A combination of periodic Hartree-Fock theory, quasiharmonic lattice dynamics, and molecular dynamics is used to study the behavior of MgF2 at elevated temperatures and/or high pressures, Particular attention is paid to the pressure-induced transition from the rutile to the fluorite structure in view of earlier theoretical estimates of the transition pressure, which differ widely. It is shown that previously reported potentials obtained by fitting to empirical data fail to reproduce thermodynamic properties. To rectify this, a new set of consistent two-body potentials has been derived from nb initio periodic Hartree-Fock calculations. Lattice dynamics calculations in the quasiharmonic approximation based on these potentials has been used to study the two phases of MgF2 at high T and P. The resulting transition pressure and that obtained directly from Hartree-Fock calculations in the static limit are both less than or equal to 30 GPa, which is close to the experimental value but appreciably lower than a previous molecular dynamics value of over 130 GPa. The variation of quantities such as (partial derivative P/dT)(V) which play a central role in the formulation of approximate equations of state is also considered. (C) 1997 American Institute of Physics.