Chemical bonding in and electronic structure of lithium and magnesium rhodium hydrides are studied theoretically using DFT methods. For Li3RhH4 with planar complex RhH4 structural units, Crystal Orbital Hamilton Populations reveal significant Rh−Rh interactions within infinite one-dimensional ∞ 1 [RhH4] stacks in addition to strong rhodium−hydrogen bonding. These metal−metal interactions are considerably weaker in the hypothetical, heavier homologue Na3RhH4. Both compounds are small-band gap semiconductors. The electronic structures of Li3RhH6 and Na3RhH6 with rhodium surrounded octahedrally by hydrogen, on the other hand, are compatible with a classical complex hydride model according to the limiting ionic formula (M+)3[RhH6]3− without any metal−metal interaction between the 18-electron hydridorhodate complexes. In MgRhH, building blocks of the composition (RhH2)4 are formed with strong rhodium−hydrogen and significant rhodium−rhodium bonding (bond lengths of 298 pm within Rh4 squares). These units are linked together to infinite two-dimensional layers ∞ 2 [(RhH2/2)4] via common hydrogen atoms. Li3RhH4 and MgRhH are accordingly examples for border cases of chemical bonding where the classical picture of hydridometalate complexes in complex hydrides is not sufficient to properly describe the chemical bonding situation.