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Theoretical Investigation of the Intercalation Chemistry of Li/Na Ions in Transition Metal Dichalcogenides Shaoxun Fan, Xiaolong Zou, Hongda Du, Lin Gan, Chengjun Xu, Wei Lv, Yan-Bing He, Quanhong Yang, Feiyu Kang, and Jia Li J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 02 Jun 2017 Downloaded from http://pubs.acs.org on June 2, 2017

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The Journal of Physical Chemistry

Theoretical Investigation of the Intercalation Chemistry of Li/Na Ions in Transition Metal Dichalcogenides Shaoxun Fan,† Xiaolong Zou,∗,‡ Hongda Du,† Lin Gan,† Chengjun Xu,† Wei Lv,¶ Yan-Bing He,¶ Quan-Hong Yang,¶,‡ Feiyu Kang,†,¶,‡ and Jia Li∗,† Guangdong Provincial Key Laboratory of Thermal Management Engineering and Materials, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, P. R. China, Tsinghua-Berkeley Shenzhen Institute (TBSI), Tsinghua University, Shenzhen 518055, P. R. China, and Engineering Laboratory for Functionalized Carbon Materials and Shenzhen Key Laboratory for Graphene-based Materials, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, P. R. China E-mail: [email protected]; [email protected]

∗

To whom correspondence should be addressed Guangdong Provincial Key Laboratory of Thermal Management Engineering and Materials, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, P. R. China ‡ Tsinghua-Berkeley Shenzhen Institute (TBSI), Tsinghua University, Shenzhen 518055, P. R. China ¶ Engineering Laboratory for Functionalized Carbon Materials and Shenzhen Key Laboratory for Graphene-based Materials, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, P. R. China †

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Abstract Among various two-dimensional compounds, transition metal dichalcogenides (TMDs or MX2 ) are a group of materials attracting growing research interest for potential applications as battery electrodes. Here we systematically investigate the electrochemical performance of a series of MX2 (M = Mo, W, Nb, Ta; X = S, Se) upon Li/Na intercalation through first-principles calculations. MoX2 and WX2 were found to have lower voltages while those of NbX2 and TaX2 were higher than 1.5 V. By applying the rigidband model, we found that the energy gained for electrons to transfer from Li/Na to MX2 could serve as a descriptor for characterizing voltages of MX2 .The linear relation between the descriptor and voltages is useful for screening candidates for electrodes with desired voltage. Migration barriers for Li/Na ions were approximately 0.3 eV in MoX2 /WX2 and 0.5 eV in NbX2 /TaX2 . The low barriers suggest a reasonable rate performance when these TMDs are used as electrodes. By stacking different MX2 with distinct properties, TMDs heterostructures could be adopted to provide tunable electrochemical properties, including voltage, capacity and electronic conductivity while keeping barriers for Li/Na ions little changed. Thus this strategy offers another degree of freedom for rational design of layered electrode materials.

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Introduction Since the discovery of graphene in 2004, 1 much effort has been devoted to searching for other two-dimensional (2D) materials that exhibit excellent physical and chemical properties. 2 In particular, 2D transition metal dichalcogenides (TMDs) have received considerable attention because of their interesting electronic, optical, and chemical properties. 3 2D TMDs are a group of layered compounds with a general chemical formula of MX2 , where M and X denote transition metal (e.g., Mo, W, etc.) and chalcogen (S, Se, Te) elements, respectively. Each layer of MX2 is three atoms thick, with one transition metal layer sandwiched between two chalcogen layers. These three layers are stacked together by weak van der Waals (vdW) interactions. 3,4 Due to the unique physical properties of 2D TMDs, many potential applications were explored, including logic integrated circuits, 5,6 photodetectors, 7,8 and light-emitting devices. 9,10 Besides their possible applications in electronics and optoelectronics, the layered structure of 2D TMDs also renders them promising applications for energy storage, such as in lithium-ion batteries (LIBs) and sodium-ion batteries (SIBs) 11–15 . Over the past decade, LIBs have become the most commonly used energy solution for portable electronic devices because of their high energy density. 16 However, the high cost of Li limits the use of LIBs in small- and mid-size energy storage applications. Compared to LIBs, SIBs are particularly suitable for grid-scale energy storage because of the natural abundance and easy accessibility of Na 17,18 . Nevertheless, LIBs and SIBs still suffer from low capacity and/or poor cycling stability of electrode materials. Further improvement of performance of LIBs and SIBs calls for search for other advanced electrode materials, including both cathode and anode materials. In this regard, 2D TMDs with tunable composition for both metals and chalcogenides have attracted considerable attention as promising electrode materials. 19 For the most extensively studied TMD, MoS2 , the electrochemical performance of Li/Na intercalation has been investigated both experimentally and theoretically. 20–23 Many MoS2 nanomaterials have been synthesized that show high capacity along with good cycling stability as LIB or SIB anode materials. 24,25 Regarding other TMD compounds, MoSe2 was 3



