom) and Bond Length bM–X (Angstrom) between Metal Atom and Chalcogen, Formation Energy Ef (eV/fu), and Band Gap Eg (Electronvolts) at GGA/PBE Level

materials	a (Å)	bM–X (Å)	Ef (eV/fu)	Eg (eV)
PtSe2	3.77	2.53	–1.51	1.36
	3.73 (ref (45))
PtTe2	4.02	2.71	–1.10	0.75
	4.03 (ref (45))
PdSe2	3.74	2.53	–1.07	0.73
PdTe2	4.03	2.70	–1.00	0.23

To analyze the defect effect, we considered four kinds of defect structures, including single-vacancy of metal atom (VPd and VPt), single-vacancy of nonmetallic atom (VSe and VTe), double vacancy (DVSe and DVTe), and the B-doping (BSe and BTe). Here, we chose boron as the doping element mainly due to the obvious difference of electronegativity between B and Se (Te). It is expected that the B-doping can introduce the band gap states to active the basal plane. With PtSe2 as an example, these defect models are shown in Figure . These defect models are constructed in a 4 × 4 supercell. To assess the thermodynamic stability of these defect structures, we analyzed the formation energies of defects. The formation energy is calculated by the formula[49]where ED and EP are the total energies of the monolayer dichalcogenides with defect structure and pristine structure in the same supercell, respectively. μ is the chemical potential of atom type i and Δn is the difference of number of atom type i in the pristine structure and defect structure. With PdSe2 as an example, we considered Se as the experimental parameter to analyze the formation of these defects. Under the thermodynamic equilibrium, the chemical potential of Se (μSe) is set in the range of [μSe(bulk) + ΔHf/2, μSe(bulk)]. Here, ΔHf is the formation heat of PdSe2 and defined by the formula, ΔHf = EPdSe – EPd – 2ESe, in which EPdSe, EPd, and ESe are the total energies of single-layer PdSe2, bulk Pd, and bulk S. The upper limit of μSe corresponds to the Se-rich condition and the down limit corresponds to the Pd-rich condition. For the B-doping, the chemical potential of B (μB) is set to that of bulk α-B.

Figure 1

Structural representation of monolayer PtSe2 with (a) pristine structure and different kinds of defects including (b) single vacancy of metal atom (VPt), (c) single vacancy of nonmetallic atom (VSe), (d) double vacancy (DVSe), and (e) the B-doping (BSe). Note that the numbers around the defect represent the potential adsorption positions of H around defects considered in this work. The structures of defect models in PdSe2, PdTe2, and PtTe2 are similar to that in PtSe2.

To get an insight into the HER catalytic activity by the interaction between H and the catalyst, we analyzed the adsorption energy on the potential active sites of the surface. The adsorption energy is defined by the formulawhere Ehost+H and Ehost are the total energies of substrate material with and without H-adsorption, respectively. EH denotes the energy of isolated H atom.

The total HER can be expressed as 2H+ + 2e– → H2. At equilibrium state, the free energy of the initial state and the final state in the reaction should be equivalent. Therefore, the free energy of the intermediate state H* (H adsorbed on the active site of catalyst) is important for the reaction rate. As an important indicator of the HER activity, the relative free energy of H* with the initial state or the finial state as the reference can be expressed as , where Ecat+H and Ecat are the total energies of the catalysts with and without H-adsorption, respectively. EH is the total energy of H2 molecule. ΔEZPE is the difference of zero-point energies between the intermediate H* and the finial state. ΔS is the entropy difference of both states. Following the work of Nørskov et al., the contribution of vibrational entropy from H in the intermediate H* is small and can be ignored.[6] ΔS can be calculated on the basis of the entropy of gas phase at standard conditions and TΔS at 300 K is about −0.2 eV. The contribution of ΔEZPE to free energy for H-adsorption is usually small and about 0.04 eV for H on Cu(111) surface. Therefore, the relative free energy can be approximately calculated by the formula[6]For ΔGH*, the positive value will obstruct the adsorption process and the negative value will restrict the desorption. Both cases hinder the HER rate.[6,50,51] According to Sabatier principle, the optimal value should be a thermoneutral value, ΔGH* ≈ 0.

