Symmetrical lattice relaxation around a vacancy, and its effect upon many electron states of the defect, were investigated. A molecular approach was used to evaluate electron-electron interactions via a semi-empirical formalism which was based upon a generalized Hubbard Hamiltonian. Coupling of the defect molecule to the surrounding bulk was also considered by using an improved Stillinger-Weber potential. A strong dependence of the electronic energy levels upon the relaxation size of the nearest-neighbor atoms indicated that, in order to obtain quantitative results, the effect of lattice relaxation should be considered. Except for the high spin state of the defect 5A2, the order of other lowest levels, especially the ground state of the vacancy 1E did not change during the relaxation. For 12% outward relaxation, there was a level crossing between 5A2 and the excited state of the well-known GR1 transition, 1T2. The reported level crossing confirmed the predicted relative energies of these states in the band-gap. By considering the outward relaxation effect, a mid-gap position was obtained for the 5A2 state; in agreement with electron paramagnetic resonance data. The position of the low-lying 3T1 level varied from 0.1 to 0.4eV with increasing outward relaxation. When the ion-ion interaction of the nearest-neighbor atoms was included, the outward relaxation lowered the energies of all electronic states. Upon considering the interaction of the first- and second-shell neighbors of the vacancy, the calculated elastic barrier restricted outward relaxation of the vacancy to 12% for the ground, and 18% for the 5A2 excited, state. The calculated equilibrium bond-lengths were in very good agreement with ab initio density functional theory and electron paramagnetic resonance data. The results also suggested that there was an outward relaxation if Hund’s rule was applicable.

Lattice Relaxation in Many-Electron States of the Diamond Vacancy. M.H.Saani, M.A.Vesaghi, K.Esfarjani, T.G.Elahi, M.Sayari, H.Hashemi, N.Gorjizadeh: Physical Review B, 2005, 71[3], 035202 (9pp)