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found to be a good anode candidate for both LIBs and SIBs, with high reversible specific capacity and excellent cycling stability. 26,27 Both 2H- and 3R-NbS2 were synthesized as electrode materials for LIBs with specific capacities of about 169.5 and 169.0 mAh/g at 0.05 C rate, respectively. 28 Meanwhile, 2H-NbS2 also showed a high specific capacity of 143.6 mAh/g in SIBs. 29 These examples highlight the potential of finding ideal electrode materials in the vast choices of layered TMDs. However, there is no systematic understanding of the electrochemical performance of TMDs to guide experimental efforts to find novel electrode materials. In this work, employing first-principles calculations, we systematically investigated the electrochemical performance of a series of bulk MX2 (M = Mo, W, Nb, Ta; X = S, Se) TMDs upon Li/Na intercalation. MoX2 and WX2 are found to be good anode materials for LIBs or SIBs due to the low voltages and good electronic conductivities after intercalation. Moreover, Li and Na ions have the lowest energy barriers for the migration in WX2 , which is beneficial for the rate performance of batteries. As for NbX2 and TaX2 , the voltages are larger than 1.5 V when the Li/Na are intercalated. And the barriers for the migration of Li/Na ions are higher in NbX2 and TaX2 . Importantly, a linear dependence between the energy gained for electrons to transfer into empty states of MX2 (Wf illing ) and the voltage of the Li/Na intercalation has been established, making Wf illing a simple descriptor for the voltages of MX2 used for LIBs or SIBs. TMDs heterostructure composed of MX2 with distinct properties, are found to be able to provide tunable electrochemical performance in electronic conductivity, voltage, and capacity, offering another strategy in rational design of electrode materials.

Computational Methods All calculations were performed using density functional theory (DFT) implemented in the Vienna ab initio Simulation Package. 30 The projected augmented wave potential 31 and gen-

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eralized gradient approximation of the Perdew–Burke–Ernzerhof functional 32 were used to describe the electron–ion interaction and exchange-correlation energy, respectively. The cutoff energy was set to 650 eV. We used 2 × 2 × 1 and 2 × 2 × 2 supercells for 2H-, and 1T-phases bulk TMDs, respectively, so that both systems consisted of two layers of TMDs including eight transition metal and sixteen chalcogen atoms. The Γ-centered 7 × 7 × 5 grid and 17 × 17 × 11 k-point samplings were used for geometry optimization and electronic structure calculations, respectively. All structures were relaxed without any symmetry restriction until the total forces acted on every atom were less than 0.01 eV/˚ A. To accurately describe vdW interactions, we used the DFT-D3 empirical correction method, 33 which has been proven reliable for describing long-range vdW interactions. The climbing-image nudged elastic band method 34 was used to determine the energy barrier and minimum energy path for the migration of Li/Na ions in the interlayer of TMDs.

Results and Discussion In TMDs, each of the transition metal atoms is coordinated to six chalcogen atoms with a triangular prismatic or octahedral structure. Based on the coordination structure of the transition metal and the stacking sequence of MX2 layers, TMDs can be classified into several phases including 1T and 2H, 3 which are the most common phases. Because other phases such as 3R possess similar intercalation environments for Li/Na ions to that of the 1T or 2H phase, only these two phases are considered in our work. Figure 1 presents the structures of the 1T and 2H phases of TMDs. In the 1T phase, transition metal atoms are surrounded by chalcogen atoms forming triangular prisms and MX2 layers are stacked in AA sequence. In the 2H phase, transition metal atoms are octahedrally coordinated, with the MX2 layers stacked in AB sequence. Both 2H- and 1T-MX2 contain two kinds of intercalation sites for Li/Na ions: octahedral sites and tetrahedral sites, as shown in Figure 1. The octahedral site is more favorable