The theoretical exchange current density (i0) is calculated on the basis of ΔGH*. The theoretical exchange current density can reveal the reaction rate during the proton transfer to the surface to some extent.[6] If the proton transfer is exothermic (ΔGH* < 0), the exchange current expression at standard conditions with pH = 0 and T = 300 K isBy contrast, if the reaction is endothermic (ΔGH* > 0), the exchange current density is calculated bywhere k0 is the rate constant (200 s–1/site) and k is Boltzmann constant.

Results and Discussion

Defects and B-Doping

In 2D materials, vacancy as a typical point defect is popular. We analyzed two kinds of single vacancies in PdSe2, PtSe2, PdTe2, and PtTe2, as shown in Figure . From the formation energy, whatever the condition of Pd-rich (Pt-rich) or Se-rich (Te-rich), the single-vacancy VSe (VTe) is more stable than VPd (VPt). It is also noticed that these nonmetal vacancies have low formation energy (less than 2 eV). This implies that they are a common type of defects in the process of experimental synthesis, especially under the condition of rich Pd to synthesize PdTe2.

Figure 2

Defect formation energy as a function of chemical potential for different materials including (a) PdSe2, (b) PdTe2, (c) PtSe2, (d) PtTe2, and (e) formation energy of B substitution (BSe for PdSe2 and PtSe2, BTe for PdTe2 and PtTe2) as a function of chemical potential calculated on the basis of the pristine structure in Figure a and single-vacancy structure in Figure c. Note that the formation energy of B substitution calculated on the basis of single-vacancy structure does not change by following the chemical potential of Te (Se) in (e).

Compared to the single vacancy VSe (or VTe), the formation of double vacancy (DVSe or DVTe) is a little difficult. In addition, in Figure , it is found that the isolated single vacancies are more popular than one double vacancy by comparing the formation energies of one double vacancy DVSe (DVTe) and two isolated single vacancies (V2Se or V2Te) at the same Se (Te) concentration. This suggests the single vacancy VSe (VTe) is dominant in PdSe2, PtSe2, PdTe2, and PtTe2.

For the B-doping, the popular way is the replacement of Se (Te) by B because B is easier to bond with Pt (Pd) than with Se (Te). The formation energy was calculated as presented in Figure e. For the four layered-compounds we considered, in B-rich condition, the B substitution becomes possible due to the low formation energy. Especially, in PtTe2, the formation energy of BTe is less than 1.8 eV. It is also possible that B will occupy the single vacancy VSe (VTe) because it is popular in the synthesis processes. With the single vacancy VSe (VTe), we found that B would likely be absorbed on the vacancy to form the defect BTe (BSe). Especially, in PtSe2, the formation energy is very low and less than 0.2 eV.

H-Adsorption and Electronic Properties of Defective Structures

To consider the adsorption in the proposed four kinds of defective models, we analyzed all the possible adsorption sites with the consideration of structural symmetry for each defective model. These adsorption sites are marked by a number, as shown in Figure . The results are listed in Table S1. For the pristine structure, the most stable adsorption site of H is at the top of Se (Te) atom for all the considered materials. For the VPd (VPt) model, the adsorbed H atom is located at the Se (Te) atom near VPd (VPt), except PdSe2. For the VSe (VTe) model, the adsorbed H atom tends to occupy the top site of the Pd (Pt) atom near VSe (VTe). In the case of double-vacancy DVSe (DVTe) model, there are two kinds of Pd (Pt) atoms near DVSe (DVTe), which are four-coordinated and five-coordinated, respectively. The adsorbed H atom is located at the middle site of the double vacancy and the H atom prefers to bind with four-coordinated Pd (Pt) atom, as shown in Figure S1c. For the B-doping model, H atom is adsorbed above the bridge site between B and Pd (Pt).

For each model in four compounds, the adsorption energy of most stable adsorption configuration is demonstrated in Figure . From the adsorption energies of hydrogen on different materials with various defects, we come to a conclusion that the adsorption energy of VPd (VPt) is the largest among the considered various defect types. It means that the interaction between Se (Te) near the defect and H in the VPd (VPt) model is strong, especially in PdSe2. Meanwhile, the interaction strength between H and other types of defects is similar.

