# Abstract:

The calculation of energy gaps of insulators is an important theory objective. A commonly used method is density functional theory. Recently it was shown that an unexpected difficulty discontinuity of the exchange correlation potential arises. This paper makes a contribution towards the understanding of this problem. The discontinuity is expressed in terms of changes of the exchange correlation energy, E sub xc, of a perfect N-particle insualtor when a a conduction electron is introduced b a valence electron is removed and c an external perturbation is applied to the perfect insulator without changing N such that the density change is equal to minus the sum of the density changes in a and b.

# Subject Categories:

• Electricity and Magnetism
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