This work provides fundamental knowledge of LnNO species and three guidelines for the application of Ln elements in catalytic decomposition of NO_x. The geometrical and electronic structure, as well as bonding nature of a series of LnNO species exhibit unique periodic trends. The structure transfer from linear oxo-NLnO featuring multiple Ln=N bonds for early Lns to triangle (h²-NO)Ln for later Ln and to linear (h¹-NO)Ln with stable Eu f⁷ and Yb f¹⁴ configurations. Correspondingly, the OS of Ln also display a “double-kirk” periodicity increasing from +III to +V and then decreasing to +I and +II for La-Gd, while it changes from +IV to +II to +I to +II for Tb-Lu. Moreover, for the Ln-N bonding, it involves significant interactions between the nitrogen 2p orbitals and both the Ln 5d and 4f orbitals in those oxo-NLnO species, while it is dominated by NO interacting with Ln 5d orbitals without any participation of the 4f orbitals in the (h²-NO)Ln structure.