To understand the role of electron-phonon interaction in superconducting MgCNi$_{3}$ we have performed density functional based linear response calculations of its lattice dynamical properties. A large coupling constant $% lambda $= 1.51 is predicted and contributing phonons are identified as displacements of Ni atoms towards octahedral interstitials of the perovskite lattice. Instabilities found for some vibrational modes emphasize the role of anharmonic effects in resolving experimental controversies.
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