II. COMPUPATIONAL DETAILS Full-electron density functional theory (DFT) implemented in the Dmol 3 package [17, 18] is used in our calculations. The Perdew, Burke, and Ernzerhof (PBE) [19] functional is used for exchange and correlation interaction in the generalized gradient approximation(GGA). The basis set is composed of double numerical basis and a polarized function (DNP) is chosen. The supercell is chosen as 20 × 20 $_{×}$c ˚ A $^{3}$, where c is the lattaice constant along the periodic direction and is varied for different TM cases [see Table I]. The corresponding Brillouin zone is sampled by a 1 × 1 × 50 Monkhorst and Pack grid.[20] All structures are fully relaxed. In order to investigate the different magnetic configurations and Peierls transition in [TM 2 (Ant)] ∞ , a supercell containing four TMs and two Ants are used. For each kind of [TM 2 (Ant)] ∞ , as shown in Figs. 1(b)-(f), five magnetic configurations are consid- ered. The combination of two characters XY ( X and Y correspond to N (non-magnetic), F (ferromagnetic) and A (anti-ferromagnetic)) are adopted for representing the related mag- netic configurations, with X and Y describing the intralayer and interlayer magnetic cou- pling of TM atoms, respectively. For example, as shown in Fig. 1(d), FA means the ferro- magnetic coupling between the inner layer TM atoms and the anti-ferromagnetic coupling between two nearest neighbor layers. After full relaxation, the calculated structural, electronic and magnetic properties of [TM 2 (Ant)] ∞ are summarized in Table I. Peierls transition does not occur in [TM 2 (Ant)] ∞ , and no magnetic moment is observed in the cases of [Sc 2 (Ant)] ∞ and [Mn 2 (Ant)] ∞ . In contrast, Ti and Fe are spin polarized, but the magnetic ground states of [Ti 2 (Ant)] ∞ and [Fe 2 (Ant)] ∞ are FA and AF , respectively. Hence, the total magnetic moments of [Ti 2 (Ant)] ∞ and [Fe 2 (Ant)] ∞ supercells are zero. In addition, our calculations predict that FF is the ground state of both [V 2 (Ant)] ∞ and [Cr 2 (Ant)] ∞ , and that the supercells of [V 2 (Ant)] ∞ and [Cr 2 (Ant)] ∞ respectively possess a magnetic moment of 2.00 µ B and 0.96 µ B per TM ion, with a finite negative magnetic moment formed on the Ant part. Further analysis shows that [V 2 (Ant)] ∞ and [Cr 2 (Ant)] ∞ are half-metallic ferromagnets which can be seen from III. RESULTS AND DISCUSSIONS 3