Figure 3

Adsorption energy of H for monolayer PdSe2, PtSe2, PdTe2, and PtTe2 with various defects in the most stable configuration.

It is noticed that the interaction between H and the defects is stronger than that of H and pristine PdSe2 (PtSe2, PdTe2, and PtTe2). To understand the atomic mechanism of interaction between H and the defects, we analyzed the change in electronic properties due to the defects. Taking PdSe2 for example, the density of states (DOS) and partial density of states (PDOS) of VPd, VSe, VSe, and BSe are plotted in Figure . The electronic band structure in Figure S2a demonstrates that pristine PdSe2 is a semiconductor with a band gap of about 0.7 eV. For VPd in Figure a, a quasi-localized state appears in the region of band gap. Fermi level is anchored at the middle of quasi-localized state. From the PDOS, this defect state can be attributed to the Se near VPd. To observe the distribution of charge in real space, we plotted the differential charge density in Figure . As shown in Figure a, from the charge distribution, the polarized covalent bond is formed between Pd and Se atom with the surplus charge transferred from Pd to Se. With VPd, there is charge accumulation near the unsaturated Se atom near the vacancy. With the H-adsorption near the defect, the hydrogen interacts with the localized electronic states from Se near VPd, as shown in Figures S1a and S3a. In addition, H also traps the other Se atom near VPd in PdSe2, resulting in the weakening of the Pd–Se bond near VPd. This phenomenon is not observed in other three compounds (Figure S4). It may be the reason why the absorption strength at VPd of PdSe2 is the largest.

Figure 4

Density of states (DOS) and partial density of states (PDOS) of PdSe2 with various defects including (a) VPd, (b) VSe, (c) VSe, and (d) BSe.

Figure 5

Differential charge density of PdSe2 with various defects including (a) VPd, (b) VSe, (c) VSe, and (d) BSe. Note that dark red color indicates charge accumulation and green color denotes charge depletion.

The localized states with high PDOS, such as the edge states from S edge-atoms in MoS2, can strengthen the interaction between H and defect. However, for the metal vacancy (VPd and VPt) in PdSe2, PtSe2, PdTe2, and PtTe2, the interaction is too strong to favor the HER based on Sabatier principle. For the VSe and DVSe in PdSe2, the weak localized states with lower PDOS is found to be formed, as shown in Figure b,c. With the participation of localized states, the H is adsorbed on Pb atom near the vacancy results in the appropriate interaction between H and defects (Figures S1 and S3). In Figure b,c, it is observed that there is a little charge accumulation near the vacancy. For BSe, the weak localized states from the contribution of Pd near B atom (Figure d) induce the accumulation of charges near the B atom (Figure d). With the H-adsorption, the localized state is modulated obviously with the charge transfer in Figure S3d. In addition, it is noticed there is a trend of charge transfer from defects to H with charge polarization in the three cases, VSe, DVSe, and BSe (Figure S1b–d). This is different from the mechanism of H-adsorption on pristine basal plane where the electron charge is transferred from H to adsorption site and its nearby sites, as shown in Figure S5.

HER Activity on Defective Structures

The relative Gibbs free energy (ΔGH*) of H-adsorption state H* with the gas phase as a reference state is an important indicator to assess the catalytic activity of catalysts. Here, we adopt ΔGH* to access the HER activity of the four materials with different defect types. As the value of ΔGH* approaches zero, the HER activity will become the best. First, we analyze the reaction activity of pristine basal plane. For PdSe2, PtSe2, PdTe2, and PtTe2, the values of ΔGH* are 0.94, 1.38, 1.10, and 1.44 eV, respectively. These large positive values imply that the HER activity of these pristine basal planes are not good. Therefore, the favorable HER activity in experiments of similar materials, such as MoS2, is usually attributed to the contribution of edge states from the edges of 2D materials.

