## Chapter 8. Time-Dependent Density-Functional Theory.

Development note This chapter will begin development after the chapter entitled Orbital-Dependent Functionals and Exact-Exchange Methods has been completed.

## 8.1. General overview.

In a future revision of this document, we will discuss how van Gisbergen et al. [216] used very accurate Slater-type orbitals (STOs) to obtain nearly exact xc potentials  ${v}_{\mathrm{xc}}$  for the He, Be, and Ne atoms, thereby avoiding the incorrect asymptotic behavior and oscillatory behavior in  ${v}_{\mathrm{xc}}$  that can result from the use of a finite set of Gaussian-type orbitals (GTOs). We will also discuss how Burke et al. [224] used the exact Kohn-Sham potentials calculated by Umrigar and Gonze [104] 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  ${f}_{\mathrm{xc}}\left(\mathbf{r},\mathbf{r\prime },t-\mathbf{t\prime }\right)$. They presented a hybrid functional for the kernel  ${f}_{\mathrm{xc}}$  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.