Eigenvalues Kohn-Sham

Kleinman L 1997 Significance of the highest occupied Kohn-Sham eigenvalue Phys. Rev. B 56 12 042-5... 

Savin, A., Umrigar, C. J., Gonze, X., 1998, Relationship of Kohn-Sham Eigenvalues to Excitation Energies , Chem. Phys. Lett., 288, 391. 

We start with a discussion of the role of relativistic xc-contributions for the band structure of Au and Pt on the basis of the RGGA, thus repeating the analysis of MacDonald et al. [25,26] with a more appropriate form for Exc[n. As relativistic effects are most important near the atomic nucleus, first the core levels are analyzed (on the basis of the Kohn-Sham eigenvalues, as usual). Table 2 shows the core levels of Au (relative to the Fermi level) for several xc-functionals, i.e. the nonrelativistic LDA, the RLDA, the nonrelativistic GGA, the RGGA for both exchange and correlation as well as a combination of the... 

We emphasize that the calculation of excitation energies from Eqs. (362) and (363) involves only known ground-state quantities, i.e., the ordinary static Kohn-Sham orbitals and the corresponding Kohn-Sham eigenvalues. Thus the scheme described here requires only one selfconsistent Kohn-Sham calculation, whereas the so-called Ajcf procedure involves linear combinations of two or more selfconsistent total energies [209]. So far, the best results are obtained with the optimized effective potential for in the KLI x-only approximation. Further improvement is expected from the inclusion of correlation terms [6,225] in the OPM. 

Vertical and adiabatic quantities are obtained if the atomic structure of the neutral system is frozen upon ionization or not. Total energy differences yield much more reliable results for / and A than HOMO and LUMO energies derived from Fock or Kohn-Sham eigenvalues. 

It has been discovered that excitations from the highest occupied orbital are in agreement with differences of Kohn-Sham eigenvalues. See CJ Umrigar, A Savin, X Gonze. In JF Dobson, G Vignale, MP Das, eds. Electronic Density Functional Theory Recent Progress and New Directions. New York Plenum Press, 1998, pp 167-176. 

Figure 2 Schematic description of some important Kohn-Sham eigenvalues relative to the vacuum level, denoted by 0, and their relation to observables. See main text for explanations.

Figure 3.13 Spin-up (upper panel) and spin-down (lower panel) density of occupied (KS) electron states for the lowest-energy isomer of Ni6. Computations have been performed within DFT-LSD-GGA. The computed Kohn-Sham eigenvalues have been convoluted with a 0.15-eV-wide Gaussian (after P. Ballone and R. O. Jones, unpublished work)...

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