Table of Contents
This chapter will begin development after the chapter entitled Orbital-Dependent Functionals and Exact-Exchange Methods has been completed.
In a future revision of this document, we will discuss how van Gisbergen et al.  used very accurate Slater-type orbitals (STOs) to obtain nearly exact xc potentials for the He, Be, and Ne atoms, thereby avoiding the incorrect asymptotic behavior and oscillatory behavior in that can result from the use of a finite set of Gaussian-type orbitals (GTOs). We will also discuss how Burke et al.  used the exact Kohn-Sham potentials calculated by Umrigar and Gonze  for the He and Be atoms to eliminate errors introduced in the calculation of the ground-state properties, and how they isolated the dependence of the excitation energies on the TDDFT exchange-correlation kernel . They presented a hybrid functional for the kernel which incorporates both the SIC-ALDA and the KLI exact-exchange only approximations. They also demonstrated the improvement of this hybrid functional over three other approximations: ALDA, the KLI exact-exchange only, and SIC-ALDA.
|...to be continued.|