The Bethe-Salpeter equation: a first-principles approach for calculating surface optical spectra

In this paper we review the first-principles theoretical framework of the Bethe–Salpeter equation which is nowadays the state-of-the-art approach for including self-energy, local fields and excitonic effects in the surface optical response. Two different approaches for calculating the dielectric screening will be described. In both cases a parallel and efficient iterative algorithm to find numerically the solution of the BSE equation has been implemented. In fact, if the surface states are not energetically separated from the bulk states and if one is interested in describing a large energy window, the traditional approach involving a full diagonalization of a very large excitonic Hamiltonian is prohibitive. The reflectance anisotropy spectrum of the monohydride Si(100) is considered and compared with experiments. A comparison of the results obtained within different treatments of the electron–hole screening is made. Convergence and numerical problems are discussed