Computational Search for Single-Layer Transition-Metal

Sep 17, 2013 - Some of the members of the family of single-layer transition-metal dichalcogenides have recently received a lot of attention for their ...
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Computational Search for Single-Layer Transition-Metal Dichalcogenide Photocatalysts Houlong L. Zhuang and Richard G. Hennig* Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, United States ABSTRACT: Some of the members of the family of single-layer transitionmetal dichalcogenides have recently received a lot of attention for their promising electronic properties, with potential applications in electronic devices. In this work, we focus on the stability of the dichalcogenides and determine their potential for photocatalytic water splitting. Using a first-principles design approach, we perform a systematic theoretical study of the dichalcogenides MX2 (M = Nb, Mo, Ta, W, Ti, V, Zr, Hf, and Pt; X = S, Se, and Te). First, we use a van der Waals functional to accurately calculate their formation energies. The results reveal that most MX2 have similar formation energies to those of singlelayer MoS2 and WS2, implying the ease of mechanically exfoliating a single-layer MX2 from their layered bulk counterparts. Next, we use the many-body G0W0 approximation to obtain the band structures, finding that about half of the MX2 are semiconductors. We then calculate conduction and valence band edge positions by combining the bandgap center energies from the density-functional calculations and the G0W0 quasiparticle bandgaps. Comparing these band edge positions to the redox potentials of water, we identify that single-layer MoS2, WS2, PtS2, and PtSe2 are potential photocatalysts for water splitting. Furthermore, we find that PtSe2 undergoes a semimetal-tosemiconductor transition when the dimension is reduced from three dimensional to two dimensional. Finally, large solvation enthalpies of these four candidate photocatalysts suggest their stability in aqueous solution.

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INTRODUCTION The family of single-layer transition-metal dichalcogenides MX2 has recently received extensive attention because several of its members, such as MoS2 and WS2, have successfully been synthesized and shown to exhibit attractive electronic properties, such as direct bandgaps.1 In addition to the wide investigation of electronic properties,2,3 the study of photochemical properties of single-layer MX2 appears to be another fast emerging research field.4 For example, theoretical studies have shown that single-layer MoS2 exhibits the potential of being used as photocatalysts for solar water splitting to generate hydrogen.4,5 To become a promising candidate semiconductor for water splitting, three criteria need to be satisfied simultaneously.6 First, the bandgap of the semiconductor must be at least 1.6− 1.7 eV to drive the kinetics of the hydrogen and oxygen evolution reactions. Second, the band edges must straddle the redox potentials of water. Finally, the semiconductor should be insoluble in an aqueous solution. On the basis of these criteria, we have suggested a general procedure of screening potential two-dimensional (2D) photocatalysts. This procedure consists of the successive evaluations of the stability of the 2D materials, their bandgaps, band edge positions, and solubility. We have successfully applied this procedure in a previous study to single-layer Gaand In-based monochalcogenides, which are all semiconductors.7 In the current work, we extend the applications of the screening procedure to the family of transition-metal dichalcogenides, differing from the monochalcogenides in not © XXXX American Chemical Society

only their chemistry and structure but also their electronic structures ranging from metals to semiconductors. To obtain accurate bandgaps and band edge positions, we perform manybody G0W0 calculations. To examine the solubility of the singlelayer MX2 compounds in water, we compute their solvation enthalpies.

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SIMULATION METHODS All calculations are based on density functional theory (DFT) and the many-body G0W0 approach using the projector augmented wave (PAW) method, as implemented in the plane wave code VASP.8−10 For the structural relaxations, we employ the generalized gradient approximation with the Perdew−Burke−Ernzerhof (PBE) parametrization.11 A cutoff energy of 400 eV for the plane wave basis set is used throughout all calculations and ensures an accuracy of the energy of 1 meV/atom. The k-point sampling uses the Monkhorst−Pack scheme12 and employs for the single-layer materials a 48 × 48 × 1 grid for the PBE functional and a 18 × 18 × 1 grid for the more expensive G0W0 calculations. We use 64 bands and 96 frequency points for all G0W0 calculations, ensuring that EQP g is converged to 1 meV. For the single-layer materials, a vacuum spacing of 18 Å ensures that the interactions between the layers are negligible. Received: June 12, 2013 Revised: September 12, 2013

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decompose the reaction 3 into two steps. In the first reaction, the solid compound is separated into isolated gas atoms, i.e.

