The structures and electronic and spin properties of the 3d TMC₅N₈ clusters have been calculated using the PBE functional. The results demonstrate that the Zn atom substituting significantly distorts the C₆N₈ clusters. TM atoms prefer to substitute the C atom which is farthest away from the biasing N atom. The TM substituting dramatically reduces the structural stability of the C₆N₈ clusters except for ScC₅N₈, TiC₅N₈ and VC₅N₈. As for the ground-state TMC₅N₈ clusters, the TM substituting improves the kinetic stability of the C₆N₈ clusters except for Ti, Cr and Cu. TM atoms in the TMC₅N₈ clusters loss certain amount of electrons. A few 4s orbital electrons of TM atoms transferred to the N atoms in the TMC₅N₈ clusters. The maximum spin values of the TM atoms occur at Mn and Ni for the TMC₅N₈ clusters.

3d TMC ₅ N ₈团簇的结构，电子和自旋性质已使用PBE函数进行了计算。结果表明，取代的Zn原子使C ₆ N ₈团簇明显变形。TM原子更喜欢取代距偏置N原子最远的C原子。除ScC ₅ N ₈，TiC ₅ N ₈和VC ₅ N ₈以外，TM替代显着降低了C ₆ N ₈团簇的结构稳定性。至于基态TMC ₅ N ₈除Ti，Cr和Cu外，TM取代能改善C ₆ N ₈团簇的动力学稳定性。TMC ₅ N ₈团簇中的TM原子损失一定数量的电子。TM原子的几个4 s轨道电子转移到TMC ₅ N ₈簇中的N原子。对于TMC ₅ N ₈簇，TM原子的最大自旋值出现在Mn和Ni处。