We performed ab initio calculations of eermanium dioxide to study its behav
ior and possible similarity to silica under high pressure. At the rutile-Ca
Cl2-type phase transition, the lattice constants, unit cell volume, and Gib
bs free energy change continuously with increasing pressure and indicate th
at this ferroelastic phase transition is close to the second order. Further
phase transitions to denser packed phases of alpha -PbO2-type and pyrite P
a (3) over bar are considered. The pressure dependence of the elastic const
ants is determined. For zero-pressure and 30-GPa phonon dispersion relation
s of rutile-type and CaCl2-type structures, respectively, are calculated. A
softening of an optical mode, linearly coupled to a shear instability, is
found. The present results confirm the analogy of the phase-transition sequ
ence between silica and germanium dioxide at high pressures.