Characterization of the negatively charged NV defect through the spin density distribution and the hyperfine coupling constants

The spin density function and hyperfine coupling constants of the NV⁻ defect (a vacancy with one nitrogen atom as a first neighbor) in its triplet ground state, are computed by using hybrid functionals, a Gaussian type all electron basis set, the supercell scheme (216 atoms before the defect formation), and the CRYSTAL code. The charged defect has been simulated by using the charge compensated (CC) scheme, in which a background of positive charge is added to restore the neutrality of the unit cell. The local geometry, charge and spin distribution are also reported and discussed. The EPR constants (Fermi contact, the hyperfine coupling and electric field gradient tensors) of the N (both ¹⁴N and ¹⁵N) and of two C (for the ¹³C isotope) atoms around the vacancy are in excellent agreement with the recent experimental results by Felton et al. (Phys. Rev. B, 79,075 203, 2009). The comparison is extended to the many other experimental data collected in the last 30 years, to simpler functionals (LDA and PBE), larger supercells (512 atoms), and to recent simulations. It is shown that the present results are much closer to experiment than previous theoretical studies, with a quantitative, rather than qualitative, agreement.