A parameter-free, self-consistent method for calculating the gradient of the total energy (i.e., forces on atoms) of point defects in semiconductors is described. It is shown that under two conditions, (i) the pseudopotential approach and (ii) the inclusion of basis-set derivatives, the Hellmann-Feynman theorem can be applied. The convergence properties of the force calculation are examined, and the method is used to study the breathing distortions of the vacancy in silicon. The results, such as the direction and amplitude of the distortions and the force constants, are compared to other calculations and to available experimental data.

• Received 9 October 1984

DOI:https://doi.org/10.1103/PhysRevB.31.6541