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Figure 1: Schematics of the structures of (a) 1T- and (b) 2H-MX2 ; (c) octahedral and (d) tetrahedral intercalation sites for 2H-MX2 . Transition metal atoms, chalcogen atoms and intercalated Li/Na atoms are represented by purple, yellow and green spheres, respectively. for lithiation than the tetrahedral site in MoS2 . 22 This is the case for all TMDs studied here upon Li or Na ion intercalation, most likely because of the higher coordination number and approximately three times larger space for inserted ions in octahedral sites than in tetrahedral ones. Therefore, we consider that all Li/Na ions intercalated only at octahedral sites to evaluate their stability and voltage profiles. The volume changes of TMDs during Li/Na intercalation to form the fully lithiated/sodiated state are listed in Table 1. These values indicate that Li or Na intercalation will tend to markedly expand the lattice in c direction, and the expansion caused by sodiation can be one to two times larger than that by lithiation because the ion radius of Na (1.02 ˚ A) is considerably larger than that of Li (0.76 ˚ A). Moreover, transition metal sulfides or selenides with transition metals in the same column of the periodic table have similar lattice constants before and after ion intercalation, especially in a and b directions. For pristine 1T-MX2 , the lattice constants are also similar to those of 2H-MX2 . The layered structure of the TMDs effectively mitigates the volume expansion issue commonly faced by electrode materials. 6


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Table 1: Lattice constants and volumes of deintercalated, and Li- and Na-ion intercalated MX2 and their maximum capacities.

2H phase MoS2 MoSe2 WS2 WSe2 NbS2 NbSe2 TaS2 TaSe2 1T phase MoS2 MoSe2 WS2 WSe2 NbS2 NbSe2 TaS2 TaSe2

a,b/˚ A

MX2 c/˚ A

V/˚ A3

a,b/˚ A

LiMX2 c/˚ A

V/˚ A3

a,b/˚ A

NaMX2 c/˚ A

V/˚ A3

Capacity/ mAh g−1

6.3 6.6 6.3 6.6 6.6 6.9 6.6 6.9

12.3 13.0 12.4 13.0 11.8 12.4 12.2 12.7

427.2 487.3 432.2 488.7 451.1 509.9 464.4 522.8

6.5 6.8 6.5 6.8 6.7 7.0 6.7 7.0

13.1 14.0 13.3 14.1 12.6 13.4 12.6 13.4

478.7 552.7 480.8 552.8 486.1 564.1 486.5 562.6

6.6 6.9 6.6 6.8 6.8 7.1 6.7 7.1

14.5 15.3 14.7 15.9 14.1 14.8 14.1 14.8

543.0 626.2 545.4 629.6 558.5 639.6 554.9 638.7

166.8 105.2 107.6 78.1 170.0 106.4 108.9 78.8

6.4 6.6 6.4 6.6 6.7 6.9 6.7 6.9

12.1 13.0 12.1 13.1 11.7 12.4 12.0 12.5

422.8 485.8 431.4 489.4 449.2 509.1 467.8 520.4

6.5 7.0 6.7 7.0 6.7 7.0 6.7 7.0

12.7 12.9 12.3 12.9 12.6 13.3 12.7 13.4

470.0 548.3 479.2 547.7 491.0 566.6 490.4 565.3

6.6 7.1 6.8 7.1 6.8 7.1 6.9 7.0

14.2 14.4 13.7 14.4 14.1 14.9 14.1 15.1

541.4 625.2 545.1 621.9 566.4 648.6 573.4 646.8

166.8 105.2 107.6 78.1 170.0 106.4 108.9 78.8

To provide insight into the electrochemical properties of the Li/Na intercalation process into MX2 , eight different intercalation states, from (Li/Na)0.125 MX2 to (Li/Na)MX2 , were chosen to study the phase transition, voltages, and ionic/electronic transport in the Li/Na intercalated states. By comparing the total energies of intercalated states in different phases (Figure 2 and Figure S1), phase transformations could be identified in the Li/Na intercalated MoX2 and WX2 from 2H phase to 1T phase, which is consistent with reported results. 20,21,35–37 For NbX2 and TaX2 , no such transformation occurred, which can be understood by analyzing the energy acquired for charge transfer as detailed below. Convex hulls 38 (Figure S2 and S3, Supporting Information) were constructed by calculating formation enthalpies of intermediate states to determine energetically stable states and thus voltage profiles of various TMDs. The equation used to derive voltages is expressed

