  Recent experiments showed the distinct observations on the transition metal
ditelluride NiTe$_2$ under pressure: one reported a superconducting phase
transition at 12 GPa, whereas another observed a sign reversal of Hall
resistivity at 16 GPa without the appearance of superconductivity. To clarify
the controversial experimental phenomena, we have carried out first-principles
electronic structure calculations on the compressed NiTe$_2$ with structure
searching and optimization. Our calculations show that the pressure can
transform NiTe$_2$ from a layered P-3m1 phase to a cubic Pa-3 phase at $\sim$10
GPa. Meanwhile, both the P-3m1 and Pa-3 phases possess nontrivial topological
properties. The calculated superconducting $T_c$'s for these two phases based
on the electron-phonon coupling theory both approach 0 K. Further magnetic
transport calculations reveal that the sign of Hall resistance for the Pa-3
phase is sensitive to the pressure and the charge doping, in contrast to the
case of the P-3m1 phase. Our theoretical predictions on the compressed NiTe$_2$
wait for careful experimental examinations.
