In this work all the computations were performed using the first-principles based DFT as implemented in the Vienna Ab-initio Simulation Package (VASP). Here all the atoms are described by projector-augmented wave (PAW) pseudopotential, and we have used generalized gradient approximations (GGA) for correlating the electron-electron interactions. All the ions are relaxed self-consistently without considering any symmetry, and the iterative relaxation processes are carried out until Hellmann-Feynman forces on each ion are converged to less than 0.01 eV/Å. For the optimization of WS 2 /graphene heterostructure, we have chosen Gamma centered kpoint mesh of 5×5×1 k-meshes. To understand the effect of van der Waals interaction we have used nonlocal DFT-D3 functional throughout calculations. The convergence of energy is set to be 10 -6 eV in all the calculations. In order to avoid the interaction of this heterostructure with its periodic image along z-axis we kept sufficiently large vacuum (≈15 Å) along this direction. We have also performed the spin-polarized calculations in all the cases, to compare the magnetic and non-magnetic solutions, but results show that system prefers to be stabilized in non-magnetic solutions. Further, denser k-mesh (45× 45 × 1) is used for deducing the electronic density of states (DOS) calculations. Further we also calculated Bader charges for all the system to understand the charge transfer in this heterostructure. Eventually, in order to investigate the energy barrier associated with the diffusion of Li atoms through the heterostructure we used climbing image nudged elastic band (CI-NEB) method, as implemented in VASP code.