Spectroscopic and thermal properties of minerals from density-functional perturbation theory

Ab-initio calculations based on density-functional theory have provento give a highly accurate description of structural and elastic properties of minerals under pressure. To evaluate spectroscopic, dielectric and thermal properties it is necessary to compute the second derivatives of the energy with respect to a displacement or electric field perturbation. While the Hellman-Feynmann theorem makes the computation of forces (first derivatives of the energy) straightforward, second derivatives depend on the linear response of the orbitals and density to the perturbation. I will sketch the variational formulation of density-function perturbation theory, and it's implementation in the CASTEP plane-wave code. The capabilities will be illustrated with calculation of the full phonon dispersion spectra and dielectric properties of a-quartz, ZrO₂ and NaHF₂.