Lowest-order vertex corrections to the energy gap in covalent semiconductors

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Abstract
The accuracy of the GW approximation is investigated by evaluating the lowest-order vertex contributions to the energy gap of covalent semiconductors. We compare for silicon the energy shifts of a plane-wave calculation with the results of a variational ansatz in local space. The gap corrections at the Γ point are found to be less than 0.1 eV. An analysis of the different diagrammatic contributions shows that there are two counteracting physical processes which lead to partial cancellations.