Multiplet splittings and Jahn-Teller energies for the vacancy in silicon

The question of the relative importance of multiplet-splitting effects and Jahn-Teller distortion energies is discussed in detail for the vacancy in silicon. The calculations are done within the self-consistent local-density approximation. It is demonstrated that the dominant contribution comes from the magnetic or exchange splitting, which for the free atom is the origin of the Hund's-rule ground state. The calculated value of this splitting is an appreciable 0.35 eV for the neutral-vacancy case. However, if multiplet and Jahn-Teller splittings are combined, the ground state is dominated by Jahn-Teller distortions while multiplet effects are practically quenched. The general results of the negative-$U$ system formed by the three charge states $V^{2+}$, $V^{+}$, and $V^0$ remain thus basically unaltered.