Variational density-functional perturbation theory for dielectrics and lattice dynamics

The application of variational density functional perturbation theory (DFPT) to lattice dynamics and dielectric properties is discussed within the plane-wave pseudopotential formalism. We derive a method to calculate the linear response of the exchange-correlation potential in the GGA at arbitrary wavevector. We introduce an efficient self-consistent solver based on all-bands conjugate-gradient minimization of the second order energy, and compare the performance of preconditioning schemes. Lattice-dynamical and electronic structure consequences of space-group symmetry are described, particularly their use in reducing the computational effort required. We discuss the implementation in the CASTEP DFT modeling code, and how DFPT calculations may be efficiently performed on parallel computers. We present results on the lattice dynamics and dielectric properties of $\ensuremath{\alpha}$-quartz, the hydrogen bonded crystal $\mathrm{Na}\mathrm{H}{\mathrm{F}}_{2}$ and the liquid-crystal-forming molecule 5CB. Excellent agreement is found between theory and experiment within the GGA.