The electronic structure and energetics of the tetragonal distortion for the fluorite-type dihydrides TiH2, ZrH2, and HfH2 are studied by means of highly accurate first-principles total-energy calculations. For HfH2, in addition to the calculations using the scalar relativistic (SR) approximation, calculations including the spin-orbit coupling have also been performed. The results show that TiH2, ZrH2, and HfH2 in the cubic phase are unstable against tetragonal strain. For the three systems, the total energy shows two minima as a function of the c/a ratio with the lowest-energy minimum at c/a < 1 in agreement with the experimental observations. The band structure of TiH2, ZrH2, and HfH2 (SR) around the Fermi level shows two common features along the two major symmetry directions of the Brillouin zone, Gamma-L and Gamma-K, a nearly flat doubly degenerate band, and a van Hove singularity, respectively. In cubic HfH2 the spin-orbit coupling lifts the degeneracy of the partially filled bands in the Gamma-L path, while the van Hove singularity in the Gamma-K path remains unchanged. The density of states of the three systems in the cubic phase shows a sharp peak at the Fermi level. We found that the tetragonal distortion produces a strong reduction in the density of states at the Fermi level resulting mainly from the splitting of the doubly-degenerate bands in the Gamma-L direction and the shift of the van Hove singularity to above the Fermi level. The validity of the Jahn-Teller model in explaining the tetragonal distortion in this group of dihydrides is discussed.