The formation energy Ef of single-layer MX2 is defined relative to the three-dimensional (3D) bulk ground-state structure as Ef = E2D/N2D − E3D/N3D

MX 2(s) ⇌ M(g) + 2X(g)

(1)

The enthalpy change of reaction 4, i.e., the cohesive energy of the MX2 compound, ΔEcoh, is calculated using the VASP code and the PBE functional. In the second reaction, the gas atoms are ionized and subsequently solvated in water, i.e.

where E2D and E3D are the total energies of single-layer and bulk MX2, respectively.13,14 N2D and N3D are the numbers of atoms in the 2D and 3D unit cells, respectively. The 3D bulk 15 structures of the MX2 are either P3m ̅ 1 or P63/mmc. To account for the van der Waals interactions, the vdw-optB88 functional is used for the calculations of the formation energies.16 We employ the method proposed by Toroker et al. to determine the band edge positions.17 The conduction band minimum (CBM) and valence band maximum (VBM) energies, ECBM and EVBM, are given by 1 ECBM/VBM = E BGC ± EgQP (2) 2 where EBGC is the bandgap center energy calculated with the PBE functional. EBGC has been shown insensitive to various exchange-correlation functionals.7 EQP in eq 2 denotes the g quasiparticle bandgap from the G0W0 calculation. The single-layer MX2 compounds exhibit a structure consisting of three atomic sublayers with the metal atom M in the center sublayer bonded to six nearest-neighbor X atoms located in the top and bottom sublayers. Figure 1 depicts the

M(g) + 2X(g) ⇌ M2n +(aq) + 2Xn −(aq)

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RESULTS AND DISCUSSION Structure and Stability of Single-Layer MX2 Compounds. Table 1 lists the formation energies as well as the structural parameters of single-layer MX2, and Figure 2 compares their formation energies. We observe that the formation energies increase for each cation group. Furthermore, most single-layer MX2 have comparable formation energies to that of single-layer MoS2. A common method to fabricate single-layer MX2, such as MoS2 and NbSe2, is micromechanical exfoliation.23 The formation energy is an important indicator of the strength of interlayer van der Waals interactions in bulk MX2. Therefore, the small formation energies indicate the ease to cleave a sheet of single-layer MX2 from bulk crystals. Recent experiments show that both the 2H and 1T phases can coexist in single-layer MoS2.24 To test whether a similar phase coexistence can occur in other MX2, we compare the energy difference ΔE between the 1T and 2H phases for each MX2, i.e. ΔE = E1T − E2H. The results of ΔE are given in Table 1. For the 2H phases, all ΔE are positive, indicating that 2H phases remain stable. Surprisingly, the ΔE of MoS2 is the second largest among all 2H phases. Similarly, for the 1T phases, the negative ΔE indicates that the 1T phases are more stable. Notably for Nb- and Ta-based dichalcogenides, their formation energies of the 2H and 1T structures are close, implying a possible coexistence of these two phases. Band Alignment of Single-Layer MX2 Compounds with Water Redox Potentials. We then determine the electronic structures of all 27 single-layer MX2. Figure 2 reveals that 13 MX2 are semiconductors, whose band edges can be classified into four categories based on the VBM and CBM positions in the reciprocal space. First, for all six molybdenum and tungsten dichalcogenides, both the VBM and CBM are located at the K point; i.e., all of these compounds are directbandgap semiconductors, arising from the strong localization of d-electron orbitals at the transition-metal atoms.25 Second, for

