The Li-Si materials system holds promise for use as an anode in Li-ion battery applications. For this system, we determine the charge capacity, voltage profiles, and energy storage density solely by ab initio methods without any experimental input. We determine the energetics of the stable and metastable Li-Si phases likely to form during the charging and discharging of a battery. Ab initio molecular dynamics simulations are used to model the structure of amorphous Li-Si as a function of composition, and a genetic algorithm coupled to density-functional theory searches the Li-Si binary phase diagram for small-cell, metastable crystal structures. Calculations of the phonon densities of states using density-functional perturbation theory for selected structures determine the importance of vibrational, including zero-point, contributions to the free energies. The energetics and local structural motifs of these metastable Li-Si phases closely resemble those of the amorphous phases, making these small unit cell crystal phases good approximants of the amorphous phase for use in further studies. The charge capacity is estimated, and the electrical potential profiles and the energy density of Li-Si anodes are predicted. We find, in good agreement with experimental measurements, that the formation of amorphous Li-Si only slightly increases the anode potential. Additionally, the genetic algorithm identifies a previously unreported member of the Li-Si binary phase diagram with composition Li5Si2 which is stable at 0 K with respect to previously known phases. We discuss its relationship to the partially occupied Li7Si3 phase. © 2013 American Physical Society.