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Vibrational modes and lattice distortion of a nitrogen-vacancy center in diamond from first-principles calculations

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.