First-principles study of the Jahn-Teller distortion in transition metal dihydrides.

The transition metal dihydrides TiH$_{2}$ and ZrH$_{2}$ present the fluorite structure (CaF$_{2})$ at high temperature but undergoes a tetragonal distortion with c/a$<$1 at low temperature. Early electronic band structure calculations have shown that TiH$_{2}$ and ZrH$_{2}$ in the cubic phase display a very flat band at the Fermi level. Thus the low temperature tetragonal distortion has been associated to a Jahn-Teller effect. Previous total energy calculations of the tetragonal distortion for TiH$_{2}$ within the Density Functional Theory (DFT), find that the ground state correspond to a tetragonal structure with c/a$>$1, in contradiction with the experimental observation (c/a$<$1). In the present work, we have performed full-potential LAPW calculations using the Local Density Approximation (LDA) and the Generalized Gradient Approximation (GGA) for the exchange correlation functional energy. Special attention was paid to the convergence of the total-energy calculations, since in TiH$_{2}$ the energy differences for a tetragonal distortion at constant volume are only fractions of 1 mRy. We find that the ground state of TiH$_{2}$ and ZrH$_{2}$ corresponds to a tetragonal distorted fluorite structure with c/a$<$1, in agreement with the experimental observations. The same behavior is predicted for HfH$_{2}$. The electronic band structure of the three systems is analyzed in the context of the Jahn-Teller effect.