The absolute concentrations of thermal mono-vacancies, and the coefficient for self-diffusion via vacancies, were calculated from first principles by using the local-density approximation and the transition-state theory of diffusion. It was found that the diffusion data were in good agreement with experimental results for high temperatures. In this theory, the migration energy was given by the energy difference between 2 static, fully-relaxed, configurations. These were the saddle-point configuration, with the moving atom halfway along the <111> direction to the vacant lattice site, and the initial configuration before the jump of the atom.

W.Frank, U.Breier, C.Elsässer, M.Fähnle: Physical Review Letters, 1996, 77[3], 518-21