A methodology is developed for the theoretical study of the polar surfaces of compound semiconductors. It is based on the calculation of the total energy in the context of density-functional theory in the pseudopotential approximation. The method is used to investigate the (2×2) reconstructions of GaAs(111). Emphasis is given to the relative chemical potential, which plays a crucial role in determining the lowest-energy geometry for surfaces with different stoichiometries. The total-energy versus chemical-potential curves indicate that there are at least two stable reconstructions. We predict one to be an As-triangle geometry and the other the Ga vacancy. © 1987 The American Physical Society.