Introduction

Hydrogen production from the water-splitting process has attracted increasing attention to meet the global energy demand and provide a viable solution to environmental issues1. An economical process for hydrogen production is based on a high-performance surface Hydrogen Evolution Reaction (HER) on an appropriate electrocatalyst2. Molybdenum and tungsten sulfides have been identified as promising noble-metal-free electrocatalysts, particularly for the HER process3,4,5,6. The basic concept of HER mechanisms has also been understood through relationships between computational approaches and corresponding experiments7,8,9,10,11,12,13,14,15. Hinnemann et al. proposed an approach based on the Density Functional Theory (DFT) in which they showed that the exposed edges of MoS2 sheets are the active sites for the adsorption of hydrogen if the binding free energy of atomic hydrogen to the electrocatalyst is close to zero9. Nevertheless, a critical issue for the application of MoS2 as an electrocatalyst in electrochemical reactions is attributed to its low electronic conductivity between two neighboring S–Mo–S sheets, bonded by van der Waals (vdW) forces16. The resistivity through the basal planes was indeed determined to be 2200 times larger than that parallel to the planes16.

There have been basically two proposed ways to improve the MoS2 electrocatalyst towards the HER: (1) increasing the density of active sites at the surface of the electrocatalyst; and (2) enhancing the electrical contact at these sites by reducing the number of layers and by placing MoS2 on highly conductive substrates, such as carbon-based materials16. Consequently, the stacking of MoS2 nanosheets with only a few layers perpendicular to a conductive substrate is expected to be an effective electrocatalyst. This can facilitate charge transfer along the edge of the electrode substrate to the active sites with minimal resistance16 while suppressing MoS2 aggregation at the same time17,18. Recent progress in heterostructures based on vdW forces at the atomic level led to new categories of vertical quantum heterostructures with sharp atomic interfaces between materials having different physicochemical properties19. Such heterostructures, including two-dimensional (2D) crystalline layers, can provide interfaces with new physical and chemical characteristics that can be potentially employed in certain applications20,21. Moreover, these 2D structures, thanks to the presence of strong covalent bonds, can already provide adequate in-plane stability. However, maintaining the stacking of these heterostructures together requires relatively weak vdW interactions22.

The design of atomic layers based on vdW heterostructures can be quite challenging when it comes to adjusting their electrocatalytic activity to the HER process, in order to render them more efficient than electrocatalysts based on metals and metal oxides23,24. It was found that no electrocatalytic activity was observed for the defect-free basal planes in most 2D layers24. However, the intrinsic electrocatalytic properties of the individual layers for a specific reaction can be significantly changed depending on the design of the various heterostructures. Such changes can be due to the electric field created between the different layers of the active electrocatalysts and the respective conductive substrates19,25,26. Namely, the vdW stacking of hexagonal boron nitride and graphene makes the corresponding heterostructure a quite active electrocatalyst towards HER despite the inactive sites of each layer2,23. In addition, to evaluate the electrochemical catalytic performance of vdW solids, the selection of the layers in the heterostructure and their sequence must be carefully considered. The importance of the stack layer sequence was addressed experimentally when the electrocatalytic activity of the vdW heterostructure of carbon nanotube (CNT) on MoS2 showed a higher HER efficiency than the layered structure of MoS2 on CNT27,28. In addition, a recent study has indicated that, when graphene is placed on top of MoS2, a higher electrocatalytic efficiency can be obtained for the HER process in acidic solution compared to the inverse configuration26.

Despite the excellent electronic properties of MoS2/carbon-derived electrocatalysts for HER, only a few studies have been carried out on the electrochemical reaction pathways of these advanced materials24,26. Specifically, a DFT calculation on MoS2/graphene complexes indicated that the presence of graphene as an underlayer of MoS2 significantly affects the charge density distribution of MoS224. In addition, the induced electric field of the MoS2/graphene hybrid provides an excess negative charge density to the system, thus improving its HER activity24. Furthermore, this sandwich configuration can also make the MoS2 basal plane near the thermo-neutral Gibbs free energy change (\({\Delta }G_{H}\) ~ 0), facilitating the activation of the MoS2 basal plane towards the HER process. Although a few studies have focused on MoS2/graphene, no report was found on the use of MoS2/CNT as a HER electrocatalyst. In the present study, we used DFT calculations to understand the molecular mechanism of the stacking sequence and subsequent layers of MoS2/CNT in the HER process. Namely, the electrocatalytic activity of a new MoS2/CNT heterostructure and the effect of MoS2 on the structural and electronic characteristics of the CNT substrate for HER were theoretically explored.

