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.