The dielectric constants of semiconductors under pressure are derived
from ab initio calculations of the complex dielectric functions epsilo
n(omega). The pressure coefficient of the refractive index is negative
for most tetrahedrally bonded compounds and trends are explained with
in a simple model. Gap deformation potentials as well as 'absolute' ba
nd edge deformation potentials are derived, and the pressure dependenc
e of the electronic structure of superlattices is discussed. Examples
from the group III-V, in particular nitrides, and II-VI (ZnS, ZnS/ZnSe
) compounds illustrate these investigations. Also, less conventional s
emiconductors, beta-FeSi2 and epsilon-FeSi, are examined. Strong elect
ron correlation effects limit the validity of LDA theory in these case
s. It is suggested that experimental pressure studies can shed new lig
ht on the properties of Kondo insulators.