the calculated total unit-cell magnetic moments per TM are shown in Fig. 3(b), in which the magnetic moments and schematic occupation of valence electrons obtained by CT model are also presented. We can find that our calculated results agree well with the CT model. Furthermore, [TM 2 (Ant)] ∞ and [TM(Cp)] ∞ are quite similar in magnetic properties, since Cp containing 5 C atoms does not obey the H¨ uckel rule, Cp tends to get one additional electron from TMs. Therefore, CT occurs in [TM(Cp)] ∞ .[12] However, according to H¨ uckel rule, Ant is a stable aromatic molecule. We want to inspect why there is so big CT in [TM 2 (Ant)] ∞ . Generally, the key factors determining the CT in this kind of polymers are: (1) the average number of carbon atom (ANC) per TM; (2) the strength of frontier orbital hybridization. From [TM(Bz)] ∞ to [TM 2 (Ant)] ∞ , the ANC increases from six to seven. This small change of ANC should not induce large CT difference between [TM(Bz)] ∞ and [TM 2 (Ant)] ∞ . Then the large CT in [TM 2 (Ant)] ∞ might arise from the second factor. Our calculations show that the HOMO-LUMO gap of Ant is 2.7 eV, which is smaller than that of Bz(5.5 eV). Comparing with Bz, the LUMO of Ant is much closer to the HOMO of TM ions. Thus, the frontier orbital hybridization between TMs and Ant is much stronger in [TM 2 (Ant)] ∞ than in [TM(Bz)] ∞ and the CT appears on [TM 2 (Ant)] ∞ . This is also illustrated clearly in Figs. 3(c) and 3(d), where the partial DOS of TM 3 d and Ant C 2 p are shown. Taking Fermi level as the reference, the HOMO of both Bz and Ant are localized around -5.5 eV. However, as the gap of Ant is smaller than that of Bz, the minimum energy of hybdridization of V 3 d and C 2 p electrons in [V 2 (Ant)] ∞ is -4 eV, which is lower than that of [V(Bz)] ∞ (-3 eV). Thus, as shown in Fig 3(c) and (d), compared with [V(Bz)] ∞ , the minority electrons of V in [V 2 (Ant)] ∞ is transferred to Ant, which can also be found in [V(Cp)] ∞ .[12] Consequently, from [V(Bz)] ∞ to [V 2 (Ant)] ∞ , the magnetic moment of V ion increases from 1 µ B to 2 µ $_{B}$. The schematic view of this opinion is also shown in Fig. 3, where the frontier orbitals (HOMO and LUMO) of Bz, V and Ant are approximately shown in the left, middle and right, respectively. The bigger arrow means the larger CT in [TM(Bz)] ∞ than that in [TM(Bz)] ∞ . Double exchange (DE) was attributed as one of the ferromagnetic origins of the in [TM(Bz)] ∞ and [TM 2 (Pn)] ∞ .[7, 15] However, in [V(Bz)] ∞ , the ferromagnetic state was be- lieved to arise from the negative polarization of carbon atoms since magnetic moments anti-polarized by TMs appears on benzene.[8] In addition, in [V(Cp)] ∞ , the ferromagnetism originates from the CT effects since there is CT between TMs and Cp. [12] In the cases of 5