two structure types that correspond to different stacking of the top and bottom X sublayers. In the 2H structure, the top and bottom X sublayers are in an eclipsing configuration, while in the 1T structure, the top X sublayer is displaced with reference to the bottom one by a vector of 1/3(a1⃗ + a2⃗ ), where a1⃗ and a2⃗ are the in-plane lattice vectors. The occurrence of these two distinctive stacking structures is due to the ionicity of MX2.18 MX2 compounds with higher ionicity favor the 1T structure, in which the X anions of the top and bottom sublayers are further apart from each other, minimizing their electrostatic repulsion. To assess the stability of single-layer MX2 in water, we calculate the solvation enthalpy, ΔHsolv, defined as the enthalpy change of the following solvation reaction: 2n+

(5)

To calculate the enthalpy change, ΔHhyd, of this reaction, we calculate the energy of the isolated atoms and the hydrated ions using Gaussian09.19 The aug-cc-pVQZ basis sets are used for all calculations, and for the heavy atoms, Mo, W, Pt, and Te, we use effective core potentials.20,21 The energy of the solvated ions is calculated using several explicit water molecules and the SMD solvation model for the solute−solvent interactions.22 Our convergence tests show that three water molecules are required to converge the hydration energy ΔHhyd to 25 kJ/mol. We also consider the effect of ion association by calculating the energy of M2n+−Xn− pairs in aqueous solution using the SMD model. The enthalpy of solvation ΔHsolv is given by the sum of the cohesive energy ΔEcoh and the enthalpy of hydration ΔHhyd. The value of n for the charge state of the M2n+(aq) and Xn−(aq) ions in aqueous solution is determined by the lowest enthalpy of hydration.

Figure 1. Two crystal structures of single-layer MX2: (a) 2H structure and (b) 1T structure.

MX 2(s) ⇌ M2n +(aq) + 2Xn −(aq)

(4)

(3)

n−

where M (aq) and X (aq) represent the M and X ions in aqueous solution, respectively. To calculate ΔHsolv, we B

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Table 1. Structural Parameters and Formation Energies Ef of Single-Layer Transition-Metal Dichalcogenides MX2 Calculated with the PBE Functionala a0

bM−X

NbS2 NbSe2 NbTe2 MoS2 MoSe2 MoTe2 TaS2 TaSe2 TaTe2 WS2 WSe2 WTe2

3.36 3.48 3.69 3.18 3.32 3.55 3.34 3.47 3.70 3.18 3.32 3.55

2.49 2.62 2.82 2.41 2.54 2.73 2.48 2.61 2.81 2.42 2.55 2.74

TiS2 TiSe2 TiTe2 VS2 VSe2 VTe2 ZrS2 ZrSe2 ZrTe2 HfS2 HfSe2 HfTe2 PtS2 PtSe2 PtTe2

3.40 3.52 3.74 3.17 3.32 3.55 3.68 3.80 3.97 3.64 3.76 3.96 3.57 3.75 4.02

2.43 2.56 2.78 2.35 2.48 2.69 2.57 2.71 2.92 2.55 2.68 2.89 2.40 2.53 2.71

bX−X

θX−M−X

Ef

ΔE

2H Structure 3.14 77.97 3.37 79.90 3.70 81.85 3.13 80.80 3.34 82.18 3.61 82.77 3.13 78.11 3.35 79.87 3.66 81.19 3.14 81.05 3.36 82.46 3.63 83.02 1T Structure 3.46 89.08 3.71 87.00 4.10 84.71 3.46 85.04 3.70 83.81 4.05 82.54 3.60 91.36 3.85 89.16 4.27 85.83 3.57 91.02 3.82 89.05 4.21 86.54 3.21 96.18 3.40 95.63 3.62 95.96

0.093 0.097 0.100 0.077 0.080 0.083 0.087 0.090 0.140 0.077 0.080 0.120

0.035 0.032 0.003 0.283 0.237 0.173 0.023 0.023 0.003 0.297 0.257 0.183

0.090 0.097 0.110 0.090 0.090 0.097 0.090 0.097 0.113 0.087 0.093 0.107 0.093 0.107 0.143

