Exchange - correlation energy and the phase diagram of

Previous first-principles calculations of the melting properties of Si, based on the local-density approximation ~LDA! for electronic exchange-correlation energy, underpredict the melting temperature by ;20 %. We present new first-principles results indicating that a large part of this problem is due to noncancellation of exchange-correlation errors between the semiconducting solid and the metallic liquid. It is shown that other sources of error, particularly those due to system size and Brillouin-zone sampling, can be made negligible. The same LDA errors cause an underprediction of the pressure of the diamond-Si → beta-tin-Si transition. The generalized-gradient approximation considerably improves both features of the Si phase diagram.