Divalent Mg2+ ions often serve as cofactors in enzyme or ribozyme-catalyzed phosphoryl transfer reactions. In this work, the interaction of Mg2+ ions and di-metal bridge complexes with phosphates, phosphoranes, and other biological ligands relevant to RNA catalysis are characterized with density functional methods. The effect of bulk solvent is treated with two continuum solvation methods (PCM and COSMO) for comparison. The relative binding affinity for different biological ligands to Mg2+ are quantified in different protonation states. The structure and stability of the single-metal and di-metal complexes are characterized, and the changes in phosphate and phosphorane geometry induced by metal ion binding are discussed. Di-metal bridge complexes are a ubiquitous motif and the key factors governing their electrostatic stabilization are outlined. The results presented here provide quantitative characterization of metal ion binding to ligands of importance to RNA catalysis, and lay the groundwork for design of new generation quantum models that can be applied to the full biological enzymatic systems.