Si is one of the most efficient anode materials for Li-ion batteries, but its potential for both Na and Mg-ion batteries is not well studied. We present a comparative computational study of diffusion barriers of Li, Na, and Mg in crystalline Si including the influence of vibrations on the storage energetics and on the diffusion barriers. Zero-point and room-temperature vibrations strongly affect both. Magnitude of the effect depends on the type of dopant and is affected by neighbouring dopant atoms. Vibrations lower the Helmholtz free energy of formation and more so for Na and Mg than for Li. The effect is stronger for dopants at neighbouring sites. Interactions between the metal atoms can locally reduce the diffusion barriers. Vibrations have a strong, dopant-type and temperature dependent lowering effect on the diffusion barrier, reaching >0.07 eV for Li at room temperature. Most calculations to date for metal ion diffusion in battery electrodes were done using plane-wave based codes. We present an analysis of the effects due to atomic-centred basis selection. To the best of our knowledge, this is the first study of the effects of vibrations and atomic-centred bases on the computed properties of battery electrodes. (C) 2013 Elsevier B.V. All rights reserved.