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Figure 2: Total energies of 1T- and 2H-MoS2 in different (a) lithiated and (b) sodiated states. Red and black points represent 1T and 2H phases, respectively. as: 39 V =−

EAx1 M X2 − (EAx2 M X2 + (x1 − x2 )EA ) (x1 − x2 )e

(1)

where A represents Li or Na, EA and EAx M X2 represent Li/Na bulk energy per atom and total energy of Ax MX2 per unit formula, respectively. Figure 3 shows calculated average voltages as a function of Li/Na concentration in various MX2 . As seen from Figure 3, for all cases, the voltages of lithiated states are higher than those of sodiated states. Moreover, the voltages of lithiated/sodiated MoX2 and WX2 are below 1 V at first, and become higher after the phase transition, while voltages of NbX2 and TaX2 exceed 1.5 V, consistent with experimental results. 28 The relatively low voltages of MoX2 and WX2 mean that they are suitable for anode materials. Specifically, the voltage of WX2 is about 0.3 V lower than that of MoX2 , so WX2 may be capable of storing more energy as anode materials than MoX2 . If matched with a cathode that has a voltage of 4 V, WX2 can provide a volumetric energy density that is 250 Wh/L (approximately 10%) higher than that of MoX2 . The migration barrier of ions is the dominant factor that determines the rate performance of batteries. Figure S4 shows the typical migration path of an intercalated ion from one octahedral site to an adjacent one through a tetrahedrally coordinated intermediate site. The migration barriers of a Li/Na ion in different 2H-A0.125 MX2 along this path are shown in Table S1. For Li ion, it has the lowest energy barriers of around 0.25 eV in WS2 and WSe2 . Although the barriers become higher for NbX2 and TaX2 , they are below 0.6 eV in all 8


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Figure 3: Average voltages as a function of (a) Li and (b) Na concentration in Nb/TaX2 and (c) Li and (d) Na concentration in Mo/WX2 . considered TMDs, which could ensure reasonable rate performance at room temperature. 40 Regarding Na ions, its migration barriers are slightly higher in MX2 and WX2 than the barriers of Li ions while those in NbX2 and TaX2 are slightly lower compared to lithium ions. The lowest barriers of 0.27 and 0.28 eV occur in WS2 and WSe2 too. In comparison, in-plane migration barriers of Li and Na ions in graphite are about 0.48 and 0.29 eV, respectively. 41 These results suggest that WS2 and WSe2 have the highest Li-ion conductivities among considered 2D materials. Moreover, the barriers may also be influenced by the concentration of inserted ions. The migration barrier of the lithium ion in Li0.031 MoS2 is calculated to be 0.44 eV, which is close to the reported result. 23 The migration barriers of Li ions in Li0.25 MoS2 and Li0.5 MoS2 are 0.23 eV and 0.19 eV, respectively. It can be concluded that as the ion concentration increases, the migration barrier would become even lower, which is probably because the intercalation of more ions can expand the interlayer spacing more, thus allowing ions to migrate more easily. Rate performance may also be influenced by the electronic properties of materials, espe-

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Figure 4: Density of states of (a) WS2 , (b) NbS2 , (c) Li0.125 WS2 , (d) Li0.125 NbS2 , (e) LiWS2 , and (f) LiNbS2 . The Fermi level was set to zero. LiWS2 is in 1T phase while others are in 2H phases. cially for semiconducting TMDs. Therefore, density of states (DOS) were also calculated to understand the change of electronic structures and conducting behaviors of TMDs during ion intercalation. Because TMDs with transition metals in the same column of the periodic table have similar behaviors upon intercalation, WS2 and NbS2 are chosen as examples in the following discussion. Figure 4 shows the DOS of WS2 and NbS2 in different lithiated states. Pristine WS2 has a bandgap of approximately 0.9 eV, suggesting its semiconducting behavior. Once Li ions are intercalated into the vdW gap, the system becomes n-type doped and turns into a conductor. It will maintain this conducting behavior after the phase transition until fully lithiated when it turns into semiconductor again as shown in Figure 4e. In contrast, NbS2 shows a different trend, transforming from a metal in the pristine form to a semiconductor after being fully lithiated. This phenomenon can be understood by considering the rigid-band model. The electronic structure of MX2 changes little when lithiated, especially in the case of low ion concentration. The intercalation of Li ions introduces additional electrons from Li-2s orbitals into the empty bands of the MX2 substrate. Thus, the Fermi level of the lithiated MX2 will move up. For WS2 , the Fermi level moves from

