Analysis of the Vignale-Kohn current functional in the calculation of the optical spectra of semiconductors

In this work, we investigate the Vignale-Kohn current functional when applied to the calculation of optical spectra of semiconductors. We discuss our results for silicon. We found qualitatively similar results for other semiconductors. These results show that there are serious limitations to the general applicability of the Vignale-Kohn functional. We show that the constraints on the degree of nonuniformity of the ground-state density and on the degree of the spatial variation of the external potential under which the Vignale-Kohn functional was derived are almost all violated. We argue that the Vignale-Kohn functional is not suited to use in the calculation of optical spectra of semiconductors since the functional was derived for a weakly inhomogeneous electron gas in the region above the particle-hole continuum, whereas the systems we study are strongly inhomogeneous and the absorption spectrum is closely related to the particle-hole continuum.