−0.137 −0.113 −0.100 −0.003 −0.007 −0.002 −0.187 −0.157 −0.097 −0.213 −0.170 −0.127 −0.598 −0.452 −0.056

Figure 3. Band structures of single-layer WS2, ZrS2, PtS2, and PtTe2 calculated with the PBE functional (solid blue lines) and the G0W0 method (red circles). The valence band maximum is set to zero.

keeping the positions of the band edges in reciprocal space unchanged. Table 2 summarizes the bandgaps calculated with the PBE functional and the G0W0 method. As expected, the PBE Table 2. Bandgaps Eg, Bandgap Center Energies EBGC, and Band Edge Positions ECBM and EVBM of Single-Layer Semiconducting Transition-Metal Dichalcogenidesa MoS2 MoSe2 MoTe2 WS2 WSe2 WTe2 ZrS2 ZrSe2 HfS2 HfSe2 PtS2 PtSe2 PtTe2

a

The structural parameters include the lattice constant a0 (Å), M−X bond length bM−X (Å), X−X bond length bX−X (Å), and X−M−X bond angle θX−M−X (degrees). ΔE refers to the energy difference between the 1T and 2H structures. All energies are in units of eV/ atom.

EPBE g

EQP g

EBGC

ECBM

EVBM

1.68 1.45 1.08 1.82 1.55 1.07 1.19 0.50 1.27 0.61 1.81 1.41 0.79

2.36 2.04 1.54 2.64 2.26 1.62 2.56 1.54 2.45 1.39 2.83 2.10 1.14

−5.10 −4.60 −4.35 −4.79 −4.33 −4.16 −5.86 −5.37 −5.75 −5.25 −5.45 −5.03 −4.38

−3.92 −3.58 −3.58 −3.47 −3.20 −3.35 −4.58 −4.60 −4.53 −4.56 −3.97 −3.98 −3.81

−6.28 −5.62 −5.12 −6.11 −5.46 −4.97 −7.14 −6.14 −6.98 −5.95 −6.80 −6.08 −4.95

a

The bandgaps are calculated with two approaches, with DFT using the PBE functional yielding E gPBE and the many-body G 0 W 0 approximation yielding the quasiparticle bandgaps EQP g . All energies are in units of eV.

Figure 2. Formation energies of single-layer transition-metal dichalcogenides. The similarity of the formation energies for the MX2 to the value for MoS2, indicated by the red dashed line, suggests the ease of mechanical exfoliation of the single-layer materials from bulk crystals.

bandgaps are smaller than the quasiparticle bandgaps and underestimate the experimental ones.26 The quasiparticle bandgaps correspond to the fundamental bandgaps measured in photoemission/inverse photoemission (PES/IPES) experiments, while the bandgaps measured by optical spectroscopy are reduced as a result of exciton binding.17 Previous calculations for single-layer MoS2 using the G0W0 method and the HSE06 hybrid density functional resulted in bandgaps of 2.50 and 2.34 eV,27−29 respectively, which are similar to our G0W0 value of 2.36 eV. Recent calculations for single-layer MoS2 and WS2 by Shi et al.27 using the self-consistent GW0 method for the quasiparticle gap and the Bethe−Salpeter

ZrS2, ZrSe2, HfS2, and HfSe2, the VBM appears at the Γ point, while the CBM is at the M point. Third, for PtS2, the VBM shows up between the Γ and K points and the CBM is between the Γ and M points. In the last category comprised of PtSe2 and PtTe2, their VBM is at the Γ point, while the CBM is between the Γ and K points. Four representative band structures from all categories are shown in Figure 3. The PBE functional and the G0W0 method are used to obtain these band structures. As seen, the G0W0 method only corrects the bandgap sizes while C

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Figure 4. Band edge positions of single-layer transition-metal dichalcogenides relative to the vacuum level. The redox potentials of water splitting at pH 0 (red dotted line) and pH 7 (green dashed line) are shown for comparison.

