▎ 摘　　要

We examine the capabilities of the ab-initio calculations within density functional theory (DFT) on the 2D monolayer MoS2, graphene, and Gr-MoS2 heterostructure. The stability, elastic properties, acoustics, electronic and optical properties of the three hexagonal MoS2, graphene, and Gr-MoS2 heterostructure is presented. The energy bandgap and both Total and partial density of states are calculated within the PBE functional and are enhanced by the HSE06 functional. Gr-MoS2 hold an indirect bandgap (0.294 ev) while MoS2 is a direct bandgap (1.83 eV); moreover, graphene is used in its metal form in our calculations. The geometrically optimized relaxed structural parameters are (a = b = 3.308 angstrom, c = 11.961 angstrom), (a = b = 3.156 angstrom, c = 12.440 angstrom), and (a = b = 2.450 angstrom, c = 7.286 angstrom) for Gr-MoS2, MoS2, and Gr, respectively. The energy bandgap of the three hexagonal crystals is induced in the pressure limit (0-40) GPa. Pressure give rise to bandgap in Gr, and does not affect the MoS2 bandgap significantly, whereas the minimal bandgap for Gr-MoS2 changes drastically under pressure. The pressure-dependent elastic moduli and related mechanical characteristics are reported. The optical properties are calculated throughout incident photon energies (0-40 eV). Most of the reported properties show a relative agreement with the cited literature. However, there are no experimental nor reliable theoretical results for the Gr-MoS2 heterostructure, and to the best of the author's knowledge many of the results of Gr-MoS2 are reported first in this work.