Methodology

The relaxation of the geometry and the calculation of the electronic structure were performed by the DFT approach. The stacked heterostructure of MoS2/CNT was investigated as our main system. In addition, an 8 × 8 CNT (a: 14.01 b: 13.91 c: 17.3 Å) containing 224 carbon atoms was applied to match a 4 × 4 MoS2 monolayer (a: 12.66 b: 12.66 c: 18.4 Å) comprising 16 molybdenum and 32 sulfur atoms. The lattice mismatch of the MoS2 and CNT layers was approximately 5%. In addition, a void space of 15 Å was considered on the Z-axis to ignore possible interactions between the periodic structures. The relaxation process was carried out for both the MoS2 and CNT layers, atoms, and cells, and then the binding energy of the heterostructure was computed using the following equation:

$$ E_{b} = E_{total} - E_{CNT} - E_{{MoS_{2} }} $$
(1)

where \( E_{total}\), \(E_{CNT} \), and \(E_{{MoS_{2} }}\) refer to the total energy of the MoS2/CNT heterostructure, the energy of a single CNT, and the energy of a single-layer of MoS2, respectively. It is worth mentioning that the stable heterostructure was such that the total energy of the MoS2/CNT heterostructure is lower than the energy of individual CNT and MoS2 (see Eq. (1)) Moreover, the DFT method was used based on the Dmol3 code with the Generalized Gradient Approximation (GGA) approach in the Materials Studio version 7.0 package29,30. Furthermore, the exchange–correlation functional used in this study was based on the work of Perdew, Burke and Ernzerhof (PBE)31 with the Gaussian double zeta plus polarization numerical base (DNP) set. To treat the core electrons, DFT semi-core pseudopotentials (DSPPs) were selected. The geometry relaxation and energy computations were chosen with 1 × 10–5 Ha, 0.002 Ha/Å, and 0.005 Å for energy, force, and displacement tolerances, respectively. Thanks to Grimme’s semi-empirical dispersion-corrected density functional theory (DFT-D2)32,33 for considering weak interactions with high accuracy, we used DFT-D2 instead of the standard PBE functional. Besides, to analyze the characteristics of the electron density difference, the CASTEP code34 of plane wave and ultra-soft pseudopotentials35 was applied with a plane-wave cutoff energy of 400 eV.

Results and discussion

Optimized structures

The optimized configurations of the CNT, MoS2, and MoS2 deposited on the CNT substrate are shown in Fig. 1. There is a good agreement between the Mo-S bond length of our optimized structure (2.42 Å) and the experimental one (2.41 Å)36,37. In addition, a distance of 3.37 Å was optimally achieved between the CNT and the nearest sulfur layer. Since both of the above distances are greater than 1.81 Å (the sum of the covalent radii of carbon and sulfur atoms), vdW forces might be established between the MoS2 and the CNT substrate as the main interactions. Furthermore, the average C–C optimized bond length in the CNT nanostructure studied in our work was calculated to be about 1.42 Å, which is in line with the previously reported DFT studies (1.43 Å)38,39. Moreover, these results agree with previously published works on graphene/ZnO40 and phosphorene/graphene41,42 equilibrium distances.

Figure 1
figure 1

The most stable configurations of: (a) CNT; (b) MoS2; (c) top view of MoS2/CNT; and (d) side view of MoS2/CNT. Gray, green and yellow spheres stand for C, Mo and S atoms, respectively.

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The stability of the MoS2/CNT interface was evaluated by computing the binding energy per C atom between MoS2 and the CNT substrate. The binding energy obtained was approximately 0.467 eV/atom, similar to the values reported for MoS2/graphene43 and MoS2/N-graphene44. Therefore, the value of binding energy can also be considered as a further evidence of the weak vdW interaction forces existing in the MoS2/CNT system.

Density of states (DOS)

The electronic properties of the system can be determined through the DOS while considering the HOMO–LUMO bandgap energy (Eg). This term is the minimum energy required to excite electrons from the valence band to the conduction band. A lower Eg can result in greater system conductivity and hydrogen adsorption capacity. During the formation of the vdW heterostructure, the electronic structure of the CNT on the one hand and of the MoS2 monolayer on the other hand were altered near the Fermi energy level. As seen in Fig. 2, the DOS of the MoS2/CNT structures was compared to the DOS of the isolated constituent monolayers.

