  We describe an empirical, self-consistent, orthogonal tight-binding model for
zirconia, which allows for the polarizability of the anions at dipole and
quadrupole levels and for crystal field splitting of the cation d orbitals.
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 polarizabilities
are exactly obtained by straightforward electrostatics, by analogy with the
Hellmann-Feynman theorem as applied in first-principles calculations. The model
correctly orders the zero temperature energies of all zirconia polymorphs. The
Zr-O matrix elements of the Hamiltonian, which measure covalency, make a
greater contribution than the polarizability to the energy differences between
phases. Results for elastic constants of the cubic and tetragonal phases and
phonon frequencies of the cubic phase are also presented and compared with some
experimental data and first-principles calculations. We suggest that the model
will be useful for studying finite temperature effects by means of molecular
dynamics.
