Implementation of the finite field perturbation method in the CRYSTAL program for calculating the dielectric constant of periodic systems

The finite field approach has been implemented in the periodic ab initio CRYSTAL program and been used for calculating the dielectric constants of crystalline LiF and MgO (FCC structure) and BeO (wurtzite structure). To maintain the periodicity along the applied field direction, a "sawtooth" potential is used in conjunction with a supercell scheme. Supercells four to five times longer than the primitive cell in the direction of the applied field provide well-converged results. The influence of the computational parameters is discussed. An alternative scheme has also been implemented, for inner check, that consists of applying a static electric field to a slab of increasing thickness in the direction orthogonal to the surface; the dielectric response at the center of the slab is shown to converge rapidly to the bulk value evaluated with the sawtooth field. The method is accurate and permits the determination of nonlinear corrections to the dielectric constant. When used in conjunction with the local density approximation (LDA) scheme, it provides for the dielectric constant of the three above-mentioned compounds values close to those recently obtained with a time-dependent density functional theory approach.