Computational data of molybdenum disulfide/graphene bilayer heterojunction under strain

The data presented in this paper refer to the research article “Dry and Hydrated Defective Molybdenum Disulfide/Graphene Bilayer Heterojunction Under Strain for Hydrogen Evolution from Water Splitting: A First-principle Study”. Here, we present the Density Functional Theory (DFT) data used to generate optimal geometries and electronic structure for the MoS2/graphene heterostructure under strain, for dry and hydrated pristine and defect configurations. We also report DFT data used to obtain hydrogen Gibbs free energies for adsorption on the MoS2 monolayer and on graphene of the heterostructure. The DFT data were calculated using the periodic DFT code CRYSTAL17, which employs Gaussian basis functions, under the hybrid functionals PBE0 and HSE06. Moreover, we also report the data used for Quantum Theory of Atoms in Molecules (QTAIM) and Non-covalent Interaction (NCI) analysis calculations. These data were obtained using the optimized unit cell configurations from the periodic DFT and inputted to Gamess program, thus generating files that could be read by the Multiwfn program used for QTAIM and NCI calculations.


Value of the Data
• We provide (a) structural and electronic information for dry and hydrated pristine and defect MoS 2 /graphene as calculated by density functional theory (DFT) and (b) outputs from quantum theory of atoms in molecules (QTAIM) and Non-covalent Interaction (NCI) calculations. Defect MoS 2 /graphene heterostructures serve as hydrogen evolution catalysts (HER). • Electronic information shows a bandgap opening at the Dirac point region, which is affected by hydration and vacancies. Thus, this bandgap could be engineered for producing efficient HER electrocatalysts. • The presence of QTAIM S-C bond critical points and NCI calculations show that MoS 2graphene interaction is var der Waals. • We also provide data that support the MoS 2 /graphene use as HER, when S and C defects are included in the lattice. These data can be further used by experimentalists to examine the needed concentration of S that produce an HER catalyst with hydrogen Gibbs energy of approximately zero. Fig. 1 shows the optimal geometries for dry and defect MoS 2 /graphene heterostructures with and without interacting waters on the S surface of the MoS 2 , as calculated by the PBE0 functional. We found no significant differences in the above optimal geometries for calculations using the HSE06 functional. Fig. 1 (g)-(l) show that one of the three waters in the unit cell dissociates at the S vacancy region. Table 1 shows the Dirac point locations (E D ), minigaps ( E), and MoS 2 bandgaps (E g ) for pristine and defect configurations of this work under the HSE06 calculations. Corresponding E D , E, and E g using the PBE0 functional are shown on Table 2 . This information is produced by electronic band structure calculations. The PBE0 cal overestimate the MoS 2 bandgaps E g relative to the HSE06 calculations, as expected. Table 3 shows the Gibbs free energy G H for H adsorption on MoS 2 and graphene for each MoS 2 /graphene configuration under the PBE0 calculations. For H/MoS 2 , G H is positive for adsorption on pristine MoS 2 and negative, when S vacancies are present. Fig. 2 shows QTAIM molecular graphs and NCI isosurfaces were obtained from the DFT optimized unit cell geometries for dry MoS 2 /graphene using Multiwfn and plotted via VMD (PBE0 calculations). Thus, for these calculations a molecular cluster has been used.

Data Description
The submitted data are grouped in five directories. Two directories contain CRYSTAL17 input and output files from electronic band structure and densities of states (DOS) calculations and from optimized geometries. Each of these directories contain information from HSE06 and PBE0 calculations, which are found in separate subdirectories. The other three directories contain HER calculations for the PBE0 functional (CRYSTAL 17 input and output files), Gamess input and output files, and QTAIM-NCI Multiwfn output files.

Experimental Design, Materials and Methods
We constructed the pristine dry MoS 2 /graphene heterostructure under comprehensive strain by using a 2H-MoS 2 three-layer 4 × 4 supercell of 48 atoms overlayered on a 3 √ 3 × 3 √ 3 R 30 • supercell monolayer graphene. This configuration contains 32 S, 16 Mo, and 54 C atoms totaling 102 atoms. Hydrated MoS 2 surfaces contain three water molecules per unit cell. These waters are placed on the S layer away from graphene. We built defective MoS 2 /graphene heterostructures by considering all combinations of single (V S ) and non-adjacent double S vacancies (V S2 ) in the MoS 2 with a single C vacancy (V C ) in the graphene layer.
Optimized geometries and electronic structure of all MoS 2 /graphene configurations were obtained using the periodic DFT code CRYSTAL17 [3] , which employs Gaussian basis functions centered at the atoms. We used two DFT hybrid functionals for our calculations: The PBE0 nonempirical/parameter-free functional [ 4 , 5 ] and the HSE06 screened hybrid functional of Heyd, Scuseria, and Ernzerhof. HSE06 provides band gaps in better agreement with experimental findings [6] . Long-range electron correlations responsible for van der Waals interactions were treated by the Grimme D3 semiempirical correction [7] . The S, C, O, and H atoms are described by all-electron basis sets optimized for crystalline calculations. Specifically, the triple-zeta valence with polarization (TZVP) functions were used for the S atoms as 73211/5111/1 for s/p/d functions, where 73211 stands for 7, 3, 2, and 1 contracted Gaussians to describe the 1s shell, 2s, 3s, and 4s shells, respectively. Moreover, the C and H atoms were described as 6211/411/1 for s/p/d functions and 311/1 for s/p functions, respectively, whereas the O atoms used the splitvalence basis set 8-411G(2d1f), where the 6 electrons on the 2s and 2p shells were described by 4 sp functions. Mo atoms use effective core potentials (ECP) and double zeta basis set with polarization for its valence as 311/41/41/1 for s/p/d functions [8] . Geometry optimizations were obtained using a 6 × 6 Monkhorst-Pack, whereas the electronic band structures calculations and DOS used a 24 × 24 grid. Band structure calculations used the following path M--K-M-, with M (1/2, 0, 0), (0, 0, 0), and K (1/3, 1/3, 0). The point of the supercell Brillouin zone (BZ) coincides with the K point of the unit cell BZ. Thus, the E D appears at the point.

Hydrogen adsorption energies E ads (H) are calculated by
where E( Mo S 2 / Graphene − H ) and E( Mo S 2 / Graphene ) are the total energies for the heterostructure with and without adsorbed H, respectively and E( H 2 ) is the energy of the free H 2 . The Gibbs free energy G H for the adsorbed hydrogen is given by where G ZPE and S H are the zero-point energy (ZPE) and entropy difference between the adsorbed and the gas phase states, respectively. G H values are approximated as [ 9 , 10 ] and NCI [11] information were obtained using the Multiwfn [12] program. This program does not accept information directly from CRYSTAL17 output files. For this reason, we extracted a cluster from the periodic layer from the CRYSTAL17 output files, which corresponds to the optimal geometry per configuration, and generated Gamess [13] input files for single energy calculations. These outputs from Gamess, served as inputs to Multiwfn. QTAIM calculations provided the electron density ( ρ( r ) ) and its Laplacian ( ∇ 2 ρ( r ) ) at all bond critical points. Since QTAIM analyses are basis set and method independent, [14] we only used the PBE0 functional here. Weak interactions were studied via the NCI method, by calculating the reduced density gradient (RDG) parameter ( ∝ | ∇ 2 ρ( r ) | ρ( r ) 4 / 3 ) and plotting the RDG map.

Ethics Statements
None.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: