  Layered molybdenum dichalchogenides are semiconductors whose gap is
controlled by delicate interlayer interactions. The gap tends to drop together
with the interlayer distance, suggesting collapse and metallization under
pressure. We predict, based on first principles calculations, that layered
semiconductors 2H$_c$-MoSe$_2$ and 2H$_c$-MoTe$_2$ should undergo metallization
at pressures between 28 and 40 GPa (MoSe$_2$) and 13 and 19 GPa (MoTe$_2$).
Unlike MoS$_2$ where a 2H$_c$ $\to$ 2H$_a$ layer sliding transition is known to
take place, these two materials appear to preserve the original 2H$_c$ layered
structure at least up to 100 GPa and to increasingly resist lubric layer
sliding under pressure. Similar to metallized MoS$_2$ they are predicted to
exhibit a low density of states at the Fermi level, and presumably very modest
superconducting temperatures if any. We also study the $\beta$-MoTe$_2$
structure, metastable with a higher enthalpy than 2H$_c$-MoTe$_2$. Despite its
ready semimetallic and (weakly) superconducting character already at zero
pressure, metallicity is not expected to increase dramatically with pressure.
