Effect of lattice relaxation on spin density of nitrogen-vacancy centers in diamond and oscillator strength calculations

Using a generalized Hubbard Hamiltonian, many-electron wavefunctions of negatively charged (NV−) and neutral nitrogen-vacancy (NV0) centers in diamond were calculated. We report the effect of symmetric relaxation of surrounding atoms on the spin density, calculated from the many electron wavefunctions in the ground and excited states. We evaluated the error, that, arises in estimation of spin density when lattice relaxation effect is neglected in Electron Paramagnetic Resonance experiment and showed that the ground state spin density distribution is accessible in outward relaxations. The computed oscillator strengths give a higher efficiency for the 1.945 eV photoluminescence (PL) line of NV− with respect to 2.156 eV PL line of NV0 which agrees well with experiment. This result is explained based on the largest the ground state spin among available values for the NV− with respect to NV0. The transition probability between degenerate ground and excited states slightly depends on the Sz value. Finally, we report on the electronic configurations which contribute to the ground and excited states and discuss the population variation of electronic configurations with relaxation