The principal approximation in the Green's-matrix method for calculating the electronic structure and total energy of point defects in crystalline solids is the choice of (finite) basis set. In this paper the results of total-energy calculations with a number of different Gaussian-orbital basis sets are presented for several defects in silicon, including the silicon lattice vacancy and the silicon self-interstitial. Particular attention is paid to the convergence of the total energy with respect to the number of atoms included in the defect cluster on which the Green's matrix is represented. Our best estimate for the formation energy of an unrelaxed neutral silicon lattice vacancy is 4.4 eV. In many cases we are interested in calculating the distortion accompanying incorporation of a point defect or the total-energy difference when a defect is displaced. As illustrative examples, the breathing relaxation around the lattice vacancy and the migration energies of the self-interstitial and of interstitial oxygen are examined. It is shown that the atoms surrounding a neutral silicon lattice vacancy relax inwards toward the site of the missing atom. On including this symmetric relaxation and the Jahn-Teller pairing distortion, the formation energy becomes 3.6 eV. Because of the importance of the long-range response to the Jahn-Teller distortion, it was not possible to calculate the pairing energy entirely ab initio. For silicon self-interstitials in the empty channels of the silicon lattice, high-temperature (midgap Fermi-level) formation energies of upwards of 4.4 eV are found. The migration energies are strongly charge-state dependent but in general substantially smaller than the formation energies. The self-interstitial displays negative-U behavior, and its electronic structure supports athermal migration. The migration energy for interstitial oxygen is calculated to be 2.5 eV, which is in good agreement with the experimental value.