Table 3. Bandgaps Eg, Bandgap Center EBGC, and Band Edge Positions ECBM and EVBM of the 3D Bulk Structures of Semiconducting MoS2, WS2, and PtS2a

equation to determine the exciton binding energy resulted in quasiparticle bandgaps that are slightly larger by 0.3 eV than our values and predict an exciton binding energy in MoS2 and WS2 of 0.6 eV. We observe that most single-layer MX2 possess quasiparticle bandgaps within the visible light energy range. Both the PBE functional and the G0W0 method show a decrease of the bandgap in each cation group because of the decrease in ionicity. Figure 4 compares the band edge positions of single-layer MX2 with the redox potentials of hydrogen evolution (H+/H2) and oxygen evolution (O2/H2O) at pH 0 and 7. While the majority of single-layer MX2 have band edge energies that are unfavorable for photocatalytic water splitting without application of an external bias potential, we find that MoS2, WS2, PtS2, and PtSe2 exhibit band edges that straddle the redox potentials of water at pH 0 and make them promising candidates for photocatalytic water splitting. These four single-layer materials should be able to split water without imposing an external bias voltage. Our conclusion that single-layer MoS2 is able to catalyze the water-splitting reaction is in agreement with previous theoretical predictions.4,5 In the above discussion, we consider a mechanism of water splitting where the exciton splits into an electron in the conduction band and a hole in the valence band, which diffuse separately and react with water. In this case, the exciton binding energy needs to be overcome and the CBM and VBM must be aligned energetically favorable with the water redox potentials. Indeed, there exists a second mechanism, where the exciton binding plays an important role. In this scenario, the exciton directly reacts with water and the exciton binding energy must not reduce the CBM and VBM levels too much as to make the redox reaction unfavorable. Assuming a similar exciton binding energy for all MX2 as calculated for MoS2 and WS2 of 0.6 eV,27 we observe that the redox reaction is still energetically favorable for MoS2, WS2, PtS2, and PtSe2. To understand why these 2D materials become promising candidate photocatalysts, we perform similar calculations of bandgaps, bandgap center, and band edge positions of their 3D counterparts. The results are shown in Table 3 for all of the MX2 compounds, except PtSe2, which is a semimetal.30 Consistent with the experimental reports, the band edge positions confirm that none of the three bulk materials is suitable for water splitting. In comparison to the bandgaps listed in Table 2, the bandgaps of MoS2, WS2, and PtS2 increase significantly because of the dimension reduction from 3D to 2D. The increase in bandgap shifts the CBM and VBM and makes these single-layer materials potential photocatalysts for water splitting. The reason why single-layer PtSe2 turns into a competitive photocatalyst is slightly different. Figure 5 shows the density of

MoS2 WS2 PtS2

EPBE g

EQP g

EBGC

ECBM

EVBM

0.94 1.05 0.73

1.30 1.48 1.13

−4.82 −4.56 −5.18

−4.17 −3.82 −4.62

−5.47 −5.30 −5.75

a

The bandgaps are calculated with two approaches, with DFT using the PBE functional yielding E gPBE and the many-body G 0 W 0 approximation yielding the quasiparticle bandgaps EQP g . All energies are in units of eV.

Figure 5. DOS of (a) bulk PtS2 calculated with the G0W0 method and the HSE06 functional and (b) single-layer PtS2 obtained from the G0W0 method.

states (DOS) of bulk and single-layer PtSe2 with the G0W0 method. For bulk PtSe2, there exist a finite number of electronic states at the Fermi level. A similar DOS is obtained from the HSE06 functional.31,32 Therefore, bulk PtSe2 is metallic, consistent with previous theoretical and experimental studies.30 In contrast, single-layer PtSe2 is semiconducting, as seen by the DOS shown in Figure 5b. The opening of a wide bandgap makes the single-layer PtSe2 a potential photocatalyst. Tuning of Band Edge Positions. Figure 4 shows that some of the band edge positions of the single-layer materials, such as MoSe2 and WSe2 are close to the oxygen redox potential of water. Several approaches can be adopted to shift these band edge positions and enable these materials to drive the oxygen evolution reaction. The first method is based on the dependence the redox potentials upon the pH values.33 Increasing the pH shifts both energy levels of H+/H2 and O2/H2O upward, as illustrated in Figure 4, making MoSe2 and WSe2 possible photocatalysts. The second method is based on applying an external bias voltage. The larger the energy D

