Chapter 8. Time-Dependent Density-Functional Theory.

[Note]Development note

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. [216] used very accurate Slater-type orbitals (STOs) to obtain nearly exact xc potentials   v xc   for the He, Be, and Ne atoms, thereby avoiding the incorrect asymptotic behavior and oscillatory behavior in   v 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 xc ( r , r′ , t - t′ ) . They presented a hybrid functional for the kernel   f 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.

[Note] be continued.

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