  An investigation of the pressure induced phase transition from the scheelite
phase (I41/a, Z=4) to the fergusonite-like phase (I2/a, Z=4)/LaTaO(P21/c, Z=4)
of LiYF4 is presented. Employing density functional theory (DFT) within the
generalized gradient approximation, the internal degrees of freedom were
relaxed for a pressure range of 0 GPa to 20 Gpa. The influence of pressure on
the lattice vibration spectrum of the scheelite phase (I41/a, Z=4) was
evaluated using the direct approach, i.e. using force constants calculated from
atomic displacements. The transition volume is in good agreement with
experiment, while the transition pressure is overestimated of 6 GPa. At 20 GPa,
a P21/c structure with apentacoordinated lithium cation is found to be the most
stable phase. This structure is compatible with a transition driven by a Bg
zone-center soft optic mode linked to a soft-acoustic mode along the [11-1]
direction as observed for the proper ferroelastic transition of BiVO4.
