  First-principle calculations with different exchange-correlation functionals,
including LDA, PBE and vdW-DF functional in form of optB88-vdW, have been
performed to investigate the electronic and elastic properties of two
dimensional transition metal dichalcogenides(TMDCs) with the formula of
MX$_2$(M=Mo,W; X=O,S,Se,Te) in both monolayer and bilayer structures. The
calculated band structures show a direct band gap for monolayer TMDCs at the K
point except for MoO$_2$ and WO$_2$. When the monolayers are stacked into
bilayer, the reduced indirect band gaps are found except for bilayer WTe$_2$,
in which direct gap is still present at the K point. The calculated in-plane
Young moduli are comparable to graphene, which promises the possible
application of TMDCs in future flexible and stretchable electronic devices. We
also evaluated the performance of different functionals including LDA, PBE, and
optB88-vdW in describing elastic moduli of TMDCs and found that LDA seems to be
the most qualified method. Moreover, our calculations suggest that the Young
moduli for bilayers are insensitive to stacking orders and the mechanical
coupling between monolayers seems to be negligible.
