To begin with, we have optimized the unit cell models of single-layer graphene and 1H-WS 2 using first-principles calculations. The obtained lattice constants of graphene and WS 2 are a=b= 2.46 and 3.17 Å, respectively, which is in good agreement with previous reports. It is well clear from their respective lattice parameters that they have an accountable lattice mismatch (= 22.4 %). Thus to avoid this, it is essential to construct supercell models of both graphene and WS 2 before stacking. Therefore we constructed a (4×4) supercell model for graphene and (3×3) supercell model for WS 2 (refer Figure , Supporting Information). At this particular combination, their lattice mismatch is only ~3.3%, which is generally acceptable. Further constructed layers have been vertically stacked to form WS 2 /graphene vdW heterostructure.