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In this paper, ab initio electronic structure calculations are applied to study half-metallic properties of Heusler alloys XMnGe (X = Sc, Fe, Ni) with both CuHgTi-type and AlCuMn-type structures using first-principles calculations based on density functional theory (DFT). The exchange-correlation energy of electrons is described in the generalized gradient approximation (GGA). The results showed that for all compounds XMnGe, the AlCuMn-type structure is energetically more stable than CuHgTi-type structure at the equilibrium volume. The ScMnGe and FeMnGe are half-metallic in the CuHgTi- and AlCuMn-type structures, respectively; finally, NiMnGe have a metallic character in both CuHgTi- and AlCuMn-type structures. [ABSTRACT FROM AUTHOR]