We present the results of a theoretical study of the diffusion barriers of titanium and copper in crystalline silicon, and of the interactions between titanium and hydrogen, and between copper and hydrogen. The calculations were performed using various molecular clusters and the Hartree-Fock method. The method of partial retention of diatomic differential overlap (PRDDO) predicts diffusion barriers of 3.29 eV for Ti+, 2.25 eV for Ti0, and 0.24 eV for Cu+. PRDDO also predicts that substitutional Ti0 is a deep trap for interstitial H, with a gain in energy of 1.84 eV relative to atomic H far outside the cluster. AB initio Hartree-Fock calculations show that a Ti+ ion at a tetrahedral interstitial site also forms a bond with interstitial H, with a dissociation energy of 2.31 eV. On the other hand, interstitial Cu+ does not form a bond with H. Several issues relevant to H passivation of interstitial 3d transition-metal impurities in Si are discussed.