Exchange-correlation potential in semiconductors and insulators

Abstract
A local density dependence for the exchange-correlation potential is derived for a model insulating system. This derivation is contrasted with the standard methods based on the jellium model and the physical origin of the exchange-correlation potential in semiconductors and insulators is discussed. It is also shown that this new derivation can account for the failure of the local density approximation to produce the correct energy gap in bandstructure calculations.