Gunnarsson O., Schonhammer K.
The band-gap problem is studied for an exactly solvable semiconductor model. The exact exchange-correlation potential is constructed and its discontinuity is studied. Depending on the parameter range, a large or a small discontinuity is obtained. The 'scissor-operator' method is compared with the local-density approximation for an impurity calculation. In general, the local-density approximation is closer to the exact solution. Some general features of the density-functional formalism are illustrated.
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