  Phonon dispersions of one typical three-dimensional topological insulator
Bi$_{2}$Se$_{3}$ have been studied within density functional theory. The soft
modes of two acoustic branches along the $Z$$-$$F$ and $\Gamma$$-$$F$
directions within the pure local density approximation will transit to show
imaginary frequency oscillating after including the spin-orbit interaction
(SOI). Similar phenomenon has also been observed for Bi$_{2}$Te$_{3}$. Besides,
we have found that the weak van der Waals forces between two Se1 layers in
Bi$_{2}$Se$_{3}$ are strengthened by turning on the SOI.
