A first-principles pseudopotential study of neutral self-interstitial defects in silicon is reported, together with calculations for Pandey's concerted exchange mechanism for self-diffusion. The energies and structures of the fully relaxed hexagonal, tetrahedral, split-110, `caged' (Clark S J and Ackland G J 1997 Phys. Rev. B 56 47), split-100, and bond-centred interstitials are calculated using supercells with up to 128 + 1 atoms. We present results obtained using the local density approximation (LDA) and the PW91 generalized gradient approximation (GGA) for the exchange-correlation energy. Both the LDA and PW91-GGA functionals give the hexagonal and split-110 defects as the lowest-energy self-interstitials. The hexagonal and split-110 defects are essentially degenerate in energy with formation energies of about 3.3 eV (LDA) and 3.80 eV (PW91-GGA). Energy barriers are studied by calculating saddle-point structures using a simple `ridge-walking' method. The energy barrier for a diffusive jump between the hexagonal and split-110 interstitial sites is calculated to be 0.15 eV (LDA) and 0.20 eV (PW91-GGA) and the barrier between neighbouring hexagonal sites is 0.03 eV (LDA) and 0.18 eV (PW91-GGA), but we have not found a low-energy path between split-110 interstitial sites. The results suggest that self-interstitial diffusion in silicon occurs via diffusive jumps between the hexagonal sites and between hexagonal and split-110 defects.