Abstract The phase stability, structural parameters, and site preference of LaCo 13− x T x (T = Cr, Mn, V, Ti) and LaCo 13H x are studied by using interatomic potentials based on Chen’s lattice inversion technique. The results show that the ternary elements can decrease the cohesive energy markedly. It is proved that these elements can stabilize LaCo 13− x T x with the NaZn 13 structure. Also, we study the volume variation of LaCo 13H x with different temperature. After introducing H atoms, lattice constants and volumes of the compounds are increased significantly. Moreover, the hydrogen atoms preferentially occupy 24d sites. The calculated results indicate that the inverted pair potentials are valid for studying the structural properties of these kinds of materials and some related hydrides.