TDDFT from molecules to solids: The role of long-range interactions

Classical Hartree effects contribute substantially to the success of time-dependent density functional theory, especially in finite systems. Moreover, exchange-correlation contributions have an asymptotic Coulomb tail similar to the Hartree term, and turn out to be crucial in describing response properties of solids. In this work, we analyze in detail the role of the long-range part of the Coulomb potential in the dielectric response of finite and infinite systems, and elucidate its importance in distinguishing between optical and electron energy loss spectra (in the long wavelength limit q → 0). We illustrate numerically and analytically how the imaginary part of the dielectric function and the loss function coincide for finite systems, and how they start to show differences as the distance between objects in an infinite array is decreased (which simulates the formation of a solid). We discuss calculations for the model case of a set of interacting and noninteracting beryllium atoms, as well as for various realistic systems, ranging from molecules to solids, and for complex systems, such as superlattices, nanotubes, nanowires, and nanoclusters.