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

Phonon spectrum and bonding properties of Bi$_{2}$Se$_{3}$: Role of strong spin-orbit interaction