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We present an implementation of the linear density response function withinthe projector-augmented wave (PAW) method with applications to the linearoptical and dielectric properties of both solids, surfaces, and interfaces. Theresponse function is represented in plane waves while the single-particleeigenstates can be expanded on a real space grid or in atomic orbital basis forincreased efficiency. The exchange-correlation kernel is treated at the levelof the adiabatic local density approximation (ALDA) and crystal local fieldeffects are included. The calculated static and dynamical dielectric functionsof Si, C, SiC, AlP and GaAs compare well with previous calculations. Whileoptical properties of semiconductors, in particular excitonic effects, aregenerally not well described by ALDA, we obtain excellent agreement withexperiments for the surface loss function of the Mg(0001) surface with plasmonenergies deviating by less than 0.2 eV. Finally, we apply the method to studythe influence of substrates on the plasmon excitations in graphene. OnSiC(0001), the long wavelength $\pi$ plasmons are significantly damped althoughtheir energies remain almost unaltered. On Al(111) the $\pi$ plasmon iscompletely quenched due to the coupling to the metal surface plasmon.

Linear density response function in the projector-augmented wave method: Applications to solids, surfaces, and interfaces