  To investigate the pressure-induced structural transitions of chromium
dioxide (CrO$_{2}$), phonon dispersions and total energy band structures are
calculated as a function of pressure. The first structural transition has been
confirmed at P$\approx$ 10 GPa from the ground state tetragonal CrO$_{2}$
(t-CrO$_{2}$) of rutile type to orthorhombic CrO$_{2}$ (o-CrO$_{2}$) of
CaCl$_{2}$ type. The half-metallic property is found to be preserved in
o-CrO$_{2}$. The softening of Raman-active B$_{1g}$ phonon mode, which is
responsible for this structural transition, is demonstrated. The second
structural transition is found to occur for P$\geq$ 61.1 GPa from ferromagnetic
(FM) o-CrO$_{2}$ to nonmagnetic (NM) monoclinic CrO$_{2}$ (m-CrO$_{2}$) of
MoO$_{2}$ type, which is related to the softening mode at {\bf q} =
R(1/2,0,1/2). The third structural transition has been newly identified at P=
88.8 GPa from m-CrO$_{2}$ to cubic CrO$_{2}$ of CaF$_{2}$ type that is a FM
insulator.
