Linear response and quasiparticle calculations as probes of the Kohn‐Sham eigenvalues in metals

Abstract

The Koh-Sham eigenvalues were formally introduced into density functional theory as Lagrange multipliers in the implementation of the minimum principle for the total energy of a many-electron system. No general results are available concerning the physical significance of these one-electron eigenvalues (with the exception of the highest occupied level, which equals the Fermi energy). Recent ab initio calculations of dynamical response in metals make explicit use of the Koh-Sham band structure, and associated wave functions, through the use of spectral representations. This opens up the possibility of examining the significance of the eigenvalues at an "empirical" level, i.e., through direct comparison with the results of spectroscopic measurements. A particularly interesting example is afforded by new inelastic x-ray scattering experiments on Al. For a special wave vector transfer, 90 = 1.5k,, the measured spectrum provides a direct mapping of the Kohn-Sham noninteracting spectrum. For a range of wave vectors about qo, the bare Kohn-Sham spectrum still reproduces all the main features of the measurements; this suggests that, in this metal, the Koh-Sham eigenvalues are good approximations to the quasiparticle energies. We also discuss the interplay between Kohr-Sham bands and the energy of the "anomalous" plasmon in Cs, whose dispersion bears a signature of the excited-state band structure. Finally, and in a more formal framework, we outline the results of a first-principles comparison between quasiparticle amplitudes and Kohn-Sham wave functions at a jellium surface; the latter turn out to be excellent approximations to the former.