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metal dichalcogenides. We found that the formation energies of single-layer transition-metal dichalcogenides are comparable to those of single-layer MoS2 and WS2, which have been successfully synthesized. In addition, the calculations of band structures reveal that 13 single-layer transition-metal dichalcogenides are semiconductors with four different types of band edge positions. Among the semiconducting transition-metal dichalcogenides, we have identified that single-layer MoS2, WS2, PtS2, and PtSe2 are potential photocatalysts for splitting water. In addition, we observed that PtSe2 transforms into a semiconductor because of the dimension reduction. Finally, we predict high enthalpies of solvation for the four single-layer materials, indicating that they are insoluble in water.

difference is between the CBM (VBM) and the energy levels of H+/H2 (O2/H2O), the larger the required bias voltage must be. A third alternative method of adjusting the bandgaps and band edge positions of a semiconductor is the application of mechanical strains. For example, applying a 4% tensile strain to single-layer ZrSe2 results in the G0W0 band structure shown in Figure 6. In comparison to the bandgap at zero strain, the

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +1-607-255-6429. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Figure 6. G0W0 band structures of single-layer ZrSe2 at the strains of 0% (red) and 4% (blue). The valence band maximum is set to zero.

ACKNOWLEDGMENTS We thank M. Spencer, D. Muller, F. Rana, D. Schlom, and L. Yang for helpful discussions. This work was supported by the National Science Foundation (NSF) through the Cornell Center for Materials Research under Award DMR-1120296 and by the CAREER Award DMR-1056587. This research used computational resources of the Texas Advanced Computing Center under Contract TG-DMR050028N and the Computation Center for Nanotechnology Innovation at Rensselaer Polytechnic Institute.

bandgap is increased by the strain from 1.54 to 2.06 eV. The tensile strain additionally affects the bandgap center energy, decreasing it from −5.37 to −5.47 eV. As a result, the CBM is shifted to −4.44 eV. Although this energy remains still insufficient to drive the hydrogen evolution reaction spontaneously, the external bias voltage needed to split water would be drastically reduced. Stability of MX2 Compounds in Water. Comparing the solvation enthalpies, ΔHhyd, for different values n for the charge state of the M2n+(aq) and Xn−(aq) ions in aqueous solution, we find that the lowest energy charge states of the transition-metal cations and chalcogen anions in aqueous solution are +2 and −1, respectively. In contrast, the energy of the solvated ions with charge states of +4 and −2 is more than 3 eV higher than the energy of the lower charge states. We furthermore also consider the effect of possible ion association consisting of M2+X− pairs in aqueous solution.34 Figure 7 compares the resulting solvation enthalpies, ΔHsolv, of single-layer MoS2, WS2, PtS2, and PtSe2 to the calculated

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REFERENCES

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Figure 7. Solvation enthalpies of single-layer MoS2, WS2, PtS2, and PtSe2. The enthalpy of insoluble HgS is also shown for comparison.

ΔHsolv of HgS, which exhibits a negligible solubility of 1.27 × 10−27 mol/100 g of water.35 For both cases of isolated and associated ions, the solvation enthalpies, ΔHsolv, of the four single-layer materials are significantly larger than that of HgS. Because the solubility of a solid compound generally decreases exponentially with increasing solvation enthalpy,7 we expect that these single-layer materials are insoluble in water.

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CONCLUSION We have performed a systematic search for potential photocatalysts for solar water splitting in the family of transitionE

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The Journal of Physical Chemistry C

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dx.doi.org/10.1021/jp405808a | J. Phys. Chem. C XXXX, XXX, XXX−XXX