Figure 2
figure 2

PDOS diagrams for: (a) CNT; (b) MoS2; and (c) MoS2/CNT. The Fermi energy level is set at zero.

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Furthermore, the projected density of states (PDOS) for the C-p orbitals in the CNT and the S-p and Mo-d orbitals in MoS2 are shown in Fig. 2a,b. It should be mentioned that CNTs are two dimensional Dirac materials with a linear dispersion near the Fermi energy level45,46, as observed in Fig. 2a. In addition, the MoS2 monolayer as a semiconductor possesses a bandgap of about 1.8 eV47. However, the bandgap obtained for MoS2 was calculated to be 2.08 eV in the current simulation (see Fig. 2b). This difference of Eg can be attributed to the unfilled d-orbital in the Mo atoms. Thus, semi-local DFT functionals cannot be used to calculate the corresponding Eg correctly, which requires the application of many-body corrections by Green’s function (GW)48 or hybrid Heyd, Scuseria, and Ernzerhof (HSE) functionals49 to compensate for the bandgap differences of 0.28 eV in the semi-local DFT functionals. However, to reduce computational costs, such bandgap corrections were ignored because the semi-empirical DFT-D2 method can achieve sufficient accuracy for the calculation of structural and electronic properties of the MoS2/CNT interface50.

Furthermore, the bottom of the conduction band and the top of the valence band originate mainly from the Mo-d orbitals and both the Mo-d and S-p orbitals, respectively (see Fig. 2b). In addition, it can be seen that the Mo-d and S-p orbitals were hybridized together at the top of the valence band (see Fig. 2b). It can be concluded from Fig. 2a that the half-filled p orbitals perpendicular to the planar structure create the π and π* bands in the electronic configuration of CNT. Moreover, at the corner of the Brillouin zone of the CNT, both bonding and antibonding bands touch at a single point near the Fermi energy level. Furthermore, the PDOS of MoS2/CNT (see Fig. 2c) is displayed relative to the partial d-DOS (blue) of Mo in MoS2 and the p-DOS (red) of C in the CNT. It can be seen that the Fermi energy level of the MoS2/CNT heterostructure is characterized by the Dirac-cone-like characteristic from CNT and a gap-like characteristic from MoS2 (see Fig. 3c). Furthermore, the location of PDOSs for CNT is similar to that of MoS2/CNT where there is also a remarkable change in the intensity and profile of the PDOSs of MoS2.

Figure 3
figure 3

Band structures of: (a) CNT; (b) MoS2; and (c) MoS2/CNT.

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Band structure analysis

To evaluate the impact of stacking configurations on the bandgap and electronic properties of the MoS2/CNT heterostructure, structural and electronic calculations were performed separately on the freestanding CNT and the MoS2 monolayer. As seen in Fig. 3a, the bandgap obtained for an isolated CNT is determined to be 0.017 eV. Besides, a bandgap structure based on a linear Dirac dispersion can be observed for the isolated CNT near the Fermi energy level. The band structure of MoS2 is illustrated in Fig. 3b, which shows a direct bandgap of 2.01 eV with the conduction and valence bands positioned at the K point. The resultant bandgap is greater than the reported experimental value (about 1.80 eV)47. However, this discrepancy can be corrected by applying the GW approximation technique, which is not the subject of our study.

The band structure of the MoS2/CNT heterostructure can be determined by the energy bands of the CNT and MoS2. Figure 3c shows the linear dispersion bands of the CNT, which are located in the large energy gap of MoS2 while the electronic energy band of the pristine CNT can be found without any major change. However, a significant change near the Fermi energy level can be observed. The results obtained from the band structure can evidently show the efficient interactions between CNT and MoS2 that improve the electronic properties of the CNT, the band gap of the heterostructure having dropped to 0.008 eV.

