Linear optical properties in the projector-augmented wave methodology

In this work we derive closed expressions for the head of the frequency-dependent microscopic polarizability matrix in the projector-augmented wave (PAW) methodology. Contrary to previous applications, the longitudinal expression is utilized, resulting in dielectric properties that are largely independent of the applied potentials. The improved accuracy of the present approach is demonstrated by comparing the longitudinal and transversal expressions of the polarizability matrix for a number of cubic semiconductors and one insulator, i.e., Si, SiC, AlP, GaAs, and diamond (C), respectively. The methodology is readily extendable to more complicated nonlocal Hamiltonians or to the calculation of the macroscopic dielectric matrix including local field effects in the random phase or density functional approximation, which is demonstrated for the previously mentioned model systems. Furthermore, density functional perturbation theory is extended to the PAW method, and the respective results are compared to those obtained by summation over the conduction band states.