Density functional calculations are used to calculate the structural and electronic properties of BaReH9 and to analyze the bonding in this compound. The high coordination in BaReH9 is due to bonding between Re 5d states and states of d-like symmetry formed from combinations of H s orbitals in the H9 cage. This explains the structure of the material, its short bond lengths and other physical properties, such as the high band gap. We compare with results for hypothetical BaMnH9, which we find to have similar bonding and cohesion to the Re compound. This suggests that it may be possible to synthesize (MnH9) 2− salts. Depending on the particular cation, such salts may have exceptionally high hydrogen contents, in excess of 10 weight %.