Determination of charge density and charge transfer

Figure S1 illustrates the variations in the average atomic charge (\({\Delta }q\)) on the sulfur and molybdenum atoms specified by Hirshfeld’s charge analysis. S1–S4 and M1–M4 represent different positions of sulfur and molybdenum atoms, respectively, in the MoS2/CNT heterostructure. The average atomic charge obtained on the MoS2 monolayer for S and Mo atoms was calculated to be − 0.114 and 0.229 a.u., respectively. Table S1 summarizes the charges on Mo and S atoms in the MoS2/CNT heterostructure. It should be noted that the charge on Mo atoms remains almost unchanged at the value of ∼ 0.229 a.u, whereas it changes negatively and significantly on sulfur atoms.

Figure 4 illustrates the difference in charge density of the current MoS2/CNT system. The charge depletion is observed at the two middle neighboring S and C planes. Moreover, no orbital overlap between the MoS2 layer and the CNT can be observed due to the weak vdW interactions between MoS2 and the CNT. Besides, the charge transfer, involving the total sum of the Hirshfeld charge populations, was analyzed and computed for the MoS2 layer. A negative charge value means that the charge is transferred from the CNT to MoS2, while the charge transfer from MoS2 to the CNT reflects its positive charge value. Hence, a negative charge value of − 0.051 a.u. obtained for MoS2/CNT implies a charge transfer from the CNT to the MoS2 monolayer.

Figure 4
figure 4

Spatial mapping of charge density differences for: (a) a MoS2 monolayer; and (b) the MoS2/CNT heterostructure. Regions of electron accumulation and depletion are denoted by blue and red lobes, respectively. BIOVIA, Dassault Systèmes, Materials Studio, version 7. https://bit.ly/38lRRQR.

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Mechanism of the Hydrogen Evolution Reaction (HER)

The superior electronic structure of MoS2/CNT relative to pristine MoS2 means that this heterostructure can be used effectively as an electrocatalyst for the HER process. A well-known mechanism of HER, known as Volmer–Heyrovsky or Volmer–Tafel mechanism, can be expressed as follows51,52:

$$ 2{\text{H}}^{ + } + 2{\text{e}}^{ - } \to 2{\text{H}}^{*} \quad \left( {{\text{Volmer}}} \right) $$
(2)
$$ {\text{H}}^{*} + {\text{H}}^{ + } \to {\text{H}}_{{2({\text{g}})}} \quad \left( {{\text{Heyrovsky}}} \right) $$
(3)
$$ {\text{H}}^{*} + {\text{H}}^{*} \to {\text{H}}_{{2({\text{g}})}} \quad \left( {{\text{Tafel}}} \right) $$
(4)

According to this mechanism, a hydronium ion first adsorbs on the surface and forms a hydrogen radical. Then, two hydrogen radicals combine and form a hydrogen molecule. Basically, HER activity can be investigated by the adsorption of hydronium ions and the activation energy barrier. The adsorption energy of the hydronium ion adsorbed on MoS2 and MoS2/CNT monolayer are calculated to be 0.0057 eV and 0.0039 eV, respectively, indicating an easier adsorption of hydronium ion on the MoS2/CNT heterostructure than on the MoS2 monolayer.

To characterize the HER activity of the proposed heterostructure, we considered the initial step of the HER process (Volmer reaction) as the rate-determining step (RDS). As illustrated in Fig. 5, the path of minimum energy for the transfer of one of the solvated protons to the MoS2 surface in the 4 × 4 supercell consists of three steps: initial, transition and final states (IS, TS and FS, respectively). It can be seen that the adsorption of H atom at each step occurs on the edge of S atom, signifying the electrocatalytic activity of the edge S atoms towards HER. In addition, the energy barrier of MoS2/CNT and MoS2 monolayer is calculated to be 0.024 eV and 0.067 eV, respectively. This observation might be ascribed to the electron redistribution of the edge S atom after the adsorption of the CNT53. From the Hirshfeld charge analysis, the edge S atom of MoS2/CNT gains − 0.190 e (see Table S1) while that of pristine MoS2 acquires − 0.114 e. This suggests that due to electrostatic attraction, the edge S atom in MoS2/CNT has a more negative charge and thus a greater interaction with the H atom. As a result, it can be seen that the CNT reduces the energy barrier (or the onset potential of HER), thus improving the intrinsic activity of MoS2.

Figure 5
figure 5

Minimum-energy pathway of the Volmer reaction on: (a) MoS2; and (b) the MoS2/CNT heterostructure. IS, TS and FS stand for initial, transition and final states, respectively. BIOVIA, Dassault Systèmes, Materials Studio, version 7. https://bit.ly/38lRRQR.

