We present a recently developed approach to calculate electron-hole excitations 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 treated within density-functional theory. Second, the single-particle spectrum of the electrons and holes is obtained within the $\mathrm{GW}$ approximation to the electron self-energy operator. Finally, the electron-hole interaction is calculated and a Bethe-Salpeter equation is solved, yielding the coupled electron-hole excitations. The resulting solutions allow the calculation of the entire optical spectrum. This holds both for bound excitonic states below the band gap, as well as for the resonant spectrum above the band gap. We discuss a number of technical developments needed for the application of the method to real systems. To illustrate the approach, we discuss the excitations and optical spectra of spatially isolated systems (atoms, molecules, and semiconductor clusters) and of extended, periodic crystals (semiconductors and insulators).

• Received 13 April 2000

DOI:https://doi.org/10.1103/PhysRevB.62.4927