Compounds crystallizing in the structure of NaZr 2 (PO 4 ) 3 (NZP) are considered as promising materials for solid state electrolytes in Li-ion batteries. Using density functional theory (DFT), a systematic computational screening of 18 NZP compounds, namely LiX 2 (LO 4 ) 3 with X = Ti, V, Fe, Zr, Nb, Ru, Hf, Ta, Os, and L = P, Mn is performed with respect to their activation energies for vacancy-mediated Li migration. It is shown how the different ionic radii of the cationic substitutions influence structural characteristics such as the octahedron volumes around Li ions on the initial and transition state sites, which affect the activation energies ("composition-structure-property" relationships). The prevalent assumption that structural bottlenecks formed by triangularly arranged oxygen atoms at a certain location along the migration path determine the energy barriers for Li migration is not supported by the DFT results. Instead, the ionic neighborhood of the migrating ion in the initial and in the transition state needs to be taken into account to relate the structure to the activation energies. This conclusion applies to Na containing NZP compounds as well. 1 arXiv:1901.09759v1 [cond-mat.mtrl-sci] 28 Jan 2019 I. INTRODUCTION A major challenge in the development of future portable energy storage devices with the potential to outreach today's battery technology in terms of capacity, energy density, charge rate, cyclability, and safety, is the identification of new materials for the use as anodes, cathodes, or electrolytes with improved properties such as ionic conductivity or thermal, chemical, electrochemical, and mechanical stability [1]. A popular approach in the search for new materials taking advantage of today's available computational resources is the virtual screening and characterization of hundreds of compounds which are systematically generated by substituting elements at specific lattice sites of a material class, with the goal of identifying compositions leading to improved battery-relevant properties [2, 3]. Apart from eventually predicting promising new materials, the data produced by such a combinatorial high-throughput screening (HTS) can be used to detect relationships between the composition, structure, and property of interest, which help to understand the underlying mechanisms better, and therefore may open up promising directions for optimization [4, 5].Present state-of-the-art battery technology could be improved significantly by replacing the liquid electrolyte by a highly ion-conducting and electrochemically stable solid-state electrolyte (SSE). Batteries consisting of SSEs could be stacked more densely, and safety concerns such as temperature stability, flammability and leakage of toxic liquids would be overcome [6,7]. However, currently known SSE materials don't yet reach the ionic conductivity of liquid electrolytes, and therefore they lead to lower power densities and slower charge/discharge rates [8]. Fast and reversible migration of the charge carrying ions is not only relevant fo...