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The thermoelectric (TE) properties of the BaM₂Ge₄X₆ compounds, where M = Rh and X = S, Se, Te, were investigated by computational approaches using density-functional theory and semi-classical Boltzmann theory for electronic transport. It was found that these compounds bear good TE properties, in particular BaRh₂Ge₄Te₆, for which the figure of merit was estimated to reach 1.51 at 300 K. As this compound has not yet been proved to be stable, we also investigated BaRh₂Ge₄S₄Te₂ by assuming that replacing tellurium by sulphur could stabilize the tellurium-containing structure. It was found that the TE properties are good. The quantum theory of atoms in molecules was used to investigate the nature of the chemical interactions that prevail in these compounds. A wide variety of interactions were evidenced, from van der Waals interactions to ionic and polar-covalent ones, which could explain the good TE performance of these compounds.