Relationship between lattice relaxation and electron delocalization in diamond vacancies

Single electron wavefunction of a vacancy in diamond lattice has been calculated in different symmetric configurations of the nearest neighbor (NN) atoms. We used ab initio  density functional theory  (DFT) and unrestricted Hartree–Fock (UHF) cluster methods. The variation of electron or spin localization on NN atoms have been investigated with respect to the lattice relaxation in the ground state of the neutral and negatively charged vacancy. Calculated variations are not symmetric with respect to the sign of the lattice relaxation. We obtain about 90% localization for electronic charge and spin density for the neutral and negatively charged vacancy, respectively. This is in good agreement with electron paramagnetic resonance (EPR) measurements on negatively charged vacancy. We discuss the sign of the lattice relaxation and the limitation in using only semi-empirical potentials for modeling this problem.