We use variable-cell first principles molecular dynamics as an optimization tool to investigate the structural and electronic properties of Mg-based anhydrous hydrotalcite-like compounds. The formation energy as a function of the ratio R between di-and trivalent cations shows a minimum at R similar to 3, in good agreement with experimental stability ranges for these materials. At the same value R similar to 3, a maximum is found in the calculated interlayer distance, suggesting a correlation between energetic stability and structure. The energies and character of the electronic states of hydrotalcites containing different interlayer anions and trivalent cations have been compared. The nature of the anions is found to have a major influence on the electronic properties. In particular, OH-anions, rather than, e.g., Cl-, lead to a significantly smaller HOMO-LUMO gap, with a LUMO spatially more localized in the interlayer region. These features are related to the observed differences in the catalytic properties of hydrotalcites containing OH- vs Cl- anions.