The tight-binding molecular dynamics method is used to study reconstructions of the Si(113) surface. Comparisons of tight-binding total energies of the 3\ifmmode\times\else\texttimes\fi{}1 and 3\ifmmode\times\else\texttimes\fi{}2 reconstructed surfaces as well as the bulk terminated and the fully relaxed 1\ifmmode\times\else\texttimes\fi{}1 surfaces show that the 3\ifmmode\times\else\texttimes\fi{}2 reconstructed surface is the most stable structure at low temperature. However, the 3\ifmmode\times\else\texttimes\fi{}1 reconstructed surface should dominate at higher temperature. A transition from the 3\ifmmode\times\else\texttimes\fi{}2 phase to the 3\ifmmode\times\else\texttimes\fi{}1 phase is predicted to occur at about 750 K, which is in agreement with experimental observations. \textcopyright{} 1996 The American Physical Society.