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Figure 5: Voltages as a function of (a) interlayer binding energy and (b) Wf illing for different MX2 . Orange and green labels represent 2H and 1T phases. Red and Black plots represent voltages of Na and Li intercalation, respectively. The dashed lines in (b) are linear fitting of the data. the valence band maximum to the conduction band when lithiated, markedly enhancing its electronic conductivity. For NbS2 , the Fermi level moves into a gap when fully lithiated; this extreme situation is potentially harmful to electron transport. More importantly, these analyses show that the intercalation process is mainly determined by charge transfer from Li/Na to TMDs, regardless of whether they are metallic or semiconducting. To gain a deeper understanding of the intercalation, we divide it into two steps: the expansion of the interlayer spaces between TMD layers when intercalated and the interaction between intercalated Li/Na atoms and the TMDs. The space expansion between TMD layers is controlled by the interlayer interaction. As a direct reflection of the energy change of intercalation, voltage might be influenced by this interaction because a stronger interaction means more energy will be required to expand the layers, thus leading to a lower voltage. We calculated the interlayer binding energies of each MX2 and compared them with their first stage voltages. As seen in Figure 5a, the interlayer binding energies of MSe2 are larger than those of MS2 , and this may be partly responsible for the voltage trends. However, the interlayer binding energies of metallic (Ta/Nb)X2 are similar to those of (Mo/W)X2 , while their voltages are much higher. In addition, the relationships between voltages and interlayer binding energies for TMDs are not monotonic. All these suggest that the difference in interlayer binding energies of the TMDs cannot account for their change of voltage. 11



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As shown above, the main effect of intercalation can be described by electron transfer from Li/Na to the TMDs. The voltage of intercalation should be strongly correlated with the energy change of this process. Because the rigid-band model is reliable in dilute cases, we used the state-filling model 42 to calculate the energy acquired when an extra electron transferred into an empty state above the Fermi level of pristine MX2 described by:

Wf illing =

Z E′

Eρ(E)dE

Ef

(2)

where E is the energy that referenced to the vacuum level by comparing local potentials of bulk MX2 and their corresponding slabs, ρ(E) is the DOS of pristine MX2 and E ′ is derived from

R E′ Ef

ρ(E)dE = 1, which assumes that there is one extra electron transferred into MX2

per supercell. The amount of charge transfer may not be precisely one, as previously shown for 2D blue phosphorus. 43 The exact values are calculated by Bader analysis and the results are shown in Table S2. The amount of charge transfer is above 0.8 in all cases. Actually, their influence on Wf illing is small, as shown in SI, and can be approximated as one here. The lower the Wf illing is, the larger the energy gain during intercalation. We take the lithiated state of A0.125 MX2 as the dilute limit, which keeps the electronic structure of MX2 in the lithiated state similar to that of the pristine one. Figure 5b plots the corresponding voltages of each MX2 upon lithiation as a function of calculated Wf illing . Intriguingly, the voltage displays a good linear dependence on Wf illing , which confirms that electron transfer plays an important role in the Li/Na intercalation process of 2H phase TMDs. This simple relation should be applicable to all TMDs or even other layered materials, as shown in Figure 5 for NbX2 and TaX2 in their 1T phases. Such a linear correlation provides guidance to explore the electrochemical performance of other materials. Besides, Wf illing could help us to understand the phase transition in TMDs. As seen in Figure 2, the energy of 1T-MoS2 decreases faster and becomes lower than that of 2H-MoS2 as lithium/sodium concentration increases. Based on the discussions above, this trend can be partly attributed to a lower Wf illing value of

