Optical Properties of Solids and Nanostructures from a Many-Body f xc Kernel

Abstract

Until the late 1990’s, the situation for the ab initio calculation of optical properties of real materials was not nearly as good as that for the quasiparticle properties. As already mentioned in Chap. 10, the description of the optical response of an interacting electron system asks for the inclusion of effects beyond single-particle excitations as electron-hole interactions (excitonic effects). The important consequence of such effects is illustrated below for many different semiconductors and insulators by comparing the computed absorption spectrum neglecting electron-hole interaction with the experimental spectrum. For wide band-gap insulators there is hardly any resemblance between the spectrum from the noninteracting theory to that of experiment. In contrast to the many-body Bether-Salpeter scheme, TDDFT using the standard local and semilocal xc functionals has a number of commonly invoked failures. One example is the difficulty encountered when studying extended systems; another one is the severe underestimation of high-lying excitation energies in molecules. For example, the fact that the strong nonlocality of the exact functional is not captured by the usual approximations for xc leads to a very poor description of the polarisability per unit-length of longconjugated molecular chains. As we will see below, the main reason of this deficiency is related to the long-range nature of the xc kernel [Onida 2002]. Indeed, the advances in the development of functionals during the last years based on many-body perturbation theory and other schemes (see contributions to Part I), have broaden the field of applicability of TDDFT, as demonstrated by the variety of examples presented in this chapter. Before discussing the applications of the many-body fxc kernel, it is important to highlight the intrinsic pathologies that should be present in DFT, and that are naturally incorporated into a many-body scheme. We know that the actual functional relation between n(r) and vxc(r) is highly nonanalytical and highly nonlocal. Some specific problems related to this inherent nonlocalities of the xc functional relevant for the description of optical properties are: