The energies and charge and spin distributions in the low-lying levels of singlet and triplet N₂V defects in diamond from direct variational calculations of the excited states

This paper reports the energies and charge and spin distributions of the low-lying excited states in singlet and triplet N₂V defects in diamond from direct Δ-SCF calculations based on Gaussian orbitals within the B3LYP, PBE0, and HSE06 functionals. They assign the observed absorption at 2.463 eV, first reported by Davies et al. [Proc. R. Soc. London 351, 245 (1976)], to the excitation of a N(sp³) lone-pair electron in the singlet and triplet states, respectively, with estimates of ∼1.1 eV for that of the unpaired electrons, C(sp³). In both cases, the excited states are predicted to be highly local and strongly excitonic with 81% of the C(sp³) and 87% of the N(sp³) excited charges localized at the three C atoms nearest neighbor (nn) to the excitation sites. Also reported are the higher excited gap states of both the N lone pair and C unpaired electron. Calculated excitation energies of the bonding sp³ hybrids of the C atoms nn to the four inner atoms are close to that of the bulk, which indicates that the N₂V defect is largely a local defect. The present results are in broad agreement with those reported by Udvarhelyi et al. [Phys. Rev. B 96, 155211 (2017)] from plane wave HSE06 calculations, notably for the N lone pair excitation energy, for which both predict an energy of ∼2.7 eV but with a difference of ∼0.5 eV for the excitation of the unpaired electron.