A simple model of local density approximation in nonconducting systems. Application to argon and silicon

A new simple model within the local density approximation (LDA) is presented for the exchange potential in systems with an energy gap in their excitation spectrum. APW band structure calculations are performed for silicon and argon and the width of the fundamental gaps is evaluated, employing the so-developed local-exchange-only potential. The results are compared with those obtained by using in the calculation the standard LDA and the exchange-only potential of Levine and Louie. A better qualitative agreement with the experiment is found by employing the presently proposed exchange potential in comparison with the other potentials we considered.