We investigate the properties of interstitial hydrogen or muonium in diamond using the ab initio Hartree-Fock approach and the method of partial retention of diatomic differential overlap. If the dangling bonds on the surface are correctly saturated, the energy profiles and spin densities are independent of cluster size in the range from C10H16 to C30H40 and the tetrahedral interstitial site (T) is a deep minimum of the total energy. However, the height of the potential barrier between two adjacent T sites varies with basis set and, to a smaller extent, with lattice relaxation. In all cases, a muon (and therefore also a proton) is localized at the T site. The hexagonal interstitial site corresponds to a saddle point of the energy (it is a maximum of the energy only along the 111 axes). The dependence of the spin densities on cluster size, basis set, and lattice relaxations is analyzed. The results indicate a highly repulsive antibonding interaction between the interstitial hydrogen (or Mu) and the diamond clusters. The impurity energy level lies deep in the gap and the associate electronic wave function has a node between the site of the impurity and its nearest neighbors. This results in a very large contact spin density at the impurity. The calculated enhancement factor f depends very little on cluster size or basis set and is larger than experimentally observed. The effect of the zero-point motion of the impurity on the contact spin density is much smaller than previously believed. The effects of various relaxations are studied using clusters containing three and four host atom shells.