The calculated ΔGH* values of various materials considered with various defects are shown in Figure a. Compared with the pristine basal plane, these point defects can decrease significantly the Gibbs free energy of H-adsorption and thus greatly improve the catalytic activity, except the VPd and VPt in PdSe2 and PtSe2. The calculated ΔGH* of Pd (Pt) vacancy in PdSe2 and PtSe2 is very negative and indicates the interaction between H and substrate materials is too strong to release H2 effectively. Compared to T′-MoS2, the ΔGH* value of Se (Te) vacancy in the case of PdSe2 and PdTe2 is a little large. The large positive value of ΔGH* implies that the weak binding of H with the catalyst will impede the Volmer adsorption process. For the rest of defect models in the considered four materials, especially for the B-doping, the calculated ΔGH* values are close to the thermoneutral, suggesting the superior HER catalytic activity.

Figure 6

(a) Values of ΔGH* and (b) volcano curve between the exchange current density i0 and ΔGH* for monolayer PdSe2, PtSe2, PdTe2, and PtTe2 with various defects.

To further directly compare the HER catalytic activity of different defect models in the four materials, the theoretical exchange current density (i0) is calculated on the basis of ΔGH*. The results are plotted in Figure b. The catalytic activity of the catalyst is reflected in the volcano curve. We can find that the double vacancy DVSe (DVTe) and B-substitution are located at the top of volcano curve and show a much higher current density. The i0 of BSe in PdSe2 and DVTe in PtTe2 are even higher than those of Pt catalyst because of the small value of ΔGH*. The results of the above analysis of the formation of defects indicate that the B-doping can improve HER activity effectively. A comparison of the overall catalytic properties of these four materials reveals that PtTe2 exhibits a slightly more superior activity than other materials.

Defect concentration may have an important effect on the HER activity, whereas a higher defect concentration means more active sites on the basal plane. To take PdSe2 as an example, we explore the concentration effect of defects. The ΔGH* values of PdSe2 with various defects including VSe, DVSe, and BSe was calculated as the functions of defect concentration in Figure a. At the low concentration less than 8%, the defect concentration does not have significant effect on the Gibbs free energy for the single vacancy VSe and double vacancy DVSe. With the increase in concentration to more than 12%, the H-adsorption strength of VSe has a trend of decrease and that of DVSe has a trend of increase. For the B-doping, the value of ΔGH* has a decreasing trend, following the increase in B concentration. The volcano curve between exchange current density and Gibbs free energy is plotted in Figure b. The B-doping is located at the top of the volcano curve, which implies a moderate H-adsorption and a superior activity, especially at low concentration less than 6%. For the concentration less than 8%, the double vacancy DVSe also has a superior activity and resides near the top site. Taking PdSe2 as an example, we also check the effect of vacancy size under the condition of rich vacancies. As shown in Figure S6, with the increase in vacancy size up to quadruple vacancy, the value of ΔGH* has a decreasing trend.

Figure 7

(a) Values of ΔGH* for VSe, DVSe, and BSe as a function of defect concentration for monolayer PdSe2. (b) Volcano curve between the exchange current density i0 and ΔGH* for defective PdSe2 with different concentration of defects.

Conclusions

We have studied the formation of defects and the modulation of electronic properties of the monolayer PdSe2, PtSe2, PdTe2, and PtTe2 by first-principle calculations. It was found that single vacancy VSe (VTe) was easier to form in Se (Te)-rich condition. In addition, B can be doped effectively into the lattice of the four compounds by the formation of BSe (BTe). We demonstrated that the catalytic activity of inert basal plane in PdSe2, PtSe2, PdTe2, and PtTe2 could be triggered efficiently through the single vacancy, double vacancy, and B-doping. This indicates that defect engineering could be used to enhance the HER activity of these compounds. The improvement in catalytic activity is found to originate from the facts that the defects can introduce quasi-localized states in the band gap and that these electronic states can interact moderately with H atom. With an overall assessment of the HER activity in terms of ΔGH* value, the activity of tellurides is found to be superior to the selenides slightly among PdSe2, PtSe2, PdTe2, and PtTe2. Moreover, B-doping is a much more effective method to enhance the HER activity in these compounds. In short, it is a feasible strategy to activate the HER activity of platinum and palladium dichalcogenides by introducing the intrinsic defect and B-doping. It is also expected that these results may shed some light on improving the HER activity of other TMDs.