  We investigate vibrational properties and lattice distortion of negatively
charged nitrogen-vacancy (NV) center in diamond. Using the first-principles
electronic structure calculations, we show that the presence of NV center leads
to appearance of a large number of quasilocalized vibrational modes (qLVMs)
with different degree of localization. The vibration patterns and the
symmetries of the qLVMs are presented and analyzed in detail for both ground
and excited orbital states of the NV center. We find that in the high-symmetry
($C_{3v}$) excited orbital state a pair of degenerate qLVMs becomes unstable,
and the stable excited state has lower ($C_{1h}$) symmetry. This is a direct
indication of the Jahn-Teller effect, and our studies suggest that dynamical
Jahn-Teller effect in the weak coupling regime takes place. We have also
performed a detailed comparison of our results with the available experimental
data on the vibrations involved in optical emission/absorption of the NV
centers. We have directly demonstrated that, among other modes, the qLVMs
crucially impact the optical properties of the NV centers in diamond, and
identified the most important groups of qLVMs. Our results are important for
deeper understanding of the optical properties and the orbital relaxation
associated with lattice vibrations of the NV centers.
