Abstract: Four systems Sm₄OC_l6, Eu₄OC_l6, Yb₄OCl₆ and Gd₆N₂Cl₁₂ were calculated by using SCC-DV-X_a method.It is found that the interstitial atom plays a determinative role in syntheses of tetrahedral cluster.There are six skeleton orbitals in the compound, three of them are formed from the interstitial atom oxygen and the rare-earth atoms, and the others are bonded by the 4f orbitals of the rare-earth atoms, pass through the embeded atom.In addition, the tetrahedral interstitial compounds may be synthesized successfully, because elements Sm, Eu etc.are in the lower valent states which make the contraction of d and f orbitals lessen and the bonding capability increase.And rich-electron f orbitals in Yb-system have become the major valence orbitals.

Key words: Rare-earth element, Tetrahedral cluster, Interstitial compound, Skeleton orbitals, DV-X_a method