  Density functional calculations are used to calculate the structural and
electronic properties of BaReH$_9$ and to analyze the bonding in this compound.
The high coordination in BaReH$_9$ is due to bonding between Re 5$d$ states and
states of $d$-like symmetry formed from combinations of H $s$ orbitals in the
H$_9$ 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 BaMnH$_9$, which we find to have similar bonding and
cohesion to the Re compound. This suggests that it may be possible to
synthesize (MnH$_9)^{2-}$ salts. Depending on the particular cation, such salts
may have exceptionally high hydrogen contents, in excess of 10 weight %
