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Abstract

Two basic methods to assess correlation effects on an ab initio level for excited states in semiconductors and insulators are presented. The construction of an effective Hamiltonian and a Green's function approach are described. Both methods are based on a local description of the correlation effects, using Wannier-type Hartree-Fock orbitals as a starting point. Numerical efficiency is derived from the combination of the correlation methods with a general incremental scheme, which allows to focus on the important correlation contributions and arranges them in rapidly converging series. This scheme also gives a guideline to the economic use of suitable approximations for different contributions. The methods suggested lead to systematically improvable numerical results. Their feasibility is demonstrated in applications to the valence bands of Si and C and the band structures of the ionic crystals LiH and LiF A good overall agreement with experiments is achieved.