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Moreover, the other two primary steps which can be plausible for H2 evolution in the second step of the HER process encompass Heyrovsky and Tafel reactions. In the case of Heyrovsky reaction (as the initial step), H2 molecule is formed through the reaction of the proton (in the water layer) with an adsorbed hydrogen (see Eq. (3)). Figure 6 displays the estimated minimum-energy paths at two dissimilar structures. It is evident that an adsorbed H atom on a sulfur one reaches an H atom of a hydronium ion in the water layer. This is followed by breaking the adsorbed H from the surface, forming H2 molecule within the water layer. In the TS (Fig. 6), the interfacial adsorbed H is separated from the surface and the S–H distance increased from 1.301 Å in the IS to 2.391 Å in the MoS2 monolayer. At the same time, the proton from H3O+ travels toward the separated H atom, forming a molecule with H–H bond lengths of 0.760 Å and 0.756 Å in the MoS2 monolayer and MoS2/CNT heterostructure, respectively. The evolved H2 molecule is detached from the surface in the FS. An activation energy of 0.68 eV was determined for MoS2 while such energy barrier drops to 0.41 eV for the MoS2/CNT heterostructure (Fig. 6). Thus, the energy barrier is far greater for the Heyrovsky reaction than that for the Volmer reaction, suggesting that the H desorption procedure would be the RDS of the Volmer − Heyrovsky pathway.

Figure 6
figure 6

Minimum-energy pathway of the Heyrovsky reaction on: (a) MoS2; and (b) MoS2/CNT heterostructure. BIOVIA, Dassault Systèmes, Materials Studio, version 7. https://bit.ly/38lRRQR.

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Furthermore, adjoining H atoms coupling to surface S atoms perform the Tafel reaction on MoS2 (see Eq. (4)). Figure 7 depicts the minimum-energy path of direct recombination of two adjoining protons adsorbed on S active sites. Due to the absence of charge transfer over the interface, the entire energies along the path are not amended for possible deviance. In the IS, the distances between the two H atoms are 3.922 Å and 3.817 Å in the MoS2 monolayer and MoS2/CNT heterostructure, respectively. The two S–H bond lengths in the MoS2 monolayer and MoS2/CNT heterostructure are 1.309 Å and 1.324 Å, respectively. However, the formed H2 molecule undergoes desorption from the surface with a H–H bond length of 0.750 Å for both of the developed structures in the FS. In the MoS2 monolayer and MoS2/CNT heterostructure, the estimated energy barrier of direct recombination values are 1.27 eV and 0.56 eV, respectively, which are markedly greater than that for the Volmer reaction. Therefore, the RDS in the Volmer–Tafel reaction is the H desorption (Tafel step).

Figure 7
figure 7

Minimum-energy pathway of the Tafel reaction on: (a) MoS2; and (b) the MoS2/CNT heterostructure. BIOVIA, Dassault Systèmes, Materials Studio, version 7. https://bit.ly/38lRRQR.

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Overall, a comparison of the energy barriers for the Heyrovsky and Tafel reactions on MoS2 monolayer and MoS2/CNT heterostructure reveals that the Tafel reaction should surmount elevated barriers of 1.27 and 0.56 eV, respectively, while it is possible for the Heyrovsky reaction to proceed more straightforwardly. This indicates more efficiency of the Heyrovsky reaction where the Volmer − Heyrovsky mechanism is the major pathway of HER. In addition, finding from the recent reports shows that HER potentially occurs through the Volmer − Heyrovsky process on the basal plane of 1 T-MoS2, 2H-MoS2 and Ni-MoS2/RGO52,54,55.

Conclusion

The present study theoretically investigates the synergistic electrocatalytic activity of the MoS2/CNT heterostructure towards the HER process by applying DFT simulations. The results indicated a weak van der Waals interaction between the CNT and the MoS2 monolayer. Moreover, a distance of 3.37 Å was determined between them, and the binding energy per C atom in this system was found to be approximately 0.467 eV. The bandgap structure indicated that the linear Dirac-like dispersion of CNT near the Fermi energy level remains unchanged in the MoS2/CNT interface as well. However, it was found that a bandgap around 8 meV was calculated at the Dirac K-point of the CNT in the MoS2/CNT interface. Finally, it was confirmed that the presence of CNT can improve the electronic conductivity while reducing the energy barrier in the MoS2/CNT heterostructure for the HER process.