A theory of classical two- and three-body interatomic potentials is developed. The ability of the classical potentials to model quantum-mechanical local-density-functional calculations for a wide range of silicon structures is explored. In developing classical models it was found to be necessary to perform new local-density-functional calculations for self-interstitial and layered silicon structures. Two different potentials are derived from fits and tests to energies of bulk, surface, layered, and self-interstitial structures. One potential models bulk energies and high-pressure properties well; the other is more appropriate for properties of the tetrahedral structure. Simulated annealing is used to find low-energy structures for silicon-atom clusters.