The Kohn-Sham Gap as Example for an Explicit Density Functional
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It is well known that the density fully characterizes the ground state of a system. The use of the total energy as a functional of the density led to the usual implementation of Kohn-Sham(KS)-DFT. But other quantities, apart from the total energy, are rarely investigated. In this work we examine the KS-gap as a functional of the density. Numerically the inversion of the KS-equation is done iteratively. Different schemes are compared.
A purpose of the work is to investigate the sensitivity of a system to inaccuracies in the density, especially in view of a subsequent calculation of excited state properties. The KS-gap acts here as an easily accessible indicator.
We also use the density-functional formulation for the band gap to discuss the relation between the Kohn-Sham gap and the electron addition and removal gap.