Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model f or zirconia, which allows for the polarizability of the anions at dipole an d quadrupole levels and for crystal field splitting of the cation d orbital s, This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polar izabilities are exactly obtained by straightforward electrostatics, by anal ogy with the Hellmann-Feynman theorem as applied in first-principles calcul ations. The model correctly orders the zero temperature energies of all zir conia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measur e covalency, make a greater contribution than the polarizability to the ene rgy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also pr esented and compared with some experimental data and first-principles calcu lations. We suggest that the model will be useful for studying finite tempe rature effects by means of molecular dynamics.