Electron-hole excitations and optical spectra from first principles

We present a recently developed approach to calculate electron-hole excitat ions and the optical spectra of condensed matter from first principles. The key concept is to describe the excitations of the electronic system by the corresponding one- and two-particle Green's function. The method combines three computational techniques. First, the electronic ground state is treat ed within density-functional theory. Second, the single particle spectrum o f the electrons and holes is obtained within the GW approximation to the el ectron self-energy operator. Finally, the electron-hole interaction is calc ulated and a Bethe-Salpeter equation is solved, yielding the coupled electr on-hole excitations. The resulting solutions allow the calculation of the e ntire optical spectrum. This holds both for bound excitonic states below th e band gap, as well as for the resonant spectrum above the band gap. We dis cuss a number of technical developments needed for the application of the m ethod to real systems. To illustrate the approach, we discuss the excitatio ns and optical spectra of spatially isolated systems (atoms, molecules, and semiconductor clusters) and of extended, periodic crystals (semiconductors and insulators).