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This chapter will begin development after the chapter entitled |

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. |

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