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about -5.1 eV for 1T-MoS2 compared to -4.2 eV for its 2H phase, which leads to a larger energy decrease when lithiated. It should be noted that the deviation of 1T-MoX2 and WX2 from the linear dependence originates from the distortion of the intercalated compound, as shown in Figure S5. For other four 1T-MX2 , their Wf illing are higher than those of their 2H phases which rationalizes the stability of their 1T phases. TMD heterojunctions have attracted much research interest recently because various combinations of different 2D TMDs could endow them with unique properties useful in electronics or other applications. 44,45 Such heterostructures can also be used as battery electrodes, and could potentially provide another degree of freedom to tune material properties. Complementary electrochemical performance incorporating merits of different TMDs could be potentially achieved in this way. For example, MoS2 has a relatively high capacity, while WS2 has a lower voltage than MoS2 and migration barrier of Li/Na ion in it is the lowest among all TMDs studied here. Therefore, we designed a MoS2 -WS2 heterostructure to investigate whether this combination is promising for LIBs. As shown in Table 2, the lattice constants, voltage ranges and capacities of the heterostructure all lie between those of its two components. Meanwhile, the migration barrier of Li ions in 2H-(MoS2 )0.50 (WS2 )0.50 is 0.25 eV, the same as in WS2 . Besides this semiconductor–semiconductor heterostructure, we also examined metal– semiconductor (NbS2 -MoS2 ) and metal–metal (NbS2 -TaS2 ) heterostructures. There are no phase transition found in these two materials during intercalation. Similar to the case of MoS2 -WS2 , their properties like lattice constants (Table 2) and voltage profiles (Figure S6) are also between those of their components. Interestingly, the metal–semiconductor heterostructure was always a metal during the whole intercalation process (Figure S7), which indicates an overall higher electronic conductivity than those of the other TMDs we studied. Given the vast number of layered materials with distinct properties, these results suggest that hetero-stacking could serves as an effective strategy to improve the electrochemical performance of electrodes based on 2D materials.

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Table 2: Lattice constants, voltage ranges and capacities of the heterostructure. MoS2 -WS2 NbS2 -TaS2 NbS2 -MoS2

a,b / ˚ A 6.3 6.6 6.5

c/˚ A 12.3 11.9 12.0

Voltage range / V 0.95 - 2.81 1.93 - 2.85 1.29 - 2.47

Capacity / mAh g−1 137.2 139.5 168.4

Conclusions To summarize, we have performed a series of DFT calculations to investigate the electrochemical properties of a group of TMDs intended for use as novel electrode materials. It was found that MoX2 and WX2 can be used as anode materials for LIBs and SIBs because they have relatively low voltages and high electronic conductivities during Li/Na intercalation. As for NbX2 and TaX2 , their voltages versus lithium/sodium are higher than those of MoX2 and WX2 . Our calculations indicated that the voltages during Li/Na intercalation were dominated by charge transfer from Li/Na to MX2 and the energy gained for the extra electron to transfer into an empty state above the Fermi level of pristine MX2 (Wf illing ) is a good descriptor for predicting the voltages of layered materials. Moreover, Li/Na ions have lowest migration barriers in WS2 and WSe2 , suggesting these materials should provide batteries with favorable rate performance. Based on the above assessment, heterostructures were investigated and shown to be good candidates for electrodes as it could combine merits of different TMDs. This may be a promising approach to design electrodes based on 2D materials with high electrochemical performance.

Supporting Information Available Electrochemical performance of TMDs, including migration barriers for Li/Na ions in various 2H-MX2 ; amount of charge transferred; formation enthalpy and convex hulls of MX2 upon Li/Na intercalation; total energies of 1T and 2H phase TMDs; schematic of migratin path of Li/Na ions in MX2 ; schematic structure of 1T-Li0.125 MoS2 ; voltage profiles of three kinds of heterosturctures and their components; density of states of NbS2 -MoS2 heterostructure in 14


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different lithation states. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement This work was supported by the Ministry of Science and Technology of China (Grant No. 2014CB932400), the National Natural Science Foundation of China (Grant No. 51232005), Shenzhen Projects for Basic Research (Grant No. KQCX20140521161756227) and the National Program for Thousand Young Talents of China. Guangzhou Supercomputing Center is also acknowledged for allowing the use of computational resources including TIANHE-2.

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