Parameter-free calculations based on the density-functional theory are used
to examine high-pressure phases of solids, mainly semiconductors. For the
elemental semiconductors, as represented by Si, the diamond --> beta-tin-->
Imma sequence is examined, and for III-V semiconductors the optimization of
the structural parameters of the Cmcm and Imm2 phases is described. The st
ructural energy differences are in several cases very small, and in some to
o small to allow a safe structure prediction on the basis of the calculatio
ns. In that context we also discuss ways to go beyond the local density app
roximation (LDA). We show that the predicted high-pressure phases may be si
gnificantly affected by inclusion of (generalized) gradient corrections (GG
A). Elemental Zn (h.c.p.) is further taken as an example where we find that
the simple LDA leads to poor results.